Singular

4.4.2 ideal expressions

An ideal expression is:

1. an identifier of type ideal
2. a function returning an ideal
3. a combination of ideal expressions by the arithmetic operations + or *
4. a power of an ideal expression (operator ^ or **)
   Note that the computation of the product i*i involves all products of generators of i while i^2 involves only the different ones, and is therefore faster.
5. a type cast to ideal

Example:

  ring r=0,(x,y,z),dp;
  ideal m = maxideal(1);
  m;
==> m[1]=x
==> m[2]=y
==> m[3]=z
  poly f = x2;
  poly g = y3;
  ideal i = x*y*z , f-g, g*(x-y) + f^4 ,0, 2x-z2y;
  ideal M = i + maxideal(10);
  timer =0;
  i = M*M;
  timer;
==> 0
  ncols(i);
==> 505
  timer =0;
  i = M^2;
  ncols(i);
==> 505
  timer;
==> 0
  i[ncols(i)];
==> x20
  vector v = [x,y-z,x2,y-x,x2yz2-y];
  ideal j = ideal(v);