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D.6.13.1 gmsring
Procedure from library gmssing.lib (see gmssing_lib).
- Usage:
- gmsring(t,s); poly t, string s
- Assume:
- characteristic 0; local degree ordering;
isolated critical point 0 of t
- Return:
| | ring G; Gauss-Manin system of t with variable s
poly gmspoly=t;
ideal gmsjacob; Jacobian ideal of t
ideal gmsstd; standard basis of Jacobian ideal
matrix gmsmatrix; matrix(gmsjacob)*gmsmatrix==matrix(gmsstd)
ideal gmsbasis; monomial vector space basis of Jacobian algebra
int Gmssing::gmsmaxdeg; maximal weight of variables
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- Note:
- gmsbasis is a C[[s]]-basis of H" and [t,s]=s^2
Example:
| | LIB "gmssing.lib";
ring @R=0,(x,y),ds;
poly t=x5+x2y2+y5;
def G=gmsring(t,"s");
setring(G);
gmspoly;
==> x2y2+x5+y5
print(gmsjacob);
==> 2xy2+5x4,
==> 2x2y+5y4
print(gmsstd);
==> 2x2y+5y4,
==> 5x5-5y5,
==> 2xy2+5x4,
==> 10y6+25x3y4
print(gmsmatrix);
==> 0,x, 1,-2xy,
==> 1,-y,0,2y2+5x3
print(gmsbasis);
==> y5,
==> y4,
==> y3,
==> y2,
==> xy,
==> y,
==> x4,
==> x3,
==> x2,
==> x,
==> 1
Gmssing::gmsmaxdeg;
==> 1
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