From eb001e2a8559c866332f69f3ca6ec85177d839f2 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Tue, 23 Jan 2024 09:56:34 -0500
Subject: [PATCH 01/14] resolved conflicts

---
 M2/Macaulay2/m2/exports.m2                    |   1 +
 M2/Macaulay2/m2/matrix1.m2                    | 139 +++++++++++-------
 M2/Macaulay2/m2/newring.m2                    |   3 +-
 .../packages/Macaulay2Doc/M2-Singular-Book.m2 |   2 +-
 M2/Macaulay2/packages/Macaulay2Doc/doc.m2     |  13 +-
 M2/Macaulay2/packages/Macaulay2Doc/doc3.m2    |   4 +-
 M2/Macaulay2/packages/Macaulay2Doc/doc7.m2    |   4 +-
 M2/Macaulay2/packages/Macaulay2Doc/doc8.m2    |   2 +-
 .../packages/Macaulay2Doc/doc_ideals.m2       |  20 ++-
 .../Macaulay2Doc/functions/comodule-doc.m2    |   4 +-
 .../functions/degreeLength-doc.m2             |   2 +-
 .../Macaulay2Doc/functions/degrees-doc.m2     |   3 +-
 .../Macaulay2Doc/functions/degreesRing-doc.m2 |   2 +-
 .../Macaulay2Doc/functions/generators-doc.m2  |   6 +-
 .../Macaulay2Doc/functions/ideal-doc.m2       |  32 ++--
 .../functions/isHomogeneous-doc.m2            |   4 +-
 .../Macaulay2Doc/functions/isIdeal-doc.m2     |   4 +-
 .../Macaulay2Doc/functions/numgens-doc.m2     |   2 +-
 .../Macaulay2Doc/functions/promote-doc.m2     |   6 +-
 .../Macaulay2Doc/functions/ring-doc.m2        |   4 +-
 .../functions/symbol-underscore-doc.m2        |  10 +-
 .../packages/Macaulay2Doc/ov_ideals.m2        |   6 +-
 .../packages/MultiprojectiveVarieties.m2      |   2 +-
 M2/Macaulay2/packages/Varieties/euler-doc.m2  |   6 +-
 M2/Macaulay2/packages/Varieties/genera-doc.m2 |   2 +-
 M2/Macaulay2/packages/Varieties/genus-doc.m2  |   4 +-
 26 files changed, 170 insertions(+), 117 deletions(-)

diff --git a/M2/Macaulay2/m2/exports.m2 b/M2/Macaulay2/m2/exports.m2
index 3bcab8f7e95..e84346704dc 100644
--- a/M2/Macaulay2/m2/exports.m2
+++ b/M2/Macaulay2/m2/exports.m2
@@ -203,6 +203,7 @@ export {
 	"Homogeneous",
 	"Homogeneous2",
 	"HorizontalSpace",
+	"LeftIdeal",
 	"Ideal",
 	"IgnoreExampleErrors",
 	"ImmutableType",
diff --git a/M2/Macaulay2/m2/matrix1.m2 b/M2/Macaulay2/m2/matrix1.m2
index 2da84a24fd8..35b5c573431 100644
--- a/M2/Macaulay2/m2/matrix1.m2
+++ b/M2/Macaulay2/m2/matrix1.m2
@@ -420,52 +420,54 @@ cokernel Matrix := Module => m -> (
 cokernel RingElement := Module => f -> cokernel matrix {{f}}
 image RingElement := Module => f -> image matrix {{f}}
 
-Ideal = new Type of HashTable
+LeftIdeal = new Type of HashTable
+Ideal = new Type of LeftIdeal 
 Ideal.synonym = "ideal"
 
 ideal = method(Dispatch => Thing, TypicalValue => Ideal)
 
-expression Ideal := (I) -> (expression ideal) unsequence apply(toSequence first entries generators I, expression)
-net Ideal := (I) -> net expression I
-toString Ideal := (I) -> toString expression I
-toExternalString Ideal := (I) -> "ideal " | toExternalString generators I
-texMath Ideal := (I) -> texMath expression I
+expression LeftIdeal := (I) -> (expression ideal) unsequence apply(toSequence first entries generators I, expression)
+net LeftIdeal := (I) -> net expression I
+toString LeftIdeal := (I) -> toString expression I
+toExternalString LeftIdeal := (I) -> "ideal " | toExternalString generators I
+texMath LeftIdeal := (I) -> texMath expression I
 
-isIdeal Ideal := I -> true
-isHomogeneous Ideal := (I) -> isHomogeneous generators I
+isIdeal LeftIdeal := I -> true
+isHomogeneous LeftIdeal := (I) -> isHomogeneous generators I
 
-degrees Ideal := I -> degrees source generators I
+degrees LeftIdeal := I -> degrees source generators I
 -- TODO: deprecate these
-degreeLength Ideal := I -> degreeLength ring I
-degreesRing Ideal := I -> degreesRing ring I
+degreeLength LeftIdeal := I -> degreeLength ring I
+degreesRing LeftIdeal := I -> degreesRing ring I
 
-promote(Ideal,Number) := 
-promote(Ideal,RingElement) := (I,R) -> ideal promote(generators I, R)
+promote(LeftIdeal,Number) :=  
+promote(LeftIdeal,RingElement) := (I,R) -> ideal promote(generators I, R)
 
 comodule Module := Module => M -> cokernel super map(M,M,1)
 quotient Module := Module => opts -> M -> comodule M
-comodule Ideal := Module => I -> cokernel generators I
-quotient Ideal := Module => opts -> I -> (ring I) / I
-module   Ideal := Module => (cacheValue symbol module) (I -> image generators I)
+comodule LeftIdeal := Module => I -> cokernel generators I
+quotient LeftIdeal := Module => opts -> I -> (ring I) / I
+module   LeftIdeal := Module => (cacheValue symbol module) (I -> image generators I)
 
-genera Ideal := (I) -> genera ((ring I)^1/I)
-genus Ideal := (I) -> genus ((ring I)^1/I)
+genera LeftIdeal := I -> genera ((ring I)^1/I)
+genus LeftIdeal := I -> genus ((ring I)^1/I)
 
-eulers(Ideal) := (I) -> eulers((ring I)^1/I)
-euler(Ideal) := (I) -> euler((ring I)^1/I)
+eulers LeftIdeal := I -> eulers((ring I)^1/I)
+euler LeftIdeal := I -> euler((ring I)^1/I)
 
+-- two-sided ideal expected
 RingElement * Ideal := Ideal => (r,I) -> ideal (r ** generators I)
 Ideal * RingElement := Ideal => (I,r) -> ideal ((generators I)**r)
 ZZ * Ideal := (r,I) -> ideal (r * generators I)
 Ideal * ZZ := (I,r) -> ideal (r * generators I)
 
-generators Ideal := Matrix => opts -> (I) -> I.generators
-Ideal_* := I -> first entries generators I
-Ideal / Function := List => (I,f) -> apply(flatten entries generators I, f)
-Function \ Ideal := List => (f,I) -> apply(flatten entries generators I, f)
+generators LeftIdeal := Matrix => opts -> (I) -> I.generators
+LeftIdeal_* := I -> first entries generators I
+LeftIdeal / Function := List => (I,f) -> apply(flatten entries generators I, f)
+Function \ LeftIdeal := List => (f,I) -> apply(flatten entries generators I, f)
 
 generator = method()
-generator Ideal := RingElement => (I) -> (
+generator LeftIdeal := RingElement => I -> (
      if I.cache.?trim then I = I.cache.trim;
      R := ring I;
      n := numgens I;
@@ -487,18 +489,34 @@ generator Module := RingElement => (M) -> (
      if n == 1 then return M_0;
      error "expected ideal to have a single generator")
 
-Ideal / Ideal := Module => (I,J) -> module I / module J
+LeftIdeal / LeftIdeal := Module => (I,J) -> module I / module J
+
+-- two-sided ideal expected
 Module / Ideal := Module => (M,J) -> M / (J * M)
 
-Ideal#AfterPrint = Ideal#AfterNoPrint = (I) ->  (Ideal," of ",ring I)
+LeftIdeal#AfterPrint = LeftIdeal#AfterNoPrint = I ->  (LeftIdeal," of ",ring I)
+Ideal#AfterPrint = Ideal#AfterNoPrint = I ->  (Ideal," of ",ring I)
 
+-- two-sided ideal expected
 Ideal ^ ZZ := Ideal => (I,n) -> ideal symmetricPower(n,generators I)
 Ideal * Ideal := Ideal => ((I,J) -> ideal flatten (generators I ** generators J)) @@ samering
 Ideal * Module := Module => ((I,M) -> subquotient (generators I ** generators M, relations M)) @@ samering
-Ideal + Ideal := Ideal => ((I,J) -> ideal (generators I | generators J)) @@ tosamering
-Ideal + RingElement := Ideal + Number := ((I,r) -> I + ideal r) @@ tosamering
-RingElement + Ideal := Number + Ideal := ((r,I) -> ideal r + I) @@ tosamering
-Ideal _ ZZ := RingElement => (I,n) -> (generators I)_(0,n)
+
+LeftIdeal + LeftIdeal := LeftIdeal => ((I,J) -> ideal (generators I | generators J)) @@ tosamering
+-- Ideal + Ideal := Ideal => ((I,J) -> ideal (generators I | generators J)) @@ tosamering
+LeftIdeal + RingElement := LeftIdeal + Number := ((I,r) -> I + ideal r) @@ tosamering
+RingElement + LeftIdeal := Number + LeftIdeal := ((r,I) -> ideal r + I) @@ tosamering
+LeftIdeal _ ZZ := RingElement => (I,n) -> (generators I)_(0,n)
+
+
+Matrix % LeftIdeal := Matrix => ((f,I) -> 
+     if numRows f === 1
+     then f % gb I
+     else 
+     error "not implemented (defined for two-sided ideals; see `code (symbol %, Matrix, Ideal)`)"
+     ) @@ samering
+
+-- two-sided ideal expected (note: R/I is a problem !!!)
 Matrix % Ideal := Matrix => ((f,I) -> 
      if numRows f === 1
      then f % gb I
@@ -508,23 +526,28 @@ Matrix % Ideal := Matrix => ((f,I) ->
 	  S := R/I;
 	  lift(promote(f,S),R))
      ) @@ samering
-Vector % Ideal := (v,I) -> new class v from {v#0%I}
-numgens Ideal := (I) -> numgens source generators I
-leadTerm Ideal := Matrix => (I) -> leadTerm generators gb I
-leadTerm(ZZ,Ideal) := Matrix => (n,I) -> leadTerm(n,generators gb I)
-jacobian Ideal := Matrix => (I) -> jacobian generators I
-Ideal _ List := (I,w) -> (module I)_w
 
-ring Ideal := (I) -> I.ring
+Vector % LeftIdeal := (v,I) -> new class v from {v#0%I}
+
+numgens LeftIdeal := I -> numgens source generators I
+leadTerm LeftIdeal := Matrix => I -> leadTerm generators gb I
+leadTerm(ZZ,LeftIdeal) := Matrix => (n,I) -> leadTerm(n,generators gb I)
+
+-- two-sided ideal expected (unless defined for non-polynomial rings!!!)
+jacobian Ideal := Matrix => I -> jacobian generators I
+
+LeftIdeal _ List := (I,w) -> (module I)_w
+
+ring LeftIdeal := I -> I.ring
 
-Ideal == Ring := (I,R) -> (
+LeftIdeal == Ring := (I,R) -> (
      if ring I =!= R
      then error "expected ideal in the given ring";
      1_R % I == 0)
 
-Ring == Ideal := (R,I) -> I == R
+Ring == LeftIdeal := (R,I) -> I == R
 
-Ideal == Ideal := (I,J) -> (
+LeftIdeal == LeftIdeal := (I,J) -> (
      samering(I,J);
      ( generators I == generators J or 
 	  -- if isHomogeneous I and isHomogeneous J  -- can be removed later
@@ -533,10 +556,10 @@ Ideal == Ideal := (I,J) -> (
 	  isSubset(I,J) and isSubset(J,I)	  -- can be removed later
 	  ))
 
-Ideal == Module := (I,M) -> module I == M
-Module == Ideal := (M,I) -> M == module I
+LeftIdeal == Module := (I,M) -> module I == M
+Module == LeftIdeal := (M,I) -> M == module I
 
-ideal Matrix := Ideal => (f) -> (
+ideal Matrix := LeftIdeal => f -> (
      R := ring f;
      if not isFreeModule target f or not isFreeModule source f 
      then error "expected map between free modules";
@@ -549,9 +572,13 @@ ideal Matrix := Ideal => (f) -> (
      	  g := map(R^1,,f);			  -- in case the degrees are wrong
      	  if isHomogeneous g then f = g;
 	  );
-     new Ideal from { symbol generators => f, symbol ring => R, symbol cache => new CacheTable } )
+     new (
+	 -- Ideal == two-sided ideal
+	 if isCommutative R or isSkewCommutative R then Ideal 
+	 else LeftIdeal
+	 ) from { symbol generators => f, symbol ring => R, symbol cache => new CacheTable } )
 
-ideal Module := Ideal => (M) -> (
+ideal Module := LeftIdeal => M -> (
      F := ambient M;
      if isSubmodule M and rank F === 1 then ideal generators M
      else error "expected a submodule of a free module of rank 1"
@@ -560,13 +587,14 @@ idealPrepare = method()
 idealPrepare RingElement := 
 idealPrepare Number := identity
 idealPrepare Matrix := m -> flatten entries m
-idealPrepare Ideal := I -> I_*
+idealPrepare LeftIdeal := I -> I_*
 idealPrepare Thing := x -> error "expected a list of numbers, matrices, ring elements or ideals"
-ideal List := ideal Sequence := Ideal => v -> ideal matrix {flatten apply(toList splice v,idealPrepare)}
-ideal RingElement := ideal Number := Ideal => v -> ideal {v}
+ideal List := ideal Sequence := LeftIdeal => v -> ideal matrix {flatten apply(toList splice v,idealPrepare)}
+ideal RingElement := ideal Number := LeftIdeal => v -> ideal {v}
 ideal Ring := R -> ideal map(R^1,R^0,0)
 
-Ideal ^ Array := (I, e) -> (
+-- not well-defined (mathwise!!!)
+Ideal ^ Array := (I, e) -> ( 
    R := ring I;
    n := numgens R;
    -- Error if input is not correct.
@@ -635,7 +663,7 @@ degree Matrix := List => (f) -> (
      if N.?generators then d = d + getshift N.generators;
      d)
 
-super(Matrix) := Matrix => (f) -> (
+super Matrix := Matrix => (f) -> (
      M := target f;
      if M.?generators then map(super M, M, M.generators) * f
      else f
@@ -644,18 +672,19 @@ super(Matrix) := Matrix => (f) -> (
 isInjective Matrix := (f) -> kernel f == 0
 isSurjective Matrix := (f) -> cokernel f == 0
 
+-- two-sided ideal expected
 scan({ZZ,QQ}, S -> (
 	  lift(Ideal,S) := opts -> (I,S) -> (
 	       -- this will be pretty slow
 	       if ring I === S then I
 	       else (ideal lift(generators I,S,opts)) + ideal (presentation ring I ** S))));
 
-content(RingElement) := Ideal => (f) -> ideal \\ last \ listForm f
-content(RingElement, RingElement) := Ideal => (f,x) -> ideal last coefficients(f, Variables => {x})
+content RingElement := LeftIdeal => f -> ideal \\ last \ listForm f
+content(RingElement, RingElement) := LeftIdeal => (f,x) -> ideal last coefficients(f, Variables => {x})
 
-cover(Matrix) := Matrix => (f) -> matrix f
+cover Matrix := Matrix => f -> matrix f
 
-rank Matrix := (f) -> (
+rank Matrix := f -> (
     if hasEngineLinearAlgebra ring f and isBasicMatrix f 
     then basicRank f 
     else rank image f
diff --git a/M2/Macaulay2/m2/newring.m2 b/M2/Macaulay2/m2/newring.m2
index 9a499802a15..3e7a79e6d38 100644
--- a/M2/Macaulay2/m2/newring.m2
+++ b/M2/Macaulay2/m2/newring.m2
@@ -75,7 +75,8 @@ tensor(QuotientRing,   QuotientRing) := monoidTensorDefaults >> optns -> (R, S)
      fg := substitute(f,(vars AB)_{0 .. m-1}) | substitute(g,(vars AB)_{m .. m+n-1});
      -- forceGB fg;  -- if the monomial order chosen doesn't restrict, then this
                      -- is an error!! MES
-     AB/image fg)
+     if isPolynomialRing A and isPolynomialRing B then AB else AB/image fg
+     )
 
 -------------------------
 -- Graph of a ring map --
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2 b/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2
index b93f253b500..c6b7765ab92 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2
@@ -496,7 +496,7 @@ document {
 	  "(gens K) % I"
 	  },
      "In Macaulay2, inclusion of ideals can be tested using ", TO (isSubset,Ideal,Ideal),
-     " and equality can be checked using ", TO (symbol==,Ideal,Ideal), ".  In both cases
+     " and equality can be checked using ", TO (symbol==,LeftIdeal,LeftIdeal), ".  In both cases
      the necessary Groebner bases are computed, if they have not already been computed.",
      EXAMPLE {
 	  "isSubset(K,I)",
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc.m2
index 823757fd50b..c6878018ad3 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc.m2
@@ -226,7 +226,7 @@ document {
 	  (symbol +, ChainComplexMap, ZZ),
 	  (symbol +, RingElement, RingElement),
 	  (symbol +, InfiniteNumber, InfiniteNumber),
-	  (symbol +, Ideal, RingElement),
+	  (symbol +, LeftIdeal, RingElement),
 	  (symbol +, RingElement, ChainComplexMap),
 	  (symbol +, MutableMatrix, MutableMatrix),
 	  (symbol +, Matrix, Matrix),
@@ -803,7 +803,8 @@ document {
 	  (symbol==, Matrix, Matrix), (symbol==, ProjectiveHilbertPolynomial, ProjectiveHilbertPolynomial),
 	  (symbol==, ZZ, ProjectiveHilbertPolynomial), (symbol==, ProjectiveHilbertPolynomial, ZZ),
 	  (symbol==, ChainComplex, ChainComplex), (symbol==, RingElement, RingElement), (symbol==, GradedModuleMap, GradedModuleMap),
-	  (symbol==, Ideal, Ideal), (symbol==, MutableMatrix, MutableMatrix), (symbol ==,Boolean,Boolean),
+	  (symbol==, LeftIdeal, LeftIdeal), 
+	  (symbol==, MutableMatrix, MutableMatrix), (symbol ==,Boolean,Boolean),
 	  (symbol ==,CC,CC), (symbol ==,CC,QQ), (symbol ==,CC,RR), (symbol ==,CC,ZZ), (symbol ==,Matrix,Number),
 	  (symbol ==,Number,Matrix), (symbol ==,QQ,CC), (symbol ==,QQ,QQ), (symbol ==,QQ,RR), (symbol ==,RR,CC),
 	  (symbol ==,RR,QQ), (symbol ==,RR,RR), (symbol ==,RR,ZZ),
@@ -837,7 +838,7 @@ document {
 	  (symbol==, GradedModuleMap, RingElement),
 	  (symbol==, RingElement, GradedModuleMap),
 	  (symbol==, String, Net),
-	  (symbol==, Ideal, Ring),
+	  (symbol==, LeftIdeal, Ring),
 	  (symbol==, ZZ, Ideal),
 	  (symbol==, Ideal, ZZ),
 	  (symbol==, Matrix, RingElement),
@@ -859,9 +860,9 @@ document {
 	  (symbol==, ChainComplexMap, ChainComplexMap),
 	  (symbol==, Net, Net),
 	  (symbol==, Net, String),
-	  (symbol==, Module, Ideal),
-	  (symbol==, Ideal, Module),
-	  (symbol==, Ring, Ideal),
+	  (symbol==, Module, LeftIdeal),
+	  (symbol==, LeftIdeal, Module),
+	  (symbol==, Ring, LeftIdeal),
 	  (symbol==, RingMap, ZZ),
 	  (symbol==, ZZ, RingMap)
 	  },
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc3.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc3.m2
index be87bd9e026..607621f2b35 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc3.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc3.m2
@@ -139,8 +139,8 @@ document {
      }
 
 document {
-     Key => { (symbol /,Ideal,Function),
-	  (symbol \,Function,Ideal)},
+     Key => { (symbol /,LeftIdeal,Function),
+	  (symbol \,Function,LeftIdeal)},
      Headline => "apply a function to generators of an ideal",
      Usage => "I/f\nf\\I",
      Inputs => { "I","f"},
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc7.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc7.m2
index 8d377f459eb..bd1ad2bbf20 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc7.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc7.m2
@@ -124,7 +124,7 @@ document {
      SeeAlso => {"leadCoefficient", "leadMonomial", "leadComponent"}
      }
 document {
-     Key => (leadTerm, Ideal),
+     Key => (leadTerm, LeftIdeal),
      Headline => "get the ideal of greatest terms",
      Usage => "leadTerm I",
      Inputs => {"I"},
@@ -183,7 +183,7 @@ document {
      SeeAlso => { "selectInSubring" }
      }
 document {
-     Key => (leadTerm, ZZ, Ideal),
+     Key => (leadTerm, ZZ, LeftIdeal),
      Headline => "get the ideal of lead polynomials",
      Usage => "leadTerm(n,I)",
      Inputs => {"n", "I"},
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc8.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc8.m2
index 91659b1d050..b5e51c4e603 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc8.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc8.m2
@@ -43,7 +43,7 @@ document {
      }
 
 document {
-     Key => (symbol /, Ideal, Ideal),
+     Key => (symbol /, LeftIdeal, LeftIdeal),
      Headline => "quotient module",
      Usage => "I/J",
      Inputs => { "I", "J" => {"in the same ring as ", TT "I"}},
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2
index 1ecc4fc1658..92beb2f3840 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2
@@ -1,6 +1,6 @@
 -- -*- coding: utf-8 -*-
 document {
-     Key => (symbol _*,Ideal),
+     Key => (symbol _*,LeftIdeal),
      Headline => "get the list of generators of an ideal",
      Usage => "I_*",
      Inputs => {"I"},
@@ -15,7 +15,13 @@ document {
 
 document {
      Key => Ideal,
-     Headline => "the class of all ideals",
+     Headline => "the class of two-sided ideals",
+     SeeAlso => {"LeftIdeal", "ideals"}
+     }
+ 
+document {
+     Key => LeftIdeal,
+     Headline => "the class of left ideals",
      SeeAlso => "ideals",
      "For basic information about ideals in ", EM "Macaulay2", ", see ",
      TO "ideals", ".",
@@ -32,16 +38,16 @@ document {
   	  },
      "Common ways to get information about an ideal:",
      UL {
-	  TO (generators, Ideal),
-	  TO (symbol _*,Ideal),
+	  TO (generators, LeftIdeal),
+	  TO (symbol _*,LeftIdeal),
 	  TO (isSubset, Ideal, Ideal),
 	  TO "MinimalPrimes :: isPrime(Ideal)"
 	  },
      "Common operations on ideals:",
      UL {
-	  TO (symbol +,Ideal,Ideal),
+	  TO (symbol +,LeftIdeal,LeftIdeal),
 	  TO (symbol *,Ideal,Ideal),
-	  TO (symbol ==,Ideal,Ideal),
+	  TO (symbol ==,LeftIdeal,LeftIdeal),
 	  TO (symbol ==,Ideal,ZZ),
 	  TO (symbol ^,Ideal,ZZ),
 	  TO (trim, Ideal)
@@ -114,7 +120,7 @@ document {
      SeeAlso => {"ideals"}
      }
 document {
-     Key => {(symbol +,Ideal,Ideal),
+     Key => {(symbol +,LeftIdeal,LeftIdeal),
 	  (symbol +,Ideal,MonomialIdeal),
 	  (symbol +,MonomialIdeal,Ideal)
 	  },
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/comodule-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/comodule-doc.m2
index e812afb90dd..a86dbd9e6d2 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/comodule-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/comodule-doc.m2
@@ -4,9 +4,9 @@
 
 document { 
      Key => {comodule,
-	  (comodule, Ideal),
+	  (comodule, LeftIdeal),
 	  (comodule, Module),
-	  (quotient, Ideal),
+	  (quotient, LeftIdeal),
 	  (quotient, Module)
 	  },
      Headline => "submodule to quotient module",
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/degreeLength-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/degreeLength-doc.m2
index d81cba6270e..aca3d3067fc 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/degreeLength-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/degreeLength-doc.m2
@@ -4,7 +4,7 @@
 
 undocumented {
     (degreeLength, Module),
-    (degreeLength, Ideal),
+    (degreeLength, LeftIdeal),
      (degreeLength, InexactField),
      (degreeLength,PolynomialRing), 
      (degreeLength,QuotientRing),
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/degrees-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/degrees-doc.m2
index d0dcde14e13..a0233f8fcef 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/degrees-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/degrees-doc.m2
@@ -11,7 +11,8 @@ document {
     	 (degrees, FractionField),
 	 (degrees, Module),
 	 (degrees, Monoid),
-	 (degrees, Ideal)},
+	 (degrees, LeftIdeal),
+	 (degrees, CoherentSheaf)},
      Headline => "degrees of generators",
      Usage => "degrees A",
      Inputs => {"A" => { ofClass Ring, ", ", ofClass Ideal, ", ", ofClass Module, ", or ", ofClass Monoid }
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/degreesRing-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/degreesRing-doc.m2
index c2d27fff8e7..4d0bc7788bc 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/degreesRing-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/degreesRing-doc.m2
@@ -3,7 +3,7 @@
 --- notes:  
 
 undocumented {
-    (degreesRing,   PolynomialRing), (degreesRing,   QuotientRing), (degreesRing,   Module), (degreesRing, Ideal),
+    (degreesRing,   PolynomialRing), (degreesRing,   QuotientRing), (degreesRing,   Module), (degreesRing, LeftIdeal),
     (degreesMonoid, PolynomialRing), (degreesMonoid, QuotientRing), (degreesMonoid, Module),
     }
 
