2017-03-06 10:51:22 -0500 received badge ● Popular Question (source) 2015-06-24 16:35:28 -0500 received badge ● Scholar (source) 2015-06-24 16:16:15 -0500 commented answer Multiplying matrices with different parents? Thank you for looking into this for me! As a new user, I'm glad to know it wasn't something ridiculous on my part. Also, thanks for the suggestion to use the polynomial ring. That will get me through what I need to do. 2015-06-24 15:52:19 -0500 received badge ● Student (source) 2015-06-24 11:44:09 -0500 commented answer Sage is not returning all solutions to equations modulo n Thanks! This will fix my current problem, but I am still concerned for when I use larger matrices, and/or a different modulus. If anyone has ideas on a really efficient way to do this in general, I would love to hear them. 2015-06-24 11:39:06 -0500 asked a question 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 2015-06-24 11:05:16 -0500 asked a question Sage is not returning all solutions to equations modulo n I am trying to find all 2x2 matrices $S$ over $Z/9Z$ such that $S^3=I$, where I is the identity matrix. I am currently using the following procedure: S = matrix(SR, 2, [[a,b],[c,d]]); S3=S^3 l=solve_mod([S3[0,0]==1,S3[0,1]==0,S3[1,0]==0,S3[1,1]==1], 9); l The list of solutions (there are 207) I receive does not include S=[[1,3],[3,1]], for example, which does in fact satisfy $S^3=I$. I am new to Sage, is there something I am missing? How can I get a complete list of solutions?