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# Hom(Module,Matrix) -- induced map on Hom

## Synopsis

• Usage:
Hom(f,g)
• Inputs:
• f, ,
• g, ,
• DegreeLimit => ...
• MinimalGenerators => ...
• Strategy => ...
• Outputs:
• , the map on Hom induced by the maps $f$ and $g$

## Synopsis

• Usage:
Hom(f,M)
Hom(M,f)
• Inputs:
• f, ,
• M, ,
• DegreeLimit => ...
• MinimalGenerators => ...
• Strategy => ...
• Outputs:
• , the map on Hom induced by the map $f$
 i1 : R = QQ[x] o1 = R o1 : PolynomialRing i2 : f = vars R o2 = | x | 1 1 o2 : Matrix R <-- R i3 : M = image f o3 = image | x | 1 o3 : R-module, submodule of R i4 : g = Hom(f,M) o4 = | x | o4 : Matrix i5 : target g o5 = image {-1} | x | 1 o5 : R-module, submodule of R i6 : source g o6 = image | x | 1 o6 : R-module, submodule of R
 i7 : R = QQ[x] o7 = R o7 : PolynomialRing i8 : f = vars R o8 = | x | 1 1 o8 : Matrix R <-- R i9 : M = image f o9 = image | x | 1 o9 : R-module, submodule of R i10 : g = Hom(M,f) o10 = {-1} | x | 1 1 o10 : Matrix R <-- R i11 : target g 1 o11 = R o11 : R-module, free, degrees {-1} i12 : source g 1 o12 = R o12 : R-module, free