NCIdeal + NCIdeal -- Sum of NCIdeals

Synopsis

Operator: +
Usage:

K = I + J
Inputs:
- I, an instance of the type NCIdeal,
- J, an instance of the type NCIdeal,
Outputs:
- K, an instance of the type NCIdeal,

This command sums two NCIdeals.

i1 : A = QQ{x,y,z}

o1 = A

o1 : NCPolynomialRing

i2 : p = y*z + z*y - x^2

            2
o2 = zy+yz-x

o2 : A

i3 : q = x*z + z*x - y^2

         2
o3 = zx-y +xz

o3 : A

i4 : r = z^2 - x*y - y*x

      2
o4 = z -yx-xy

o4 : A

i5 : I = ncIdeal{p,q}

                             2      2
o5 = Two-sided ideal {zy+yz-x , zx-y +xz}

o5 : NCIdeal

i6 : J = ncIdeal r

                       2
o6 = Two-sided ideal {z -yx-xy}

o6 : NCIdeal

i7 : I + J

                             2      2      2
o7 = Two-sided ideal {zy+yz-x , zx-y +xz, z -yx-xy}

o7 : NCIdeal