Defines the sum of NCRingMaps. Though a linear combination of ring maps is not a ring map in general, this routine is useful in constructing ring maps programmatically. The sum is defined only on generators of the common source of f and g, while for higher degree monomials m, one no longer has f(m) + g(m) = h(m) (so it is only the sum on words of length 1).
i1 : A = QQ{x,y} o1 = A o1 : NCPolynomialRing |
i2 : f = ncMap(A,A,{x,y}) o2 = NCRingMap A <--- A o2 : NCRingMap |
i3 : g = ncMap(A,A,{y,x}) o3 = NCRingMap A <--- A o3 : NCRingMap |
i4 : h = 3*f + 4*g o4 = NCRingMap A <--- A o4 : NCRingMap |
i5 : matrix h o5 = | 4*y+3*x 3*y+4*x | o5 : NCMatrix |
i6 : k = h^3 o6 = NCRingMap A <--- A o6 : NCRingMap |
i7 : matrix k o7 = | 172*y+171*x 171*y+172*x | o7 : NCMatrix |