I'm curious how I might get a k-basis for a quotient ring of the form R = k[x_1,...x_n] / I, where I is some ideal in the polynomial ring.
For example, given I = {x^3}, and R = Q[x]/I, I would want Sage to give me the vector space basis {1,x,x^2}.
Any help is appreciated!! :)
I.normal_basis()
You're welcome! If you want to know the algorithm behind it, I think it is done by using a Groebner basis $I = \langle g_1, \ldots, g_s \rangle$: take all the monomials which are not in $LM(I) = \langle LM(g_1), \ldots, LM(g_s) \rangle$ (at least this is a way to do it).
Asked: 2019-02-03 19:59:06 +0100
Seen: 1,054 times
Last updated: Feb 03 '19
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