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weyl.m2
-- Tests of standard ideal/matrix operations but in the Weyl algebra, to check -- consistency -- no test yet assert(true) end restart needsPackage "Dmodules" W = makeWA(QQ[x,y]) W * Matrix := (f,M) -> error "cannot multiply matrices on left" W * Ideal := (f,M) -> error "cannot multiply ideal on left" prevMult = lookup(symbol*, W, W) W * W := (f,g) -> prevMult(g,f) x * dx describe W I = ideal(x*dx) f = dx f * I -- want to disallow this for Weyl algebras -- it is: if I = (g1, ..., gr), is f*I = (f*g1, ..., f*gr) -- but: this has no good meaning -- instead, want: W = QQ[a..d] a * ideal(b,c) I * f f * (gens I) matrix{{f}} * (gens I) -- this is what we want gens(I*f) to be. (gens I) * f f * (gens I) gens (f*I) (gens I) * matrix{{f}} -- these are OK matrix{{f}} * (gens I) (gens I) ** matrix{{f}} -- want to disallow tensor product in this case, as it doesn't really mean what -- we usually want it to mean. matrix{{f}} ** (gens I)