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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_sp1.1.10.html" title="methods for creating ring maps">Singular Book 1.1.10</a></div>
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<div><h1>Singular Book 1.1.10 -- methods for creating ring maps</h1>
<div>In Macaulay2, ring maps from a polynomial ring are defined and used as follows.<table class="examples"><tr><td><pre>i1 : A = QQ[a,b,c];</pre>
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<tr><td><pre>i2 : f = a+b+a*b+c^3;</pre>
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<tr><td><pre>i3 : B = QQ[x,y,z];</pre>
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<tr><td><pre>i4 : F = map(B,A,{x+y, x-y, z})
o4 = map(B,A,{x + y, x - y, z})
o4 : RingMap B <--- A</pre>
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Notice that ring maps are defined by first giving the target ring, then the source ring, and finally the data.<p/>
Parentheses for functions with one parameter are optional.<table class="examples"><tr><td><pre>i5 : g = F f
3 2 2
o5 = z + x - y + 2x
o5 : B</pre>
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<tr><td><pre>i6 : A1 = QQ[x,y,c,b,a,z];</pre>
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<tr><td><pre>i7 : substitute(f,A1)
3
o7 = c + b*a + b + a
o7 : A1</pre>
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To map the first variable of A to the first variable of A1, the second variable of A to the second variable of A1, and so on, create the list of the first generators of A1<table class="examples"><tr><td><pre>i8 : v = take(gens A1, numgens A)
o8 = {x, y, c}
o8 : List</pre>
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<tr><td><pre>i9 : G = map(A1,A,v)
o9 = map(A1,A,{x, y, c})
o9 : RingMap A1 <--- A</pre>
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<tr><td><pre>i10 : G f
3
o10 = c + x*y + x + y
o10 : A1</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_substitution_spand_spmaps_spbetween_springs.html" title="">substitution and maps between rings</a></span></li>
<li><span><a href="_map.html" title="make a map">map</a> -- make a map</span></li>
<li><span><a href="_substitute.html" title="substituting values for variables">substitute</a> -- substituting values for variables</span></li>
<li><span><a href="___Ring__Map.html" title="the class of all ring maps">RingMap</a> -- the class of all ring maps</span></li>
<li><span><a href="_generators.html" title="provide matrix or list of generators">generators</a> -- provide matrix or list of generators</span></li>
<li><span><a href="_numgens.html" title="the number of generators">numgens</a> -- the number of generators</span></li>
<li><span><a href="_take.html" title="take some elements from a list">take</a> -- take some elements from a list</span></li>
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