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<head><title>Singular Book 2.1.26 -- computation of 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_sp2.1.26.html" title="computation of Hom">Singular Book 2.1.26</a></div>
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<div><h1>Singular Book 2.1.26 -- computation of Hom</h1>
<div><table class="examples"><tr><td><pre>i1 : A = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : M = cokernel matrix(A, {{1,2,3},{4,5,6},{7,8,9}})
o2 = cokernel | 1 2 3 |
| 4 5 6 |
| 7 8 9 |
3
o2 : A-module, quotient of A</pre>
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<tr><td><pre>i3 : N = cokernel matrix{{x,y},{z,0}}
o3 = cokernel | x y |
| z 0 |
2
o3 : A-module, quotient of A</pre>
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<tr><td><pre>i4 : H = Hom(M,N)
o4 = subquotient (| 1 0 |, | y x 0 0 0 0 |)
| 0 1 | | 0 z 0 0 0 0 |
| -2 0 | | 0 0 y x 0 0 |
| 0 -2 | | 0 0 0 z 0 0 |
| 1 0 | | 0 0 0 0 y x |
| 0 1 | | 0 0 0 0 0 z |
6
o4 : A-module, subquotient of A</pre>
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H is a subquotient module. In Macaulay2, the most general form of a module is as a subquotient: a submodule of a cokernel module. For more about subquotient modules, see <a href="_modules.html" title="">modules</a>. <table class="examples"><tr><td><pre>i5 : f = homomorphism H_{0}
o5 = | 1 -2 1 |
| 0 0 0 |
o5 : Matrix</pre>
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<tr><td><pre>i6 : target f === N
o6 = true</pre>
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<tr><td><pre>i7 : source f === M
o7 = true</pre>
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<tr><td><pre>i8 : matrix f
o8 = | 1 -2 1 |
| 0 0 0 |
2 3
o8 : Matrix A <--- A</pre>
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Macaulay2 has a <tt>modulo</tt> command (it was initially introduced in the original Macaulay, in the late 1980's), but it is not needed very often. It is used internally in Macaulay2 to implement kernels of module homomorphisms.</div>
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