Trac #10483: deprecate the misuse of symbolic variables as polynomial variable

Also-by: Simon King <[email protected]>

Author: rwst

src/sage/categories/rings.py

@@ -947,14 +947,7 @@ def __getitem__(self, arg):
                 ...
                 TypeError: power series rings must have at least one variable
 
-            Some flexibility is allowed when specifying variables::
-
-                sage: QQ["x", SR.var('y'), polygen(CC, 'z')]
-                Multivariate Polynomial Ring in x, y, z over Rational Field
-                sage: QQ[["x", SR.var('y'), polygen(CC, 'z')]]
-                Multivariate Power Series Ring in x, y, z over Rational Field
-
-            but more baroque expressions do not work::
+            These kind of expressions do not work::
 
                 sage: QQ['a,b','c']
                 Traceback (most recent call last):

src/sage/coding/linear_code.py

@@ -3555,7 +3555,7 @@ def weight_enumerator(self, names=None, name2=None, bivariate=True):
             sage: C.weight_enumerator(names="var1, var2")
             var1^7 + 7*var1^4*var2^3 + 7*var1^3*var2^4 + var2^7
             sage: (var1, var2) = var('var1, var2')
-            sage: C.weight_enumerator(names=(var1, var2))
+            sage: C.weight_enumerator(names=('var1', 'var2'))
             var1^7 + 7*var1^4*var2^3 + 7*var1^3*var2^4 + var2^7
             sage: C.weight_enumerator(bivariate=False)
             x^7 + 7*x^4 + 7*x^3 + 1

src/sage/functions/piecewise.py

@@ -996,10 +996,10 @@ def trapezoid(cls, self, parameters, variable, N):
                 sage: f.trapezoid(2)
                 piecewise(y|-->1/2*y on (0, 1/2), y|-->3/2*y - 1/2 on (1/2, 1), y|-->7/2*y - 5/2 on (1, 3/2), y|-->-7/2*y + 8 on (3/2, 2); y)
             """
-            x = QQ[self.default_variable()].gen()
             def func(x0, x1):
                 f0, f1 = self(x0), self(x1)
-                return [[(x0,x1),f0+(f1-f0)*(x1-x0)**(-1)*(x-x0)]]
+                return [[(x0,x1), f0 + (f1-f0) * (x1-x0)**(-1)
+                    * (self.default_variable()-x0)]]
             rsum = []
             for domain, f in parameters:
                 for interval in domain:

src/sage/matrix/matrix2.pyx

@@ -10983,7 +10983,7 @@ cdef class Matrix(Matrix1):
             sage: p, S = A.cyclic_subspace(v, var='T'); p
             T^3 - 9*T^2 + 24*T - 16
             sage: gen = polygen(QQ, 'z')
-            sage: p, S = A.cyclic_subspace(v, var=gen); p
+            sage: p, S = A.cyclic_subspace(v, var='z'); p
             z^3 - 9*z^2 + 24*z - 16
             sage: p.degree() == E.dimension()
             True

src/sage/rings/polynomial/polynomial_element.pyx

@@ -6654,9 +6654,10 @@ cdef class Polynomial(CommutativeAlgebraElement):
 
         The following examples show that :trac:`11782` has been fixed::
 
-            sage: ZZ.quo(81)[x](3*x^2 + 3*x + 3).discriminant()
+            sage: x = var('x')
+            sage: ZZ.quo(81)['x'](3*x^2 + 3*x + 3).discriminant()
             54
-            sage: ZZ.quo(9)[x](2*x^3 + x^2 + x).discriminant()
+            sage: ZZ.quo(9)['x'](2*x^3 + x^2 + x).discriminant()
             2
 
         This was fixed by :trac:`15422`::

src/sage/rings/polynomial/polynomial_ring_constructor.py

@@ -72,7 +72,7 @@ def PolynomialRing(base_ring, *args, **kwds):
 
     - ``name`` -- a string
 
-    - ``names`` -- a list or tuple of names, or a comma separated string
+    - ``names`` -- a list or tuple of names (strings), or a comma separated string
 
     - ``var_array`` -- a list or tuple of names, or a comma separated string
 

src/sage/rings/quotient_ring.py

@@ -107,6 +107,7 @@
 # (at your option) any later version.
 #                  http://www.gnu.org/licenses/
 #*****************************************************************************
+
 from __future__ import absolute_import
 from six.moves import range
 
@@ -185,7 +186,9 @@ def QuotientRing(R, I, names=None):
 
     ::
 
-        sage: S = QuotientRing(QQ[x], QQ[x].ideal(x^2 - 2)); S
+        sage: P.<x> = QQ[]
+        sage: S.<xbar> = QuotientRing(P, P.ideal(x^2 - 2))
+        sage: S
         Univariate Quotient Polynomial Ring in xbar over Rational Field with
         modulus x^2 - 2
         sage: xbar = S.gen(); S.gen()
@@ -197,7 +200,8 @@ def QuotientRing(R, I, names=None):
 
     Sage coerces objects into ideals when possible::
 
-        sage: R = QuotientRing(QQ[x], x^2 + 1); R
+        sage: P.<x> = QQ[]
+        sage: R.<xbar> = QuotientRing(P, x^2 + 1); R
         Univariate Quotient Polynomial Ring in xbar over Rational Field with
         modulus x^2 + 1
 

src/sage/rings/ring.pyx

@@ -983,9 +983,8 @@ cdef class Ring(ParentWithGens):
 
         Make sure :trac:`10481` is fixed::
 
-            sage: var(x)
-            x
-            sage: R.<a>=ZZ[x].quo(x^2)
+            sage: x = var('x')
+            sage: R.<a> = ZZ['x'].quo(x^2)
             sage: R.fraction_field()
             Traceback (most recent call last):
             ...