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D.6.9.3 gmscoeffs

Procedure from library gmssing.lib (see gmssing_lib).

Usage:
gmscoeffs(p,K); poly p, int K

Assume:
basering constructed by gmsring

Return:
 
list l;
  matrix l[1];  C[[s]]-basis representation of p mod s^(K+1)
  ideal l[2];  p==matrix(gmsbasis)*l[1]+l[2]

Note:
computation can be continued by setting p=l[2]

Example:
 
LIB "gmssing.lib";
ring R=0,(x,y),ds;
poly t=x5+x2y2+y5;
def G=gmsring(t,"s");
setring(G);
list l0=gmscoeffs(gmspoly,0);
print(l0[1]);
==> -1/2,
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0    
list l1=gmscoeffs(gmspoly,1);
print(l1[1]);
==> -1/2,
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 0,   
==> 1/2s 
list l=gmscoeffs(l0[2],1);
print(l[1]);
==> 0,  
==> 0,  
==> 0,  
==> 0,  
==> 0,  
==> 0,  
==> 0,  
==> 0,  
==> 0,  
==> 0,  
==> 1/2s