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# ring(NCIdeal) -- Returns the ring of an NCIdeal or NCGroebnerBasis

- Function: ring
- Usage:
    `A = ring I`
- Inputs:
  - I, an instance of the type NCIdeal,
- Outputs:
  - A, an instance of the type NCRing,

## Description

Returns the ring of an NCIdeal.

    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,r}

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

    o5 : NCIdeal

    i6 : ring I

    o6 = A

    o6 : NCPolynomialRing

## Ways to use this method:

- `ring(NCGroebnerBasis)`
- ring(NCIdeal) -- Returns the ring of an NCIdeal or NCGroebnerBasis

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NCAlgebra/NCAlgebraDoc.m2:2024:0.