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Macaulay2Doc :: homomorphism'

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

Synopsis

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

See also

Ways to use homomorphism' :

For the programmer

The object homomorphism' is a method function.