Hi Travis and John, On 2018-06-17, Travis Scrimshaw <tsc...@ucdavis.edu> wrote: > IMO, proper way to implement this is as a CategoryWithAxiom as a part of > SuperAlgebras[WithBasis]. So you add a class > "Commutative(CategoryWithAxiom_over_base_ring)" to the > SuperAlgebras[WithBasis] category and do the normal category implementation > stuff there.
I disagree. In a previous post (IIRC), John has emphasised that he is dealing with graded commutative algebras, which are of course not commutative algebras (indeed, x*y=-y*x when x,y are of odd degree). So, it would actually be mathematically wrong to use the axiom "Commutative" here (in one way or another) because graded commutative algebras are not commutative, and are thus not sub-categories of CommutativeMonoids (which would be the effect of using the "Commutative" axiom. I think the proper way to proceed is: Add a new axiom "GradedCommutative", that is defined for GradedRings(). Then, GradedAlgebrasWithBasis(QQ).GradedCommutative() would automatically be available (as GradedAlgebrasWithBasis(QQ) is a sub-category of GradedAlgebras(QQ), returning the "Category of graded commutative graded algebras with basisover Rational Field", and I think that's what John wanted (if I recall his previous post correctly). Best regards, Simon -- You received this message because you are subscribed to the Google Groups "sage-devel" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-devel+unsubscr...@googlegroups.com. To post to this group, send email to sage-devel@googlegroups.com. Visit this group at https://groups.google.com/group/sage-devel. For more options, visit https://groups.google.com/d/optout.
