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NCAlgebra :: gddKernel

gddKernel -- Computes a homogeneous generating set of the kernel of a ring map.

Synopsis

Usage:

kern = gddKernel(n,phi)
Inputs:
- n, an integer
- phi, an instance of the type NCRingMap
Outputs:
- kern, a list

Description

This function returns a generating set of the kernel of a ring map up to a specified degree.

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

o1 = A

o1 : NCPolynomialRing

i2 : B = skewPolynomialRing(QQ,(-1)_QQ, {a,b,c})
--Calling Bergman for NCGB calculation.
Complete!

o2 = B

o2 : NCQuotientRing

i3 : phi = ncMap(B,A,{a,b,c})

o3 = NCRingMap B <--- A

o3 : NCRingMap

i4 : gddKernel(4,phi)
Computing kernel in degree 1
Computing kernel in degree 2
Computing kernel in degree 3
Computing kernel in degree 4

o4 = {yx+xy, zx+xz, zy+yz}

o4 : List

Ways to use `gddKernel` :

"gddKernel(ZZ,NCRingMap)"

For the programmer

The object gddKernel is a method function.