ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 24 May 2016 13:47:57 +0200Find the kernel of a matrix $A$ and make it a matrix.https://ask.sagemath.org/question/33533/find-the-kernel-of-a-matrix-a-and-make-it-a-matrix/ I am trying to write a function that computes the monic genrator of an ideal $I\in k[x_1,\dots,x_n]$, i.e., the generator of $I\cap k[x_i]$ for each $i$. For this I need to use linear algebra for the set
$$\{1, x_i, x_i^2,\dots\}$$
I write each one of them in terms of the basis for the quotient ring $k[x_1,\dots,x_n]/I$, and see if they are linearly dependent.
Since I add in one more power a time, when I find a linearly dependent set, it should have nullity $1$. So if I can get the one element in basis of the kernel, I am done. But the $A.kernel()$ command in Sage gives me this:
N=M.kernel();N
Vector space of degree 2 and dimension 1 over Rational Field
Basis matrix:
[0 1]
Is there a way to assign it as a vector using the kernel command? Or do I have to write my own function to implement it? Thank you for your help!KittyLTue, 24 May 2016 13:47:57 +0200https://ask.sagemath.org/question/33533/