Macaulay2 » Documentation
Packages » Macaulay2Doc » ideals » sums, products, and powers of ideals
next | previous | forward | backward | up | index | toc

# 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.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/Macaulay2Doc/ov_ideals.m2:192:0.