On Tue, May 16, 2023 at 07:41:15AM -0700, Sid Andal wrote:
> Obtained the tensor product, TA, of A2 and A3 as before with the following
> tensor basis:
>
> B11 := tensor(E1, F1)$TA
>
>
> (18) E1 # F1
> B12 := tensor(E1, F2)$TA
>
>
> (19) E1 # F2
> B13 := tensor(E1, F3)$TA
>
>
> (20) E1 # F3
> B21 := tensor(E2, F1)$TA
>
>
> (21) E2 # F1
> B22 := tensor(E2, F2)$TA
>
>
> (22) E2 # F2
> B23 := tensor(E2, F3)$TA
>
>
> (23) E2 # F3
> (24) ->
>
>
> The vector V, defined below, fails to form the product with itself:
>
>
> (24) -> V := 2 * B11 + 3 * B23
>
> (24) 2 E1 # F1 + 3 E2 # F3
> (25) ->
>
>
> (25) -> V * V
> There are 31 exposed and 40 unexposed library operations named *
> having 2 argument(s) but none was determined to be applicable.
> Use HyperDoc Browse, or issue
> )display op *
> to learn more about the available operations. Perhaps
> package-calling the operation or using coercions on the arguments
> will allow you to apply the operation.
>
> Cannot find a definition or applicable library operation named *
> with argument type(s)
> TensorProduct(PrimeField(11),OrderedVariableList([E1,E2]),OrderedVariableList([F1,F2,F3]),AlgebraGivenByStructuralConstants(PrimeField(11),2,[E1,E2],[[[10,7],[3,8]],[[9,2],[5,1]]]),AlgebraGivenByStructuralConstants(PrimeField(11),3,[F1,F2,F3],[[[5,3,10],[9,4,7],[2,10,1]],[[4,2,5],[6,1,7],[10,5,8]],[[7,3,9],[8,1,5],[4,2,7]]]))
> TensorProduct(PrimeField(11),OrderedVariableList([E1,E2]),OrderedVariableList([F1,F2,F3]),AlgebraGivenByStructuralConstants(PrimeField(11),2,[E1,E2],[[[10,7],[3,8]],[[9,2],[5,1]]]),AlgebraGivenByStructuralConstants(PrimeField(11),3,[F1,F2,F3],[[[5,3,10],[9,4,7],[2,10,1]],[[4,2,5],[6,1,7],[10,5,8]],[[7,3,9],[8,1,5],[4,2,7]]]))
>
> Perhaps you should use "@" to indicate the required return type,
> or "$" to specify which version of the function you need.
>
> (25) ->
>
>
> Just wondering, is the tensor product, TA, only a vector-space
module
or is it an
> algebra too?
No, ATM one needs to define ring/algebra structure separately.
--
Waldek Hebisch
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