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ScalarProduct

scalar product
Syntax

ScalarProduct(L, M):OBJECT

where each of L and M is of type VECTOR or LIST


Description
This function returns the sum of the product of the components of L and M; precisely:

ScalarProduct(L,M) = Sum([L[I]*M[I]|I In 1..Min(Len(L),Len(M))])).

Thus, the function works even if the lengths of L and M are different. The function works whenever the product of the components of L and M are defined (see Algebraic Operators).

Example
ScalarProduct([1,2,3],[5,0,-1]);
2
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ScalarProduct([1,2,3],[5,0]);
5
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Use R ::= Q[x,y];
ScalarProduct([Ideal(x,y),Ideal(x^2-xy)],[x^2,y]);
Ideal(x^3, x^2y, x^2y - xy^2)
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See Also