How to overload the operator "*" as KroneckerProduct

Question

Can I use the expression below

a * b * c * d

for short to instead

KroneckerProduct[a,b,c,d]

automatically when a,b,c,d are matrix.

The number of elements (a,b,c,d) is arbitrary, such as a*b, a*b*c and a*b*c*d*e*f all can work well.

It seems overriding the operator * in Mathematica is not a good method. And my special applicaon that importing expressions from external file in string format has some others ways.

Why does it have to be *? Why not use a different symbol instead? Overloading Times[] is usually not the way to go. — J. M.'s missing motivation, May 29 '16 at 16:02
@J.M. Using "*" will make the expression look like a primitive math expression naturally and a loog expression can be easily understood. — cmc, May 29 '16 at 16:07
⊗ would be the more traditional symbol for the Kronecker product, then. — J. M.'s missing motivation, May 29 '16 at 16:10
Well, then... Unprotect[NonCommutativeMultiply]; NonCommutativeMultiply = KroneckerProduct; Protect[NonCommutativeMultiply]; Don't try this at home, kids! — J. M.'s missing motivation, May 29 '16 at 16:12
@J.M. To avoid to use esc ... esc . Some special symbols will not be copied right. — cmc, May 29 '16 at 16:29
How about telling us why you're unable or unwilling to use the traditional method of entering special characters? — J. M.'s missing motivation, May 29 '16 at 16:31
@J.M. I want to generate some math expression in a .txt file and then load them into Mathematica for calculation. So I would like to use a way to wirte the expressions in plain string and as possible as native math expression while it can be directly understood by Mathematica. — cmc, May 29 '16 at 16:37
Please take a look at this. This glyph is available for uses such as you propose. — m_goldberg, May 29 '16 at 20:03
@cmc please add to your question information from comment, that you want to import to Mathematica expressions from a text file, that has some specific format. This is very different problem than overriding built-in function for expressions that are already in Mathematica. — jkuczm, May 30 '16 at 11:53

jkuczm · Answer 1 · 2016-05-30T12:29:59.323

It was clarified in comments that expressions are supposed to be read into Mathematica from a text file. To achieve what OP wants one can read the file as list of held expressions, perform appropriate replacements, then release hold.

If we have a test.txt file with following contents:

a * b * c * d
a^dag

We can read it in following way:

ReadList["test.txt", HoldComplete@Expression]
% /. {Times -> KroneckerProduct, x_^dag :> ConjugateTranspose[x]} // ReleaseHold
(* {HoldComplete[a b c d], HoldComplete[a^dag]} *)
(* {KroneckerProduct[a, b, c, d], ConjugateTranspose[a]} *)

If we have more control over format of this text file and can accept non-ASCII characters, then we could use operators without built‐in meaning, as already suggested in comments. With unicode.txt file:

a ⊗ b ⊗ c ⊗ d
a^†

we could do this:

ReadList["unicode.txt", HoldComplete@Expression]
% /. {
    CircleTimes -> KroneckerProduct,
    x_^\[Dagger] :> ConjugateTranspose[x]
} // ReleaseHold
(* {a ⊗ b ⊗ c ⊗ d, a^†} *)
(* {KroneckerProduct[a, b, c, d], ConjugateTranspose[a]} *)

That doc page link is so useful. Thank you jkuczm! – matheorem Sep 25 '16 at 01:34 — matheorem, Sep 25 '16 at 01:34

How to overload the operator "*" as KroneckerProduct

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