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 instance of the type NCRingMap,
• Outputs:
  • kern, an instance of the type NCMatrix,

Description

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 : kernelComponent(2,phi)

o4 = | y*x+x*y z*x+x*z z*y+y*z |

o4 : NCMatrix