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 "$" to specify which version of the function you need.
(25) ->
Just wondering, is the tensor product, TA, only a vector-space or is it an
algebra too?
On Wednesday, May 10, 2023 at 1:57:24 PM UTC-5 Waldek Hebisch wrote:
> On Wed, May 10, 2023 at 11:27:25AM -0700, Sid Andal wrote:
> > The patch file ALGSC.diff was applied to the file naalg.spad (no
> ALGSC.spad
> > file in the installation src dir)
> > containing the AlgebraGivenByStructuralConstants entry and compiled.
> >
> > The Algs A2 and A3 with bases V2 and V3 are as before.
> >
> > The call to TensorProduct gives an invalid type error:
> >
> > (22) -> TA := TensorProduct(FN, V2, V3, A2, A3)
> >
> > V2 is not a valid type.
>
>
> Yes. The patch uses OrderedVariableList. So you need:
>
> o2 := OVAR(['E1, 'E2])
> o3 := OVAR(['F1, 'F2, 'F3])
>
> Then
>
> tP := TensorProduct(FN, o2, o3, A2, A3)
>
> works and you can do
>
> tensor((basis()$A2)(1), (basis()$A3)(1))$tP
>
>
> --
> Waldek Hebisch
>
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