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/generators-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/generators-doc.m2
index 1c8567250d1..1eca448a95e 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/generators-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/generators-doc.m2
@@ -35,10 +35,10 @@ document {
      }
 
 document {
-     Key => {generator,(generator,Ideal),(generator,Module)},
+     Key => {generator,(generator,LeftIdeal),(generator,Module)},
      Headline => "provide a single generator",
      Usage => "generator I",
-     Inputs => { "I" => {ofClass{Ideal,Module}}},
+     Inputs => { "I" => {ofClass{LeftIdeal,Module}}},
      Outputs => {{"the single generator of ", TT "I", ", if it has just one"}},
      PARA {"If the number of apparent generators is greater than 1, then ", TO "trim", " will be called."},
      EXAMPLE lines ///
@@ -112,7 +112,7 @@ document {
      SeeAlso => {monoid}
      }
 document {
-     Key => {(generators, Ideal),
+     Key => {(generators, LeftIdeal),
 	  (generators, MonomialIdeal)},
      Headline => "the generator matrix of an ideal",
      Usage => "generators I\ngens I",
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/ideal-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/ideal-doc.m2
index 1f6c81678ce..0ada00dd9dd 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/ideal-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/ideal-doc.m2
@@ -15,9 +15,12 @@ document {
 	  "L" => {"or a ", TO2("Sequence","sequence"), " of ", TO2("RingElement", "ring elements")}
 	  },
      Outputs => {
-	  Ideal => {"which is generated by the ", TO2("List","list"), " or ",
+	  LeftIdeal => {"which is generated by the ", TO2("List","list"), " or ",
 	  TO2("Sequence","sequence"), " of ",  TO2("RingElement", "ring elements")}
 	  },
+     PARA {
+	 "If the input (generators) is in a commutative or skew-commutative ring the type of the output is a (two-sided) ", TO "Ideal","." 
+	 },
      EXAMPLE {
 	  "R = ZZ/101[w,x,y,z];",
 	  "ideal{x^2-w*y, x*y-w*z, x*z-y^2}",
@@ -37,7 +40,7 @@ document {
      ideal ()
      promote(oo,R)
      ///,
-     SeeAlso => {Ideal, PolynomialRing}
+     SeeAlso => {LeftIdeal, Ideal, PolynomialRing}
      }
 document { 
      Key => (ideal,Matrix),
@@ -46,8 +49,11 @@ document {
 	  "M" => {"whose ", TO "entries", " are ", TO2("RingElement", "ring elements")}
 	  },
      Outputs => {
-	  Ideal => {"which is generated by all the entries in ", TT "M"}
+	  LeftIdeal => {"which is generated by all the entries in ", TT "M"}
 	  },
+     PARA {
+	 "If the input (generators) is in a commutative or skew-commutative ring the type of the output is a (two-sided) ", TO "Ideal","." 
+	 },
      EXAMPLE {
 	  "R = ZZ/7[w,x,y,z];",
 	  "f = vars R",
@@ -68,8 +74,11 @@ document {
 	  "r"
 	  },
      Outputs => {
-	  Ideal => {"which is generated by the ", TO2("RingElement", "ring element"), " ", TT "r"}
+	  LeftIdeal => {"which is generated by the ", TO2("RingElement", "ring element"), " ", TT "r"}
 	  },
+      PARA {
+	 "If the input (generator) is in a commutative or skew-commutative ring the type of the output is a (two-sided) ", TO "Ideal","." 
+	 },
      EXAMPLE {
 	  "ideal 7",
 	  "R = ZZ/2[x,y];",
@@ -101,9 +110,14 @@ document {
      Outputs => {
 	  Ideal => {"which is the defining ideal of ", TT "R"}
 	  },
-     "A ", TO2("QuotientRing","quotient ring"), " is a the quotient of its ", TO "ambient", 
-     " ", TO2("Ring","ring"), " by its defining ideal.  Other rings have no ambient ring,
-     and the defining ideal is its zero ideal.", 
+     PARA {
+	 "If the input (generators) is in a commutative or skew-commutative ring the type of the output is a (two-sided) ", TO "Ideal","." 
+	 },
+     PARA {
+     	 "A ", TO2("QuotientRing","quotient ring"), " is a the quotient of its ", TO "ambient", 
+     	 " ", TO2("Ring","ring"), " by its defining ideal.  Other rings have no ambient ring,
+     	 and the defining ideal is its zero ideal."
+	 }, 
      EXAMPLE {
 	  "S = ZZ/2[x,y,z];",
 	  "ideal S",
@@ -141,7 +155,7 @@ document {
 	  "I * ideal I",
 	  "I + ideal(x*y+y*z)"
 	  },
-     SeeAlso => {monomialIdeal, (generators,Ideal)}
+     SeeAlso => {monomialIdeal, (generators,LeftIdeal)}
      }
 document { 
      Key => (ideal,Module),
@@ -151,7 +165,7 @@ document {
 	  "M" => "which is a submodule of a free module of rank 1"
 	  },
      Outputs => {
-	  Ideal => {"given by the generators of ", TT "M"}
+	  LeftIdeal => {"given by the generators of ", TT "M"}
 	  },
      EXAMPLE {
 	  "R = QQ[w,x,y,z];",
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/isHomogeneous-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/isHomogeneous-doc.m2
index eae43af934e..27ed869b5f7 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/isHomogeneous-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/isHomogeneous-doc.m2
@@ -19,7 +19,7 @@ document {
 	  (isHomogeneous,ChainComplex),
 	  (isHomogeneous,RingMap),
 	  (isHomogeneous,Vector),
-	  (isHomogeneous,Ideal)},
+	  (isHomogeneous,LeftIdeal)},
      Headline => "whether something is homogeneous (graded)",
      Usage => "isHomogeneous x",
      Inputs => {
@@ -27,7 +27,7 @@ document {
 	       TO RingElement, ", ",
 	       TO Vector, ", ",
 	       TO Matrix, ", ",
-	       TO Ideal, ", ",
+	       TO LeftIdeal, ", ",
 	       TO Module, ", ",
 	       TO RingMap, ", ",
 	       TO ChainComplex, ", or ",
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/isIdeal-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/isIdeal-doc.m2
index d6fb954b80e..beb9127ad22 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/isIdeal-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/isIdeal-doc.m2
@@ -3,14 +3,14 @@
 --- notes: 
 
 document { 
-     Key => {isIdeal, (isIdeal,Thing), (isIdeal,Module),(isIdeal, Ideal),(isIdeal, MonomialIdeal)},
+     Key => {isIdeal, (isIdeal,Thing), (isIdeal,Module),(isIdeal, LeftIdeal),(isIdeal, MonomialIdeal)},
      Headline => "whether something is an ideal",
      Usage => "isIdeal I",
      Inputs => {
 	  "I" => Thing
 	  },
      Outputs => {
-	  Boolean => {TO "true", " if ", TT "I", " is either an ", TO2("Ideal", "ideal"), 
+	  Boolean => {TO "true", " if ", TT "I", " is either an ", TO2("LeftIdeal", "ideal"), 
 	       ", a ", TO2("MonomialIdeal", "monomial ideal"), " or a ", TO2("Module", "module"), 
 	       " which is a submodule of a free module of rank 1 with generators in degree 0 and ", 
 	       TO "false", " otherwise"}
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/numgens-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/numgens-doc.m2
index a742a29214a..1aa1443c7d5 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/numgens-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/numgens-doc.m2
@@ -53,7 +53,7 @@ document {
      SeeAlso => {monoid}
      }
 document { 
-     Key => (numgens,Ideal),
+     Key => (numgens,LeftIdeal),
      Headline => "number of generators of an ideal",
      Usage => "numgens I",
      Inputs => {
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/promote-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/promote-doc.m2
index cfaa8ade0a0..900de39663d 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/promote-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/promote-doc.m2
@@ -20,8 +20,8 @@ promote(Vector,type of RingElement)
 
 undocumented {(promote,CC,CC_*),
      (promote, Matrix, InexactNumber),(promote, Number, InexactNumber),
-     (promote, Ideal, Number),
-     (promote, Ideal, RingElement),
+     (promote, LeftIdeal, Number),
+     (promote, LeftIdeal, RingElement),
      (promote, List, QQ, CC_*),
      (promote, List, QQ, QQ),
      (promote, List, QQ, RR_*),
@@ -99,7 +99,7 @@ document {
      Headline => "promote to another ring",
      Usage => "promote(f,R)",
      Inputs => {
-	  "f" => {ofClass{RingElement, Ideal, Matrix}, " over some base ring of R"},
+	  "f" => {ofClass{RingElement, LeftIdeal, Matrix}, " over some base ring of R"},
 	  "R" => Ring
 	  },
      Outputs => {
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/ring-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/ring-doc.m2
index 660f463c89e..c81cf5ad104 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/ring-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/ring-doc.m2
@@ -6,8 +6,8 @@ document {
      Key => {ring, (ring,Vector), (ring,RingElement), (ring,GradedModule),
 	  (ring,ChainComplexMap),(ring, GradedModuleMap),(ring, GroebnerBasis),(ring, Number),
 	  (ring,Module),(ring,ChainComplex),(ring,Matrix),
-	  (ring,MutableMatrix),(ring,Ideal), (ring,CC),(ring,RR),(ring,RRi),(ring,Resolution),
-	  (ring,MonomialIdeal)},
+	  (ring,MutableMatrix),(ring,LeftIdeal), (ring,CC),(ring,RR),(ring,RRi),(ring,Resolution),
+	  (ring,CoherentSheaf),(ring,MonomialIdeal)},
      Headline => "get the associated ring of an object",
      Usage => "ring M",
      Inputs => {"M" => "an object with a ring associated to it"},
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/symbol-underscore-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/symbol-underscore-doc.m2
index 92888e5dd20..30da9213c8a 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/symbol-underscore-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/symbol-underscore-doc.m2
@@ -316,7 +316,7 @@ document {
 
 document { 
      Key => {"generators of ideals and modules",
-	  (symbol _, Ideal, ZZ),
+	  (symbol _, LeftIdeal, ZZ),
 	  (symbol _, MonomialIdeal, ZZ),
 	  (symbol _, Module, ZZ),
 	  (symbol _, Matrix, ZZ)},
@@ -325,7 +325,7 @@ document {
 	  Heading => "Synopsis",
      	  Usage => "L_i",
      	  Inputs => {
-	       "L" => ofClass{Ideal,MonomialIdeal,Module,Matrix},
+	       "L" => ofClass{LeftIdeal,MonomialIdeal,Module,Matrix},
 	       "i" => ZZ
 	       },
      	  Outputs => {
@@ -442,11 +442,11 @@ document {
      }
 
 document {
-     Key => {(symbol _, Module, List), (symbol _, Ideal, List)},
+     Key => {(symbol _, Module, List), (symbol _, LeftIdeal, List)},
      Headline => "map from free module to some generators",
      Usage => "M_p",
      Inputs => {
-	  "M" => {"or ", ofClass Ideal},
+	  "M" => {"or ", ofClass LeftIdeal},
 	  "p" => "of integers"
 	  },
      Outputs => {
@@ -466,7 +466,7 @@ document {
 	  source g
 	  target g
 	  ///,
-     SeeAlso => { (module, Ideal), (symbol _, Module, ZZ) }
+     SeeAlso => { (module, LeftIdeal), (symbol _, Module, ZZ) }
      }
 
 document { 
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2 b/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2
index bf4eee0b669..9743b3d88c7 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2
@@ -181,7 +181,7 @@ document {
 	  "I*J",
 	  "I^2"
 	  },
-     "For more information see ", TO (symbol+,Ideal,Ideal), ", 
+     "For more information see ", TO (symbol+,LeftIdeal,LeftIdeal), ", 
      ", TO (symbol*,Ideal,Ideal), ", and ", TO (symbol^,Ideal,ZZ), "."
      }
 
@@ -191,7 +191,7 @@ document {
      (or quotient of a polynomial ring) is checked by comparing their 
      respective Groebner bases.",     
      SUBSECTION "equal and not equal",
-       "Use ", TO (symbol==,Ideal,Ideal), " to test if two ideals in 
+       "Use ", TO (symbol==,LeftIdeal,LeftIdeal), " to test if two ideals in 
        the same ring 
        are equal.",
        EXAMPLE {
@@ -236,7 +236,7 @@ document {
 	    "S == 0"
 	    },
      SeeAlso => {
-	  (symbol==,Ideal,Ideal),
+	  (symbol==,LeftIdeal,LeftIdeal),
 	  (symbol==,Ideal,ZZ),
 	  symbol!=,
 	  (symbol%,RingElement,Ideal),
diff --git a/M2/Macaulay2/packages/MultiprojectiveVarieties.m2 b/M2/Macaulay2/packages/MultiprojectiveVarieties.m2
index 50440e6ba50..0d949eafd7d 100644
--- a/M2/Macaulay2/packages/MultiprojectiveVarieties.m2
+++ b/M2/Macaulay2/packages/MultiprojectiveVarieties.m2
@@ -2733,7 +2733,7 @@ EXAMPLE {"O = 0_(PP_(ZZ/101)^{2,1});",
 "X = random({2,1},O);",
 "Y = random({1,1},O);",
 "X * Y"},
-SeeAlso => {(symbol +,MultiprojectiveVariety,MultiprojectiveVariety),(symbol +,Ideal,Ideal),(⋂,List)}}
+SeeAlso => {(symbol +,MultiprojectiveVariety,MultiprojectiveVariety),(symbol +,LeftIdeal,LeftIdeal),(⋂,List)}}
 
 document {Key => {⋂,(⋂,List)}, 
 Headline => "intersection of multi-projective varieties", 
diff --git a/M2/Macaulay2/packages/Varieties/euler-doc.m2 b/M2/Macaulay2/packages/Varieties/euler-doc.m2
index b5d8b78e83c..9dcfb1db3e3 100644
--- a/M2/Macaulay2/packages/Varieties/euler-doc.m2
+++ b/M2/Macaulay2/packages/Varieties/euler-doc.m2
@@ -86,9 +86,9 @@ document {
      }
 
 document {
-     Key => (euler,Ideal),
+     Key => (euler,LeftIdeal),
      "This needs to be documented.",
-     SeeAlso => {(eulers,Ideal),genus}
+     SeeAlso => {(eulers,LeftIdeal),genus}
      }
 
 document { 
@@ -130,7 +130,7 @@ document {
      SeeAlso => {genera,genus}
      }
 document { 
-     Key => (eulers,Ideal),
+     Key => (eulers,LeftIdeal),
      Usage => "eulers I",
      Inputs => {"I"
 	  },
diff --git a/M2/Macaulay2/packages/Varieties/genera-doc.m2 b/M2/Macaulay2/packages/Varieties/genera-doc.m2
index 3565855f714..69c253271e4 100644
--- a/M2/Macaulay2/packages/Varieties/genera-doc.m2
+++ b/M2/Macaulay2/packages/Varieties/genera-doc.m2
@@ -47,7 +47,7 @@ document {
      SeeAlso => {euler}
      }
 document { 
-     Key => (genera,Ideal),
+     Key => (genera,LeftIdeal),
      Usage => "genera I",
      Inputs => {"I"
 	  },
diff --git a/M2/Macaulay2/packages/Varieties/genus-doc.m2 b/M2/Macaulay2/packages/Varieties/genus-doc.m2
index d355fede049..ae1622854f5 100644
--- a/M2/Macaulay2/packages/Varieties/genus-doc.m2
+++ b/M2/Macaulay2/packages/Varieties/genus-doc.m2
@@ -8,9 +8,9 @@ document {
      SeeAlso => {genera, euler}
      }
 document { 
-     Key => {(genus,CoherentSheaf),(genus,Module),(genus, Ideal)},
+     Key => {(genus,CoherentSheaf),(genus,Module),(genus, LeftIdeal)},
      Usage => "genus F",
-     Inputs => {"F" => {ofClass{CoherentSheaf,Module,Ideal} }},
+     Inputs => {"F" => {ofClass{CoherentSheaf,Module,LeftIdeal} }},
      Outputs => {ZZ },
      "Computes the arithmetic genus of the coherent sheaf ", TT "F", " that is (-1)^dim-support * (chi(F) - 1)).  If ", TT "F", " is a module
      over a ring, then the genus of ", TT "F~", " is computed.  If ", TT "I", " is an ideal in a ring ", TT "R", " then the genus of ", TT "(R/I)~", " is

From 87f0f2794552f84cd7a7c3d5f8adf14d64f0048d Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Tue, 3 Oct 2023 12:32:54 -0400
Subject: [PATCH 02/14] LeftIdeal update: more packages install now; checks
 pass for Dmodules, but not for BernsteinSato yet

---
 M2/Macaulay2/m2/gb.m2                         |  2 +-
 M2/Macaulay2/m2/intersect.m2                  | 12 ++---
 M2/Macaulay2/m2/matrix2.m2                    | 12 ++---
 M2/Macaulay2/m2/modules2.m2                   | 10 ++--
 M2/Macaulay2/m2/newring.m2                    | 14 ++++--
 M2/Macaulay2/m2/ringmap.m2                    | 12 ++---
 .../BernsteinSato/DOC/Drestriction.m2         |  4 +-
 .../packages/BernsteinSato/DOC/bFunctions.m2  |  8 ++--
 .../packages/BernsteinSato/Dresolution.m2     |  6 +--
 .../packages/BernsteinSato/bFunction.ideal.m2 |  6 +--
 .../packages/BernsteinSato/globalBFunction.m2 |  8 ++--
 .../packages/BernsteinSato/localBFunction.m2  |  8 ++--
 .../packages/WeylAlgebras/DOC/basics.m2       | 46 +++++++++----------
 M2/Macaulay2/packages/WeylAlgebras/Dbasic.m2  | 17 +++----
 M2/Macaulay2/packages/WeylAlgebras/Gbw.m2     |  8 ++--
 .../packages/WeylAlgebras/TST/Dbasic.m2       |  7 +--
 .../packages/WeylAlgebras/makeCyclic.m2       |  2 +-
 .../packages/WeylAlgebras/stafford.m2         |  6 +--
 18 files changed, 95 insertions(+), 93 deletions(-)

diff --git a/M2/Macaulay2/m2/gb.m2 b/M2/Macaulay2/m2/gb.m2
index 64e7f7200c4..21872a87040 100644
--- a/M2/Macaulay2/m2/gb.m2
+++ b/M2/Macaulay2/m2/gb.m2
@@ -304,7 +304,7 @@ degreeToHeft = (R, d) -> (
 -----------------------------------------------------------------------------
 
 gb = method(TypicalValue => GroebnerBasis, Options => gbDefaults)
-gb Ideal  := GroebnerBasis => opts -> I -> gb (module I, opts)
+gb LeftIdeal  := GroebnerBasis => opts -> I -> gb (module I, opts)
 gb Module := GroebnerBasis => opts -> M -> (
     if M.?relations then (
 	if not M.cache#?"full gens" then M.cache#"full gens" = generators M | relations M;
diff --git a/M2/Macaulay2/m2/intersect.m2 b/M2/Macaulay2/m2/intersect.m2
index 197adf05efc..ddd751f475a 100644
--- a/M2/Macaulay2/m2/intersect.m2
+++ b/M2/Macaulay2/m2/intersect.m2
@@ -68,7 +68,7 @@ moduleIntersectOpts := {
     }
 
 -- ideally this should be unnecessary, but some code seems to depend on this
-intersect Ideal  := Ideal  =>  idealIntersectOpts >> opts -> I -> doTrim(opts, I)
+intersect LeftIdeal  := LeftIdeal  =>  idealIntersectOpts >> opts -> I -> doTrim(opts, I)
 intersect Module := Module => moduleIntersectOpts >> opts -> M -> doTrim(opts, M)
 
 -- intersect is a MethodFunctionBinary, so arbitrary lists
@@ -77,12 +77,12 @@ intersect Module := Module => moduleIntersectOpts >> opts -> M -> doTrim(opts, M
 --   installing a method (intersect, S, T) => T enables intersect(S, T, T, ...)
 --   installing a method (intersect, S, S) => S enables intersect(S, S, T, T, ...)
 --   installing a method (intersect, T, S) => S enables intersect(S, T, S, T, ...)
-intersect(Ideal,  Ideal)  :=  Ideal =>  idealIntersectOpts >> opts -> L -> intersectHelper(L, (intersect, Ideal,  Ideal),  opts)
+intersect(LeftIdeal,  LeftIdeal)  :=  LeftIdeal =>  idealIntersectOpts >> opts -> L -> intersectHelper(L, (intersect, LeftIdeal,  LeftIdeal),  opts)
 intersect(Module, Module) := Module => moduleIntersectOpts >> opts -> L -> intersectHelper(L, (intersect, Module, Module), opts)
 
 -- Specializations for intersecting many objects at once, e.g. Modules,
 -- can be installed on (symbol intersect, T), which calls T.intersect
-Ideal.intersect  =  idealIntersectOpts >> opts -> L -> intersectHelper(L, (intersect, Ideal,  Ideal),  opts)
+LeftIdeal.intersect  =  idealIntersectOpts >> opts -> L -> intersectHelper(L, (intersect, LeftIdeal,  LeftIdeal),  opts)
 Module.intersect = moduleIntersectOpts >> opts -> L -> intersectHelper(L, (intersect, Module, Module), opts)
 
 -----------------------------------------------------------------------------
@@ -112,7 +112,7 @@ scan({Default}, strategy ->
 
 -----------------------------------------------------------------------------
 
-algorithms#(intersect, Ideal, Ideal) = new MutableHashTable from {
+algorithms#(intersect, LeftIdeal, LeftIdeal) = new MutableHashTable from {
     Default => (opts, L) -> ideal intersect(opts, apply(L, module)),
 
     -- TODO: can this be extended to do more than 2 at once?
@@ -145,6 +145,6 @@ algorithms#(intersect, Ideal, Ideal) = new MutableHashTable from {
 	    newMonomialIdeal(R, rawIntersect(raw monomialIdeal I, raw monomialIdeal J)))),
     }
 
--- Installing hooks for intersect(Ideal, Ideal)
+-- Installing hooks for intersect(LeftIdeal, LeftIdeal)
 scan({Default, "Elimination", Monomial}, strategy ->
-    addHook(key := (intersect, Ideal, Ideal), algorithms#key#strategy, Strategy => strategy))
+    addHook(key := (intersect, LeftIdeal, LeftIdeal), algorithms#key#strategy, Strategy => strategy))
diff --git a/M2/Macaulay2/m2/matrix2.m2 b/M2/Macaulay2/m2/matrix2.m2
index 8bd42f69535..077664457ea 100644
--- a/M2/Macaulay2/m2/matrix2.m2
+++ b/M2/Macaulay2/m2/matrix2.m2
@@ -136,7 +136,7 @@ complement Matrix := Matrix => (f) -> (
      else error "complement: expected matrix over affine ring or finitely generated ZZ-algebra")
 
 -- the method is declared in gb.m2
-mingens Ideal  := Matrix => opts -> I -> mingens(module I, opts)
+mingens LeftIdeal  := Matrix => opts -> I -> mingens(module I, opts)
 mingens Module := Matrix => opts -> (cacheValue symbol mingens) ((M) -> (
         c := runHooks((mingens, Module), (opts, M));
         if c =!= null then c else error "mingens: no method implemented for this type of module"))
@@ -175,7 +175,7 @@ trim QuotientRing := opts -> (R) -> (
      A/(trim(ideal f,opts)))
 
 -- TODO: why is the caching key an Option?
-trim Ideal  := Ideal  => opts -> (cacheValue (symbol trim => opts)) ((I) -> ideal trim(module I, opts))
+trim LeftIdeal  := LeftIdeal  => opts -> (cacheValue (symbol trim => opts)) ((I) -> ideal trim(module I, opts))
 trim Module := Module => opts -> (cacheValue symbol trim) (M -> (
 	if isFreeModule M then return M;
 	c := runHooks((trim, Module), (opts, M));
@@ -405,12 +405,12 @@ RingElement % Matrix := (r,f) -> (
      else error "expected target of matrix to be free, and of rank 1"
      )
 
-RingElement % Ideal := (r,I) -> (
+RingElement % LeftIdeal := (r,I) -> (
      R := ring I;
      if ring r =!= R then error "expected ring element and ideal for the same ring";
      if r == 0 then return r;
      r % if isHomogeneous I and heft R =!= null then gb(I, DegreeLimit => degree r) else gb I)
-Number % Ideal := (r,I) -> (
+Number % LeftIdeal := (r,I) -> (
      R := ring I;
      r = promote(r,R);
      if r == 0 then return r;
@@ -441,7 +441,7 @@ support = method()
 support RingElement := support Matrix := (f) -> (
      x := rawIndices raw f;
      apply(x, i -> (ring f)_i))
-support Ideal := (I) -> rsort toList sum apply(flatten entries generators I, f -> set support f)
+support LeftIdeal := (I) -> rsort toList sum apply(flatten entries generators I, f -> set support f)
 --------------------
 -- homogenization --
 --------------------
@@ -489,7 +489,7 @@ homogenize(Module,RingElement) := Module => (M,z) -> (
 	  if M.?generators then homogenize(generators gb M.generators,z),
 	  if M.?relations then homogenize(generators gb M.relations,z)))
 
-homogenize(Ideal,RingElement) := Ideal => (I,z) -> ideal homogenize(module I, z)
+homogenize(LeftIdeal,RingElement) := LeftIdeal => (I,z) -> ideal homogenize(module I, z)
 
 homogenize(Module,RingElement,List) := Module => (M,z,wts) -> (
      if isFreeModule M then M
diff --git a/M2/Macaulay2/m2/modules2.m2 b/M2/Macaulay2/m2/modules2.m2
index 1dc3a660a14..78738d2d6fc 100644
--- a/M2/Macaulay2/m2/modules2.m2
+++ b/M2/Macaulay2/m2/modules2.m2
@@ -114,8 +114,8 @@ issub := (f, g) -> (
 -- TODO: we can do better in the homogeneous case!
 addHook(ContainmentHooks, Strategy => Inhomogeneous, (f, g) -> -1 === rawGBContains(raw gb g, raw f))
 
-ZZ == Ideal := (n,I) -> I == n
-Ideal == ZZ := (I,n) -> (
+ZZ == LeftIdeal := (n,I) -> I == n
+LeftIdeal == ZZ := (I,n) -> (
      if n === 0
      then I.generators == 0
      else if n === 1
@@ -367,9 +367,9 @@ isSubset(Module,Module) := (M,N) -> (
 	  false
 	  )
      )
-isSubset(Ideal,Ideal) := (I,J) -> isSubset(module I, module J)
-isSubset(Module,Ideal) := (M,J) -> isSubset(M, module J)
-isSubset(Ideal,Module) := (I,N) -> isSubset(module I, N)
+isSubset(LeftIdeal,LeftIdeal) := (I,J) -> isSubset(module I, module J)
+isSubset(Module,LeftIdeal) := (M,J) -> isSubset(M, module J)
+isSubset(LeftIdeal,Module) := (I,N) -> isSubset(module I, N)
 
 -- Local Variables:
 -- compile-command: "make -C $M2BUILDDIR/Macaulay2/m2 "
diff --git a/M2/Macaulay2/m2/newring.m2 b/M2/Macaulay2/m2/newring.m2
index 3e7a79e6d38..9194f7f237f 100644
--- a/M2/Macaulay2/m2/newring.m2
+++ b/M2/Macaulay2/m2/newring.m2
@@ -62,7 +62,13 @@ QuotientRing ** PolynomialRing :=
 PolynomialRing ** QuotientRing :=
 QuotientRing ** QuotientRing := (R,S) -> tensor(R,S)
 
-tensor(PolynomialRing, PolynomialRing) :=
+tensor(PolynomialRing, PolynomialRing) := monoidTensorDefaults >> optns -> (R, S) -> (
+     k := coefficientRing R;
+     if k =!= coefficientRing S 
+     then error "expected rings to have the same coefficient ring";
+     k tensor(monoid R, monoid S, optns)
+     )
+
 tensor(QuotientRing,   PolynomialRing) :=
 tensor(PolynomialRing, QuotientRing) :=
 tensor(QuotientRing,   QuotientRing) := monoidTensorDefaults >> optns -> (R, S) -> (
@@ -71,11 +77,11 @@ tensor(QuotientRing,   QuotientRing) := monoidTensorDefaults >> optns -> (R, S)
      then error "expected rings to have the same coefficient ring";
      f := presentation R; A := ring f; M := monoid A; m := numgens M;
      g := presentation S; B := ring g; N := monoid B; n := numgens N;
-     AB := k tensor(M, N, optns);
-     fg := substitute(f,(vars AB)_{0 .. m-1}) | substitute(g,(vars AB)_{m .. m+n-1});
+     MN := k tensor(M, N, optns);
+     fg := substitute(f,(vars MN)_{0 .. m-1}) | substitute(g,(vars MN)_{m .. m+n-1});
      -- forceGB fg;  -- if the monomial order chosen doesn't restrict, then this
                      -- is an error!! MES
-     if isPolynomialRing A and isPolynomialRing B then AB else AB/image fg
+     MN/image fg
      )
 
