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About: About this document ideal expressions (plural)

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


ring r=0,(x,y,z),dp;
def R=nc_algebra(-1,0); // an anticommutative algebra
setring R;
ideal m = maxideal(1);
==> 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);
i = M*M;
==> 598
i = M^2;
==> 690
==> x20
vector v = [x,y-z,x2,y-x,x2yz2-y];
ideal j = ideal(v);
==> j[1]=x
==> j[2]=y-z
==> j[3]=x2
==> j[4]=-x+y
==> j[5]=x2yz2-y