# Singular

#### D.6.7.1 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 ```

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 ```