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<head><title>homomorphisms (maps) between modules -- including elements of modules</title>
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<div><h1>homomorphisms (maps) between modules -- including elements of modules</h1>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y];</pre>
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<tr><td><pre>i2 : M = image vars R
o2 = image | x y |
1
o2 : R-module, submodule of R</pre>
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<tr><td><pre>i3 : N = coker presentation M
o3 = cokernel {1} | -y |
{1} | x |
2
o3 : R-module, quotient of R</pre>
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<tr><td><pre>i4 : f = map(M,N,1)
o4 = {1} | 1 0 |
{1} | 0 1 |
o4 : Matrix</pre>
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<tr><td><pre>i5 : isWellDefined f
o5 = true</pre>
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<tr><td><pre>i6 : isIsomorphism f
o6 = true</pre>
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<tr><td><pre>i7 : g = map(M,cover M,1)
o7 = {1} | 1 0 |
{1} | 0 1 |
o7 : Matrix</pre>
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<tr><td><pre>i8 : isWellDefined g
o8 = true</pre>
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<tr><td><pre>i9 : isIsomorphism g
o9 = false</pre>
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<tr><td><pre>i10 : h = map(cover M,M,1)
o10 = {1} | 1 0 |
{1} | 0 1 |
o10 : Matrix</pre>
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<tr><td><pre>i11 : isWellDefined h
o11 = false</pre>
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