 -------------------------
diff --git a/M2/Macaulay2/m2/ringmap.m2 b/M2/Macaulay2/m2/ringmap.m2
index b26c8a18462..1a865c48ee2 100644
--- a/M2/Macaulay2/m2/ringmap.m2
+++ b/M2/Macaulay2/m2/ringmap.m2
@@ -197,7 +197,7 @@ RingMap Vector := Vector => (p,m) -> (
      f := p new Matrix from m;
      new target f from f)
 
-RingMap Ideal  := Ideal  => (f, I) -> ideal f module I
+RingMap LeftIdeal  := LeftIdeal  => (f, I) -> ideal f module I
 RingMap Module := Module => (f, M) -> (
     (S, R) := (target f, source f);
     if R =!= ring M then error "expected module over source ring";
@@ -413,18 +413,18 @@ substitute(RingElement,Matrix) := RingElement => (r,f) -> (map(ring f,ring r,f))
 substitute(Vector,Matrix) := Vector => (v,f) -> (map(ring f,ring v,f)) v
 substitute(Matrix,Matrix) := Matrix => (m,f) -> (map(ring f,ring m,f)) m
 substitute(Module,Matrix) := Module => (M,f) -> (map(ring f,ring M,f)) M
-substitute(Ideal,Matrix) := Ideal => (I,f) -> (map(ring f,ring I,f)) I
+substitute(LeftIdeal,Matrix) := LeftIdeal => (I,f) -> (map(ring f,ring I,f)) I
 
 substitute(Matrix,Ring) := Matrix => (m,S) -> (map(S,ring m)) m
 substitute(Module,Ring) := Module => (M,S) -> (map(S,ring M)) M
-substitute(Ideal,Ring) := Ideal => (I,S) -> (map(S,ring I)) I
+substitute(LeftIdeal,Ring) := LeftIdeal => (I,S) -> (map(S,ring I)) I
 substitute(Vector,Ring) := Vector => (v,S) -> (map(S,ring v)) v
 substitute(Number,Ring) := 
 substitute(RingElement,Ring) := RingElement => (r,S) -> (map(S,ring r)) r
 
 substitute(Matrix,RingFamily) := Matrix => (m,S) -> substitute(m, default S)
 substitute(Module,RingFamily) := Module => (M,S) -> substitute(M, default S)
-substitute(Ideal,RingFamily) := Ideal => (I,S) -> substitute(I, default S)
+substitute(LeftIdeal,RingFamily) := LeftIdeal => (I,S) -> substitute(I, default S)
 substitute(Vector,RingFamily) := Vector => (v,S) -> substitute(v, default S)
 substitute(Number,RingFamily) := 
 substitute(RingElement,RingFamily) := RingElement => (r,S) -> substitute(r, default S)
@@ -493,13 +493,13 @@ sub2 = (S,R,v) -> (				   -- S is the target ring or might be null, meaning targ
 
 substitute(Matrix,List) := Matrix => (f,v) -> (sub2(,ring f,v)) f
 substitute(Module,List) := Module => (M,v) -> (sub2(,ring M,v)) M
-substitute(Ideal,List) := Ideal => (I,v) -> (sub2(,ring I,v)) I
+substitute(LeftIdeal,List) := LeftIdeal => (I,v) -> (sub2(,ring I,v)) I
 substitute(Vector,List) := Vector => (f,v) -> (sub2(,ring f,v)) f
 substitute(RingElement,List) := RingElement => (f,v) -> (sub2(,ring f,v)) f
 
 substitute(Matrix,Option) := (f,v) -> (sub2(,ring f,{v})) f
 substitute(Module,Option) := (M,v) -> (sub2(,ring M,{v})) M
-substitute(Ideal,Option) := (I,v) -> (sub2(,ring I,{v})) I
+substitute(LeftIdeal,Option) := (I,v) -> (sub2(,ring I,{v})) I
 substitute(Vector,Option) := (f,v) -> (sub2(,ring f,{v})) f
 substitute(RingElement,Option) := (f,v) -> (sub2(,ring f,{v})) f
 
diff --git a/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2 b/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2
index e06b9943426..fd870b58ece 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2
@@ -24,8 +24,8 @@ document {
      }
 
 document {
-     Key => {Dresolution, (Dresolution,Module), (Dresolution,Ideal,List), 
-	  (Dresolution,Module,List), (Dresolution,Ideal)},
+     Key => {Dresolution, (Dresolution,Module), (Dresolution,LeftIdeal,List), 
+	  (Dresolution,Module,List), (Dresolution,LeftIdeal)},
      Headline => "resolution of a D-module",
      Usage => "Dresolution M, Dresolution I, Dresolution(M,w), Dresolution(I,w)",
      Inputs => {
diff --git a/M2/Macaulay2/packages/BernsteinSato/DOC/bFunctions.m2 b/M2/Macaulay2/packages/BernsteinSato/DOC/bFunctions.m2
index a96e2d72440..464fe12b545 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DOC/bFunctions.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DOC/bFunctions.m2
@@ -2,7 +2,7 @@ document {
      Key => bFunction,
      Headline => "b-function",
      UL {
-	  {TO (bFunction, Ideal,List), " - for an ideal"},
+	  {TO (bFunction, LeftIdeal,List), " - for an ideal"},
 	  {TO (bFunction, Module,List,List), " - for a module"}  
 	  }
      }
@@ -40,7 +40,7 @@ document {
      }
 
 document {
-     Key => (bFunction, Ideal, List),
+     Key => (bFunction, LeftIdeal, List),
      Headline => "b-function of an ideal",
      Usage => "b = bFunction(I,w)",
      Inputs => {
@@ -310,7 +310,7 @@ document {
      }
 
 document {
-     Key => {(globalB, Ideal, RingElement), globalB},
+     Key => {(globalB, LeftIdeal, RingElement), globalB},
      Headline => "compute global b-function and b-operator 
           for a D-module and a polynomial",
      Usage => "H = globalB(I,f)", 
@@ -350,7 +350,7 @@ document {
      } 
 
 document { 
-     Key => {(localBFunction,RingElement,Ideal), localBFunction},
+     Key => {(localBFunction,RingElement,LeftIdeal), localBFunction},
      Headline => "local b-function (a.k.a. the local Bernstein-Sato polynomial)",
      Usage => "b = localBFunction(f,P)",
      Inputs => {
diff --git a/M2/Macaulay2/packages/BernsteinSato/Dresolution.m2 b/M2/Macaulay2/packages/BernsteinSato/Dresolution.m2
index b5f38ac6ac4..13f3c81a3ae 100644
--- a/M2/Macaulay2/packages/BernsteinSato/Dresolution.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/Dresolution.m2
@@ -63,7 +63,7 @@ kerGB := m -> (
 --------------------------------------------------------------------------------
 
 Dresolution = method( Options => {Strategy => Schreyer, LengthLimit => infinity} )
-Dresolution Ideal  := options -> I -> Dresolution(comodule I, options)
+Dresolution LeftIdeal  := options -> I -> Dresolution(comodule I, options)
 Dresolution Module := options -> M -> (
 
      pInfo (1, "ENTERING Dresolution ... ");
@@ -100,9 +100,7 @@ Dresolution Module := options -> M -> (
      M.cache.resolution
      )
 
-Dresolution (Ideal, List) := options -> (I, w) -> (
-     Dresolution ((ring I)^1/I, w, options)
-     )
+Dresolution (LeftIdeal, List) := options -> (I, w) -> Dresolution ((ring I)^1/I, w, options)
 
 Dresolution (Module, List) := options -> (M, w) -> (
 
diff --git a/M2/Macaulay2/packages/BernsteinSato/bFunction.ideal.m2 b/M2/Macaulay2/packages/BernsteinSato/bFunction.ideal.m2
index 09a8d60f1fb..bc38f61ad1f 100644
--- a/M2/Macaulay2/packages/BernsteinSato/bFunction.ideal.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/bFunction.ideal.m2
@@ -40,7 +40,7 @@ makeQQ := f -> (
 
 -- trivial intersection strategy (internal)
 bfIntRing := method()
-bfIntRing(Ideal, List) :=  (I, w) -> (
+bfIntRing(LeftIdeal, List) :=  (I, w) -> (
      local tInfo;
      -- prep work
      if not (ring I).?IntRing then
@@ -91,7 +91,7 @@ bfIntRing(Ideal, List) :=  (I, w) -> (
 
 -- TryGeneric or NonGeneric strategy (internal)
 bfGenericOrNonGeneric := method(Options => {Strategy => TryGeneric})
-bfGenericOrNonGeneric(Ideal, List) := o -> (I, w) -> (
+bfGenericOrNonGeneric(LeftIdeal, List) := o -> (I, w) -> (
      local tInfo;
      -- prep work
      if not (ring I).?ThetaRing then
@@ -195,7 +195,7 @@ bfGenericOrNonGeneric(Ideal, List) := o -> (I, w) -> (
      makeQQ bfcn     	
      );
 
-bFunction(Ideal, List) := RingElement => o -> (I, w) -> (
+bFunction(LeftIdeal, List) := RingElement => o -> (I, w) -> (
      result := (
 	  if o.Strategy == IntRing then bfIntRing(I, w)
      	  else if o.Strategy == TryGeneric or o.Strategy == NonGeneric 
diff --git a/M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2 b/M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2
index 35096086649..12ebed03374 100644
--- a/M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2
@@ -20,7 +20,7 @@ makeMonic := f -> ( if coefficientRing ring f === QQ
 
 -- also used in multiplierIdeals.m2
 star = method()
-star (Ideal,List) := (I,vw) -> (
+star (LeftIdeal,List) := (I,vw) -> (
      W := ring I;
      n := numgens W;
      u := symbol u;
@@ -116,7 +116,7 @@ globalRBAnnFs (RingElement,Ideal,Boolean) := RingElement => (f,AnnI,isRed) -> (
 --------------------------------------------------------------------------------
 globalB = method()
 
-globalB(Ideal, RingElement) := HashTable => (I, f) -> (
+globalB(LeftIdeal, RingElement) := HashTable => (I, f) -> (
      W := ring I;
      AnnI := AnnIFs (I,f);
      Ws := ring AnnI;
@@ -210,10 +210,10 @@ generalB (List, RingElement) := RingElement => o->(F,g) -> (
 	  inw(intersect(AnnI, ideal sub(g, DY)), -w|w)
 	  ) 
      else if m===null and o.Strategy===StarIdeal then (
-	  star(AnnI,-w|w) + sub(g*ideal F,DY)
+	  star(AnnI,-w|w) + sub(ideal(g*F),DY)
 	  )
      else if m=!=null then (
-	  star(AnnI,-w|w) + (sub(ideal F, DY))^m
+	  star(AnnI,-w|w) + ideal symmetricPower(m, gens sub(ideal F, DY))
 	  )
      else error "uknwnown Strategy";
      
diff --git a/M2/Macaulay2/packages/BernsteinSato/localBFunction.m2 b/M2/Macaulay2/packages/BernsteinSato/localBFunction.m2
index e4d904468a1..099f8fdabbc 100644
--- a/M2/Macaulay2/packages/BernsteinSato/localBFunction.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/localBFunction.m2
@@ -1,7 +1,7 @@
 -- internal, also used in multiplierIdeals.m2
 -- TODO: move to Dbasic?
 eliminateWA = method()
-eliminateWA(Ideal, List) := Ideal => (I, v) -> (
+eliminateWA(LeftIdeal, List) := LeftIdeal => (I, v) -> (
     R := ring I;
     if not isSubset(v, gens R) then error "expected generators of the ring";
     w := apply(gens R, g -> if member(g, v) then 1 else 0);
@@ -17,7 +17,7 @@ protect s						    -- is this right?  should s be visible to the user?
 
 -- internal
 computeJf = method()
-computeJf RingElement := Ideal => f -> (
+computeJf RingElement := LeftIdeal => f -> (
      if #(options (ring f).monoid)#WeylAlgebra > 0 -- isWA
      then (
 	  D := ring f;
@@ -87,7 +87,7 @@ exceptionalLocusB (RingElement,RingElement) := RingElement => o -> (f,b) -> (
 protect ColonIdeal
 
 -- this version performs the computation given (ring f, I3, b)
-exceptionalLocusB (Ring,Ideal,RingElement) := RingElement => o -> (R,I3,b) -> (
+exceptionalLocusB (Ring,LeftIdeal,RingElement) := RingElement => o -> (R,I3,b) -> (
      Rs := ring I3;
      K := coefficientRing Rs;
      s := Rs_0;
@@ -176,7 +176,7 @@ localBFunctionStrata RingElement := HashTable => f -> (
      )
 
 localBFunction = method(TypicalValue => RingElement)
-localBFunction (RingElement,Ideal) := RingElement => (f,P) -> (
+localBFunction (RingElement,LeftIdeal) := RingElement => (f,P) -> (
      if ring f =!= ring P then error "same ring for polynomial and ideal expected";
      R := ring f;
      D := makeWeylAlgebra(R,SetVariables=>false);
diff --git a/M2/Macaulay2/packages/WeylAlgebras/DOC/basics.m2 b/M2/Macaulay2/packages/WeylAlgebras/DOC/basics.m2
index 7eb776a0262..12cd2c7288f 100644
--- a/M2/Macaulay2/packages/WeylAlgebras/DOC/basics.m2
+++ b/M2/Macaulay2/packages/WeylAlgebras/DOC/basics.m2
@@ -1,7 +1,7 @@
 doc ///
   Key
     gbw
-    (gbw, Ideal, List)
+    (gbw, LeftIdeal, List)
     (gbw, Matrix, List)
     [gbw, Strategy]
   Headline
@@ -10,7 +10,7 @@ doc ///
     gbI = gbw(I, w)
     gbM = gbw(M, w)
   Inputs
-    I:Ideal
+    I:LeftIdeal
       in the Weyl algebra
     M:Matrix
       with entries in the Weyl algebra
@@ -19,7 +19,7 @@ doc ///
     Strategy=>Thing
       if set to @TT "homogenize"@ the input is homogenized in the homogeneous Weyl algebra
   Outputs
-    gbI:Ideal
+    gbI:LeftIdeal
       with the generators forming a Gröbner basis of the ideal with respect to the weight vector
     gbM:Matrix
       with the columns forming a Gröbner basis of the submodule generated by the columns of the
@@ -54,7 +54,7 @@ doc ///
     inw
     (inw, Matrix, List)
     (inw, RingElement, List)
-    (inw, Ideal, List)
+    (inw, LeftIdeal, List)
   Headline
     get the initial term or ideal with respect to a weight vector
   Usage
@@ -63,14 +63,14 @@ doc ///
     inM = inw(M, w)
   Inputs
     F:RingElement
-    I:Ideal
+    I:LeftIdeal
     M:Matrix
     w:List
       of weights
   Outputs
     inF:RingElement
       the initial form of @EM "F"@ with respect to the weight vector
-    inI:Ideal
+    inI:LeftIdeal
       the initial ideal of @EM "I"@ with respect to the weight vector
     inM:Matrix
       with the columns generating the initial module of the image of @EM "M"@ with respect to the weight vector
@@ -113,12 +113,12 @@ doc ///
      Fourier
      (Fourier,Matrix)
      (Fourier,RingElement)
-     (Fourier,Ideal)
+     (Fourier,LeftIdeal)
      (Fourier,Module)
      (Fourier,ChainComplex)
       FourierInverse
      (FourierInverse, ChainComplex)
-     (FourierInverse, Ideal)
+     (FourierInverse, LeftIdeal)
      (FourierInverse, Matrix)
      (FourierInverse, Module)
      (FourierInverse, RingElement)
@@ -128,10 +128,10 @@ doc ///
     Fourier A
     FourierInverse A
    Inputs
-     A:{Matrix, RingElement, Ideal, ChainComplex}
+     A:{Matrix, RingElement, LeftIdeal, ChainComplex}
        over the Weyl algebra
    Outputs
-     :{Matrix, RingElement, Ideal, ChainComplex}
+     :{Matrix, RingElement, LeftIdeal, ChainComplex}
        the Fourier transform of @TT "A"@ as a matrix, function, ideal, or chain complex over the Weyl algebra
    Description
     Text
@@ -184,7 +184,7 @@ doc ///
    Key
      Dtransposition
      (Dtransposition,Matrix)
-     (Dtransposition,Ideal)
+     (Dtransposition,LeftIdeal)
      (Dtransposition,ChainComplex)
      (Dtransposition,RingElement)
    Headline
@@ -247,16 +247,16 @@ doc ///
 doc ///
    Key
      stafford
-     (stafford, Ideal)
+     (stafford, LeftIdeal)
    Headline
      computes 2 generators for a given ideal in the Weyl algebra
    Usage
      stafford I
    Inputs
-     I:Ideal
+     I:LeftIdeal
        of the Weyl algebra
    Outputs
-     :Ideal
+     :LeftIdeal
        with 2 generators (that has the same extension as I in k(x)<dx>)
    Description
     Text
@@ -282,7 +282,7 @@ doc ///
   Key
     isHolonomic
     (isHolonomic, Module)
-    (isHolonomic, Ideal)
+    (isHolonomic, LeftIdeal)
   Headline
     determines whether a D-module (or ideal in Weyl algebra) is holonomic
   Usage
@@ -319,7 +319,7 @@ doc ///
   Key
     DsingularLocus
     (DsingularLocus,Module)
-    (DsingularLocus,Ideal)
+    (DsingularLocus,LeftIdeal)
   Headline
     singular locus of a D-module
   Usage
@@ -328,10 +328,10 @@ doc ///
   Inputs
     M:Module
       over the Weyl algebra @EM "D"@
-    I:Ideal
+    I:LeftIdeal
       which represents the module @EM "M = D/I"@
   Outputs
-    :Ideal
+    :LeftIdeal
       the singular locus of @EM "M"@
   Description
     Text
@@ -357,7 +357,7 @@ doc ///
 doc ///
   Key
     characteristicIdeal
-    (characteristicIdeal,Ideal)
+    (characteristicIdeal,LeftIdeal)
     (characteristicIdeal,Module)
   Headline
     characteristic ideal of a D-module
@@ -366,10 +366,10 @@ doc ///
   Inputs
     M:Module
       over the Weyl algebra @EM "D"@
-    I:Ideal
+    I:LeftIdeal
       which represents the module @EM "M = D/I"@
   Outputs
-    :Ideal
+    :LeftIdeal
       the characteristic ideal of @EM "M"@
   Description
     Text
@@ -408,7 +408,7 @@ doc ///
   Key
     holonomicRank
     (holonomicRank,Module)
-    (holonomicRank,Ideal)
+    (holonomicRank,LeftIdeal)
   Headline
     holonomic rank of a D-module
   Usage
@@ -461,7 +461,7 @@ doc ///
 doc ///
   Key
     Ddim
-    (Ddim,Ideal)
+    (Ddim,LeftIdeal)
     (Ddim,Module)
   Headline
     dimension of a D-module
diff --git a/M2/Macaulay2/packages/WeylAlgebras/Dbasic.m2 b/M2/Macaulay2/packages/WeylAlgebras/Dbasic.m2
index c297a8599be..113ab7b2203 100644
--- a/M2/Macaulay2/packages/WeylAlgebras/Dbasic.m2
+++ b/M2/Macaulay2/packages/WeylAlgebras/Dbasic.m2
@@ -121,7 +121,7 @@ createCommAlgebra PolynomialRing := W -> (
 
 -- These routines compute the Fourier transform which is the automorphism
 -- of the Weyl algebra sending x -> -dx, dx -> x.
--- Input: RingElement f, Matrix m, Ideal I, ChainComplex C, or Module M
+-- Input: RingElement f, Matrix m, LeftIdeal I, ChainComplex C, or Module M
 -- Output: Fourier transform of f, m, I, C, or M
 Fourier = method()
 FourierLocal := M -> (
@@ -145,7 +145,7 @@ FourierLocal := M -> (
      FMap M
      )
 Fourier RingElement := M -> (FourierLocal M)
-Fourier Ideal := M -> (FourierLocal M)
+Fourier LeftIdeal := M -> (FourierLocal M)
 Fourier Matrix := M -> (FourierLocal M)
 Fourier ChainComplex := M -> (FourierLocal M)
 Fourier Module := M -> (cokernel FourierLocal relations prune M)
@@ -172,7 +172,7 @@ FourierInverseLocal := M -> (
      FInvMap M
      )
 FourierInverse RingElement := M -> (FourierInverseLocal M)
-FourierInverse Ideal := M -> (FourierInverseLocal M)
+FourierInverse LeftIdeal := M -> (FourierInverseLocal M)
 FourierInverse Matrix := M -> (FourierInverseLocal M)
 FourierInverse ChainComplex := M -> (FourierInverseLocal M)
 FourierInverse Module := M -> (cokernel FourierInverseLocal relations prune M)
@@ -214,7 +214,7 @@ Dtransposition Matrix := m -> (
      mtrans
      )
 
-Dtransposition Ideal := I -> (
+Dtransposition LeftIdeal := I -> (
      ideal Dtransposition gens I
      )
 
@@ -236,7 +236,7 @@ Dtransposition ChainComplex := C -> (
 
 -- This routine computes the dimension of a D-module
 Ddim = method()
-Ddim Ideal := (cacheValue Ddim) (I -> (
+Ddim LeftIdeal := (cacheValue Ddim) (I -> (
      -- preprocessing
      W := ring I;
      -- error checking
@@ -269,7 +269,7 @@ addHook((codim, Module), Strategy => WeylAlgebra,
 
 -- This routine determines whether a D-module is holonomic
 isHolonomic = method()
-isHolonomic Ideal := I -> (
+isHolonomic LeftIdeal := I -> (
      -- preprocessing
      W := ring I;
      -- error checking
@@ -296,10 +296,7 @@ isHolonomic Module := M -> (
 -- This routine computes the rank of a D-module
 -- QUESTION: this changes the current ring?
 holonomicRank = method()
-holonomicRank Ideal := I -> (
-     holonomicRank ((ring I)^1/I)
-     )
-
+holonomicRank LeftIdeal := I -> holonomicRank cokernel gens I
 holonomicRank Module := M -> (
      W := ring M;
      createDpairs W;
diff --git a/M2/Macaulay2/packages/WeylAlgebras/Gbw.m2 b/M2/Macaulay2/packages/WeylAlgebras/Gbw.m2
index 80010b6b3db..d59e8e5dbde 100644
--- a/M2/Macaulay2/packages/WeylAlgebras/Gbw.m2
+++ b/M2/Macaulay2/packages/WeylAlgebras/Gbw.m2
@@ -22,7 +22,7 @@ inw (RingElement, List) := (L, w) -> (
      mw := max apply(lf,t->sum(#w,i->t#0#i*w#i));
      part(mw,w,L)
      )
-inw(Ideal,  List) := (I, w) -> ideal inw(gens I, w)
+inw(LeftIdeal,  List) := (I, w) -> ideal inw(gens I, w)
 inw(Matrix, List) := (m, w) -> (
      -- preprocessing
      W := ring m;
@@ -120,7 +120,7 @@ inw(Matrix, List) := (m, w) -> (
 -- this routine computes a grobner basis of an ideal or matrix with respect
 -- a weight vector w.
 gbw = method(Options => { Strategy => null })
-gbw(Ideal,  List) := opts -> (I, w) -> ideal gbw(gens I, w, opts)
+gbw(LeftIdeal,  List) := opts -> (I, w) -> ideal gbw(gens I, w, opts)
 gbw(Matrix, List) := opts -> (m, w) -> (
      -- preprocessing
      W := ring m;
@@ -187,7 +187,7 @@ gbw(Matrix, List) := opts -> (m, w) -> (
 
 -- This routine computes the characteristic ideal of a D-module
 characteristicIdeal = method()
-characteristicIdeal Ideal := I -> (
+characteristicIdeal LeftIdeal := I -> (
     if not isWeylAlgebra(W := ring I) then error "expected an ideal in a Weyl algebra";
     createDpairs W;
     w := apply( toList(0..numgens W - 1),
@@ -209,7 +209,7 @@ characteristicIdeal Module := M -> (
 -- This routine computes the singular locus of a D-ideal
 -- SHOULD IT BE CHANGED SO THAT OUTPUT IS IN POLY SUBRING?
 DsingularLocus = method()
-DsingularLocus Ideal  := I -> DsingularLocus comodule I
+DsingularLocus LeftIdeal  := I -> DsingularLocus comodule I
 DsingularLocus Module := M -> (
     if not isWeylAlgebra(W := ring M) then error "expected a module over a Weyl algebra";
     createDpairs W;
diff --git a/M2/Macaulay2/packages/WeylAlgebras/TST/Dbasic.m2 b/M2/Macaulay2/packages/WeylAlgebras/TST/Dbasic.m2
index b7c95995c7f..e02d1442895 100644
--- a/M2/Macaulay2/packages/WeylAlgebras/TST/Dbasic.m2
+++ b/M2/Macaulay2/packages/WeylAlgebras/TST/Dbasic.m2
@@ -55,9 +55,10 @@ TEST///
   D = QQ[u,v,Du,Dv, WeylAlgebra => {u => Du, v => Dv}];
   assert (Dtransposition (u*Du) ==-Du*u);
   assert (Dtransposition ideal (u*Dv^2+Du^2*Dv) == ideal (u*Dv^2-Du^2*Dv));
-  assert (entries Dtransposition matrix {{u*Du, v}, {v*Dv^2, u^2}} == entries matrix {{-Du*u, v}, {Dv^2*v, u^2}});
-  C1 = Dtransposition res ideal(u*Du);
-  C2 = res ideal(-Du*u);
+  assert (entries Dtransposition matrix {{u*Du, v}, {v*Dv^2, u^2}} == entries matrix {{-Du*u, v}, {Dv^2*v, u^2}});  
+  needsPackage "BernsteinSato"
+  C1 = Dtransposition Dres ideal(u*Du);
+  C2 = Dres ideal(-Du*u);
   assert (C1_1==C2_1);
 ///
 
diff --git a/M2/Macaulay2/packages/WeylAlgebras/makeCyclic.m2 b/M2/Macaulay2/packages/WeylAlgebras/makeCyclic.m2
index 85b334498bd..3b16b73c353 100644
--- a/M2/Macaulay2/packages/WeylAlgebras/makeCyclic.m2
+++ b/M2/Macaulay2/packages/WeylAlgebras/makeCyclic.m2
@@ -211,7 +211,7 @@ assert (singLocus h.AnnG == singLocus cokernel M)
 -- R^1 / dx^3  
 -------------------------
 use R
-M = presentation image map( R^1/ideal dx^3, R^3, matrix{{1, x, x^2}} )
+M = presentation image map( cokernel matrix{{dx^3}}, R^3, matrix{{1, x, x^2}} )
 h = makeCyclic M 
 b1 = bFunction(ideal dx^3, {1})
 b2 = bFunction(cokernel M, {1}, {0,-1,-2})
diff --git a/M2/Macaulay2/packages/WeylAlgebras/stafford.m2 b/M2/Macaulay2/packages/WeylAlgebras/stafford.m2
index 24dd2903cc9..078d7bf488d 100644
--- a/M2/Macaulay2/packages/WeylAlgebras/stafford.m2
+++ b/M2/Macaulay2/packages/WeylAlgebras/stafford.m2
@@ -326,7 +326,7 @@ mainStep = (a,b,c) -> (
      )
 
 stafford = method();
-stafford Ideal := I -> (
+stafford LeftIdeal := I -> (
      g := first entries gens I;
      while #g>2 do g = mainStep(g#0,g#1,g#2) | drop(g,3);
      ideal g
@@ -607,7 +607,7 @@ isAll (ZZ,Matrix) := (k,M) -> (
      t := target M;
      all(toList(0..numgens t - 1), i->reduceInCalR(k,t_{i},M)==0)
      )
-isAll (ZZ, Ideal) := (k,I) -> (
+isAll (ZZ, LeftIdeal) := (k,I) -> (
      return isAll(k, gens gb I);
      R := ring I;
      n := numgens R // 2;
@@ -645,4 +645,4 @@ R = QQ[x_1..x_n,D_1..D_n, WeylAlgebra=>(apply(n,i->x_(i+1)=>D_(i+1)))]
 a = D_1; b = D_2; c = D_3; d = D_4;
 stafford ideal (a,b,c,d)
 assert(ideal(a,b,c,d)==oo)
-///
\ No newline at end of file
+///

