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AssociativeAlgebras :: ncKernel

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

Synopsis

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:  Parallel F4 Algorithm not available over current coefficient ring.
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 :

For the programmer

The object ncKernel is a method function with options.