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BUG (or misunderstanding): tensor simplification

Charles Gillingham
Posted 12 years ago

I'm using Mathematica 9, so tell me if this is fixed in 10.

Steps to reproduce:

Enter and Evaluate:

Assuming[Element[M , Matrices[{2, 2}]] && Element[Z , Matrices[{2, 2}] ], Simplify[M == M Z]]

False

This returns "False". However, this is not correct. Consider:

Assuming[Element[M , Matrices[{2, 2}]] && Element[Z , Matrices[{2, 2}] ], Simplify[M == M Z /. Z -> {{1, 1}, {1, 1}}]]

True

Obviously, {{1,1},{1,1}} is n element of the domain, which Mathematica knows:

Element[{{1,1},{1,1}}, Matrices[{2,2}]
POSTED BY: Charles Gillingham
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Yes, I think we agree.

Yes

I hope it was obvious that I was saying it should return "M == M Z", rather than "False"

Yes

There are solutions where M is not all zeros and Z is not all ones.

True - and that means, that the mentioned result is not almost always correct (as I said), because there is not a finite set of exceptions, but an infinite set of exceptions.
POSTED BY: Udo Krause
POSTED BY: Udo Krause

Yes, I think we agree. I hope it was obvious that I was saying it should return "M == M Z", rather than "False"

There are solutions where M is not all zeros and Z is not all ones. Consider:

M = {{0,2},{0,3}} and Z = {{4,1},{5,1}}

The fact that TensorDimensions[M Z] fails is probably a clue to where the problems lie.

POSTED BY: Charles Gillingham
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