From 72b1f4003d7a7c2064abe69d89bd1f9fe46c5c12 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Wed, 15 Nov 2023 22:03:50 -0500
Subject: [PATCH 03/14] docs in packages/Macaulay2Doc/... fixed

---
 .../packages/Macaulay2Doc/M2-Singular-Book.m2    |  2 +-
 M2/Macaulay2/packages/Macaulay2Doc/doc.m2        |  6 +++---
 M2/Macaulay2/packages/Macaulay2Doc/doc8.m2       |  2 +-
 M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2 | 14 +++++++-------
 .../packages/Macaulay2Doc/doc_ringmaps.m2        | 14 +++++++-------
 .../packages/Macaulay2Doc/functions/gb-doc.m2    |  2 +-
 .../Macaulay2Doc/functions/intersect-doc.m2      | 16 ++++++++--------
 .../Macaulay2Doc/functions/isSubset-doc.m2       |  4 ++--
 .../Macaulay2Doc/functions/mingens-doc.m2        |  2 +-
 .../functions/minimalPresentation-doc.m2         |  2 +-
 .../Macaulay2Doc/functions/support-doc.m2        |  2 +-
 .../Macaulay2Doc/functions/symbol-percent-doc.m2 |  4 ++--
 .../packages/Macaulay2Doc/functions/trim-doc.m2  |  2 +-
 M2/Macaulay2/packages/Macaulay2Doc/groebner.m2   |  2 +-
 M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2  |  8 ++++----
 .../packages/Macaulay2Doc/ov_ringmaps.m2         |  2 +-
 16 files changed, 42 insertions(+), 42 deletions(-)

diff --git a/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2 b/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2
index c6b7765ab92..13f530a16ed 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/M2-Singular-Book.m2
@@ -495,7 +495,7 @@ document {
 	  "K = ideal(f,x^2*y^7+y^14);",
 	  "(gens K) % I"
 	  },
-     "In Macaulay2, inclusion of ideals can be tested using ", TO (isSubset,Ideal,Ideal),
+     "In Macaulay2, inclusion of ideals can be tested using ", TO (isSubset,LeftIdeal,LeftIdeal),
      " and equality can be checked using ", TO (symbol==,LeftIdeal,LeftIdeal), ".  In both cases
      the necessary Groebner bases are computed, if they have not already been computed.",
      EXAMPLE {
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc.m2
index c6878018ad3..90f64f21db4 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc.m2
@@ -432,7 +432,7 @@ document {
 	  (symbol %, RR, RR),
 	  (symbol %, RR, ZZ),
 	  (symbol %, Number, GroebnerBasis),
-	  (symbol %, Number, Ideal),
+	  (symbol %, Number, LeftIdeal),
 	  (symbol %, ZZ, MonomialIdeal),
 	  (symbol %, ZZ, ZZ)
 	  },	  
@@ -839,8 +839,8 @@ document {
 	  (symbol==, RingElement, GradedModuleMap),
 	  (symbol==, String, Net),
 	  (symbol==, LeftIdeal, Ring),
-	  (symbol==, ZZ, Ideal),
-	  (symbol==, Ideal, ZZ),
+	  (symbol==, ZZ, LeftIdeal),
+	  (symbol==, LeftIdeal, ZZ),
 	  (symbol==, Matrix, RingElement),
 	  (symbol==, MonomialIdeal, Ideal),
 	  (symbol==, ZZ, GradedModuleMap),
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc8.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc8.m2
index b5e51c4e603..318a2994618 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc8.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc8.m2
@@ -269,7 +269,7 @@ document {
 -----------------------------------------------------------------------------
 
 document {
-     Key => {homogenize,(homogenize, Ideal, RingElement),(homogenize, Matrix, RingElement),
+     Key => {homogenize,(homogenize, LeftIdeal, RingElement),(homogenize, Matrix, RingElement),
 	  (homogenize, Matrix, RingElement, List),(homogenize, Module, RingElement),
 	  (homogenize, Module, RingElement, List),(homogenize, RingElement, RingElement),(homogenize, RingElement, RingElement, List),
 	  (homogenize, Vector, RingElement),(homogenize, Vector, RingElement, List)},
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2
index 92beb2f3840..6223fb620e3 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc_ideals.m2
@@ -40,7 +40,7 @@ document {
      UL {
 	  TO (generators, LeftIdeal),
 	  TO (symbol _*,LeftIdeal),
-	  TO (isSubset, Ideal, Ideal),
+	  TO (isSubset, LeftIdeal, LeftIdeal),
 	  TO "MinimalPrimes :: isPrime(Ideal)"
 	  },
      "Common operations on ideals:",
@@ -48,9 +48,9 @@ document {
 	  TO (symbol +,LeftIdeal,LeftIdeal),
 	  TO (symbol *,Ideal,Ideal),
 	  TO (symbol ==,LeftIdeal,LeftIdeal),
-	  TO (symbol ==,Ideal,ZZ),
+	  TO (symbol ==,LeftIdeal,ZZ),
 	  TO (symbol ^,Ideal,ZZ),
-	  TO (trim, Ideal)
+	  TO (trim, LeftIdeal)
 	  },
      "Gröbner bases, normal forms, free resolutions",
      UL {
@@ -58,7 +58,7 @@ document {
 	  TO leadTerm,
 	  TO codim,
 	  TO dim,
-	  TO (symbol%,Matrix,Ideal),
+	  TO (symbol%,Matrix,LeftIdeal),
 	  TO resolution,
 	  TO betti
 	  },
@@ -115,7 +115,7 @@ document {
 	  "I = ideal(a,(t+1)*c) * ideal(a^2,b^2)"
 	  },
      "The generators produced are not generally minimal.  Use ",
-     TO (trim,Ideal), " or ", TO (mingens,Ideal), " to find a smaller
+     TO (trim,LeftIdeal), " or ", TO (mingens,LeftIdeal), " to find a smaller
      generating set.",
      SeeAlso => {"ideals"}
      }
@@ -135,7 +135,7 @@ document {
 	  "I = ideal(a,(t+1)*c) + ideal(a^2,b^2)"
 	  },
      "The generators produced are not generally minimal.  Use ",
-     TO (trim,Ideal), " or ", TO (mingens,Ideal), " to find a smaller
+     TO (trim,LeftIdeal), " or ", TO (mingens,LeftIdeal), " to find a smaller
      generating set.",
      EXAMPLE {
 	  "trim I"
@@ -156,7 +156,7 @@ document {
 	  "I^3"
 	  },
      "The generators produced are often not minimal.  Use ",
-     TO (trim,Ideal), " or ", TO (mingens,Ideal), " to find a smaller
+     TO (trim,LeftIdeal), " or ", TO (mingens,LeftIdeal), " to find a smaller
      generating set.",
      EXAMPLE {
 	  "trim I^3"
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/doc_ringmaps.m2 b/M2/Macaulay2/packages/Macaulay2Doc/doc_ringmaps.m2
index b48b6805d5a..4785eae2035 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/doc_ringmaps.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/doc_ringmaps.m2
@@ -16,7 +16,7 @@ document {
 
 document {
      Key => {(symbol SPACE, RingMap, RingElement),
-	  (symbol SPACE, RingMap, Ideal),
+	  (symbol SPACE, RingMap, LeftIdeal),
 	  (symbol SPACE, RingMap, Matrix),
 	  (symbol SPACE, RingMap, Vector),
 	  (symbol SPACE, RingMap, Module),
@@ -57,13 +57,13 @@ document {
 	  (substitute, Vector, Option),
 	  (substitute, Product, Thing),
 	  (substitute, Matrix, List),
-	  (substitute, Ideal, List),
+	  (substitute, LeftIdeal, List),
 	  (substitute, Module, Matrix),
 	  (substitute, Matrix, Ring),
 	  (substitute, Matrix, ZZ),
-	  (substitute, Ideal, Ring),
+	  (substitute, LeftIdeal, Ring),
 	  (substitute, Module, Option),
-	  (substitute,Ideal,RingFamily),
+	  (substitute,LeftIdeal,RingFamily),
 	  (substitute,Matrix,RingFamily),
 	  (substitute,Module,RingFamily),
 	  (substitute,Number,RingFamily),
@@ -74,13 +74,13 @@ document {
 	  (substitute, Vector, Ring),
 	  (substitute, RingElement, Option),
 	  (substitute, Matrix, Matrix),
-	  (substitute, Ideal, Matrix),
+	  (substitute, LeftIdeal, Matrix),
 	  (substitute, Module, List),
 	  (substitute, Divide, Thing),
 	  (substitute, Module, Ring),
 	  (substitute, Matrix, Option),
 	  (substitute, Sum, Thing),
-	  (substitute, Ideal, Option),
+	  (substitute, LeftIdeal, Option),
 	  (substitute, Vector, Matrix),
 	  (substitute, RingElement, List),
 	  (substitute, Power, Thing),
@@ -91,7 +91,7 @@ document {
      Inputs => {
 	  "f" => {ofClass RingElement, ", ",
 	         ofClass Matrix,", ",
-		 ofClass Ideal,", ",
+		 ofClass LeftIdeal,", ",
 		 ofClass Module,", ",
 		 ofClass Vector,", or ",
 		 ofClass Expression, " over a ring ", TT "R"},
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/gb-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/gb-doc.m2
index d588a342765..e30d7eabf97 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/gb-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/gb-doc.m2
@@ -7,7 +7,7 @@ undocumented (NewFromMethod, GroebnerBasis, Sequence)
 
 document { 
      Key => {gb,
-	  (gb,Ideal),
+	  (gb,LeftIdeal),
 	  (gb,Matrix),
 	  (gb,Module),
 	  [gb,Algorithm],
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/intersect-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/intersect-doc.m2
index cb11f913e91..c2b74cc5bee 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/intersect-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/intersect-doc.m2
@@ -5,10 +5,10 @@
 doc ///
 Node
   Key
-     (intersect, Ideal, Ideal)
-    [(intersect, Ideal, Ideal), Strategy]
-    [(intersect, Ideal, Ideal), MinimalGenerators]
-     (intersect, Ideal)
+     (intersect, LeftIdeal, LeftIdeal)
+    [(intersect, LeftIdeal, LeftIdeal), Strategy]
+    [(intersect, LeftIdeal, LeftIdeal), MinimalGenerators]
+     (intersect, LeftIdeal)
      (intersect, Module, Module)
     [(intersect, Module, Module), Strategy]
     [(intersect, Module, Module), MinimalGenerators]
@@ -19,15 +19,15 @@ Node
     intersect(M, N)
     intersect(M, N, ..., P)
   Inputs
-    :{Ideal,Module}
-    :{Ideal,Module}
+    :{LeftIdeal,Module}
+    :{LeftIdeal,Module}
       submodules of the same module or ideals in the same ring
     Strategy=>Thing
       specifies the algorithm
     MinimalGenerators=>Boolean
       indicates whether the output should be @TO2 {trim, "trimmed"}@
   Outputs
-    :{Ideal,Module}
+    :{LeftIdeal,Module}
       the intersection of the sequence of objects
   Description
     Text
@@ -52,7 +52,7 @@ Node
       Multiple strategies are implemented via @TO2 {"Macaulay2Doc :: using hooks", "hooks"}@ and
       can be listed using the function @TO hooks@. More strategies may be added using @TO addHook@.
     Example
-      hooks(intersect, Ideal, Ideal)
+      hooks(intersect, LeftIdeal, LeftIdeal)
       hooks(intersect, Module, Module)
     Text
       By default, the strategies are attempted in the reverse order in which the were added, until one is successful.
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/isSubset-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/isSubset-doc.m2
index 76e2be98bd3..dac20b55980 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/isSubset-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/isSubset-doc.m2
@@ -26,7 +26,7 @@ document {
      }
 
 document { 
-     Key => {(isSubset,Module,Module),(isSubset,Ideal,Module),(isSubset,Module,Ideal)},
+     Key => {(isSubset,Module,Module),(isSubset,LeftIdeal,Module),(isSubset,Module,LeftIdeal)},
      Usage => "isSubset(M,N)",
      Inputs => { "M", "N" },
      Outputs => { Boolean => {"whether ", TT "M", " is contained in ", TT "N"} },
@@ -40,7 +40,7 @@ document {
      }
 
 document {
-     Key => {(isSubset,Ideal,Ideal)},
+     Key => {(isSubset,LeftIdeal,LeftIdeal)},
      Usage => "isSubset(I,J)",
      Inputs => { "I", "J" },
      Outputs => { Boolean => {"whether ", TT "I", " is contained in ", TT "J"} },
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/mingens-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/mingens-doc.m2
index 3d66c92cf52..7abba3c39a7 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/mingens-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/mingens-doc.m2
@@ -63,7 +63,7 @@ document {
      }
 
 document { 
-     Key => {(mingens,Module),(mingens,Ideal)},
+     Key => {(mingens,Module),(mingens,LeftIdeal)},
      Usage => "mingens I",
      Inputs => {
 	  "I" => "or an ideal"
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/minimalPresentation-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/minimalPresentation-doc.m2
index acb915d6f9b..49552676362 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/minimalPresentation-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/minimalPresentation-doc.m2
@@ -88,7 +88,7 @@ document {
 	  I = ideal(x-x^2-y,z+x*y,w^2-u^2);
 	  minimalPresentation(I, Exclude=>{1})
           ///,
-     SeeAlso => {(minimalPresentation,Ring), (trim, Ideal)}
+     SeeAlso => {(minimalPresentation,Ring), (trim, LeftIdeal)}
      }
 
 document { 
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/support-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/support-doc.m2
index 666ac38f95d..d940ffab758 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/support-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/support-doc.m2
@@ -40,7 +40,7 @@ document {
      }
 
 document { 
-     Key => {(support,Ideal)},
+     Key => {(support,LeftIdeal)},
      Headline => "list of variables occurring in the generators of an ideal",
      Usage => "support I",
      Inputs => { "I" => "an ideal in a polynomial ring" },
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/symbol-percent-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/symbol-percent-doc.m2
index 9c4b25cc105..edac4d90c20 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/symbol-percent-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/symbol-percent-doc.m2
@@ -6,11 +6,11 @@
 document { 
      Key => {
 	  "methods for normal forms and remainder",
-	  (symbol %, RingElement, Ideal),
+	  (symbol %, RingElement, LeftIdeal),
 	  (symbol %, RingElement, MonomialIdeal),
 	  (symbol %, RingElement, Matrix),
 	  (symbol %, RingElement, RingElement),
-	  (symbol %, Matrix, Ideal),
+	  (symbol %, Matrix, LeftIdeal),
 	  (symbol %, Matrix, MonomialIdeal),
 	  (symbol %, Matrix, RingElement),
 	  (symbol %, Matrix, Module),
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/trim-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/trim-doc.m2
index a483b1efb4f..8f606d220cc 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/trim-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/trim-doc.m2
@@ -43,7 +43,7 @@ Node
 Node
   Key
     trim
-   (trim, Ideal)
+   (trim, LeftIdeal)
    (trim, Ring)
    (trim, Module)
    (trim, MonomialIdeal)
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/groebner.m2 b/M2/Macaulay2/packages/Macaulay2Doc/groebner.m2
index 665472640c0..dea789847b8 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/groebner.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/groebner.m2
@@ -134,7 +134,7 @@ document {
        f = x^3+y^3+z^3
        f % I
        ///,
-     SeeAlso => {"Gröbner bases", (symbol %, RingElement, Ideal)},
+     SeeAlso => {"Gröbner bases", (symbol %, RingElement, LeftIdeal)},
      }
 
 -- we should be able to link to the right nodes without this:
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2 b/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2
index 9743b3d88c7..ae47f4d6eee 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2
@@ -203,7 +203,7 @@ document {
 	    },
 
      SUBSECTION "normal form with respect to a Groebner basis and membership",
-       "The function ", TO (symbol%,RingElement,Ideal), 
+       "The function ", TO (symbol%,RingElement,LeftIdeal), 
        " reduces an element with 
        respect to a Groebner basis of the ideal.", 
        EXAMPLE {
@@ -237,10 +237,10 @@ document {
 	    },
      SeeAlso => {
 	  (symbol==,LeftIdeal,LeftIdeal),
-	  (symbol==,Ideal,ZZ),
+	  (symbol==,LeftIdeal,ZZ),
 	  symbol!=,
-	  (symbol%,RingElement,Ideal),
-	  (isSubset,Ideal,Ideal),
+	  (symbol%,RingElement,LeftIdeal),
+	  (isSubset,LeftIdeal,LeftIdeal),
 	  "MinimalPrimes :: radicalContainment"
 	  }
      }     
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/ov_ringmaps.m2 b/M2/Macaulay2/packages/Macaulay2Doc/ov_ringmaps.m2
index 5f1ad98f295..d9e4db12f72 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/ov_ringmaps.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/ov_ringmaps.m2
@@ -68,7 +68,7 @@ document {
      UL {
 	  TO (symbol SPACE, RingMap, RingElement),
 	  TO (symbol SPACE, RingMap, Matrix),
-	  TO (symbol SPACE, RingMap, Ideal),
+	  TO (symbol SPACE, RingMap, LeftIdeal),
 	  TO (symbol SPACE, RingMap, Module),
 	  TO (symbol *, RingMap, RingMap),
 	  },

From 7a0a5dccef8017cfebaffeb3afb74c49f8f8b4c4 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Sat, 18 Nov 2023 08:44:21 -0500
Subject: [PATCH 04/14] LeftIdeal --> Macaulay2Doc, HolonomicSystems; breaks at
 B-S

---
 M2/Macaulay2/m2/matrix1.m2                    |  4 ++--
 .../HolonomicSystems/DOC/canonicalSeries.m2   | 24 +++++++++----------
 .../HolonomicSystems/canonicalSeries.m2       | 22 ++++++++---------
 .../Macaulay2Doc/functions/hooks-doc.m2       |  2 +-
 4 files changed, 26 insertions(+), 26 deletions(-)

diff --git a/M2/Macaulay2/m2/matrix1.m2 b/M2/Macaulay2/m2/matrix1.m2
index 35b5c573431..980a2616717 100644
--- a/M2/Macaulay2/m2/matrix1.m2
+++ b/M2/Macaulay2/m2/matrix1.m2
@@ -574,8 +574,8 @@ ideal Matrix := LeftIdeal => f -> (
 	  );
      new (
 	 -- Ideal == two-sided ideal
-	 if isCommutative R or isSkewCommutative R then Ideal 
-	 else LeftIdeal
+	 if isWeylAlgebra R then LeftIdeal 
+	 else Ideal
 	 ) from { symbol generators => f, symbol ring => R, symbol cache => new CacheTable } )
 
 ideal Module := LeftIdeal => M -> (
diff --git a/M2/Macaulay2/packages/HolonomicSystems/DOC/canonicalSeries.m2 b/M2/Macaulay2/packages/HolonomicSystems/DOC/canonicalSeries.m2
index b9008b46fe1..29c4284e020 100644
--- a/M2/Macaulay2/packages/HolonomicSystems/DOC/canonicalSeries.m2
+++ b/M2/Macaulay2/packages/HolonomicSystems/DOC/canonicalSeries.m2
@@ -87,7 +87,7 @@ doc ///
 doc ///
    Key
      distraction
-     (distraction, Ideal, Ring)
+     (distraction, LeftIdeal, Ring)
      (distraction, RingElement, Ring)
    Headline
      the image in the thetaRing of a torus-fixed element or ideal in a Weyl algebra
@@ -95,7 +95,7 @@ doc ///
      distraction(I,thetaRing)
      distraction(f,thetaRing)
    Inputs
-     I:Ideal
+     I:LeftIdeal
      f:RingElement
      thetaRing:PolynomialRing
        a stand in for the subring $k[\theta]$ generated by @TT "theta = x*dx"@
@@ -128,13 +128,13 @@ doc ///
 doc ///
    Key
      indicialIdeal
-     (indicialIdeal, Ideal, List)
+     (indicialIdeal, LeftIdeal, List)
    Headline
      the image in the thetaRing of an indicial ideal in a Weyl algebra
    Usage
      indicialIdeal(I,w)
    Inputs
-     I:Ideal
+     I:LeftIdeal
        in a WeylAlgebra that is torus-fixed
      w:List
        (generic) weights for $I$, of length half the number of variables in the Weyl algebra
@@ -167,13 +167,13 @@ doc ///
 doc ///
    Key
      cssExpts
-     (cssExpts, Ideal, List)
+     (cssExpts, LeftIdeal, List)
    Headline
      the exponents of the canonical series solutions of I in the direction of a weight vector
    Usage
      cssExpts(I,w)
    Inputs
-     I:Ideal
+     I:LeftIdeal
        (regular) holonomic ideal in the Weyl algebra
      w:List
        (generic) weights for $I$, of length half the number of variables in the Weyl algebra
@@ -200,13 +200,13 @@ doc ///
 doc ///
    Key
      cssExptsMult
-     (cssExptsMult, Ideal, List)
+     (cssExptsMult, LeftIdeal, List)
    Headline
      the exponents and multiplicities of the canonical series solutions
    Usage
      cssExptsMult(I,w)
    Inputs
-     I:Ideal
+     I:LeftIdeal
        (regular) holonomic ideal in the Weyl algebra
      w:List
        (generic) weights for $I$, of length half the number of variables in the Weyl algebra
@@ -236,13 +236,13 @@ doc ///
 doc ///
    Key
      isTorusFixed
-     (isTorusFixed, Ideal)
+     (isTorusFixed, LeftIdeal)
    Headline
      checks if an ideal in a Weyl algebra is torus-fixed
    Usage
      isTorusFixed I
    Inputs
-     I:Ideal
+     I:LeftIdeal
        in a WeylAlgebra
    Outputs
      :Boolean
@@ -298,13 +298,13 @@ doc ///
 doc ///
    Key
      cssLeadTerm
-    (cssLeadTerm, Ideal, List)
+    (cssLeadTerm, LeftIdeal, List)
    Headline
      lead term of the canonical series solutions of I
    Usage
      cssLeadTerm(I, w)
    Inputs
-     I:Ideal
+     I:LeftIdeal
        (regular) holonomic ideal in the Weyl algebra
      w:List
        (generic) weights for $I$, of length half the number of variables in the Weyl algebra
diff --git a/M2/Macaulay2/packages/HolonomicSystems/canonicalSeries.m2 b/M2/Macaulay2/packages/HolonomicSystems/canonicalSeries.m2
index 0b8d1825fe3..b4db57a0d50 100644
--- a/M2/Macaulay2/packages/HolonomicSystems/canonicalSeries.m2
+++ b/M2/Macaulay2/packages/HolonomicSystems/canonicalSeries.m2
@@ -12,7 +12,7 @@
 --Input: J an ideal in a Weyl algebra
 --Output: True if ideal is torus fixed, as in SST Lem. 2.3.1. False if not.
 isTorusFixed = method();
-isTorusFixed(Ideal) := Boolean => (J)->(
+isTorusFixed LeftIdeal := Boolean => J->(
     n := numgens ring J//2;
     J' := ideal flatten apply(J_*,f->( 
 	    apply(apbFactor(f
@@ -66,7 +66,7 @@ distraction = method()
 --Input: torus-fixed left D-ideal J
 --Output: the distraction of J, viewed in ThetaRing
 --Note: this was called thetaIdeal in the past
-distraction(Ideal, Ring) := Ideal => (J, ThetaRing) -> sum(J_*, j -> ideal distraction(j, ThetaRing))
+distraction(LeftIdeal, Ring) := Ideal => (J, ThetaRing) -> sum(J_*, j -> ideal distraction(j, ThetaRing))
 --Input: element in a torus-fixed left D-ideal
 --Output: list of corresponding gens from homogeneous pieces in the distraction, viewed in ThetaRing
 distraction(RingElement, Ring) := List => (f, ThetaRing) -> (
@@ -81,7 +81,7 @@ distraction(RingElement, Ring) := List => (f, ThetaRing) -> (
 --Input: holonomic ideal I, weight w in the form of a List
 --Output: the indicial ideal of I with respect to w
 indicialIdeal = method();
-indicialIdeal(Ideal, List) := Ideal => (I, w) -> distraction(inw(I, -w|w), first createThetaRing ring I)
+indicialIdeal(LeftIdeal, List) := Ideal => (I, w) -> distraction(inw(I, -w|w), first createThetaRing ring I)
 
 --Input: 0-dimensional primary ideal I
 --Output: corresponding point, as a vector
@@ -94,7 +94,7 @@ solveMax Ideal := List => I -> first entries lift(vars ring I % radical I, coeff
 --Output: list of 0-dimensional ideals encoding css exponents and their multiplicities
 -- internal
 beginExptComp = method();
-beginExptComp(Ideal,List,ZZ,Ring) := List => (H,w,n,S)->(
+beginExptComp(LeftIdeal,List,ZZ,Ring) := List => (H,w,n,S)->(
     	if not isHolonomic(H) then error "ideal is not holonomic";
 	if #w != n then error "weight vector has wrong length";
 	J := inw(H,(-w)|w);
@@ -105,7 +105,7 @@ beginExptComp(Ideal,List,ZZ,Ring) := List => (H,w,n,S)->(
 --Input: holonomic D-ideal H, weight vector w as List
 --Output: list of starting monomial exponents for H wrt w
 cssExpts = method();
-cssExpts(Ideal,List) := List => (H,w)->(
+cssExpts(LeftIdeal,List) := List => (H,w)->(
 	n:= (numgens ring H)//2;
 	t := symbol t;
 	S := QQ(monoid [t_1..t_n]);
@@ -116,7 +116,7 @@ cssExpts(Ideal,List) := List => (H,w)->(
 --Input: holonomic D-ideal H, weight vector w as List, 
 --Output: list of starting monomial exponents for H wrt w, with multiplicities
 cssExptsMult = method();
-cssExptsMult(Ideal,List) := List => (H,w)->(
+cssExptsMult(LeftIdeal,List) := List => (H,w)->(
 	n:= (numgens ring H)//2;
 	t := symbol t;
 	S := QQ(monoid [t_1..t_n]);
@@ -246,7 +246,7 @@ solveFrobeniusIdeal(Ideal, Ring) := List => (I, W) -> (
 --Input: I regular holonomic ideal in a Weyl algebra on n vars, weight vector w in \ZZ^n as a List
 --Output: starting monomials for the css for I for weight w, as a List of ring elements in vars for I and their logs
 cssLeadTerm = method()
-cssLeadTerm(Ideal, List) := List => (I, w) -> solveFrobeniusIdeal(indicialIdeal(I, w), ring I)
+cssLeadTerm(LeftIdeal, List) := List => (I, w) -> solveFrobeniusIdeal(indicialIdeal(I, w), ring I)
 
