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# ncKernel -- Compute the graph ideal of a ring map between noncommutative rings.

- Usage:
    `I = ncKernel f`
- Inputs:
  - f, a ring map,
- Optional inputs:
  - DegreeLimit => ..., default value 10
  - Strategy => ..., default value "F4"
- Outputs:
  - I, an ideal,

## Description

This function computes (a Groebner basis of) the kernel of a ring map between noncommutative rings.

    i1 : A = QQ<|a,b,c|>

    o1 = A

    o1 : FreeAlgebra

    i2 : B = QQ<|x,y|>

    o2 = B

    o2 : FreeAlgebra

    i3 : f = map(B,A,{x*y*x,y*x*y,x*y})

    o3 = map (B, A, {x*y*x, y*x*y, x*y})

    o3 : RingMap B <-- A

    i4 : K = ncKernel f
    Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
    Converting to Naive algorithm.

    o4 = ideal 0

    o4 : Ideal of A

The generators returned by this function are in fact a Groebner basis of the kernel, so it may not be a minimal generating set.

The DegreeLimit and Strategy options are forwarded on to the call to the Groebner basis routine NCGB.

## Ways to use ncKernel:

- `ncKernel(RingMap)`

## For the programmer

The object ncKernel is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/AssociativeAlgebras/doc.m2:1365:0.