Graded-commutative ideals

[trevorkarn]

A graded-commutative ring is a mildly noncommutative ring in which x*y = (-1)**(x.deg()*y.deg())*y*x for the right notion of degree. This ticket aims to implement ideals of graded-commutative rings inside of sage.rings.noncommutative_ideals via the class Ideal_gc.

CC: @tscrim @trevorkarn @jhpalmieri

Component: algebra

Keywords: gsoc2021 gradedcommutative ideal graded

Author: Trevor K. Karn

Branch/Commit: u/tkarn/sc-ideals-32249 @ 1a79ed0

Issue created by migration from https://trac.sagemath.org/ticket/32249

[trevorkarn]

Description changed:

--- 
+++ 
@@ -1 +1 @@
-A supercommutative ring is a mildly noncommutative ring in which `x*y = (-1)**(x.deg()*y.deg())*y*x` for the right notion of degree. This ticket aims to implement ideals of supercommutative rings inside of `sage.rings.ideal` via the class `Ideal_supercommutative`. 
+A supercommutative ring is a mildly noncommutative ring in which `x*y = (-1)**(x.deg()*y.deg())*y*x` for the right notion of degree. This ticket aims to implement ideals of supercommutative rings inside of `sage.rings.noncommutative_ideals` via the class `Ideal_supercommutative`. 

[trevorkarn]

New commits:

1a79ed0

Initial commit of supercommutative ideal

[trevorkarn]

Commit: 1a79ed0

[trevorkarn]

Branch: u/tkarn/sc-ideals-32249

[nbruin]

comment:3

Searching on google for the synonymous term "graded-commutative" returns "About 5,310,000 results" whereas for "supercommutative" it returns "About 13,400 results". This suggests to me that the former is the more entrenched term and therefore is probably the one to use in a general-purpose CAS such as sage.

[trevorkarn]

comment:4

It is also a more general idea, I had the definition of supercommutative slightly off. It is an instance of a graded-commutative algebra with only degree 0 and degree 1 things. I agree the name should change.

[trevorkarn]

Description changed:

--- 
+++ 
@@ -1 +1 @@
-A supercommutative ring is a mildly noncommutative ring in which `x*y = (-1)**(x.deg()*y.deg())*y*x` for the right notion of degree. This ticket aims to implement ideals of supercommutative rings inside of `sage.rings.noncommutative_ideals` via the class `Ideal_supercommutative`. 
+A graded-commutative ring is a mildly noncommutative ring in which `x*y = (-1)**(x.deg()*y.deg())*y*x` for the right notion of degree. This ticket aims to implement ideals of graded-commutative rings inside of `sage.rings.noncommutative_ideals` via the class `Ideal_gc`. 

[trevorkarn]

Changed keywords from gsoc2021 supercommutative ideal to gsoc2021 gradedcommutative ideal graded

[trevorkarn]

comment:6

Here is a reference: https://d-nb.info/1012919684/34

[mjungmath]

comment:7

Please notice that graded superalgebras already exist, though under a different name (see here).