sums, products, and powers of ideals

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);

For more information about quotient rings see quotient rings.

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

For more information see Ideal + Ideal, Ideal * Ideal, and Ideal ^ ZZ.