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<head><title>Singular Book 2.1.7 -- maps induced by Hom</title>
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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_basic_spcommutative_spalgebra.html" title="">basic commutative algebra</a> > <a href="___M2__Singular__Book.html" title="Macaulay2 examples for the Singular book">M2SingularBook</a> > <a href="___Singular_sp__Book_sp2.1.7.html" title="maps induced by Hom">Singular Book 2.1.7</a></div>
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<div><h1>Singular Book 2.1.7 -- maps induced by Hom</h1>
<div><table class="examples"><tr><td><pre>i1 : A = QQ[x,y,z]
o1 = A
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : M = matrix(A, {{1,2,3},{4,5,6},{7,8,9}})
o2 = | 1 2 3 |
| 4 5 6 |
| 7 8 9 |
3 3
o2 : Matrix A <--- A</pre>
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<tr><td><pre>i3 : Hom(M,A^2)
o3 = | 1 0 4 0 7 0 |
| 0 1 0 4 0 7 |
| 2 0 5 0 8 0 |
| 0 2 0 5 0 8 |
| 3 0 6 0 9 0 |
| 0 3 0 6 0 9 |
6 6
o3 : Matrix A <--- A</pre>
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<tr><td><pre>i4 : Hom(A^2,M)
o4 = | 1 2 3 0 0 0 |
| 4 5 6 0 0 0 |
| 7 8 9 0 0 0 |
| 0 0 0 1 2 3 |
| 0 0 0 4 5 6 |
| 0 0 0 7 8 9 |
6 6
o4 : Matrix A <--- A</pre>
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Notice that the basis that Macaulay2 uses for Hom(A^3,A^2) is different than the basis used by Singular.<p/>
The function contraHom of the Singular book in example 2.1.7 could be coded in the following way.<table class="examples"><tr><td><pre>i5 : contraHom = (M, s) -> (
(n,m) := (numgens target M, numgens source M);
R := mutableMatrix(ring M, s*n, s*m);
for b from 0 to m-1 do
for a from 0 to s-1 do
for c from 0 to n-1 do
R_(a*n+c,a*m+b) = M_(b,c);
matrix R
)
o5 = contraHom
o5 : FunctionClosure</pre>
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Let's try an example.<table class="examples"><tr><td><pre>i6 : contraHom(M,2)
o6 = | 1 4 7 0 0 0 |
| 2 5 8 0 0 0 |
| 3 6 9 0 0 0 |
| 0 0 0 1 4 7 |
| 0 0 0 2 5 8 |
| 0 0 0 3 6 9 |
6 6
o6 : Matrix A <--- A</pre>
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