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- 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]]
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