I'm trying to define some multilinear forms to study differential geometry. What I need is only symbolic. My intention is symplify computations involving multilinear forms.

For example, to create an symbolic inner product "g" I used the command "define" like in this post:

http://www.mapleprimes.com/questions/203480-Define-And-Use-Abstract-Linear-Operator

So I tipped:

define(g, orderless, multilinear);

My doubt is: how can I declare that g(x,y) is always scalar?

With it I would simplify things like g(g(z,w)*x,y) = g(z,w)*g(x,y)

In my case, specifically, I type:

v:=(X,Y,Z)->g(Y,Z)*X-g(X,Z)*Y;

r:=(X,Y,Z,W)->g(v(X,Y,Z),W)-g(Y,T)*g(v(X,T,Z),W)+g(X,T)*g(v(Y,T,Z),W);

expand(r(X,Y,Z,W));

and the result is:

g(W,g(Y,Z)*X)-g(W,g(X,Z)*Y)-g(T,Y)*g(W,g(T,Z)*X)+g(T,Y)*g(W,g(X,Z)*T)+g(T,X)*g(W,g(T,Z)*Y)-g(T,X)*g(W,g(Y,Z)*T)

But I would enjoy that it were:

g(Y,Z)*g(W,X)-g(X,Z)*g(W,Y)-g(T,Z)*g(T,Y)*g(W,X)+g(X,Z)*g(T,Y)*g(W,T)+g(T,Z)*g(T,X)*g(W,Y)-g(Y,Z)*g(T,X)*g(W,T)

Is there a way to declare that g(x,y) is always scalar?

Thanks.