# sums, products, and powers of ideals

Arithmetic for ideals uses the standard symbols. Below are examples of the basic arithmetic functions for ideal.
 i1 : R = ZZ/101[a..d]/(b*c-a*d,c^2-b*d,b^2-a*c);
 i2 : I = ideal (a*b-c,d^3); o2 : Ideal of R i3 : J = ideal (a^3,b*c-d); o3 : Ideal of R i4 : I+J 3 3 o4 = ideal (a*b - c, d , a , a*d - d) o4 : Ideal of R i5 : I*J 4 3 2 3 3 4 4 o5 = ideal (a b - a c, a b*d - a*b*d - a*c*d + c*d, a d , a*d - d ) o5 : Ideal of R i6 : I^2 3 2 3 3 6 o6 = ideal (a c - 2a d + b*d, a*b*d - c*d , d ) o6 : Ideal of R