D.5.4.1 gmsring
...............
Procedure from library gaussman.lib (see gaussman_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 gmsmaxdeg;  maximal weight of variables

Note:
gmsbasis is a C[[s]]-basis of H" and [t,s]=s^2

Example:
LIB "gaussman.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,
==> 2xy2+5x4,
==> 5x5-5y5,
==> 10y6+25x3y4
print(gmsmatrix);
==> 0,1,x, -2xy,  
==> 1,0,-y,2y2+5x3
print(gmsbasis);
==> y5,
==> y4,
==> y3,
==> y2,
==> xy,
==> y,
==> x4,
==> x3,
==> x2,
==> x,
==> 1
gmsmaxdeg;
==> 1

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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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