I was sent here from StackOverflow.
I have a vector space with given basis (it is also a Hopf algebra, but this is not part of the problem). How do I make it into a graded vector space? E. g., I know that in order to make it into an algebra, I have to define a function called
Once this is done, I would like to do linear algebra on the graded components. They are each finite-dimensional, with basis a part of the combinatorial basis of the big space, so there shouldn't be any problem. I have defined two maps and want to know, e. g., whether the image of one lies inside the image of the other. Is there an abstract way to do this in Sage or do I have to translate these maps into matrices?
Context (not important): I have (successfully, albeit stupidly) implemented the Malvenuto-Reutenauer Hopf algebra of permutations:
Now I want to check some of its properties. This checking cannot be automated on the whole space, but it is a finite problem on each of its graded components, so I would like to check it, say, on the fifth one.
Good luck -- I am personally interested in computations with differential graded algebras so I would love to see how you implement your classes.
Asked: Jan 26 '12
Seen: 257 times
Last updated: Jan 27 '12
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