ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 06 May 2016 17:59:45 -0500Exterior and tensor product of algebrashttp://ask.sagemath.org/question/33337/exterior-and-tensor-product-of-algebras/Hi,
I've been trying to construct something like $\Lambda^2 A \otimes A$ where $A$ is a free associative $\mathbb{Q}$-algebra on some generators, say, $x$ and $y$, without success. I think I understand the basics of the FreeAlgebra object in Sage, but I could not find more specific information about this kind of construction in the documentation or here in this forum. Ultimately, I would like to form and calculate with expressions like $x y \wedge xx \otimes xy$ where $x,y\in \mathbb{Q}\langle x,y\rangle$, the free associative unital algebra, and such that, for instance, $xy \wedge xx \otimes xy = - xx \wedge xy \otimes xy$. Does anyone know whether this is or is not possible to achieve in Sage at the moment? Any help will be greatly appreciated.
Cheers,
WaldeckWaldeckFri, 06 May 2016 17:59:45 -0500http://ask.sagemath.org/question/33337/convert polynomial rings from Sage to Singularhttp://ask.sagemath.org/question/32596/convert-polynomial-rings-from-sage-to-singular/Suppose I have a ring R in sage (I have in mind a polynomial ring modulo some ideal). Is there a way to convert it into a ring in Singular?
I want to use the tensor product function (which singular provides) on two rings (and then convert back to sage) but singular doesn't have (natural) constructors for the rings I'd like to tensor. admiraltsoFri, 19 Feb 2016 12:03:01 -0600http://ask.sagemath.org/question/32596/Tensor Product of Two Matrices coming from Algebra Representationshttp://ask.sagemath.org/question/8100/tensor-product-of-two-matrices-coming-from-algebra-representations/Is there a command in sage to compute the tensor product of two Matrices coming from Algebra representations? In groups, x(v tensor w) = xv tensor xw, and the sage command Matrix1.tensor_product(Matrix2) appears to give the matrix corresponding to this. But in an algebra x(v tensor w) = xv tensor w + v tensor xw. How can I compute the corresponding matrix here?ChrisBergTue, 03 May 2011 04:06:56 -0500http://ask.sagemath.org/question/8100/Tensor products in Sagehttp://ask.sagemath.org/question/7995/tensor-products-in-sage/Computing the tensor product of two matrices A, B is quite straightforward through A.tensor_product(B).
What about computing the tensor product of some field extensions L and K over $\mathbb{Q}$? Or the tensor products of some ring of integers $\mathcal{O}_K$ of a field extension K and $\mathbb{Z}/\mathbb{pZ}$ over $\mathbb{Z}$.
Other instances of tensor product computations in Sage is welcomed, not necessarily as constructive, but illustrative enough to aid in studying Tensor products. WeaamSun, 13 Mar 2011 04:58:43 -0500http://ask.sagemath.org/question/7995/What is the name of a tensor product?http://ask.sagemath.org/question/8750/what-is-the-name-of-a-tensor-product/I have a tensor like
tensor([a,b,c])
where a, b, c lie in some CombinatorialFreeModule. Where (in Sage syntax) does this tensor lie? (I need to know, because I am writing a function using module_morphism, and it requires me to explicitly specify its codomain.)
Writing
type(tensor([a,b,c]))
doesn't help (it just gives generic trash).darijgrinbergMon, 27 Feb 2012 11:33:16 -0600http://ask.sagemath.org/question/8750/