7.2.1.2 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

Example:

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