#### 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

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