# ncMap -- Make a map to or from an NCRing

## Synopsis

• 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 => , default value false
• Outputs:

## 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