 --TODO: where should this go?
 --Input: cone C, weight vector k
@@ -261,7 +261,7 @@ truncate(Cone, List, ZZ) := List => {} >> o -> (C, w, k) -> polyhedronFromHData(
 --NOTE: We are assuming that the ideal I is provided with LT of weight 0.
 --We will adjust to this case using nonpositiveWeightGens
 nilssonSupport = method()
-nilssonSupport(Ideal, List) := Cone => (I, w) -> (
+nilssonSupport(LeftIdeal, List) := Cone => (I, w) -> (
     -- See description before SST Thm 2.5.14
     n := length w;
     G := gbw(I, fw := -w|w);
@@ -275,12 +275,12 @@ nilssonSupport(Ideal, List) := Cone => (I, w) -> (
     tailCone polar polyhedronFromHData(concatRows first L, concatRows last L))
 --Input: I regular holonomic ideal in a Weyl algebra on n vars, weight vector w in \ZZ^n as a List, weight k
 --Output: lattice points in cone of weight \leq k, as a List of Lists
-nilssonSupport(Ideal, List, ZZ) := List => (I, w, k) -> entries transpose concatCols latticePoints truncate(nilssonSupport(I, w), w, k)
+nilssonSupport(LeftIdeal, List, ZZ) := List => (I, w, k) -> entries transpose concatCols latticePoints truncate(nilssonSupport(I, w), w, k)
 
 --Input: I regular holonomic ideal in a Weyl algebra on n vars, weight vector w in \ZZ^n as a List
 --Output: list of generators of gbw(I) times monomial in variables, so that all inw terms have w-weight zero
 nonpositiveWeightGens = method()
-nonpositiveWeightGens(Ideal, List) := List => (I, w) -> (
+nonpositiveWeightGens(LeftIdeal, List) := List => (I, w) -> (
     W := ring I;
     n := length w;
     G := gbw(I, fw := -w|w);
@@ -293,7 +293,7 @@ nonpositiveWeightGens(Ideal, List) := List => (I, w) -> (
     )
 
 truncatedCanonicalSeries = method()
-truncatedCanonicalSeries(Ideal, List, ZZ) := List => (I, w, k) -> (
+truncatedCanonicalSeries(LeftIdeal, List, ZZ) := List => (I, w, k) -> (
     W := ring I;
     n := numgens W // 2;
     r := holonomicRank I;
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/hooks-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/hooks-doc.m2
index 9829e577a43..b818936b817 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/hooks-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/hooks-doc.m2
@@ -160,7 +160,7 @@ Node
       of those hooks associated with @TT "key"@ or stored in @TT "store"@
   Description
     Example
-      hooks(intersect, Ideal, Ideal)
+      hooks(intersect, LeftIdeal, LeftIdeal)
       code 0
       hooks(quotient, Strategy => Iterate)
   SeeAlso

From a1ac40185885712df40f2b2b1f4c833b97dd5f12 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Mon, 20 Nov 2023 08:32:24 -0500
Subject: [PATCH 05/14] working on B.-S.: stuck on colon ideal

---
 .../packages/BernsteinSato/multiplierIdeals.m2 | 18 +++++++++++++++---
 1 file changed, 15 insertions(+), 3 deletions(-)

diff --git a/M2/Macaulay2/packages/BernsteinSato/multiplierIdeals.m2 b/M2/Macaulay2/packages/BernsteinSato/multiplierIdeals.m2
index 25c4062500d..ebac78d3cf2 100644
--- a/M2/Macaulay2/packages/BernsteinSato/multiplierIdeals.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/multiplierIdeals.m2
@@ -18,6 +18,18 @@ isInMultiplierIdeal(RingElement, Ideal, QQ) := o -> (g,I,c) -> (
      -c > max roots
      )
 
+-- power of a (left) ideal and
+-- quotient -- LeftIdeal:RingElement
+-- product -- RingElement:LeftIdeal
+--   are _not_ well defined in general in the Weyl algebra, 
+--   ... but are used by some methods below in a limited context (for commuting elements) 
+powerIdealZZ = method()
+powerIdealZZ(LeftIdeal,ZZ) := (I,n) -> ideal symmetricPower(n,generators I)
+quotientInWeylAlgebra = method()
+quotientInWeylAlgebra(LeftIdeal,RingElement) := (I,f) -> (new Ideal from I) : (new Ideal from ideal f)  
+productInWeylAlgebra = method()
+productInWeylAlgebra(RingElement,LeftIdeal) := (f,I) -> f * (new Ideal from ideal I)  
+
 multiplierIdeal = method(Options => {Strategy=>ViaElimination, DegreeLimit=>null})
 multiplierIdeal (Ideal, ZZ) := o -> (a,c) -> multiplierIdeal(a, promote(c,QQ), Strategy=>o.Strategy, DegreeLimit=>o.DegreeLimit)
 multiplierIdeal (Ideal, QQ) := o -> (a,c) -> first multiplierIdeal(a, {c}, Strategy=>o.Strategy, DegreeLimit=>o.DegreeLimit) 
@@ -51,7 +63,7 @@ multiplierIdeal (Ideal, List) := o -> (a,cs) -> (
      	  SXring := K(monoid [SX,MonomialOrder=>Eliminate 1]);
      	  SDYtoSX := map(SXring,SDY, gens SXring | toList(n+2*r:0) );
 	  --
-	  I2' := sub(Istar,SDY) + (sub(a, SDY))^m + ideal (SDY_0 + sum(r,i->dT#i*T#i)); -- Istar + a^m + (s-\sigma)
+	  I2' := sub(Istar,SDY) + powerIdealZZ(sub(a, SDY),m) + ideal (SDY_0 + sum(r,i->dT#i*T#i)); -- Istar + a^m + (s-\sigma)
      	  if o.Strategy == ViaElimination then I2 := SDYtoSX eliminateWA(I2', notSX);
      	  pInfo(1, "J_I("|toString m|") = "|toString I2);
      	  -- b-function part
@@ -97,7 +109,7 @@ multiplierIdeal (Ideal, List) := o -> (a,cs) -> (
      	       	    while d <= o.DegreeLimit do (
 		    	 -- add reductions of all monomials of degree d times b(s)
 			 new'monoms = false;
-    		    	 for f in ((ideal X)^d)_* do (
+    		    	 for f in (powerIdealZZ(ideal X,d))_* do (
 			      -- taking monomials not in the initial ideal of ret 
 			      -- could be optimized more: delete the initial terms discovered on the previous step from monoms and f'b'sigma (MutableList? MutableHashTable?)
 			      if ret === null or sub(f,R) % ideal( (flatten entries gens gb ret)/ leadMonomial ) != 0 
@@ -122,7 +134,7 @@ multiplierIdeal (Ideal, List) := o -> (a,cs) -> (
 	       else if o.Strategy == ViaElimination then
 	       exceptionalLocusB(R,I2,b) -- ring I2 has to eliminate s 
 	       else if o.Strategy == ViaColonIdeal then (
-	  	    I2'' := I2' : ( (map(SDY, ring b, {sigma})) b ); 
+	  	    I2'' := quotientInWeylAlgebra(I2',(map(SDY, ring b, {sigma})) b); 
 		    notX := {SDY_0}|notSX;
      	       	    SDYtoSX eliminateWA(I2'', notX)
 		    )

From 422a508832006250e0c4d07b8956094dbb7c4569 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Wed, 22 Nov 2023 17:21:34 -0500
Subject: [PATCH 06/14] BernsteinSato; added quotientHelper
 quotient(LeftIdeal,RingElement)

---
 M2/Macaulay2/packages/BernsteinSato/DHom.m2   | 81 ++++++++++---------
 .../packages/BernsteinSato/DOC/DHom.m2        | 50 ++++++------
 .../packages/BernsteinSato/DOC/Dlocalize.m2   |  6 +-
 .../BernsteinSato/DOC/Drestriction.m2         | 54 ++++++-------
 .../packages/BernsteinSato/DOC/WeylClosure.m2 |  8 +-
 .../packages/BernsteinSato/DOC/annFs.m2       |  4 +-
 .../packages/BernsteinSato/DOC/localCohom.m2  | 38 ++++-----
 .../packages/BernsteinSato/Dlocalize.m2       |  8 +-
 .../packages/BernsteinSato/Dresolution.m2     |  4 +-
 .../packages/BernsteinSato/Drestriction.m2    | 48 +++++------
 .../packages/BernsteinSato/TST/tests.m2       |  2 +-
 .../packages/BernsteinSato/WeylClosure.m2     |  6 +-
 M2/Macaulay2/packages/BernsteinSato/annFs.m2  |  6 +-
 .../BernsteinSato/intersectionCohom.m2        |  2 +-
 .../packages/BernsteinSato/localCohom.m2      | 40 ++++-----
 .../BernsteinSato/multiplierIdeals.m2         |  2 +-
 .../packages/BernsteinSato/paramBpoly.m2      |  7 +-
 M2/Macaulay2/packages/Saturation.m2           | 32 ++++++--
 18 files changed, 210 insertions(+), 188 deletions(-)

diff --git a/M2/Macaulay2/packages/BernsteinSato/DHom.m2 b/M2/Macaulay2/packages/BernsteinSato/DHom.m2
index 38edc51a51e..38c0afe0c91 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DHom.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DHom.m2
@@ -56,7 +56,7 @@ divideOutGCD Matrix := m -> (
 --------------------------------------------------------------------------------
 
 Ddual = method()
-Ddual Ideal  := I -> Ddual comodule I
+Ddual LeftIdeal  := I -> Ddual comodule I
 Ddual Module := M -> (
      pInfo(1, "ENTERING Ddual ... ");
      W := ring M;
@@ -86,11 +86,11 @@ Ddual Module := M -> (
 --------------------------------------------------------------------------------
 polynomialSolutions = method(Options => {Alg => GD} )
 
-polynomialSolutions Ideal := options -> I -> ( 
-     polynomialSolutions((ring I)^1/I, options) )
+polynomialSolutions LeftIdeal := options -> I -> ( 
+     polynomialSolutions(coker gens I, options) )
 
-polynomialSolutions(Ideal,List) := options -> (I,w) -> ( 
-     polynomialSolutions((ring I)^1/I, w, options) )
+polynomialSolutions(LeftIdeal,List) := options -> (I,w) -> ( 
+     polynomialSolutions(coker gens I, w, options) )
 
 polynomialSolutions Module := options -> M -> (
      W := ring M;
@@ -255,8 +255,8 @@ polynomialSolutions(Module, List) := options -> (M, w) -> (
 --------------------------------------------------------------------------------
 --------------------------------------------------------------------------------
 polynomialExt = method(Options => {Strategy => Schreyer})
-polynomialExt Ideal := options -> I -> (
-     polynomialExt ((ring I)^1/I, options)
+polynomialExt LeftIdeal := options -> I -> (
+     polynomialExt (coker gens I, options)
      )
 
 polynomialExt Module := options -> (M) -> (
@@ -273,8 +273,8 @@ polynomialExt Module := options -> (M) -> (
      homologyTable
      )
 
-polynomialExt(ZZ, Ideal) := options -> (k, I) -> (
-     if not I.?quotient then I.quotient = (ring I)^1/I;
+polynomialExt(ZZ, LeftIdeal) := options -> (k, I) -> (
+     if not I.?quotient then I.quotient = coker gens I;
      polynomialExt (k, I.quotient, options)
      )
 
@@ -297,7 +297,7 @@ polynomialExt(ZZ, Module) := options -> (k, M) -> (
 --------------------------------------------------------------------------------
 --------------------------------------------------------------------------------
 rationalFunctionSolutions = method()
-rationalFunctionSolutions(Ideal) := (I) -> (
+rationalFunctionSolutions(LeftIdeal) := (I) -> (
      W := ring I;
      createDpairs W;
      w := toList(#W.dpairVars#0: 1);
@@ -305,19 +305,19 @@ rationalFunctionSolutions(Ideal) := (I) -> (
      rationalFunctionSolutions(I, f, w)
      )
 
-rationalFunctionSolutions(Ideal, List) := (I, w) -> (
+rationalFunctionSolutions(LeftIdeal, List) := (I, w) -> (
      f := (singLocus I)_0;
      rationalFunctionSolutions(I, f, w)
      )
 
-rationalFunctionSolutions(Ideal, RingElement) := (I, f) -> (
+rationalFunctionSolutions(LeftIdeal, RingElement) := (I, f) -> (
      W := ring I;
      createDpairs W;
      w := toList(#W.dpairVars#0: 1);
      rationalFunctionSolutions(I, f, w)
      )
 
-rationalFunctionSolutions(Ideal, RingElement, List) := (I, f, w) -> (
+rationalFunctionSolutions(LeftIdeal, RingElement, List) := (I, f, w) -> (
      W := ring I;
      bfunc := (globalB(I, f))#Bpolynomial;
      k := (max getIntRoots bfunc) + 1;
@@ -332,7 +332,7 @@ rationalFunctionSolutions(Ideal, RingElement, List) := (I, f, w) -> (
      solsList
      )
 
-rationalFunctionSolutions(Ideal, List, List) := (I, f, w) -> (
+rationalFunctionSolutions(LeftIdeal, List, List) := (I, f, w) -> (
      W := ring I;
      createDpairs W;
      bfuncs := apply(f, i -> (globalB(I, i))#Bpolynomial);
@@ -353,10 +353,10 @@ rationalFunctionSolutions(Ideal, List, List) := (I, f, w) -> (
 
 -- internal
 TwistOperator = method()
-TwistOperator(Ideal, RingElement, ZZ) := (I, f, k) -> (
+TwistOperator(LeftIdeal, RingElement, ZZ) := (I, f, k) -> (
      ideal apply((entries gens I)#0, L -> TwistOperator(L, f, k))
      )
-TwistOperator(Ideal, List, List) := (I, f, k) -> (
+TwistOperator(LeftIdeal, List, List) := (I, f, k) -> (
      ideal apply((entries gens I)#0, L -> TwistOperator(L, f, k))
      )
 
@@ -450,7 +450,7 @@ TwistOperator(RingElement, List, List) := (L, f, k) -> (
 --------------------------------------------------------------------------------
 rationalFunctionExt = method(Options => {Strategy => Schreyer} )
 
-rationalFunctionExt Ideal := options -> I -> (
+rationalFunctionExt LeftIdeal := options -> I -> (
      f := (singLocus(I))_0;
      rationalFunctionExt (I, f)
      )
@@ -468,8 +468,8 @@ rationalFunctionExt Module := options -> M -> (
      )
 
 
-rationalFunctionExt(Ideal, RingElement) := options -> (I, f) -> (
-     rationalFunctionExt ((ring I)^1/I, f, options)
+rationalFunctionExt(LeftIdeal, RingElement) := options -> (I, f) -> (
+     rationalFunctionExt (coker gens I, f, options)
      )
 
 rationalFunctionExt(Module, RingElement) := options -> (M, f) -> (
@@ -499,13 +499,13 @@ rationalFunctionExt(ZZ, Module) := options -> (k, M) -> (
      rationalFunctionExt (k, M, f)
      )
 
-rationalFunctionExt(ZZ, Ideal) := options -> (k, I) -> (
+rationalFunctionExt(ZZ, LeftIdeal) := options -> (k, I) -> (
      f := (singLocus(I))_0;
      rationalFunctionExt (k, I, f)
      )
 
-rationalFunctionExt(ZZ, Ideal, RingElement) := options -> (k, I, f) -> (
-     rationalFunctionExt (k, (ring I)^1/I, f, options)
+rationalFunctionExt(ZZ, LeftIdeal, RingElement) := options -> (k, I, f) -> (
+     rationalFunctionExt (k, coker gens I, f, options)
      )
 
 rationalFunctionExt(ZZ, Module, RingElement) := options -> (k, M, f) -> (
@@ -531,12 +531,12 @@ rationalFunctionExt(ZZ, Module, RingElement) := options -> (k, M, f) -> (
 
 DHom = method(Options => {Strategy => Schreyer})
 
-DHom(Ideal, Ideal) := options -> (I, J) -> (
+DHom(LeftIdeal, LeftIdeal) := options -> (I, J) -> (
      W := ring I;
      createDpairs W;
      n := #W.dpairVars#0;
      w := toList(2*n:1);
-     DHom(W^1/I, W^1/J, w, options)
+     DHom(coker gens I, coker gens J, w, options)
      )
      
 DHom(Module, Module) := options -> (M, N) -> (
@@ -903,20 +903,19 @@ compareSpans (List, List) := (list1, list2) -> (
 
 
 
-TEST ///
 -- TESTS TO WRITE (exported symbols);
---    polynomialExt Ideal
+--    polynomialExt LeftIdeal
 --    polynomialExt Module
---    polynomialExt (ZZ, Ideal)
+--    polynomialExt (ZZ, LeftIdeal)
 --    polynomialExt (ZZ, Module)
 
---    rationalFunctionExt Ideal
+--    rationalFunctionExt LeftIdeal
 --    rationalFunctionExt Module
---    rationalFunctionExt (Ideal, RingElement)
+--    rationalFunctionExt (LeftIdeal, RingElement)
 --    rationalFunctionExt (Module, rationalFunctionExt)
 --    rationalFunctionExt (ZZ, Module)
---    rationalFunctionExt (ZZ, Ideal)
---    rationalFunctionExt (ZZ, Ideal, RingElement)
+--    rationalFunctionExt (ZZ, LeftIdeal)
+--    rationalFunctionExt (ZZ, LeftIdeal, RingElement)
 --    rationalFunctionExt (ZZ, Module, RingElement)
 
 --    DHom (Module, Module, List)
@@ -934,12 +933,14 @@ TEST ///
 --    divideOutGCD RingElement
 --    divideOutGCD Matrix
 
---    TwistOperator (Ideal, RingElement, ZZ)
---    TwistOperator (Ideal, List, List)
+--    TwistOperator (LeftIdeal, RingElement, ZZ)
+--    TwistOperator (LeftIdeal, List, List)
 --    TwistOperator (RingElement, RingElement, ZZ)
 --    TwistOperator (RingElement, List, List)
 
+TEST ///
 importFrom_"BernsteinSato" {"compareSpans"}
+
 ---------------- TESTS for compareSpan -----------------------
 -- Test 1:
 S = QQ[x,y,z];
@@ -962,14 +963,14 @@ mylist1 = {1, x, y};
 mylist2 = {x + y, x-y};
 assert(not compareSpans(mylist1, mylist2));
 
-
 ----------------------- TESTS for ^ -----------------------
 x = symbol x; y = symbol y; z = symbol z;
 R = QQ[x,y,z];
 assert({x,y,z}^{2,3,4} == x^2*y^3*z^4);
+///
 
-
-
+TEST///
+importFrom_"BernsteinSato" {"compareSpans"}
 ----------------------- TESTS for polynomialSolutions -------------------------
 -- Test 1: Simple example 
 x = symbol x; Dx = symbol Dx;
@@ -998,11 +999,12 @@ ansGD = polynomialSolutions(I, weight);
 R = ring ansGD#0;
 ansDuality = polynomialSolutions(I, Alg => Duality) / (f -> sub(f, R));
 assert(compareSpans(ansGD, ansDuality));
-
+///
 
 --------------------- TESTS for polynomialExt -----------------------
 
-
+TEST///
+importFrom_"BernsteinSato" {"compareSpans"}
 --------------------- TESTS for rationalFunctionSolutions -----------------------
 -- Test 1: 
 x = symbol x; Dx = symbol Dx;
@@ -1025,8 +1027,9 @@ ans = {(-x+y)/(-y^4 + 3*y^3 - 3*y^2 + y), (-x*y^3 + 3*x*y^2 - 3*x*y + 4*x - 3*y)
 
 thelcd = lcm((allSols | ans) / denominator);
 assert compareSpans( thelcd*allSols / (f -> lift(f, R)), thelcd*ans / (f -> lift(f, R)));
+///
 
-
+TEST///
 ---------------------- TESTS forDHom and DExt ------------------------
 -- Test 1: Simple ODE examples
 x = symbol x; dx = symbol dx;
diff --git a/M2/Macaulay2/packages/BernsteinSato/DOC/DHom.m2 b/M2/Macaulay2/packages/BernsteinSato/DOC/DHom.m2
index 1bd8c12ed5d..6d82f867441 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DOC/DHom.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DOC/DHom.m2
@@ -4,14 +4,14 @@ document {
 	  TO [Dresolution,Strategy]
 }
 document {
-     Key => {DHom, (DHom,Module,Module), (DHom,Module,Module,List), (DHom,Ideal,Ideal)},
+     Key => {DHom, (DHom,Module,Module), (DHom,Module,Module,List), (DHom,LeftIdeal,LeftIdeal)},
      Headline=>"D-homomorphisms between holonomic D-modules",
      Usage => "DHom(M,N), DHom(M,N,w), DHom(I,J)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
 	  "N" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
-	  "J" => Ideal => {"which represents the module ", EM "N = D/J"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
+	  "J" => LeftIdeal => {"which represents the module ", EM "N = D/J"},
 	  "w" => List => "a positive weight vector"  
 	  },
      Outputs => { 
@@ -37,8 +37,8 @@ document {
 	  the restriction algorithm."},
      EXAMPLE lines ///
 	     W = QQ[x, D, WeylAlgebra=>{x=>D}]
-	     M = W^1/ideal(D-1)
-	     N = W^1/ideal((D-1)^2)
+	     M = coker gens ideal(D-1)
+	     N = coker gens ideal((D-1)^2)
 	     DHom(M,N)
 	     ///,
      Caveat => {"Input modules ", EM "M", ", ", EM "N", ", ", 
@@ -102,8 +102,8 @@ document {
 	  the restriction algorithm."},
      EXAMPLE lines ///
 	     W = QQ[x, D, WeylAlgebra=>{x=>D}]
-	     M = W^1/ideal(x*(D-1))
-	     N = W^1/ideal((D-1)^2)
+	     M = coker gens ideal(x*(D-1))
+	     N = coker gens ideal((D-1)^2)
 	     DExt(M,N)
 	     ///,
      Caveat =>{
@@ -115,12 +115,12 @@ document {
      }
 
 document {
-     Key => {Ddual, (Ddual,Module), (Ddual,Ideal)},
+     Key => {Ddual, (Ddual,Module), (Ddual,LeftIdeal)},
      Headline => "holonomic dual of a D-module",
      Usage => "Ddual M, Ddual I",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"}
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"}
 	  },
      Outputs => {
 	  Module => {"the holonomic dual of ", EM "M"}
@@ -148,12 +148,12 @@ document {
 	  TO [Dresolution,Strategy]
 }
 document {
-     Key => {polynomialExt, (polynomialExt,Module), (polynomialExt,ZZ,Ideal), (polynomialExt,ZZ,Module), (polynomialExt,Ideal)},
+     Key => {polynomialExt, (polynomialExt,Module), (polynomialExt,ZZ,LeftIdeal), (polynomialExt,ZZ,Module), (polynomialExt,LeftIdeal)},
      Headline => "Ext groups between a holonomic module and a polynomial ring",
      Usage => "polynomialExt M, polynomialExt I; rationalFunctionExt(i,M), rationalFunctionExt(i,I)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "i" => ZZ => "nonnegative"  
 	  },
      Outputs => {
@@ -172,7 +172,7 @@ document {
 	  the restriction algorithm."},
      EXAMPLE lines ///
 	     W = QQ[x, D, WeylAlgebra=>{x=>D}]
-	     M = W^1/ideal(x^2*D^2)
+	     M = coker gens ideal(x^2*D^2)
 	     polynomialExt(M)
 	     ///,
      Caveat =>{"Does not yet compute explicit representations of
@@ -187,15 +187,15 @@ document {
 }
 
 document {
-     Key => {rationalFunctionExt, (rationalFunctionExt,Module), (rationalFunctionExt,ZZ,Ideal,RingElement), (rationalFunctionExt,ZZ,Ideal), 
-	  (rationalFunctionExt,Ideal,RingElement), (rationalFunctionExt,Ideal),(rationalFunctionExt,ZZ,Module,RingElement), 
+     Key => {rationalFunctionExt, (rationalFunctionExt,Module), (rationalFunctionExt,ZZ,LeftIdeal,RingElement), (rationalFunctionExt,ZZ,LeftIdeal), 
+	  (rationalFunctionExt,LeftIdeal,RingElement), (rationalFunctionExt,LeftIdeal),(rationalFunctionExt,ZZ,Module,RingElement), 
 	  (rationalFunctionExt,ZZ,Module), (rationalFunctionExt,Module,RingElement)},
      Headline => "Ext(holonomic D-module, polynomial ring localized at the singular locus)",
      Usage => "rationalFunctionExt M, rationalFunctionExt I; rationalFunctionExt(M,f), rationalFunctionExt(I,f);
                rationalFunctionExt(i,M), rationalFunctionExt(i,I); rationalFunctionExt(i,M,f), rationalFunctionExt(i,I,f)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "f" => RingElement => "a polynomial",
 	  "i" => ZZ => "nonnegative"  
 	  },
@@ -215,7 +215,7 @@ document {
 	  the restriction algorithm."},
      EXAMPLE lines ///
 	     W = QQ[x, D, WeylAlgebra=>{x=>D}]
-	     M = W^1/ideal(x*D+5)
+	     M = coker gens ideal(x*D+5)
 	     rationalFunctionExt M
 	     ///,
      Caveat =>{"Input modules M or D/I should be holonomic."},
@@ -226,9 +226,9 @@ doc ///
   Key
     polynomialSolutions
     (polynomialSolutions,Module)
-    (polynomialSolutions,Ideal,List)
+    (polynomialSolutions,LeftIdeal,List)
     (polynomialSolutions,Module,List)
-    (polynomialSolutions,Ideal)
+    (polynomialSolutions,LeftIdeal)
   Headline
     polynomial solutions of a holonomic system
   Usage
@@ -239,7 +239,7 @@ doc ///
   Inputs
     M:Module
       over the Weyl algebra $D$
-    I:Ideal
+    I:LeftIdeal
       holonomic ideal in the Weyl algebra $D$
     w:List
       a weight vector
@@ -292,11 +292,11 @@ document {
 doc ///
   Key
     rationalFunctionSolutions
-    (rationalFunctionSolutions,Ideal,List,List)
-    (rationalFunctionSolutions,Ideal,RingElement,List)
-    (rationalFunctionSolutions,Ideal,List)
-    (rationalFunctionSolutions,Ideal,RingElement)
-    (rationalFunctionSolutions,Ideal)
+    (rationalFunctionSolutions,LeftIdeal,List,List)
+    (rationalFunctionSolutions,LeftIdeal,RingElement,List)
+    (rationalFunctionSolutions,LeftIdeal,List)
+    (rationalFunctionSolutions,LeftIdeal,RingElement)
+    (rationalFunctionSolutions,LeftIdeal)
   Headline
     rational solutions of a holonomic system
   Usage
@@ -306,7 +306,7 @@ doc ///
     rationalFunctionSolutions(I,ff)
     rationalFunctionSolutions(I,ff,w)
   Inputs
-    I:Ideal
+    I:LeftIdeal
       holonomic ideal in the Weyl algebra @EM "D"@
     f:RingElement
       a polynomial
diff --git a/M2/Macaulay2/packages/BernsteinSato/DOC/Dlocalize.m2 b/M2/Macaulay2/packages/BernsteinSato/DOC/Dlocalize.m2
index ed46c86b7a6..4f1d76cd581 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DOC/Dlocalize.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DOC/Dlocalize.m2
@@ -38,7 +38,7 @@ document {
 
