Singular

You don't need a computer to see that your book is wrong.
Multiply f1 with x and you see that x is in G.

I have a problem with the exercise.

[code]ring A = 0 , (x,y,z), dp; // a global ordering
poly f = x2yz + xy2z + y2z + z3 + xy;
poly f1 = xy + y2 -1
poly f2 = xy;
ideal G = f1, f2;
ideal S = std(G) //a standard basis of <G>
S;[/code]

In my book I have a result:
//-> S[1]=xy
//-> S[2]=y2-1

but in Singular the returns:
//-> S[1]=x
//-> S[2]=y2-1

Why?

Cheers







and the programme returns:
//-> S[1]=x
//-> S[2]=y2-1