Hi, I am trying to implement the infinite polynomial ring as a free
commutative algebra.
I am unsure of exactly how to do this. So far I have:
-----------------------------------------------------------------------------------
X.<x>=InfinitePolynomialRIng(QQ)
----------------------------------------------------------------------------------
class Practice3(CombinatorialFreeModule):
def __init__(self, R, X, **keywords):
self._group= X
CombinatorialFreeModule.__init__(self, R, self._group,
category=AlgebrasWithBasis(QQ))
return
-----------------------------------------------------------------------------------
I define:
def product_on_basis(self,left,right):
return self.monomial(left*right)
This is exactly how the SymmetricGroupAlgebra(QQ,n) is built from
permutations of size n.
My problem is that my algebra uses all of X as a basis. I have poked
and prodded the problem in quite a few ways but I have absolutely no
idea how to make a basis for the infintepolynomials.
My question is there any way to easily implement this algebra?
- I can make an algebra indexed by an infinite set so is there any
way to make the elements of the algebra inherit the commutative
multiplication of the polynomial ring?
-Or conversely can I coerce the polynomialring into a free
commutative algebra (since it is one?)
if not than I suggest that someone should make a class that takes an
object with a basis and builds a basis object. If I can use an
infinitepolynomial ring as a basis for my algebra then why couldn't an
object X.basis() be made for my algebra?
thanks
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