      EXAMPLE lines ///
 	W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}]
-     	M = W^1/(ideal(x*Dx+1, Dy))
+     	M = coker gens ideal(x*Dx+1, Dy)
      	f = x^2-y^3
      	Mf = Dlocalize(M, f)
 	///,
@@ -61,7 +61,7 @@ document {
      " that computes the localization map.",
      EXAMPLE lines ///
 	W = QQ[x,y,Dx,Dy, WeylAlgebra => {x=>Dx,y=>Dy}]
-     	M = W^1/(ideal(x*Dx+1, Dy))
+     	M = coker gens ideal(x*Dx+1, Dy)
      	f = x^2-y^3
      	DlocalizeMap(M, f)
 	///,
@@ -105,7 +105,7 @@ doc ///
 	    $s$ such that (the images of) the generators of $M$ are $f^{-s}$ times the generators of $M_f$.
 	Example
 	    W = makeWeylAlgebra(QQ[x,y])
-	    M = W^1/ideal(x*dx + 1, dy)
+	    M = coker gens ideal(x*dx + 1, dy)
 	    f = x^2 - y^3
 	    Mfall = DlocalizeAll(M, f)
 	    gens image Mfall.LocMap == f^(-Mfall.GeneratorPower) * gens Mfall.LocModule
diff --git a/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2 b/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2
index fd870b58ece..87cb56db404 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DOC/Drestriction.m2
@@ -30,7 +30,7 @@ document {
      Usage => "Dresolution M, Dresolution I, Dresolution(M,w), Dresolution(I,w)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector"
 	  },
      Outputs => {
@@ -81,14 +81,14 @@ document {
 	  }
 
 document {
-     Key => {Drestriction, (Drestriction,ZZ,Module,List), (Drestriction,Ideal,List), 
-	  (Drestriction,Module,List), (Drestriction,ZZ,Ideal,List)},
+     Key => {Drestriction, (Drestriction,ZZ,Module,List), (Drestriction,LeftIdeal,List), 
+	  (Drestriction,Module,List), (Drestriction,ZZ,LeftIdeal,List)},
      Headline => "restriction modules of a D-module",
      Usage => "N = Drestriction(M,w), NI = Drestriction(I,w), Ni = Drestriction(i,M,w),
      NIi = Drestriction(i,I,w)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector",
 	  "i" => ZZ => "nonnegative"  
 	  },
@@ -131,15 +131,15 @@ document {
      }
 
 document {
-     Key => {DrestrictionIdeal, (DrestrictionIdeal, Ideal, List)},
+     Key => {DrestrictionIdeal, (DrestrictionIdeal, LeftIdeal, List)},
      Headline => "restriction ideal of a D-module",
      Usage => "DrestrictionIdeal(I,w)",
      Inputs => {
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector"
 	  },
      Outputs => {
-     	  Ideal => {"the restriction ideal of ", EM "M", " w.r.t. the weight vector ", EM "w"}
+     	  LeftIdeal => {"the restriction ideal of ", EM "M", " w.r.t. the weight vector ", EM "w"}
 	  },
      "A supplementary function for ", TO "Drestriction", 
      " that computes the restriction ideal.",   
@@ -156,12 +156,12 @@ document {
 }
 
 document {
-     Key => {DrestrictionAll, (DrestrictionAll, Module, List), (DrestrictionAll, Ideal, List)},
+     Key => {DrestrictionAll, (DrestrictionAll, Module, List), (DrestrictionAll, LeftIdeal, List)},
      Headline => "restriction modules of a D-module (extended version)",
      Usage => "N = DrestrictionAll(M,w), NI = DrestrictionAll(I,w)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector"
 	  },
      Outputs => {
@@ -184,12 +184,12 @@ document {
 }
 
 document {
-     Key => {DrestrictionComplex, (DrestrictionComplex, Module, List), (DrestrictionComplex, Ideal, List)},
+     Key => {DrestrictionComplex, (DrestrictionComplex, Module, List), (DrestrictionComplex, LeftIdeal, List)},
      Headline => "derived restriction complex of a D-module",
      Usage => "N = DrestrictionComplex(M,w), NI = DrestrictionComplex(I,w)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector"
 	  },
      Outputs => {
@@ -212,14 +212,14 @@ document {
 
 
 document {
-     Key => {DrestrictionClasses, (DrestrictionClasses,ZZ,Module,List), (DrestrictionClasses,Ideal,List), (DrestrictionClasses,Module,List),
-      (DrestrictionClasses,ZZ,Ideal,List)},
+     Key => {DrestrictionClasses, (DrestrictionClasses,ZZ,Module,List), (DrestrictionClasses,LeftIdeal,List), (DrestrictionClasses,Module,List),
+      (DrestrictionClasses,ZZ,LeftIdeal,List)},
      Headline => "restriction classes of a D-module",
      Usage => "N = DrestrictionClasses(M,w), NI = DrestrictionClasses(I,w), Ni = DrestrictionClasses(i,M,w),
      NIi = DrestrictionClasses(i,I,w), ",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector",
 	  "i" => ZZ => "nonnegative"  
 	  },
@@ -297,14 +297,14 @@ document {
 }
 
 document {
-     Key => { Dintegration, (Dintegration,ZZ,Module,List), (Dintegration,Ideal,List), 
-	  (Dintegration,Module,List), (Dintegration,ZZ,Ideal,List) },
+     Key => { Dintegration, (Dintegration,ZZ,Module,List), (Dintegration,LeftIdeal,List), 
+	  (Dintegration,Module,List), (Dintegration,ZZ,LeftIdeal,List) },
      Headline => "integration modules of a D-module",
      Usage => "N = Dintegration(M,w), NI = Dintegration(I,w), Ni = Dintegration(i,M,w),
      NIi = Dintegration(i,I,w), ",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector",
 	  "i" => ZZ => "nonnegative"  
 	  },
@@ -344,15 +344,15 @@ document {
  }
 
 document {
-     Key => {DintegrationIdeal, (DintegrationIdeal, Ideal, List)},
+     Key => {DintegrationIdeal, (DintegrationIdeal, LeftIdeal, List)},
      Headline => "integration ideal of a D-module",
      Usage => "DintegrationIdeal(I,w)",
      Inputs => {
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector"
 	  },
      Outputs => {
-     	  Ideal => {"the integration ideal of ", EM "M", " w.r.t. the weight vector ", EM "w"}
+     	  LeftIdeal => {"the integration ideal of ", EM "M", " w.r.t. the weight vector ", EM "w"}
 	  },
      "A supplementary function for ", TO "Dintegration", 
      " that computes the integration ideal.",   
@@ -369,12 +369,12 @@ document {
 }
 
 document {
-     Key => {DintegrationAll, (DintegrationAll, Module, List), (DintegrationAll, Ideal, List)},
+     Key => {DintegrationAll, (DintegrationAll, Module, List), (DintegrationAll, LeftIdeal, List)},
      Headline => "integration modules of a D-module (extended version)",
      Usage => "N = DintegrationAll(M,w), NI = DintegrationAll(I,w)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector"
 	  },
      Outputs => {
@@ -397,12 +397,12 @@ document {
 }
 
 document {
-     Key => {DintegrationComplex, (DintegrationComplex, Module, List), (DintegrationComplex, Ideal, List)},
+     Key => {DintegrationComplex, (DintegrationComplex, Module, List), (DintegrationComplex, LeftIdeal, List)},
      Headline => "derived integration complex of a D-module",
      Usage => "N = DintegrationComplex(M,w), NI = DintegrationComplex(I,w)",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector"
 	  },
      Outputs => {
@@ -425,14 +425,14 @@ document {
 
 
 document {
-     Key => {DintegrationClasses, (DintegrationClasses,ZZ,Module,List), (DintegrationClasses,Ideal,List), (DintegrationClasses,Module,List),
-      (DintegrationClasses,ZZ,Ideal,List)},
+     Key => {DintegrationClasses, (DintegrationClasses,ZZ,Module,List), (DintegrationClasses,LeftIdeal,List), (DintegrationClasses,Module,List),
+      (DintegrationClasses,ZZ,LeftIdeal,List)},
      Headline => "integration classes of a D-module",
      Usage => "N = DintegrationClasses(M,w), NI = DintegrationClasses(I,w), Ni = DintegrationClasses(i,M,w),
      NIi = DintegrationClasses(i,I,w), ",
      Inputs => {
 	  "M" => Module => {"over the Weyl algebra ", EM "D"},
-	  "I" => Ideal => {"which represents the module ", EM "M = D/I"},
+	  "I" => LeftIdeal => {"which represents the module ", EM "M = D/I"},
 	  "w" => List => "a weight vector",
 	  "i" => ZZ => "nonnegative"  
 	  },
diff --git a/M2/Macaulay2/packages/BernsteinSato/DOC/WeylClosure.m2 b/M2/Macaulay2/packages/BernsteinSato/DOC/WeylClosure.m2
index 06bf8056cd1..a8d877e4495 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DOC/WeylClosure.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DOC/WeylClosure.m2
@@ -1,20 +1,20 @@
 doc ///
   Key
     WeylClosure
-    (WeylClosure, Ideal)
-    (WeylClosure, Ideal, RingElement)
+    (WeylClosure, LeftIdeal)
+    (WeylClosure, LeftIdeal, RingElement)
   Headline
     Weyl closure of an ideal
   Usage
     WeylClosure I
     WeylClosure(I,f)
   Inputs
-    I:Ideal
+    I:LeftIdeal
       a left ideal of the Weyl Algebra
     f:RingElement
       a polynomial
   Outputs
-    :Ideal
+    :LeftIdeal
       the Weyl closure (w.r.t. $f$) of $I$
   Description
     Text
diff --git a/M2/Macaulay2/packages/BernsteinSato/DOC/annFs.m2 b/M2/Macaulay2/packages/BernsteinSato/DOC/annFs.m2
index dd9cd987851..b17e5399896 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DOC/annFs.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DOC/annFs.m2
@@ -27,7 +27,7 @@ doc ///
 ///
 
 document {
-     Key => {(AnnIFs, Ideal,RingElement), AnnIFs}, 
+     Key => {(AnnIFs, LeftIdeal,RingElement), AnnIFs}, 
      Headline => "the annihilating ideal of f^s for an arbitrary D-module", 
      Usage => "AnnIFs(I,f)",
      Inputs => {
@@ -40,7 +40,7 @@ document {
 	       " (should contain no differential variables)"}
 	  },      
      Outputs => {
-	  Ideal => {"the annihilating ideal of ", TEX "A_n[f^{-1},s] f^s", " tensored with ",
+	  LeftIdeal => {"the annihilating ideal of ", TEX "A_n[f^{-1},s] f^s", " tensored with ",
 	       TEX "A_n/I", " over the ring of polynomials" }
 	  },
      EXAMPLE lines ///
diff --git a/M2/Macaulay2/packages/BernsteinSato/DOC/localCohom.m2 b/M2/Macaulay2/packages/BernsteinSato/DOC/localCohom.m2
index a6c57992b3a..390f8010330 100644
--- a/M2/Macaulay2/packages/BernsteinSato/DOC/localCohom.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/DOC/localCohom.m2
@@ -69,20 +69,20 @@ document {
      Headline => "local cohomology",
      "Local cohomology of a polynomial ring:",
      UL {
-	  {TO (localCohom, Ideal)},
-	  {TO (localCohom, List, Ideal)},
-	  {TO (localCohom, ZZ, Ideal)}
+	  {TO (localCohom, LeftIdeal)},
+	  {TO (localCohom, List, LeftIdeal)},
+	  {TO (localCohom, ZZ, LeftIdeal)}
 	  },
      "Local cohomology of a holonomic module:",
      UL {
-	  {TO (localCohom, Ideal, Module)},
-	  {TO (localCohom, ZZ, Ideal, Module)},
-	  {TO (localCohom, List, Ideal, Module)}
+	  {TO (localCohom, LeftIdeal, Module)},
+	  {TO (localCohom, ZZ, LeftIdeal, Module)},
+	  {TO (localCohom, List, LeftIdeal, Module)}
 	  },
      SeeAlso => {"pruneLocalCohom"} 
      }
 document {
-     Key => (localCohom, Ideal),
+     Key => (localCohom, LeftIdeal),
      Headline => "local cohomology of a polynomial ring",
      Usage => "H = localCohom I", 
      Inputs => {
@@ -109,12 +109,12 @@ document {
      }  
 
 document {
-     Key => (localCohom, List, Ideal),
+     Key => (localCohom, List, LeftIdeal),
      Headline => "local cohomology of a polynomial ring",
      Usage => "localCohom(l,I)",
      Inputs => { "l", "I" },
      Outputs => { { "the local cohomology of ", TT "I", " in the degrees specified by ", EM "l" } },
-     "See ", TO (localCohom, Ideal), " for the full description.",
+     "See ", TO (localCohom, LeftIdeal), " for the full description.",
      EXAMPLE { 
 	  "W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}]",
      	  "I = ideal (X*(Y-Z), X*Y*Z)",
@@ -125,12 +125,12 @@ document {
      }
 
 document {
-     Key => (localCohom, ZZ, Ideal),
+     Key => (localCohom, ZZ, LeftIdeal),
      Headline => "local cohomology of a polynomial ring",
      Usage => "localCohom(d,I)",
      Inputs => { "d", "I" },
      Outputs => {{ "the local cohomology of ", TT "I", " in degree ", EM "d" }},
-     "See ", TO (localCohom, Ideal), " for the full description.",
+     "See ", TO (localCohom, LeftIdeal), " for the full description.",
      EXAMPLE { 
 	  "W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}]",
      	  "I = ideal (X*(Y-Z), X*Y*Z)",
@@ -141,7 +141,7 @@ document {
      }
 
 document {
-     Key => (localCohom, Ideal, Module),
+     Key => (localCohom, LeftIdeal, Module),
      Headline => "local cohomology of a D-module",
      Usage => "H = localCohom(I,M)", 
      Inputs => {
@@ -163,7 +163,7 @@ document {
      EXAMPLE {
 	  "W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}]",
      	  "I = ideal (X*(Y-Z), X*Y*Z)",
-     	  "h = localCohom(I, W^1 / ideal{dX,dY,dZ})",
+     	  "h = localCohom(I, coker gens ideal{dX,dY,dZ})",
      	  "pruneLocalCohom h"
 	  },
      Caveat => {"The modules returned are not simplified, 
@@ -172,7 +172,7 @@ document {
      }
 
 document {
-     Key => (localCohom, ZZ, Ideal, Module),
+     Key => (localCohom, ZZ, LeftIdeal, Module),
      Headline => "local cohomology of a D-module",
      Usage => "localCohom(d,I,M)",
      Inputs => { "d", "I", "M" },
@@ -181,18 +181,18 @@ document {
 	  EM {"H", SUB "I", "(M)"}, " in degree ", EM "d", ", where ", EM "I", 
 	  " is an ideal in a polynomial ring and ", EM "M", " is a D-module"
 	  }},
-     "See ", TO "localCohom(Ideal,Module)", " for the full description.",
+     "See ", TO "localCohom(LeftIdeal,Module)", " for the full description.",
      EXAMPLE {
 	  "W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}]",
      	  "I = ideal (X*(Y-Z), X*Y*Z)",
-	  "h = localCohom(2, I, W^1 / ideal{dX,dY,dZ})",
+	  "h = localCohom(2, I, coker gens ideal{dX,dY,dZ})",
 	  "pruneLocalCohom h"
 	  },
      SeeAlso => {"pruneLocalCohom"} 
      }
 
 document {
-     Key => (localCohom, List, Ideal, Module),
+     Key => (localCohom, List, LeftIdeal, Module),
      Headline => "local cohomology of a D-module",
      Usage => "localCohom(l,I,M)",
      Inputs => { "l", "I", "M" },
@@ -202,11 +202,11 @@ document {
 	  ", where ", EM "I", 
 	  " is an ideal in a polynomial ring and ", EM "M", " is a D-module"
 	  }},
-     "See ", TO "localCohom(Ideal,Module)", " for the full description.",
+     "See ", TO "localCohom(LeftIdeal,Module)", " for the full description.",
      EXAMPLE {
 	  "W = QQ[X, dX, Y, dY, Z, dZ, WeylAlgebra=>{X=>dX, Y=>dY, Z=>dZ}]",
      	  "I = ideal (X*(Y-Z), X*Y*Z)",
-	  "h = localCohom({1,2}, I, W^1 / ideal{dX,dY,dZ})",
+	  "h = localCohom({1,2}, I, coker gens ideal{dX,dY,dZ})",
 	  "pruneLocalCohom h"
 	  },
      SeeAlso => {"pruneLocalCohom"} 
diff --git a/M2/Macaulay2/packages/BernsteinSato/Dlocalize.m2 b/M2/Macaulay2/packages/BernsteinSato/Dlocalize.m2
index 1d4947e91a0..a3a15c93b19 100644
--- a/M2/Macaulay2/packages/BernsteinSato/Dlocalize.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/Dlocalize.m2
@@ -110,7 +110,7 @@ computeLocalization = (M, f, output, options) -> (
      	bestPower := min (getIntRoots (bpoly));
         if bestPower == infinity then bestPower = 0;
      	locIdeal := substitute(substitute(AnnI, {Ws_(ns-1) => bestPower}), W);
-     	locModule := W^1/locIdeal;
+     	locModule := coker gens locIdeal;
      	local locMap;
 	
      	if member (LocMap, output) then (
@@ -122,7 +122,7 @@ computeLocalization = (M, f, output, options) -> (
 		       bestPower = 0;
 		       locIdeal = substitute(substitute(AnnI, 
 			    	 {Ws_(ns-1) => bestPower}), W);
-     		       locModule = W^1/locIdeal;
+     		       locModule = coker gens locIdeal;
 		       locMap = map(locModule, M, matrix{{f^(-bestPower)}})
 		       )
 	     	  else locMap = map(locModule, M, matrix{{f^(-bestPower)}});
@@ -315,7 +315,7 @@ computeLocalization = (M, f, output, options) -> (
    )
 
 AnnIFs2 = method()
-AnnIFs2(Ideal, RingElement) := (I, f) -> (
+AnnIFs2(LeftIdeal, RingElement) := (I, f) -> (
      pInfo(1, "computing AnnIFs... ");
      W := ring I;
      n := numgens W;
@@ -402,7 +402,7 @@ u = symbol u; Du = symbol Du;
 n = 4;
 W = QQ[u_1..u_n, Du_1..Du_n, WeylAlgebra => 
      apply(toList(1..n), i -> u_i => Du_i)];
-M = W^1/ideal(Du_1..Du_n);
+M = coker gens ideal(Du_1..Du_n);
 f = sum(toList(1..n), i -> u_i^2);
 assert(Dlocalize(M, f) == Dlocalize(M, f, Strategy => Oaku));
 assert(DlocalizeMap(M, f) == DlocalizeMap(M, f, Strategy => Oaku));
diff --git a/M2/Macaulay2/packages/BernsteinSato/Dresolution.m2 b/M2/Macaulay2/packages/BernsteinSato/Dresolution.m2
index 13f3c81a3ae..a24b3d54488 100644
--- a/M2/Macaulay2/packages/BernsteinSato/Dresolution.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/Dresolution.m2
@@ -100,7 +100,7 @@ Dresolution Module := options -> M -> (
      M.cache.resolution
      )
 
-Dresolution (LeftIdeal, List) := options -> (I, w) -> Dresolution ((ring I)^1/I, w, options)
+Dresolution (LeftIdeal, List) := options -> (I, w) -> Dresolution (coker gens I, w, options)
 
 Dresolution (Module, List) := options -> (M, w) -> (
 
@@ -250,10 +250,8 @@ I = ideal 0_W;
 J = ideal 1_W;
 w = {-1,1}
 assert( Dres(I) == Dres(I, w) );
-assert( Dres(W^1/I) == Dres(W^1/I, w) );
 assert( Dres(module I) == Dres(module I, w) );
 assert( Dres(J) == Dres(J, w) );
-assert( Dres(W^1/J) == Dres(W^1/J, w) );
 assert( Dres (module J) == Dres(module J, w) );
 
 -- Resolutions in the same res Grobner cone
diff --git a/M2/Macaulay2/packages/BernsteinSato/Drestriction.m2 b/M2/Macaulay2/packages/BernsteinSato/Drestriction.m2
index 9b5b3be75e4..b2405dcf39a 100644
--- a/M2/Macaulay2/packages/BernsteinSato/Drestriction.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/Drestriction.m2
@@ -72,7 +72,7 @@ ensureQuotientModule(Module, String) := (M,errorString) -> (
 --------------------------------------------------------------------------------
 
 Drestriction = method( Options => {Strategy => Schreyer} )
-Drestriction(Ideal,  List) := options -> (I,w) -> Drestriction(comodule I, w, options)
+Drestriction(LeftIdeal,  List) := options -> (I,w) -> Drestriction(comodule I, w, options)
 Drestriction(Module, List) := options -> (M,w) -> (
      ensureQuotientModule(M, 
 	  "Drestriction currently only handles quotient modules");
@@ -83,7 +83,7 @@ Drestriction(Module, List) := options -> (M,w) -> (
      outputTable#HomologyModules
      )
 
-Drestriction(ZZ, Ideal, List) := options -> (k,I,w) -> Drestriction (k, comodule I, w, options)
+Drestriction(ZZ, LeftIdeal, List) := options -> (k,I,w) -> Drestriction (k, comodule I, w, options)
 Drestriction(ZZ,Module,List) := options -> (k,M,w) -> (
      ensureQuotientModule(M, 
 	  "Drestriction currently only handles quotient modules");
@@ -101,7 +101,7 @@ Drestriction(ZZ,Module,List) := options -> (k,M,w) -> (
 --------------------------------------------------------------------------------
 
 DrestrictionClasses = method( Options => {Strategy => Schreyer} )
-DrestrictionClasses(Ideal, List) := options -> (I,w) -> DrestrictionClasses(comodule I, w, options)
+DrestrictionClasses(LeftIdeal, List) := options -> (I,w) -> DrestrictionClasses(comodule I, w, options)
 DrestrictionClasses(Module, List) := options -> (M,w) -> (
      ensureQuotientModule(M, 
 	  "Drestriction currently only handles quotient modules");
@@ -116,7 +116,7 @@ DrestrictionClasses(Module, List) := options -> (M,w) -> (
      outputTable
      )
 
-DrestrictionClasses(ZZ, Ideal, List) := options -> (k,I,w) -> DrestrictionClasses (k, comodule I, w, options)
+DrestrictionClasses(ZZ, LeftIdeal, List) := options -> (k,I,w) -> DrestrictionClasses (k, comodule I, w, options)
 DrestrictionClasses(ZZ,Module,List) := options -> (k,M,w) -> (
      ensureQuotientModule(M, 
 	  "Drestriction currently only handles quotient modules");
@@ -147,8 +147,8 @@ DrestrictionClasses(ZZ,Module,List) := options -> (k,M,w) -> (
 --------------------------------------------------------------------------------
 
 DrestrictionComplex = method( Options => {Strategy => Schreyer} )
-DrestrictionComplex(Ideal,List) := options -> (I,w) -> (
-     DrestrictionComplex ((ring I)^1/I, w, options)     )
+DrestrictionComplex(LeftIdeal,List) := options -> (I,w) -> (
+     DrestrictionComplex (coker gens I, w, options)     )
 
 protect RestrictComplex
 
@@ -165,10 +165,10 @@ DrestrictionComplex(Module, List) := options -> (M,w) -> (
 --------------------------------------------------------------------------------
 
 DrestrictionIdeal = method( Options => {Strategy => Schreyer} )
-DrestrictionIdeal(Ideal,List) := options -> (I,w) -> (
+DrestrictionIdeal(LeftIdeal,List) := options -> (I,w) -> (
      d := #positions(w, i -> (i>0));
      outputRequest := {RestrictComplex, Explicit};
-     outputTable := computeRestriction ((ring I)^1/I, w, -1, 1, 
+     outputTable := computeRestriction (coker gens I, w, -1, 1, 
 	  outputRequest, options);
      M := cokernel (outputTable#RestrictComplex).dd#1;
      R := ring M;
@@ -184,8 +184,8 @@ DrestrictionIdeal(Ideal,List) := options -> (I,w) -> (
 --------------------------------------------------------------------------------
 
 DrestrictionAll = method( Options => {Strategy => Schreyer} )
-DrestrictionAll(Ideal,List) := options -> (I,w) -> (
-     DrestrictionAll ((ring I)^1/I, w, options)     )
+DrestrictionAll(LeftIdeal,List) := options -> (I,w) -> (
+     DrestrictionAll (coker gens I, w, options)     )
 
 DrestrictionAll(Module, List) := options -> (M,w) -> (
      ensureQuotientModule(M, 
@@ -212,8 +212,8 @@ DrestrictionAll(Module, List) := options -> (M,w) -> (
 --------------------------------------------------------------------------------
 
 Dintegration = method( Options => {Strategy => Schreyer} )
-Dintegration(Ideal,List) := options -> (I,w) -> (
-     Dintegration ((ring I)^1/I, w, options)     )
+Dintegration(LeftIdeal,List) := options -> (I,w) -> (
+     Dintegration (coker gens I, w, options)     )
 
 Dintegration(Module, List) := options -> (M,w) -> (
      W := ring M;
@@ -235,8 +235,8 @@ Dintegration(Module, List) := options -> (M,w) -> (
      Mout
      )     
 
-Dintegration(ZZ, Ideal, List) := options -> (k,I,w)  -> (
-     Dintegration (k, (ring I)^1/I, w, options)	 )
+Dintegration(ZZ, LeftIdeal, List) := options -> (k,I,w)  -> (
+     Dintegration (k, coker gens I, w, options)	 )
 
 Dintegration(ZZ, Module, List) := options -> (k,M,w)  -> (
      W := ring M;
@@ -261,8 +261,8 @@ Dintegration(ZZ, Module, List) := options -> (k,M,w)  -> (
 --------------------------------------------------------------------------------
 
 DintegrationClasses = method( Options => {Strategy => Schreyer} )
-DintegrationClasses(Ideal,List) := options -> (I,w) -> (
-     DintegrationClasses ((ring I)^1/I, w, options)     )
+DintegrationClasses(LeftIdeal,List) := options -> (I,w) -> (
+     DintegrationClasses (coker gens I, w, options)     )
 
 DintegrationClasses(Module, List) := options -> (M,w) -> (
      W := ring M;
@@ -294,8 +294,8 @@ DintegrationClasses(Module, List) := options -> (M,w) -> (
      hashTable outputList
      )
 
-DintegrationClasses(ZZ,Ideal,List) := options -> (k,I,w) -> (
-     DintegrationClasses (k, (ring I)^1/I, w, options)     )
+DintegrationClasses(ZZ,LeftIdeal,List) := options -> (k,I,w) -> (
+     DintegrationClasses (k, coker gens I, w, options)     )
 
 DintegrationClasses(ZZ,Module,List) := options -> (k,M,w) -> (
      W := ring M;
@@ -343,8 +343,8 @@ DintegrationClasses(ZZ,Module,List) := options -> (k,M,w) -> (
 --------------------------------------------------------------------------------
 
