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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+3A,3B],[3C,1+3D]]) garbage=matrix(SR,2,[[2,1],[2,6]]);garbageinverse=matrix(SR,2,[[6,8],[7,2]]) expand(garbageSigmagarbageinverse);(Sigmagarbageinverse)[0,0]garbage[1,0]+(Sigmagarbageinverse)[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(garbageSigmagarbageinverse);(Sigmagarbageinverse)[0,0]garbage[1,0]+(Sigmagarbageinverse)[1,0]garbage[1,1]

[ 36A + 42B + 18C + 21D + 19 48A + 12B + 24C + 6D + 18] [36A + 42B + 108C + 126D + 54 48A + 12B + 144C + 36D + 28] 36A + 42B + 108C + 126D + 54 [ 6B + 3D + 1 3A + 3B + 6C + 6D] [ 0A + 0D 3A + 0D + 1] 6B + 0D

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(garbageSigmagarbageinverse);(Sigmagarbageinverse)[0,0]garbage[1,0]+(Sigmagarbageinverse)[1,0]garbage[1,1]
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(garbageSigmagarbageinverse);(Sigmagarbageinverse)[0,0]garbage[1,0]+(Sigmagarbageinverse)[1,0]garbage[1,1]
expand(garbage*Sigma*garbageinverse);(Sigma*garbageinverse)[0,0]*garbage[1,0]+(Sigma*garbageinverse)[1,0]*garbage[1,1]
  
[  36A 36*A + 42B 42*B + 18C 18*C + 21D 21*D + 19    48A 48*A + 12B 12*B + 24C 24*C + 6D 6*D + 18]
[36A [36*A + 42B 42*B + 108C 108*C + 126D 126*D + 54  48A 48*A + 12B 12*B + 144C 144*C + 36D 36*D + 28]
36A 36*A + 42B 42*B + 108C 108*C + 126D 126*D + 54
[        6B 6*B + 3D 3*D + 1 3A 3*A + 3B 3*B + 6C 6*C + 6D]
6*D]
[            0A 0*A + 0D 0*D  3A 3*A + 0D 0*D + 1]
6B 6*B + 0D0*D

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

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

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