Singular Manual: satstd

  | #### D.17.1.1 satstd `Syntax:` `satstd(` ideal I `)` `satstd(` ideal I, ideal J `)` `Type:` ideal `Assume:` J is generated by variables `Purpose:` Starts a standard basis computation in which elements are freely divided by the generators of J. Hence returns a standard basis of an ideal between I and the saturation . In particular, if I is saturated with respect to J, returns a standard basis of I. If J is unspecified, it is assumed to be the ideal generated by all variables in the base ring. `Example:`
      LIB "customstd.so";
      ring r = 0,(x,y,z),dp;
      ideal I = x2+x,y2+y,z2;
      satstd(I,ideal(x));
      ==> _[1]=x+1
      ==> _[2]=z2
      ==> _[3]=y2+y
      satstd(I,ideal(x,y));
      ==> _[1]=y+1
      ==> _[2]=x+1
      ==> _[3]=z2
      satstd(I,ideal(z));
      ==> _[1]=1
      satstd(I);
      ==> _[1]=1

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