 DintegrationComplex = method( Options => {Strategy => Schreyer} )
-DintegrationComplex(Ideal, List) := options -> (I,w) -> (
-     DintegrationComplex ((ring I)^1/I, w, options)     )
+DintegrationComplex(LeftIdeal, List) := options -> (I,w) -> (
+     DintegrationComplex (coker gens I, w, options)     )
 
 DintegrationComplex(Module, List) := options -> (M,w) -> (
      W := ring M;
@@ -365,13 +365,13 @@ DintegrationComplex(Module, List) := options -> (M,w) -> (
 --------------------------------------------------------------------------------
 
 DintegrationIdeal = method( Options => {Strategy => Schreyer} )
-DintegrationIdeal(Ideal,List) := options -> (I,w) -> (
+DintegrationIdeal(LeftIdeal,List) := options -> (I,w) -> (
      W := ring I;
      d := #positions(w, i -> (i>0));
      n := numgens W;
      IF := Fourier I; 
      outputRequest := {RestrictComplex, Explicit};
-     outputTable := computeRestriction (W^1/IF, w, -1, 1, 
+     outputTable := computeRestriction (coker gens IF, w, -1, 1, 
 	  outputRequest, options);
      M := cokernel (outputTable#RestrictComplex).dd#1;
      resW := ring M;
@@ -390,8 +390,8 @@ DintegrationIdeal(Ideal,List) := options -> (I,w) -> (
 --------------------------------------------------------------------------------
 
 DintegrationAll = method( Options => {Strategy => Schreyer} )
-DintegrationAll(Ideal,List) := options -> (I,w) -> (
-     DintegrationAll ((ring I)^1/I, w, options)     )
+DintegrationAll(LeftIdeal,List) := options -> (I,w) -> (
+     DintegrationAll (coker gens I, w, options)     )
 
 DintegrationAll(Module, List) := options -> (M,w) -> (
      W := ring M;
diff --git a/M2/Macaulay2/packages/BernsteinSato/TST/tests.m2 b/M2/Macaulay2/packages/BernsteinSato/TST/tests.m2
index b4c3e2a96fb..a878c52db5d 100644
--- a/M2/Macaulay2/packages/BernsteinSato/TST/tests.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/TST/tests.m2
@@ -7,7 +7,7 @@ TEST ///
   I = PolyAnn f;
   J = RatAnn f;
   K = RatAnn (u-v^2, f);
-  L = directSum (W^1/I, W^1/J);
+  L = directSum (coker gens I, coker gens J);
   assert ( isHolonomic I );
   assert ( isHolonomic J );
   assert ( isHolonomic K );
diff --git a/M2/Macaulay2/packages/BernsteinSato/WeylClosure.m2 b/M2/Macaulay2/packages/BernsteinSato/WeylClosure.m2
index 77ec81aaded..6d01bd4b4ba 100644
--- a/M2/Macaulay2/packages/BernsteinSato/WeylClosure.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/WeylClosure.m2
@@ -8,7 +8,7 @@
 --------------------------------------------------------------------------------
 --------------------------------------------------------------------------------
 WeylClosure = method()
-WeylClosure(Ideal, RingElement) := (I, f) -> (
+WeylClosure(LeftIdeal, RingElement) := (I, f) -> (
      W := ring I;
      if W.monoid.Options.WeylAlgebra === {} then
      error "Expected a Weyl algebra" ;
@@ -22,7 +22,7 @@ WeylClosure(Ideal, RingElement) := (I, f) -> (
      ideal gens gb J
      )
      
-WeylClosure Ideal := I -> (
+WeylClosure LeftIdeal := I -> (
      W := ring I;
      outputList :={};
      if W.monoid.Options.WeylAlgebra === {} then
@@ -66,4 +66,4 @@ f = (x^3-y^2*z^2);
 I = ideal(f^2*Dx+3*x^2, f^2*Dy-2*y*z^2, f^2*Dz-2*y^2*z);
 assert ( WeylClosure(I) == 
      I + ideal(y*Dy-z*Dz, y^2*z^3*Dz-(2/3)*x^4*Dx-2*x^3*z*Dz-2));
-///
\ No newline at end of file
+///
diff --git a/M2/Macaulay2/packages/BernsteinSato/annFs.m2 b/M2/Macaulay2/packages/BernsteinSato/annFs.m2
index 397dfe2886f..db98d2275b2 100644
--- a/M2/Macaulay2/packages/BernsteinSato/annFs.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/annFs.m2
@@ -4,7 +4,7 @@
 
 ---------------------------------------------------------------------------------
 AnnFs = method()
-AnnFs RingElement := Ideal => f -> (
+AnnFs RingElement := LeftIdeal => f -> (
 -- Input:   f, a polynomial in n variables 
 --             (has to be an element of A_n, the Weyl algebra).
 -- Output:  Ann f^s, an ideal in A_n[s].	
@@ -67,7 +67,7 @@ MalgrangeIdeal List := Ideal => F -> (
 ------------------------------------------------------------------------------
 --This needs documentation.
 AnnIFs = method()
-AnnIFs(Ideal, RingElement) := Ideal => (I, f) -> (
+AnnIFs(LeftIdeal, RingElement) := LeftIdeal => (I, f) -> (
      pInfo(1, "AnnIFs: Warning! The method expects an f-saturated module"); 
      W := ring I;
      createDpairs W;
@@ -354,7 +354,7 @@ rationalFunctionAnnihilator(RingElement, RingElement) := (g,f) -> (
     if a == -1 and g == 1_W then Ia
     else (
     	compensate := -1 - a;
-    	F := map(W^1/Ia, W^1, matrix{{g*f^compensate}});
+    	F := map(coker gens Ia, W^1, matrix{{g*f^compensate}});
     	ideal mingens kernel F)
     )
 
diff --git a/M2/Macaulay2/packages/BernsteinSato/intersectionCohom.m2 b/M2/Macaulay2/packages/BernsteinSato/intersectionCohom.m2
index fd3defcae04..7b4a235aef5 100644
--- a/M2/Macaulay2/packages/BernsteinSato/intersectionCohom.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/intersectionCohom.m2
@@ -27,7 +27,7 @@ IHmodule(Ideal) := options -> I -> (
 	for i from 0 to c-1 do J=J+ideal(sub(g#i,W)); -- submodule of H^c_I(R) generated by F^-1
 	m := minors (c,jacobian(I));      
 	l := (flatten entries (mingens m))#0;
-	image map(W^1/J, W^1, matrix{{sub(l,W)}}) -- D-mod generated by fundamental class
+	image map(coker gens J, W^1, matrix{{sub(l,W)}}) -- D-mod generated by fundamental class
 	)
     else (
     	S := flatten entries mingens(ideal singularLocus P);
diff --git a/M2/Macaulay2/packages/BernsteinSato/localCohom.m2 b/M2/Macaulay2/packages/BernsteinSato/localCohom.m2
index 7bafd7f12b7..4a95715ae38 100644
--- a/M2/Macaulay2/packages/BernsteinSato/localCohom.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/localCohom.m2
@@ -18,9 +18,9 @@ localCohom = method(Options => {Strategy => Walther, LocStrategy => null})
 -- option: Strategy (sets the way localizations are computed)
 ----------------------------------------------------------------------------------------
 
-localCohom(      Ideal) := HashTable => o ->    I  -> localCohom(toList (0..numgens I), I, o)
-localCohom(ZZ,   Ideal) := HashTable => o -> (n,I) -> (localCohom({n}, I, o))#n
-localCohom(List, Ideal) := HashTable => o -> (l,I) -> (
+localCohom(      LeftIdeal) := HashTable => o ->    I  -> localCohom(toList (0..numgens I), I, o)
+localCohom(ZZ,   LeftIdeal) := HashTable => o -> (n,I) -> (localCohom({n}, I, o))#n
+localCohom(List, LeftIdeal) := HashTable => o -> (l,I) -> (
      -- Promote I to the Weyl algebra if it is not already there
      if #(ring I).monoid.Options.WeylAlgebra == 0
      then I = sub(I, makeWA ring I); -- TODO: what degrees are best for the differentials?
@@ -30,7 +30,7 @@ localCohom(List, Ideal) := HashTable => o -> (l,I) -> (
      else (
 	  R := ring I;
 	  createDpairs R;
-	  localCohom(l, I, R^1 / ideal R.dpairVars#1, o)
+	  localCohom(l, I, coker gens ideal R.dpairVars#1, o)
 	  )
      );
 
@@ -104,9 +104,9 @@ localCohomUli = (l, I) -> (
 -- option:  Strategy (sets the way localizations are computed)
 ----------------------------------------------------------------------
 
-localCohom(      Ideal, Module) := HashTable => o ->   (I,M) -> localCohom(toList (0..numgens I), I, M, o)
-localCohom(ZZ,   Ideal, Module) := HashTable => o -> (n,I,M) -> localCohom({n}, I, M, o)
-localCohom(List, Ideal, Module) := HashTable => o -> (l,I,M) -> (
+localCohom(      LeftIdeal, Module) := HashTable => o ->   (I,M) -> localCohom(toList (0..numgens I), I, M, o)
+localCohom(ZZ,   LeftIdeal, Module) := HashTable => o -> (n,I,M) -> localCohom({n}, I, M, o)
+localCohom(List, LeftIdeal, Module) := HashTable => o -> (l,I,M) -> (
      -- Promote I to the Weyl algebra if it is not already there
      if #(ring I).monoid.Options.WeylAlgebra == 0
      then (
@@ -130,7 +130,7 @@ localCohom(List, Ideal, Module) := HashTable => o -> (l,I,M) -> (
 -- iterated localizations + localize by Oaku 
 ----------------------------------------------------------
 localCohomILOaku = method()
-localCohomILOaku(List, Ideal, Module) := (l, I, M) -> (
+localCohomILOaku(List, LeftIdeal, Module) := (l, I, M) -> (
      -- error checking to be added
      -- I is assumed to be an ideal in WA generated by polynomials
      f := first entries gens I;
@@ -169,7 +169,7 @@ localCohomILOaku(List, Ideal, Module) := (l, I, M) -> (
 		    subMap := map(W, ring I, vars W | matrix {{(FPower#i)_W}});
 		    locIdeal := ideal subMap gens I; 
 		    L#theta = new HashTable from {
-			 LocModule => W^1/locIdeal, 
+			 LocModule => coker gens locIdeal, 
 			 Generator => L#theta'#Generator * (f_i)^(-FPower#i)
 			 };
 		    theta => L#theta#LocModule
@@ -220,7 +220,7 @@ localCohomILOaku(List, Ideal, Module) := (l, I, M) -> (
 -- iterated localizations + localize by OTW 
 ----------------------------------------------------------
 localCohomILOTW = method()
-localCohomILOTW(List, Ideal, Module) := (l, I, M) -> (
+localCohomILOTW(List, LeftIdeal, Module) := (l, I, M) -> (
      -- error checking to be added
      -- I is assumed to be an ideal in WA generated by polynomials
      f := first entries gens I;
@@ -298,7 +298,7 @@ localCohomILOTW(List, Ideal, Module) := (l, I, M) -> (
 -- caveat: not smart, does not iterate localizations. 
 ----------------------------------------------------------------------------------------
 localCohomRegular = method()
-localCohomRegular(List,Ideal,Module) := (l, I, M) -> (
+localCohomRegular(List,LeftIdeal,Module) := (l, I, M) -> (
      -- error checking to be added
      -- I is assumed to be an ideal in WA generated by polynomials
      f := first entries gens I;
@@ -383,13 +383,13 @@ pruneLocalCohom(HashTable) := HashTable => h -> (
 --------------------------------------------------------------------------------
 
 localCohomOT = method()
-localCohomOT(Ideal, Ideal) := (I, J) -> (
-     if not J.?quotient then J.quotient = (ring J)^1/J;
+localCohomOT(LeftIdeal, LeftIdeal) := (I, J) -> (
+     if not J.?quotient then J.quotient = coker gens J;
      localCohomOT(I, J.quotient)
      )
-localCohomOT(Ideal, Module) := (I, M) -> computeLocalCohomOT(I, M, 0, min(numgens I, (dim ring I)//2))
+localCohomOT(LeftIdeal, Module) := (I, M) -> computeLocalCohomOT(I, M, 0, min(numgens I, (dim ring I)//2))
 
-localCohomOT(List, Ideal, Module) := (l, I, M) -> (
+localCohomOT(List, LeftIdeal, Module) := (l, I, M) -> (
      locOut := computeLocalCohomOT(I, M, min l, max l);
      locOut = hashTable apply(keys locOut, 
 	  i -> if member(i, l) then i => locOut#i);
@@ -461,7 +461,7 @@ I = ideal (x*(y-z), x*y*z)
 J = ideal (dx, dy, dz)
 
 time h = localCohom I
-time h = localCohom (I, W^1/J, Strategy=>Walther)
+time h = localCohom (I, coker gens J, Strategy=>Walther)
 time h = localCohom (I, Strategy=>Walther, LocStrategy=>OaTaWa)
 time h = localCohom (I, Strategy=>Walther, LocStrategy=>Oaku)
 time h = localCohom (I, Strategy=>OaTa)
@@ -473,7 +473,7 @@ J = ideal (dx, dy);
 K = ideal(x^3,y^3);
 
 time h = localCohom I
-time h = localCohom (I, W^1/J, Strategy=>Walther)
+time h = localCohom (I, coker gens J, Strategy=>Walther)
 time h = localCohom (I, Strategy=>Walther, LocStrategy=>OTW)
 time h = localCohom (I, Strategy=>Walther, LocStrategy=>Oaku)
 time h = localCohom (I, Strategy=>OaTa)
@@ -486,14 +486,14 @@ assert (rank L#1 == 0);
 assert (rank L#2 == 1);
 Mat = Dprune localCohom(2,I);
 assert (sub((minimalPrimes charIdeal Mat)_0,W)==ideal(x,y));
-L' = localCohom (m, W^1/K, Strategy=>OaTa);
-assert (L'#0==W^1/ideal(x^3,y^3));
+L' = localCohom (m, coker gens K, Strategy=>OaTa);
+assert (L'#0==coker gens ideal(x^3,y^3));
 
 ---------------------------------------------------------------
 x = symbol x; dx = symbol dx; 
 W = QQ[x, dx, WeylAlgebra=>{x=>dx}]
 I = ideal {x, x^2, x^2+x, x^3, x^4+2*x}
-M = W^1 / ideal dx 
+M = coker gens ideal dx 
 time h = localCohom (I, M, Strategy=>Walther, LocStrategy=>Oaku)
 time h' = localCohom (ideal x)  
 h = pruneLocalCohom h
diff --git a/M2/Macaulay2/packages/BernsteinSato/multiplierIdeals.m2 b/M2/Macaulay2/packages/BernsteinSato/multiplierIdeals.m2
index ebac78d3cf2..d104688d728 100644
--- a/M2/Macaulay2/packages/BernsteinSato/multiplierIdeals.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/multiplierIdeals.m2
@@ -26,7 +26,7 @@ isInMultiplierIdeal(RingElement, Ideal, QQ) := o -> (g,I,c) -> (
 powerIdealZZ = method()
 powerIdealZZ(LeftIdeal,ZZ) := (I,n) -> ideal symmetricPower(n,generators I)
 quotientInWeylAlgebra = method()
-quotientInWeylAlgebra(LeftIdeal,RingElement) := (I,f) -> (new Ideal from I) : (new Ideal from ideal f)  
+quotientInWeylAlgebra(LeftIdeal,RingElement) := (I,f) -> quotient(I,f)  
 productInWeylAlgebra = method()
 productInWeylAlgebra(RingElement,LeftIdeal) := (f,I) -> f * (new Ideal from ideal I)  
 
diff --git a/M2/Macaulay2/packages/BernsteinSato/paramBpoly.m2 b/M2/Macaulay2/packages/BernsteinSato/paramBpoly.m2
index 68d4b7bd4c6..7143b8f697a 100644
--- a/M2/Macaulay2/packages/BernsteinSato/paramBpoly.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/paramBpoly.m2
@@ -535,7 +535,7 @@ gbWparam(Ideal, List) := (I, w) -> (
 -- computes in_w(I). The result is a WA ideal (as opposed to 
 -- an ideal in the associated commutative ring) 
 inWparam = method()
-inWparam(Ideal,List) := (I, w) -> (
+inWparam(LeftIdeal,List) := (I, w) -> (
      I2 := homGBparam(I, w);
      GB := paramGB (I2);    
      I3 := leadTerm(1, gensGB GB);
@@ -923,8 +923,9 @@ isdivisible := (f,g) -> (
 --        ChangeMatrix=>false: option
 -- output: { Groebner basis generators for I [, changematrix] }
 
-paramGB = I -> (
-    if class I === Ideal then I = gens I;
+paramGB = method()
+paramGB LeftIdeal := I -> paramGB gens I
+paramGB Matrix := I -> (
     R := ring I;
     WAflag := R.monoid.Options.WeylAlgebra =!= {};
     if WAflag then (
diff --git a/M2/Macaulay2/packages/Saturation.m2 b/M2/Macaulay2/packages/Saturation.m2
index ef46f130b68..0a024fa3cd6 100644
--- a/M2/Macaulay2/packages/Saturation.m2
+++ b/M2/Macaulay2/packages/Saturation.m2
@@ -49,6 +49,7 @@ override' := (def, opts) -> nonnull apply(keys def, key -> if opts#?key and opts
 ambient' = method()
 ambient' Module := Module => ambient
 ambient' Ideal  := Ideal  => I -> (if instance(I, MonomialIdeal) then monomialIdeal else ideal) 1_(ring I)
+ambient' LeftIdeal  := LeftIdeal  => I -> ideal 1_(ring I)
 
 -- TODO: remove this once the Ideal vs. MonomialIdeal dichotomy is resolved
 uniform' := L -> all(L, l -> instance(l, Ideal)) or uniform L
@@ -123,7 +124,7 @@ QuotientComputation = new Type of Computation
 QuotientComputation.synonym = "quotient computation"
 
 -- TODO: try to find a compatible context that can be used in the computation
-new QuotientContext from Sequence := (C, S) -> ( (A, B) := S; QuotientContext{ mingens B } )
+new QuotientContext from Sequence := (C, S) -> ( (A, B) := S; QuotientContext{ if instance(B,RingElement) then matrix{{B}} else mingens B } )
 new QuotientComputation from Sequence := (C, S) -> new QuotientComputation from {
     BasisElementLimit => (S#2).BasisElementLimit,
     DegreeLimit       => (S#2).DegreeLimit,
@@ -151,6 +152,9 @@ Ideal  : Ideal                := Ideal  =>         (I, J) -> quotient(I, J)
 Ideal  : Number               :=
 Ideal  : RingElement          := Ideal  =>         (I, f) -> quotient(I, f)
 
+-- LeftIdeal
+quotient(LeftIdeal,  RingElement) := LeftIdeal  => opts -> (I, f) -> quotientHelper(I, f, (quotient, LeftIdeal, RingElement), opts)
+
 -- TODO: why is this the right thing to do?
 quotient(MonomialIdeal, RingElement) := MonomialIdeal => opts -> (I, f) -> (
     quotient(I, if size f === 1 and leadCoefficient f == 1 then monomialIdeal f else ideal f, opts))
@@ -183,19 +187,19 @@ quotientHelper = (A, B, key, opts) -> (
     -- this logic runs the strategies in order, or the specified strategy
     computation := (opts, container) -> (
 	if R =!= ring B then error "expected objects in the same ring";
-	if instance(B, RingElement) then B = ideal B;
-	if uniform' {A, B} and ambient' A != ambient' B
+	idealOrModuleB := if instance(B, RingElement) then ideal B else B;
+	if uniform' {A, idealOrModuleB} and ambient' A != ambient' idealOrModuleB
 	then error "expected objects to be contained in the same ambient object";
 	-- note: if B \subset A then A:B should be "everything", but computing
 	-- a gb for A can be slow, so isSubset' doesn't compute a gb
-	if isSubset'(B, A) then return if uniform' {A, B} then cast 1_R else ambient' A;
+	if isSubset'(idealOrModuleB, A) then return if uniform' {A, idealOrModuleB} then cast 1_R else ambient' A;
 	-- note: ideal(..A..) :         f    = A <==> f is nzd / A
 	-- note: ideal(..A..) : ideal(..B..) = A <==>
 	-- note: module(.A.)  : ideal(..B..) = A <==> B is not contained in any associated primes of A
 	-- TODO: can either of the above be efficiently checked?
 	-- TODO: module(.A.)  : module(.B.)  = ? <==> A \subset B
-	if instance(B, Ideal) then -- see the above TODO item
-	if isSubset'(ambient' A, B) then return A;
+	if instance(idealOrModuleB, Ideal) then -- see the above TODO item
+	if isSubset'(ambient' A, idealOrModuleB) then return A;
 	-- TODO: add speedup for when isSubset'(A, B), being cautious of (a3):(a3,bc) in kk[abc]/ac
 
 	-- TODO: what would adding {SyzygyLimit => opts.BasisElementLimit, BasisElementLimit => null} do?
@@ -263,6 +267,22 @@ algorithms#(quotient, Ideal, Ideal) = new MutableHashTable from {
 scan({Quotient, Iterate-*, Linear*-, Monomial}, strategy ->
     addHook(key := (quotient, Ideal, Ideal), algorithms#key#strategy, Strategy => strategy))
 
+-- Installing a hook for LeftIdeal : RingElement
+addHook(
+    (quotient, LeftIdeal, RingElement),
+    (opts, I, f) -> (
+	R := ring I;
+	g := syz gb(
+	    matrix{{f}} | gens I, 
+	    opts,
+	    Strategy   => LongPolynomial,
+	    Syzygies   => true,
+	    SyzygyRows => 1);
+	ideal g
+	),     
+    Strategy => Quotient
+    )
+
 --------------------------------------------------------------------
 -- Algorithms for Module : Ideal
 algorithms#(quotient, Module, Ideal) = new MutableHashTable from {

From 401837d2a0fdc24946b8365c22919acd7dbf95db Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Thu, 30 Nov 2023 08:08:22 -0500
Subject: [PATCH 07/14] one more B-S method needed LeftIdeal

---
 M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2 | 2 +-
 M2/Macaulay2/packages/BernsteinSato/localCohom.m2      | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2 b/M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2
index 12ebed03374..a7909363b17 100644
--- a/M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/globalBFunction.m2
@@ -79,7 +79,7 @@ globalRB (RingElement,Boolean) := RingElement => (f,isRed) -> (
      globalRBAnnFs(f, AnnI, isRed);
 )
 
-globalRBAnnFs (RingElement,Ideal,Boolean) := RingElement => (f,AnnI,isRed) -> (
+globalRBAnnFs (RingElement,LeftIdeal,Boolean) := RingElement => (f,AnnI,isRed) -> (
      W := ring f;
      Ws := ring AnnI;
      ns := numgens Ws;
diff --git a/M2/Macaulay2/packages/BernsteinSato/localCohom.m2 b/M2/Macaulay2/packages/BernsteinSato/localCohom.m2
index 4a95715ae38..7dfda741eec 100644
--- a/M2/Macaulay2/packages/BernsteinSato/localCohom.m2
+++ b/M2/Macaulay2/packages/BernsteinSato/localCohom.m2
@@ -71,7 +71,7 @@ localCohomUli = (l, I) -> (
 	 
      -- Step 3.
      -- Compute the Cech complex 
-	 C := applyValues(subISets, S -> directSum apply(S, theta -> (theta => W^1 / J#theta)));
+	 C := applyValues(subISets, S -> directSum apply(S, theta -> (theta => coker gens J#theta)));
 	 M := new HashTable from apply(Lmaps, k -> k => map (C#(k+1), C#k, (i,j) -> (
 		i0 := (indices C#k)_j;
 		j0 := (indices C#(k+1))_i;

From 3ec8cd7373e3b54cfe5228fd63d0a41ff9853575 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Thu, 7 Dec 2023 11:02:29 -0500
Subject: [PATCH 08/14] lift and eliminate take LeftIdeal now

---
 M2/Macaulay2/m2/matrix1.m2                    |  2 +-
 M2/Macaulay2/m2/matrix2.m2                    |  2 +-
 M2/Macaulay2/packages/Elimination.m2          | 21 ++++++++-----------
 .../Macaulay2Doc/functions/lift-doc.m2        | 10 ++++-----
 4 files changed, 16 insertions(+), 19 deletions(-)

diff --git a/M2/Macaulay2/m2/matrix1.m2 b/M2/Macaulay2/m2/matrix1.m2
index 980a2616717..fc01daa3c8a 100644
--- a/M2/Macaulay2/m2/matrix1.m2
+++ b/M2/Macaulay2/m2/matrix1.m2
@@ -674,7 +674,7 @@ isSurjective Matrix := (f) -> cokernel f == 0
 
 -- two-sided ideal expected
 scan({ZZ,QQ}, S -> (
-	  lift(Ideal,S) := opts -> (I,S) -> (
+	  lift(LeftIdeal,S) := opts -> (I,S) -> (
 	       -- this will be pretty slow
 	       if ring I === S then I
 	       else (ideal lift(generators I,S,opts)) + ideal (presentation ring I ** S))));
diff --git a/M2/Macaulay2/m2/matrix2.m2 b/M2/Macaulay2/m2/matrix2.m2
index 077664457ea..c0a3d40cc4c 100644
--- a/M2/Macaulay2/m2/matrix2.m2
+++ b/M2/Macaulay2/m2/matrix2.m2
@@ -680,7 +680,7 @@ newCoordinateSystem(PolynomialRing, Matrix) := (S,x) -> (
   ( map(S,R,vars S * toS n), map(R,S,vars R * n^(-1)) )
   )
 
-lift(Ideal,RingElement) := Ideal => opts -> (I,S) -> (
+lift(LeftIdeal,RingElement) := Ideal => opts -> (I,S) -> (
      -- provisional, just for quotient rings
      T := ring I;
      if T === S then I
diff --git a/M2/Macaulay2/packages/Elimination.m2 b/M2/Macaulay2/packages/Elimination.m2
index 69c09b8c842..dc2de84c8b1 100644
--- a/M2/Macaulay2/packages/Elimination.m2
+++ b/M2/Macaulay2/packages/Elimination.m2
@@ -81,7 +81,7 @@ eliminate1 = (elimindices,I) -> (
      ideal mingens ideal toR selectInSubring(1,generators gb J)
      )
 
-eliminate (List, Ideal) := (v,I) -> (     
+eliminate (List, LeftIdeal) := (v,I) -> (     
      R := ring I;
      -- if R is a quotient ring, then give error
      if not isFlatPolynomialRing R then
@@ -92,9 +92,9 @@ eliminate (List, Ideal) := (v,I) -> (
      eliminate1(varlist, I)
      )
 
-eliminate (Ideal, RingElement) := (I,v) -> eliminate({v},I)
-eliminate (Ideal, List) := (I,v) -> eliminate(v,I)
-eliminate(RingElement, Ideal) := (v,I) -> eliminate({v},I)
+eliminate (LeftIdeal, RingElement) := (I,v) -> eliminate({v},I)
+eliminate (LeftIdeal, List) := (I,v) -> eliminate(v,I)
+eliminate(RingElement, LeftIdeal) := (v,I) -> eliminate({v},I)
 
 -----------------------------------------------
 -- Sylvester matrix, resultant, discriminant --
@@ -173,17 +173,14 @@ document {
      SeeAlso => {"sylvesterMatrix", "discriminant", "eliminate"}
      }
 
