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
|