ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 02 Jul 2020 09:25:26 +0200Is there any graded Hopf algebra functionality?https://ask.sagemath.org/question/52298/is-there-any-graded-hopf-algebra-functionality/In the SAGE Reference Manual, there's a brief section on graded Hopf algebras: https://doc.sagemath.org/html/en/reference/categories/sage/categories/graded_hopf_algebras.html
Can one actually define graded Hopf algebras and do computations in them? If not, what is this doing there?davidac897Thu, 02 Jul 2020 09:25:26 +0200https://ask.sagemath.org/question/52298/How to get the graded part of a graded ring?https://ask.sagemath.org/question/47623/how-to-get-the-graded-part-of-a-graded-ring/I have a graded quotient of a graded polynomial ring, say something like
P = PolynomialRing(QQ, , 'x,y,z', order=TermOrder('wdegrevlex',(1,2,3)))
I = P.ideal(x*y^2 + x^5, z*y + x^3*y)
Q = P.quotient(I)
I would like to get the vector space over QQ consisting on vectors of degree, say 9, in Q.
heluaniTue, 27 Aug 2019 15:34:06 +0200https://ask.sagemath.org/question/47623/How to get graded component of graded ringhttps://ask.sagemath.org/question/47622/how-to-get-graded-component-of-graded-ring/I have a graded quotient of a graded polynomial ring, say something like
P = PolynomialRing(QQ, , 'x,y,z', order=TermOrder('wdegrevlex',(1,2,3)))
I = P.ideal(x*y^2 + x^5, z*y + x^3*y)
Q = P.quotient(I)
I would like to get the vector space over QQ consisting on vectors of degree, say 9, in Q.
heluaniTue, 27 Aug 2019 15:32:45 +0200https://ask.sagemath.org/question/47622/What does cohomology_generators actually do?https://ask.sagemath.org/question/46609/what-does-cohomology_generators-actually-do/ I don't understand the output of the function "cohomology_generators" of commutative differential graded algebras. Look at this simple exmaple:
A.<x,y,z,t> = GradedCommutativeAlgebra(QQ, degrees = (2,2,1,2))
B = A.cdg_algebra({z:x-y})
B.cohomology_generators(5)
{2: [t, y, x]}
It's apparently telling me that t, x and y are all generators of the cohomology algebra in degree 2. But in cohomology, x = y, since dz = x - y!wutututTue, 21 May 2019 16:46:44 +0200https://ask.sagemath.org/question/46609/How do I define a homomorphism of a graded commutative algebra?https://ask.sagemath.org/question/42202/how-do-i-define-a-homomorphism-of-a-graded-commutative-algebra/Why does the following throw a `TypeError: images do not define a valid homomorphism`?
E = GradedCommutativeAlgebra(QQ,'x,y',degrees=(1,1))
E.inject_variables()
f = E.hom([x,y])
I expected it to define $f$ to be the identity homomorphism of $E$. What is the right way to define a homomorphism of $E$? I'm more interested in the one that switches $x$ and $y$ than the identity homomorphism, but this seemed a more obvious version of the question.ronnoSat, 28 Apr 2018 19:14:46 +0200https://ask.sagemath.org/question/42202/