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Results tagged with computer-algebra
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user 1306
Using computer-aid approach to solve algebraic problems. Questions with this tag should typically include at least one other tag indicating what sort of algebraic problem is involved, such as ac.commutative-algebra or rt.representation-theory or ag.algebraic-geometry.
1
vote
Degree 8 multilinear operations on Jordan algebras
I managed to run Albert on a very powerful computer at work, and the computation of the desired dimension converged: it seems equal to 19089. I would very much like to confirm that it is correct (I am …
- 16.9k
10
votes
2
answers
214
views
Degree 8 multilinear operations on Jordan algebras
I am interested in the dimension, or, even better, in the $S_8$-module structure of the space of degree 8 multilinear operations on Jordan algebras.
Recall that a Jordan algebra is a commutative but n …
- 16.9k
3
votes
0
answers
114
views
Checking the generic rank of a matrix
Suppose that $A,B\in M_{p,q}(\mathbb{Z})$ are two rectangular integer matrices of the same size. Suppose that one has a conjecture stating that the rank of the matrix $A+tB$ for Zariski generic values …
- 16.9k
3
votes
Grobner basis of a submodule of a free module over polynomial ring
What exactly you Googled? There are many standard references, e.g.
"Gröbner bases and primary decomposition of modules", by Elizabeth W.Rutman
(https://www.sciencedirect.com/science/article/pii/074771 …
- 16.9k
56
votes
Accepted
Minimal polynomial of cos(π/n)
The minimal polynomial of $\cos(2\pi/n)$ (by William Watkins and Joel Zeitlin, The American Mathematical Monthly
Vol. 100, No. 5 (May, 1993), pp. 471-474) has full clarity on this matter (just take th …
- 16.9k
10
votes
2
answers
520
views
Monomial orderings in noncommutative setting
An ordering of monomials in the free associative algebra $k\langle x_1,\ldots,x_n\rangle$ is called a monomial ordering (EDIT: it seems that an equally common term used in this context is "term orderi …
- 16.9k
4
votes
Open source mathematical software
For all sorts of Groebner bases-related computation (I believe you might need some at least for questions in algebraic geometry), I would recommend Bergman (http://servus.math.su.se/bergman/).
30
votes
Computer algebra errors
A friend of mine told me about his experience with Maple (version 5 or 6, I think) when dealing with matrices over $\mathbb{Q}(\sqrt{2},\sqrt{3})$. When he computed the rank and the determinant for on …