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, 09 Aug 2016 16:51:57 +0200Does right_kernel_matrix support assumptions over the symbolic ring?https://ask.sagemath.org/question/34385/does-right_kernel_matrix-support-assumptions-over-the-symbolic-ring/I'm trying to a basis for the kernel of a symbolic matrix. However, exactly quite what the kernel is depends on the assumptions that have been made. It seems that although other matrix functions (e.g. calculating the inverse) respect assumptions the kernel function doesn't. Here is an example:
var('x,y')
M = Matrix(SR, [[x, 0],[0,y]])
print(~M) # Gives expected inverse [[1/x, 0], [0,1/y]]
print(M.right_kernel_matrix()) # Gives [] as expected (if x, y != 0 then M is invertible so has trivial kernel)
assume(x == 0)
# print(~M) # Throws an error (ZeroDivisionError)
print(M.right_kernel_matrix()) # Still gives [], whereas the kernel now has basis [(1, 0)]
Am I missing something here? Is it possible to use this function with assumptions?exodusTue, 09 Aug 2016 16:51:57 +0200https://ask.sagemath.org/question/34385/Multiplying matrices with different parents?https://ask.sagemath.org/question/27196/multiplying-matrices-with-different-parents/I want to conjugate a symbolic matrix, Sigma, by a matrix, garbage, over Z/9Z.
If I define both matrices as symbolic matrices, I get the right answer. If I define garbage over Z/9Z, I get confusing answers. Can anyone explain my results?
Sigma=matrix(SR,2,[[1+3*A,3*B],[3*C,1+3*D]])
garbage=matrix(SR,2,[[2,1],[2,6]]);garbageinverse=matrix(SR,2,[[6,8],[7,2]])
expand(garbage*Sigma*garbageinverse);(Sigma*garbageinverse)[0,0]*garbage[1,0]+(Sigma*garbageinverse)[1,0]*garbage[1,1]
R=Integers(9)
garbage=matrix(R,2,[[2,1],[2,6]]);garbageinverse=matrix(R,2,[[6,8],[7,2]])
expand(garbage*Sigma*garbageinverse);(Sigma*garbageinverse)[0,0]*garbage[1,0]+(Sigma*garbageinverse)[1,0]*garbage[1,1]
[ 36*A + 42*B + 18*C + 21*D + 19 48*A + 12*B + 24*C + 6*D + 18]
[36*A + 42*B + 108*C + 126*D + 54 48*A + 12*B + 144*C + 36*D + 28]
36*A + 42*B + 108*C + 126*D + 54
[ 6*B + 3*D + 1 3*A + 3*B + 6*C + 6*D]
[ 0*A + 0*D 3*A + 0*D + 1]
6*B + 0*D
AcantiWed, 24 Jun 2015 18:39:06 +0200https://ask.sagemath.org/question/27196/