ambient(NCRingMap) -- Extends an NCRingMap to the ambient ring of the source.

Synopsis

Function: ambient
Usage:

g = ambient f
Inputs:
- f, an instance of the type NCRingMap,
Outputs:
- g, an instance of the type NCRingMap,

Description

If f:R->S is a ring map and R=A/I is a quotient ring, this method returns the NCRingMap g:A->S obtained by composing f with the natural map. This method is called by isWellDefined(NCRingMap) and can be used to determine what ideal to mod out of the target so the map becomes well-defined.

i1 : A = skewPolynomialRing(QQ,(-1)_QQ,{w,x,y,z})
--Calling Bergman for NCGB calculation.
Complete!

o1 = A

o1 : NCQuotientRing

i2 : B = QQ{w,x,y,z}/ncIdeal{w*x+x*w,w*y+y*w,x*y+y*x}
--Calling Bergman for NCGB calculation.
Complete!

o2 = B

o2 : NCQuotientRing

i3 : f = ncMap(B,A,gens B)

o3 = NCRingMap B <--- A

o3 : NCRingMap

i4 : isWellDefined f

o4 = false

i5 : g = ambient f

o5 = NCRingMap B <--- QQ{w, x, y, z}

o5 : NCRingMap

i6 : (gens ideal A)/g

o6 = {0, 0, 0, zw+wz, zx+xz, zy+yz}

o6 : List

Ways to use this method: