homomorphism' -- get the element of Hom from a homomorphism

Synopsis

• Usage:
homomorphism' f
• Inputs:
• f, of the form M --> N
• Outputs:
• the map R^1 --> Hom(M,N), corresponding to the map f

Description

 i1 : R = QQ[x,y,z] o1 = R o1 : PolynomialRing i2 : f = vars R ++ vars R o2 = | x y z 0 0 0 | | 0 0 0 x y z | 2 6 o2 : Matrix R <--- R i3 : g = homomorphism' f -- ker (35) called with OptionTable: OptionTable{SubringLimit => infinity} -- ker (35) returned CacheFunction: -*a cache function*- -- ker (35) called with Matrix: 0 -- 12 -- ker (35) returned Module: R assert( ker(map(R^0,R^{{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}},0)) === (R^{{1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}, {1}})) o3 = {-1} | x | {-1} | 0 | {-1} | y | {-1} | 0 | {-1} | z | {-1} | 0 | {-1} | 0 | {-1} | x | {-1} | 0 | {-1} | y | {-1} | 0 | {-1} | z | 12 1 o3 : Matrix R <--- R i4 : target g === Hom(source f, target f) o4 = true

We can undo the process with homomorphism.

 i5 : f' = homomorphism g o5 = | x y z 0 0 0 | | 0 0 0 x y z | 2 6 o5 : Matrix R <--- R i6 : f === f' o6 = true