Consider 3 non-commutative elements $A,B,C$ and we have the relation $CB=\alpha BC$.
I want to compute things like : $(A\otimes BC ) ( B \otimes B) = AB \otimes \alpha B^2C$
Is there any package doing this ?
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4$\begingroup$ Check the NCAlgebra package (I am not very familiar with it so I can't give an answer, but it's the biggest/oldest package dealing with such problems). $\endgroup$– SzabolcsCommented Mar 21, 2019 at 8:25
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$\begingroup$ try www.github.com/NCAlgebra/NC $\endgroup$– Slepecky MamutCommented Mar 21, 2019 at 8:39
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$\begingroup$ This package deals with non commutative algebra but it doesn't seem to treat tensor products $\endgroup$– Nico045Commented Mar 21, 2019 at 10:16
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1$\begingroup$ You don't need a package. Just give Mathematica the rules for working with non-commutative multiplication and tensor product. $\endgroup$– SomosCommented Mar 21, 2019 at 14:46
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$\begingroup$ See also mathematica.stackexchange.com/questions/126671/… $\endgroup$– Mauricio de OliveiraCommented Dec 5, 2021 at 20:50
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1 Answer
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Using Dot for your noncommutative multiplication, we can encode your relation with:
B /: C . B := α B . C
Using KroneckerProduct for your "⊗" operation, the output you want to get can then be obtained with:
KroneckerProduct[A, B.C].KroneckerProduct[B, B] //TensorExpand
α KroneckerProduct[A.B, B.B.C]
answered Mar 21, 2019 at 20:44
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$\begingroup$ What does this symbol "/:" do? (not easy to google such a thing) $\endgroup$ Commented Aug 15, 2021 at 15:08
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$\begingroup$ @StevenSagona Look up "/:" in the help. It stands for either TagSet or TagSetDelayed. $\endgroup$ Commented Aug 17, 2021 at 1:50