-
-undocumented {
-	  (eliminate, Ideal, RingElement), 
-	  (eliminate, Ideal, List)
-     }
 document {
      Key => {eliminate,
-	  (eliminate, RingElement, Ideal), 
-	  (eliminate, List, Ideal)
+	  (eliminate, RingElement, LeftIdeal), 
+	  (eliminate, LeftIdeal, RingElement), 
+	  (eliminate, LeftIdeal, List),
+	  (eliminate, List, LeftIdeal)
 	  },
-     Usage => "eliminate(v,J)",
+     Usage => "eliminate(v,J)\neliminate(J,v)",
      Inputs => {
 	  "v" => Nothing => {ofClass RingElement, " or ", ofClass List, ", a variable or list of variables of a polynomial ring ", TT "R"},
 	  "J" => Ideal => {"in the ring ", TT "R"},
diff --git a/M2/Macaulay2/packages/Macaulay2Doc/functions/lift-doc.m2 b/M2/Macaulay2/packages/Macaulay2Doc/functions/lift-doc.m2
index fdf1168cc71..6709cc5e736 100644
--- a/M2/Macaulay2/packages/Macaulay2Doc/functions/lift-doc.m2
+++ b/M2/Macaulay2/packages/Macaulay2Doc/functions/lift-doc.m2
@@ -18,13 +18,13 @@ lift(MutableMatrix,type of RingElement)
 
 document { 
      Key => {lift,
-	  (lift,Ideal,RingElement),[lift,Verify],
+	  (lift,LeftIdeal,RingElement),[lift,Verify],
 	  (lift,Matrix,RingElement),
 	  (lift, CC, QQ),
 	  (lift, CC, RR_*),
 	  (lift, CC, ZZ),
-	  (lift, Ideal, QQ),
-	  (lift, Ideal, ZZ),
+	  (lift, LeftIdeal, QQ),
+	  (lift, LeftIdeal, ZZ),
 	  (lift,Matrix,CC_*,QQ),
 	  (lift,Matrix,CC_*,RR_*),
 	  (lift,Matrix,CC_*,ZZ),
@@ -54,14 +54,14 @@ document {
      Usage => "lift(f,R)",
      Inputs => {
 	  "f" => {"a ", TO2(RingElement,"ring element"), ", ",
-	       TO2(Ideal, "ideal"), ", or ", 
+	       TO2(LeftIdeal, "ideal"), ", or ", 
 	       TO2(Matrix, "matrix")},
 	  "R" => Ring,
 	  Verify => Boolean => {"whether to give an error message if lifting is not possible, or, alternatively, to return ", TO "null"}
 	  },
      Outputs => {
 	  {"a ", TO2(RingElement,"ring element"), ", ",
-	       TO2(Ideal, "ideal"), ", or ", 
+	       TO2(LeftIdeal, "ideal"), ", or ", 
 	       TO2(Matrix, "matrix"), ", over the ring ", TT "R"}
 	  },
      PARA {

From caa7271226ca83f5b32af28956fc3715bc9a1c88 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Sat, 9 Dec 2023 10:13:03 -0500
Subject: [PATCH 09/14] fixes in Core and ComputationsBook; Module / LeftIdeal
 special usage for backward compatibility; Matrix % LeftIdeal convenience
 implementation (no good meaning for the output as a map of one-sided Modules)

---
 M2/Macaulay2/m2/matrix1.m2                    | 14 ++++----
 M2/Macaulay2/m2/newring.m2                    |  5 ++-
 .../tests/ComputationsBook/d-modules/test.m2  |  6 ++--
 .../d-modules/test.out.expected               | 32 +++++++++----------
 4 files changed, 31 insertions(+), 26 deletions(-)

diff --git a/M2/Macaulay2/m2/matrix1.m2 b/M2/Macaulay2/m2/matrix1.m2
index fc01daa3c8a..00359d3c8c7 100644
--- a/M2/Macaulay2/m2/matrix1.m2
+++ b/M2/Macaulay2/m2/matrix1.m2
@@ -493,6 +493,11 @@ LeftIdeal / LeftIdeal := Module => (I,J) -> module I / module J
 
 -- two-sided ideal expected
 Module / Ideal := Module => (M,J) -> M / (J * M)
+Module / LeftIdeal := Module => (M,J) -> (
+    if isFreeModule M and rank M == 1 
+    then comodule J
+    else "not defined for a left ideal (in general)" 
+    )
 
 LeftIdeal#AfterPrint = LeftIdeal#AfterNoPrint = I ->  (LeftIdeal," of ",ring I)
 Ideal#AfterPrint = Ideal#AfterNoPrint = I ->  (Ideal," of ",ring I)
@@ -509,12 +514,9 @@ RingElement + LeftIdeal := Number + LeftIdeal := ((r,I) -> ideal r + I) @@ tosam
 LeftIdeal _ ZZ := RingElement => (I,n) -> (generators I)_(0,n)
 
 
-Matrix % LeftIdeal := Matrix => ((f,I) -> 
-     if numRows f === 1
-     then f % gb I
-     else 
-     error "not implemented (defined for two-sided ideals; see `code (symbol %, Matrix, Ideal)`)"
-     ) @@ samering
+-- Matrix % Ideal is a convenience function... and so is Matrix % LeftIdeal 
+-- the result of the latter has even less (natural) meaning as a map (on a one-sided module)
+Matrix % LeftIdeal := Matrix => ((f,I) -> map(target f, source f, apply(entries f, row -> matrix row % gb I))) @@ samering
 
 -- two-sided ideal expected (note: R/I is a problem !!!)
 Matrix % Ideal := Matrix => ((f,I) -> 
diff --git a/M2/Macaulay2/m2/newring.m2 b/M2/Macaulay2/m2/newring.m2
index 9194f7f237f..8906e5919da 100644
--- a/M2/Macaulay2/m2/newring.m2
+++ b/M2/Macaulay2/m2/newring.m2
@@ -132,6 +132,7 @@ coerce(Thing,Thing) := (x,Y) -> if instance(x,Y) then x else error("no method fo
 coerce(Ideal,Ring) := quotient @@ first
 coerce(Thing,Nothing) := (x,Nothing) -> null		    -- avoid using this one, to save time earlier
 coerce(Ring,Ideal) := (R,Ideal) -> ideal R		    -- avoid using this one, to save time earlier
+coerce(Ring,Ideal) := (R,LeftIdeal) -> ideal R		    -- avoid using this one, to save time earlier
 preprocessResultTemplate = (narrowers,r) -> (
      if instance(r,ZZ) then r = r:null;
      r = apply(sequence r,x -> if x === null then Thing else x);
@@ -192,7 +193,9 @@ triv := R -> (
 flattenRing Ring := opts -> R -> (
      resultTemplate := preprocessResultTemplate(1:Ring, opts.Result);
      k := opts.CoefficientRing;
-     if k === R or k === null and (R.?isBasic or isField R) then flatCoerce(R,resultTemplate,triv R)
+     if k === R or k === null and (R.?isBasic or isField R) and 
+     not isWeylAlgebra R -- for WeylAlgebra flatCoerce doesn't work as is, since R/I is not defined for a left ideal I 
+     then flatCoerce(R,resultTemplate,triv R)
      else unable())
 
 flattenRing GaloisField := opts -> (cacheValue (symbol flattenRing => opts)) (F -> (
diff --git a/M2/Macaulay2/tests/ComputationsBook/d-modules/test.m2 b/M2/Macaulay2/tests/ComputationsBook/d-modules/test.m2
index d6f610477ec..4ec88333f02 100644
--- a/M2/Macaulay2/tests/ComputationsBook/d-modules/test.m2
+++ b/M2/Macaulay2/tests/ComputationsBook/d-modules/test.m2
@@ -46,7 +46,7 @@ Jfgh=ideal relations Rfgh.LocModule;
 JH3=Jfgh+ideal(f^2,g,h);
 JH3gb=gens gb JH3
 testmTorsion = method();
-testmTorsion Ideal := (L) -> (
+testmTorsion LeftIdeal := (L) -> (
      LL = ideal generators gb L;
      n = numgens (ring (LL)) // 2;
      LLLL = ideal select(first entries gens LL, f->(
@@ -71,7 +71,7 @@ Ifgh=ideal relations Rfgh.LocModule;
 IH3=Ifgh+ideal(f,g,h);
 IH3gb=gens gb IH3
 findSocle = method();
-findSocle(Ideal, RingElement):= (L,P) -> (
+findSocle(LeftIdeal, RingElement):= (L,P) -> (
      createDpairs(ring(L));
      v=(ring L).dpairVars#0;
      myflag = true;
@@ -86,7 +86,7 @@ findSocle(Ideal, RingElement):= (L,P) -> (
 D = ring JH3
 findSocle(JH3,1_D)
 findLength = method();
-findLength Ideal := (I) -> (   
+findLength LeftIdeal := (I) -> (   
      l = 0;
      while I != ideal 1_(ring I) do (
           l = l + 1;
diff --git a/M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected b/M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected
index abd0a3e4aca..c3b6e79ce06 100644
--- a/M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected
+++ b/M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected
@@ -11,7 +11,7 @@ i3 : Delta = ideal(Dx,Dy,Dz)
 
 o3 = ideal (Dx, Dy, Dz)
 
-o3 : Ideal of D
+o3 : LeftIdeal of D
 
 i4 : (Dx * x)^2
 
@@ -67,19 +67,19 @@ i10 : AnnFs(f)
 
 o10 = ideal (w*Dz - z*Dw, w*Dy - y*Dw, z*Dy - y*Dz, w*Dx - x*Dw, z*Dx - x*Dz, y*Dx - x*Dy, x*Dx + y*Dy + z*Dz + w*Dw - 2s)
 
-o10 : Ideal of QQ[x..z, w, Dx, Dy, Dz, Dw, s]
+o10 : LeftIdeal of QQ[x..z, w, Dx, Dy, Dz, Dw, s]
 
 i11 : L=ideal(x,y,Dz,Dw)
 
 o11 = ideal (x, y, Dz, Dw)
 
-o11 : Ideal of D
+o11 : LeftIdeal of D
 
 i12 : AnnIFs(L,f)
 
 o12 = ideal (y, x, w*Dz - z*Dw, z*Dz + w*Dw - 2s)
 
-o12 : Ideal of QQ[x..z, w, Dx, Dy, Dz, Dw, s]
+o12 : LeftIdeal of QQ[x..z, w, Dx, Dy, Dz, Dw, s]
 
 i13 : f
 
@@ -117,7 +117,7 @@ i18 : I1 = ideal((x*Dx)^2+1)
              2  2
 o18 = ideal(x Dx  + x*Dx + 1)
 
-o18 : Ideal of D1
+o18 : LeftIdeal of D1
 
 i19 : f1 = x;
 
@@ -175,7 +175,7 @@ i27 : D = QQ[x,y,z,Dx,Dy,Dz, WeylAlgebra => {x=>Dx, y=>Dy, z=>Dz}];
 
 i28 : Delta = ideal(Dx,Dy,Dz);
 
-o28 : Ideal of D
+o28 : LeftIdeal of D
 
 i29 : f=x^3+y^3+z^3;
 
@@ -217,7 +217,7 @@ i33 : D= QQ[x,y,z,u,v,w,Dx,Dy,Dz,Du,Dv,Dw, WeylAlgebra =>
 
 i34 : Delta=ideal(Dx,Dy,Dz,Du,Dv,Dw);
 
-o34 : Ideal of D
+o34 : LeftIdeal of D
 
 i35 : R=D^1/Delta;
 
@@ -268,11 +268,11 @@ o42 = -2
 
 i43 : Jfgh=ideal relations Rfgh.LocModule;
 
-o43 : Ideal of D
+o43 : LeftIdeal of D
 
 i44 : JH3=Jfgh+ideal(f^2,g,h);
 
-o44 : Ideal of D
+o44 : LeftIdeal of D
 
 i45 : JH3gb=gens gb JH3
 
@@ -283,7 +283,7 @@ o45 : Matrix D  <-- D
 
 i46 : testmTorsion = method();
 
-i47 : testmTorsion Ideal := (L) -> (
+i47 : testmTorsion LeftIdeal := (L) -> (
            LL = ideal generators gb L;
            n = numgens (ring (LL)) // 2;
            LLLL = ideal select(first entries gens LL, f->(
@@ -309,7 +309,7 @@ i52 : h=x*w-y*z;
 
 i53 : Delta=ideal(Dx,Dy,Dz,Dw);
 
-o53 : Ideal of D
+o53 : LeftIdeal of D
 
 i54 : R=D^1/Delta;
 
@@ -333,11 +333,11 @@ i57 : Rfgh=DlocalizeAll(Rfg.LocModule,h, Strategy => Oaku);
 
 i58 : Ifgh=ideal relations Rfgh.LocModule;
 
-o58 : Ideal of D
+o58 : LeftIdeal of D
 
 i59 : IH3=Ifgh+ideal(f,g,h);
 
-o59 : Ideal of D
+o59 : LeftIdeal of D
 
 i60 : IH3gb=gens gb IH3
 
@@ -348,7 +348,7 @@ o60 : Matrix D  <-- D
 
 i61 : findSocle = method();
 
-i62 : findSocle(Ideal, RingElement):= (L,P) -> (
+i62 : findSocle(LeftIdeal, RingElement):= (L,P) -> (
            createDpairs(ring(L));
            v=(ring L).dpairVars#0;
            myflag = true;
@@ -375,7 +375,7 @@ o64 : D
 
 i65 : findLength = method();
 
-i66 : findLength Ideal := (I) -> (   
+i66 : findLength LeftIdeal := (I) -> (   
            l = 0;
            while I != ideal 1_(ring I) do (
                 l = l + 1;
@@ -480,7 +480,7 @@ i89 : I = gkz(matrix{{1,2}}, {5})
 o89 = ideal (x D  + 2x D  - 5, D  - D )
               1 1     2 2       1    2
 
-o89 : Ideal of QQ[x ..x , D ..D ]
+o89 : LeftIdeal of QQ[x ..x , D ..D ]
                    1   2   1   2
 
 i90 : PolySols I

From 29af24fa3888e2dde05c7e4fd9f7d1c6673de28b Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Sun, 10 Dec 2023 07:45:40 -0500
Subject: [PATCH 10/14] some forgotten files in tests/normal

---
 M2/Macaulay2/tests/normal/isSkewCommutative.m2 | 4 ----
 M2/Macaulay2/tests/normal/monoids.m2           | 4 +++-
 M2/Macaulay2/tests/normal/polyrings.m2         | 6 ++++++
 3 files changed, 9 insertions(+), 5 deletions(-)

diff --git a/M2/Macaulay2/tests/normal/isSkewCommutative.m2 b/M2/Macaulay2/tests/normal/isSkewCommutative.m2
index dbfd0d19eb4..0880c24333f 100644
--- a/M2/Macaulay2/tests/normal/isSkewCommutative.m2
+++ b/M2/Macaulay2/tests/normal/isSkewCommutative.m2
@@ -8,9 +8,5 @@ R = QQ[x,y,z,SkewCommutative => {x,y}]
 assert( isSkewCommutative R )
 R = QQ[x,y,z]/z^2
 assert( not isSkewCommutative R )
-R = QQ[x,y,z,WeylAlgebra => {x => y}]/z^2
-assert( not isSkewCommutative R )
 R = QQ[x,y,z,SkewCommutative => true]/z^2
 assert( isSkewCommutative R )
-R = QQ[x,y,z,SkewCommutative => {x,y}]/z^2
-assert( isSkewCommutative R )
diff --git a/M2/Macaulay2/tests/normal/monoids.m2 b/M2/Macaulay2/tests/normal/monoids.m2
index 103f465e01e..4b6ba981812 100644
--- a/M2/Macaulay2/tests/normal/monoids.m2
+++ b/M2/Macaulay2/tests/normal/monoids.m2
@@ -241,11 +241,13 @@ A = QQ[t, dt, WeylAlgebra => {t => dt}]
 M = monoid A
 assert(A.WeylAlgebra == {{0, 1}})
 assert(M.Options.WeylAlgebra == {{M_0, M_1}})
-B = first flattenRing(A[t])
+-* 
+B = first flattenRing(A[t]) -- flattenRing doesn't work for WeylAlgebra at the moment
 assert(gens B == {t_0, t_1, dt})
 N = monoid B
 assert(B.WeylAlgebra == {{1, 2}})
 assert(N.Options.WeylAlgebra == {{N_1, N_2}})
+*-
 
 -- test of adjoining variables with local variables
 needsPackage "BernsteinSato"
diff --git a/M2/Macaulay2/tests/normal/polyrings.m2 b/M2/Macaulay2/tests/normal/polyrings.m2
index a5fbb3dcbe0..e6a2e8ebb5c 100644
--- a/M2/Macaulay2/tests/normal/polyrings.m2
+++ b/M2/Macaulay2/tests/normal/polyrings.m2
@@ -14,6 +14,8 @@ A = ZZ[a,b]/(a^3-b^3)
 B = A[x,y]
 assert(B_2^3 == B_3^3)
 
+-* 
+-- Ring/LeftIdeal is not a ring
 C = ZZ/3[x,dx,k,WeylAlgebra => x => dx]/(k^3-x^3)	    -- I made this ZZ/3 so x^3 would be in the center [dan]
 del(dx,x,1)
 
@@ -22,6 +24,7 @@ assert(D_1^3==D_3^3)
 com(x,t)
 com(dx,t)
 del(D_2,D_1,1)
+*-
 
 E = A[s,ds,WeylAlgebra => s => ds]
 com(a*1_E,b*1_E)
@@ -31,6 +34,8 @@ com(a,ds)
 com(b,ds)
 del(ds,s,1)
 
+-* 
+-- C is not valid (see above) 
 F = C[r,dr,WeylAlgebra => r => dr]
 del(dx*1_F,x*1_F,1)
 del(dr,r,1)
@@ -38,6 +43,7 @@ com(dx,dr)
 com(dx,r)
 com(x,dr)
 com(x,r)
+*-
 
 G = ZZ[p,SkewCommutative => true]
 assert( p^2 == 0 )

From e181bf04003f479900735dead4fa481750ccc006 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Tue, 12 Dec 2023 14:37:03 -0500
Subject: [PATCH 11/14] one line in ComputationsBook

---
 M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected b/M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected
index c3b6e79ce06..4f1a684a449 100644
--- a/M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected
+++ b/M2/Macaulay2/tests/ComputationsBook/d-modules/test.out.expected
@@ -481,7 +481,7 @@ o89 = ideal (x D  + 2x D  - 5, D  - D )
               1 1     2 2       1    2
 
 o89 : LeftIdeal of QQ[x ..x , D ..D ]
-                   1   2   1   2
+                       1   2   1   2
 
 i90 : PolySols I
 

From 66b93a0deb31b48eb0fbffce19ea72fdc8db5fd3 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Thu, 21 Nov 2024 14:43:01 -0500
Subject: [PATCH 12/14] fixed bug in support

---
 M2/Macaulay2/m2/matrix2.m2 | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/M2/Macaulay2/m2/matrix2.m2 b/M2/Macaulay2/m2/matrix2.m2
index e9b01710437..c4b9e4ecd3a 100644
--- a/M2/Macaulay2/m2/matrix2.m2
+++ b/M2/Macaulay2/m2/matrix2.m2
@@ -438,7 +438,7 @@ indices Matrix := (f) -> rawIndices raw f
 support = method()
 support RingElement :=
 support Matrix      := f -> apply(try rawIndices raw f else {}, i -> (ring f)_i)
-support LeftIdeal := I -> rsort toList sum apply(flatten entries generators I, f -> set support f)
+support LeftIdeal   := I -> support generators I
 
 --------------------
 -- homogenization --

From 50803b302a2057b085b98edc8e6c74c74d6c007d Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Tue, 26 Nov 2024 12:50:24 -0500
Subject: [PATCH 13/14] PolynomialRing ** PolynomialRing fixed to work in all
 cases

---
 M2/Macaulay2/m2/matrix1.m2 |  2 +-
 M2/Macaulay2/m2/matrix2.m2 |  8 ++------
 M2/Macaulay2/m2/newring.m2 | 26 +++++++++++++-------------
 3 files changed, 16 insertions(+), 20 deletions(-)

diff --git a/M2/Macaulay2/m2/matrix1.m2 b/M2/Macaulay2/m2/matrix1.m2
index 4e733f2a301..45a5c803025 100644
--- a/M2/Macaulay2/m2/matrix1.m2
+++ b/M2/Macaulay2/m2/matrix1.m2
@@ -689,7 +689,7 @@ super Matrix := Matrix => (f) -> (
 isInjective Matrix := (f) -> kernel f == 0
 isSurjective Matrix := (f) -> cokernel f == 0
 
--- two-sided ideal expected
+-- AL: `**` may cause problems in the noncommutative case 
 scan({ZZ,QQ}, S -> (
 	  lift(LeftIdeal,S) := opts -> (I,S) -> (
 	       -- this will be pretty slow
diff --git a/M2/Macaulay2/m2/matrix2.m2 b/M2/Macaulay2/m2/matrix2.m2
index c4b9e4ecd3a..a2e4ae40aba 100644
--- a/M2/Macaulay2/m2/matrix2.m2
+++ b/M2/Macaulay2/m2/matrix2.m2
@@ -141,10 +141,6 @@ complement Matrix := Matrix => (f) -> (
 -----------------------------------------------------------------------------
 -- the method is declared in gb.m2
 mingens LeftIdeal  := Matrix => opts -> I -> mingens(module I, opts)
-mingens Module := Matrix => opts -> (cacheValue symbol mingens) ((M) -> (
-        c := runHooks((mingens, Module), (opts, M));
-        if c =!= null then c else error "mingens: no method implemented for this type of module"))
-
 -- TODO: the strategies should be separated
 mingens Module := Matrix => opts -> M -> if isFreeModule M then generators M else cacheHooks(
     symbol mingens, M, (mingens, Module), (opts, M), (opts, M) -> (
@@ -174,8 +170,8 @@ trim = method (Options => { Strategy => null -* TODO: add DegreeLimit => {} *-})
 trim Ring         := Ring => o -> identity
 trim QuotientRing := Ring => o -> R -> quotient trim(ideal presentation R, o)
 
--- trim Ideal  := Ideal  => opts -> I -> ideal trim(module I, opts)
-trim LeftIdeal  := LeftIdeal  => opts -> (cacheValue (symbol trim => opts)) ((I) -> ideal trim(module I, opts))
+trim LeftIdeal  := LeftIdeal  => opts -> I -> ideal trim(module I, opts)
+-- old or new version???: trim LeftIdeal  := LeftIdeal  => opts -> (cacheValue (symbol trim => opts)) ((I) -> ideal trim(module I, opts))
 trim Module := Module => opts -> M -> if isFreeModule M then M else cacheHooks(
     (symbol trim, opts), M, (trim, Module), (opts, M), (opts, M) -> (
 	if opts.Strategy === null then opts = opts ++ { Strategy => Complement };
diff --git a/M2/Macaulay2/m2/newring.m2 b/M2/Macaulay2/m2/newring.m2
index 6d83be2bfb5..cd8ee7bf7c1 100644
--- a/M2/Macaulay2/m2/newring.m2
+++ b/M2/Macaulay2/m2/newring.m2
@@ -64,13 +64,7 @@ QuotientRing ** PolynomialRing :=
 PolynomialRing ** QuotientRing :=
 QuotientRing ** QuotientRing := (R,S) -> tensor(R,S)
 
-tensor(PolynomialRing, PolynomialRing) := monoidTensorDefaults >> optns -> (R, S) -> (
-     k := coefficientRing R;
-     if k =!= coefficientRing S 
-     then error "expected rings to have the same coefficient ring";
-     k tensor(monoid R, monoid S, optns)
-     )
-
+tensor(PolynomialRing, PolynomialRing) := 
 tensor(QuotientRing,   PolynomialRing) :=
 tensor(PolynomialRing, QuotientRing) :=
 tensor(QuotientRing,   QuotientRing) := monoidTensorDefaults >> optns -> (R, S) -> (
@@ -79,12 +73,18 @@ tensor(QuotientRing,   QuotientRing) := monoidTensorDefaults >> optns -> (R, S)
      then error "expected rings to have the same coefficient ring";
      f := presentation R; A := ring f; M := monoid A; m := numgens M;
      g := presentation S; B := ring g; N := monoid B; n := numgens N;
-     MN := k tensor(M, N, optns);
-     fg := substitute(f,(vars MN)_{0 .. m-1}) | substitute(g,(vars MN)_{m .. m+n-1});
-     -- forceGB fg;  -- if the monomial order chosen doesn't restrict, then this
-                     -- is an error!! MES
-     AB := MN;
-     RS := AB/image fg;
+     AB := k tensor(M, N, optns);
+     -- need "if" below, since for non-commutative R or S `image fg` is a (zero) LeftIdeal
+     --   alt: need to prohibit tensoring non-commutative rings???
+     --   alt (future???): quotients of non-commutative rings would be allowed and
+     --                    `presentation R` then returns a potentially nontrivial two-sided ideal;
+     --                    e.g., WA with some commuting variables
+     RS := if class R === PolynomialRing and class S === PolynomialRing then AB else (
+	 fg := substitute(f,(vars AB)_{0 .. m-1}) | substitute(g,(vars AB)_{m .. m+n-1});
+	 -- forceGB fg;  -- if the monomial order chosen doesn't restrict, then this
+	 -- is an error!! MES
+	 AB/image fg
+	 );
      setupPromote map(RS,R,(vars AB)_{0 .. m-1});
      setupLift map(R,RS,generators A | toList(n:0));
      if S =!= R then (

From f8fa2faa9684689e8021e1cdad3fffd8248f9e54 Mon Sep 17 00:00:00 2001
From: Anton Leykin <anton.leykin@gmail.com>
Date: Mon, 9 Dec 2024 11:12:33 -0500
Subject: [PATCH 14/14] long comment on Module / LeftIdeal

---
 M2/Macaulay2/m2/matrix1.m2 | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/M2/Macaulay2/m2/matrix1.m2 b/M2/Macaulay2/m2/matrix1.m2
index 45a5c803025..e9db5323baa 100644
--- a/M2/Macaulay2/m2/matrix1.m2
+++ b/M2/Macaulay2/m2/matrix1.m2
@@ -468,6 +468,7 @@ euler LeftIdeal := I -> euler((ring I)^1/I)
 -- two-sided ideal expected
 RingElement * Ideal := Ideal => (r,I) -> ideal (r ** generators I)
 Ideal * RingElement := Ideal => (I,r) -> ideal ((generators I)**r)
+LeftIdeal * RingElement := Ideal => (I,r) -> ideal ((generators I)*r) -- staying away from ** 
 ZZ * Ideal := (r,I) -> ideal (r * generators I)
 Ideal * ZZ := (I,r) -> ideal (r * generators I)
 
@@ -503,6 +504,11 @@ LeftIdeal / LeftIdeal := Module => (I,J) -> module I / module J
 
 -- two-sided ideal expected
 Module / Ideal := Module => (M,J) -> M / (J * M)
+
+-- This function exist because there is a lot of user (package?) code 
+-- where `R^1/I` means R/I as a _left_ R-module and, in non-commutative setting,
+-- (however, R^1 is a currently a right module over R^{op}). 
+-- It is never used for `M/I` where M is not `R^1`. 
 Module / LeftIdeal := Module => (M,J) -> (
     if isFreeModule M and rank M == 1 
     then comodule J