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NCAlgebra :: kernelComponent

kernelComponent -- Computes a basis of the kernel of a ring map in a specified degree.

Synopsis

Usage:
kern = kernelComponent(n,phi)
Inputs:
- n, an integer
- phi, an object of class NCRingMap
Outputs:
- kern, an object of class NCMatrix

Description

This function returns a basis of the kernel of a ring map in 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.
--running: bergman -i /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12273-0/0.init -on-error exit --silent > /var/folders/46/9b86vqxj4hjcngvy7kd7sb140000gn/T/M2-12273-0/3.ter ... Complete!

o2 = B

o2 : NCQuotientRing

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

o3 = NCRingMap B <--- A

o3 : NCRingMap

i4 : kernelComponent(2,phi)

o4 = | yx+xy  zx+xz  zy+yz |

o4 : NCMatrix

Ways to use `kernelComponent` :

kernelComponent(ZZ,NCRingMap)