ncMap -- Make a map to or from an NCRing

Usage:

f = ncMap(B,A,m)
Inputs:
- A, an instance of the type NCRing, or a Ring
- B, an instance of the type NCRing, or a Ring
- m, a list, the images of the generators of A.
Optional inputs:
- Derivation => a Boolean value, default value false
Outputs:
- f, an instance of the type NCRingMap,

Description

NCRingMaps are linear and multiplicative by definition, but need not be well-defined or homogeneous. The user has the option to define an NCRingMap to be a derivation. Such a map must have the same source and target.

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

o1 = A

o1 : NCQuotientRing

i2 : B = QQ{a,b,c}

o2 = B

o2 : NCPolynomialRing

i3 : f = ncMap(B,A,{a^3,b^2,a+b,a-b})

o3 = NCRingMap B <--- A

o3 : NCRingMap

i4 : f(w*x+2*y)

         3 2
o4 = 2b+a b +2a

o4 : B

i5 : g = ncMap(B,B,{a*b,b^2,c*a*c},Derivation=>true)

o5 = NCRingMap B <--- B

o5 : NCRingMap

i6 : g(a*b)==g(a)*b+a*g(b)

o6 = true

i7 : g(promote(1,B))

o7 = 0

o7 : B

i8 : g(c*a+2*b)

                2
o8 = caca+cab+2b

o8 : B

Ways to use ncMap:

ncMap(NCRing,NCRing,List)
ncMap(NCRing,Ring,List)
ncMap(Ring,NCRing,List)

For the programmer

The object ncMap is a method function with options.

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/NCAlgebra/NCAlgebraDoc.m2:2988:0.

ncMap -- Make a map to or from an NCRing

Description

See also

Ways to use ncMap:

For the programmer