sm1_wTensor0

sm1_wTensor0([f,g,v,w]|proc=p)

:: It computes the D-module theoretic 0-th tensor product of f and g.

return

List

p

Number

f, g, v, w

List

• It returns the D-module theoretic 0-th tensor product of f and g.
• v is a list of variables. w is a list of weights. The integer w[i] is the weight of the variable v[i].
• sm1_wTensor0 calls wRestriction0 of ox_sm1, which requires a generic weight vector w to compute the restriction. If w is not generic, the computation fails.
• Let F and G be solutions of f and g respectively. Intuitively speaking, the 0-th tensor product is a system of differential equations which annihilates the function FG.
• The answer is a submodule of a free module D^r in general even if the inputs f and g are left ideals of D.

[258]  sm1_wTensor0([[x*dx -1, y*dy -4],[dx+dy,dx-dy^2],[x,y],[1,2]]);
[[-y*x*dx-y*x*dy+4*x+y],[5*x*dx^2+5*x*dx+2*y*dy^2+(-2*y-6)*dy+3],
 [-25*x*dx+(-5*y*x-2*y^2)*dy^2+((5*y+15)*x+2*y^2+16*y)*dy-20*x-8*y-15],
 [y^2*dy^2+(-y^2-8*y)*dy+4*y+20]]

• sm1_reduction

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