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[MUG] abstract algebra impossible in Maple?
| [MUG] abstract algebra impossible in Maple? |
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Author: Charles James Leonardo Quarra Cappiello
Posted: Fri, 20 Dec 2002 10:39:57 -0400
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>> From: "Charles James Leonardo Quarra Cappiello" "charsquarra"
Hi,
The dot product on Maple ( '.' operator ) has no effect upon undefined
objects, even if the effect of such operation may depend only on the
conmutative properties.
a desired capability would be the following:
>(A + t*B).(A + t*B);
(A + tB)(A + tB)
>expand(%);
2 2 2
A + 2 A t B + t B
>collect(%,t) assuming conmute(t,[A,B]); (t conmutes with A and B)
2 2 2
A + t(BA + AB) + t (B )
currently this doesnt seem to be possible
Other thing that 'should' be easily computable but seem to not be
implemented yet is bra-ket formalism
ie:
> <psi|:=a*<e1| + b*<e2| + c*<e3|: //(a basis)
> expand( <psi|rho> );
a*<e1|rho> + b*<e2|rho> + c*<e3|rho>
> Projector:= |psi><psi|:
> Projector.|psi>;
_ _ _ _ _ _
( a*|e1> + b*|e2> + c*|e3> )*(aa<e1|e1> + ab<e1|e2> + ac<e1|e3> +
_ _ _ _ _ _
ba<e2|e1> + bb<e2|e2> + bc<e2|e3> + ca<e3|e1> + cb<e3|e2> + cc<e3|e3>)
>% assuming(real,a,b,c), additionally( orthonormal, |e1> , |e2> , |e3> );
2 2 2
( a*|e1> + b*|e2> + c*|e3> )*(a + b + c )
But again, this doesnt seem to be possible, and im not aware what language
resources are available to Maple to implement it. Any hints about this?
Greetings,
Charles Quarra
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