In your commutators.mac you start with
defining a bilinear property (which I have copied
into bilinear.mac).
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declare (bilinear, feature);
bilinearp (e) := featurep (e, bilinear);
declare (comm, bilinear);
matchdeclare (xx, bilinearp);
matchdeclare ([aa, bb, cc], all);
defrule (rbilineara1, xx (aa + bb, cc), map (lambda ([u], xx (u, cc)), bb));
defrule (rbilineara2, xx (cc, aa + bb), map (lambda ([u], xx (cc, u)), bb));
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and with these rules in place we get:
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(%i1) load(bilinear);
(%o1) "c:/work5/bilinear.mac"
(%i2) apply1(comm(a + b,c),rbilineara1);
(%o2) comm(b,c)+comm(a,c)
(%i3) apply1(comm(a ,b + c),rbilineara2);
(%o3) comm(a,c)+comm(a,b)
(%i4) map (lambda ([u], yy (u, c)), b);
Improper argument to map: b
-- an error. To debug this try: debugmode(true);
(%i5) map (lambda ([u], yy (u, c)),a + b);
(%o5) yy(b,c)+yy(a,c)
(%i6) declare (zz,bilinear)$
(%i7) map (lambda ([u], zz (u, c)), b);
Improper argument to map: b
-- an error. To debug this try: debugmode(true);
(%i8) map (lambda ([u], zz (u, c)), a + b);
(%o8) zz(b,c)+zz(a,c)
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I don't understand why rule rbilineara1 definition in terms
of the lambda function doesn't refer to aa as well as bb.
How is your definition able to get the job done?
Ted Woollett