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2017-11-14 19:50:18 +0100 | commented question | Exterior algebra error Thanks for the response FredericC. The documentation says that ExteriorAlgebra can take as input R a free module over a base ring. Can I get sage to treat $V3$ as a free module (vector space)? It knows that $V3$ lies in the category of vector spaces with basis over $\mathbb{Q}$. If not, can you think of any other way to create an exterior algebra with bi-indexed basis, such that $w_{i,j} = w_{j,i}$? |
2017-11-14 05:42:23 +0100 | asked a question | Exterior algebra error Hi, I'm new to Sage, and I've been having a lot of trouble constructing a particular algebra. I want to construct the exterior algebra (over $\mathbb{Q}$) on generators $w_{i,j} = w_{j,i}$ where $1 \le i < j \le n$ for some $n$ (for concreteness, say $n = 6$). I want this particular generating set so that I can define an $S_n$ action, but that's the next challenge. I've been attempting the following rough outline:
Several possible data structures for $V$ (FiniteRankFreeModule, VectorSpace, FreeModule) seem to fail at step 2. Are tensor products implemented for these? The most promising structure, CombinatorialFreeModule, fails at step 4 for an unknown reason. I get an error "base must be a ring or a subcategory of Rings()", even though the base is $\mathbb{Q}$. Here's the specific code I've tried. The last line gives an error, "base must be a ring or a subcategory of Rings()". The command Any help would be appreciated, either in fixing this error or approaching the construction in a different way. |