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7.7.5.0. annRat
Procedure from library dmodapp.lib (see dmodapp_lib).
- Usage:
- annRat(g,f); f, g polynomials
- Return:
- ring (a Weyl algebra) containing an ideal 'LD'
- Purpose:
- compute the annihilator of the rational function g/f in the
corresponding Weyl algebra
- Assume:
- basering is commutative and over a field of characteristic 0
- Note:
- Activate the output ring with the
setring command.
In the output ring, the ideal 'LD' (in Groebner basis) is the
annihilator of g/f.
The algorithm uses the computation of Ann(f^{-1}) via D-modules,
see (SST).
- Display:
- If printlevel =1, progress debug messages will be printed,
if printlevel>=2, all the debug messages will be printed.
Example:
| | LIB "dmodapp.lib";
ring r = 0,(x,y),dp;
poly g = 2*x*y; poly f = x^2 - y^3;
def B = annRat(g,f);
setring B;
LD;
==> LD[1]=3*y^2*Dx^2*Dy+2*x*Dx*Dy^2+9*y*Dx^2+4*Dy^2
==> LD[2]=3*y^3*Dx^2-10*x*y*Dx*Dy-8*y^2*Dy^2+10*x*Dx
==> LD[3]=y^3*Dy^2-x^2*Dy^2-6*x*y*Dx+2*y^2*Dy+4*y
==> LD[4]=3*x*Dx+2*y*Dy+1
==> LD[5]=y^4*Dy-x^2*y*Dy+2*y^3+x^2
// Now, compare with the output of Macaulay2:
ideal tst = 3*x*Dx + 2*y*Dy + 1, y^3*Dy^2 - x^2*Dy^2 + 6*y^2*Dy + 6*y,
9*y^2*Dx^2*Dy-4*y*Dy^3+27*y*Dx^2+2*Dy^2, 9*y^3*Dx^2-4*y^2*Dy^2+10*y*Dy -10;
option(redSB); option(redTail);
LD = groebner(LD);
tst = groebner(tst);
print(matrix(NF(LD,tst))); print(matrix(NF(tst,LD)));
==> 0,0,0,0,0
==> 0,0,0,0,0
// So, these two answers are the same
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See also:
annPoly.
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