//SINGULAR Example 1.7.9


ring A  = 0,(x,y),dp;   //global ordering: degrevlex
ideal I = x10+x9y2,y8-x2y7;
ideal J = std(I);
J;

ring A1 = 0,(x,y),lp;   //global ordering: lex
ideal I = fetch(A,I);
ideal J = std(I);
J;

ring B  = 0,(x,y),ds;   //local ordering: local degrevlex
ideal I = fetch(A,I);
ideal J = std(I);
J;

ring B1 = 0,(x,y),ls;   //local ordering: negative lex
ideal I = fetch(A,I);
ideal J = std(I);
J;

intmat O[3][3]=1,1,1,0,-1,-1,0,0,-1;
ring  C = 0,(t,x,y),M(O);     //global ordering: matrix O
ideal I = homog(imap(A,I),t); //gives a standard basis for 
                              //local degrevlex
ideal J = std(I);             //cf. Exercise 1.7.5
      J = subst(J,t,1);
J;