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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_substitution_spand_spmaps_spbetween_springs.html" title="">substitution and maps between rings</a> > <a href="_evaluation_spand_spcomposition_spof_spring_spmaps.html" title="">evaluation and composition of ring maps</a></div>
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<div><h1>evaluation and composition of ring maps</h1>
<div><h2>evaluating ring maps</h2>
Once a ring map <tt>F</tt> is defined, the image of an element <tt>m</tt> in the source ring can be found by applying the map as <tt>F(m)</tt>.<table class="examples"><tr><td><pre>i1 : R = ZZ[x,y,z];</pre>
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<tr><td><pre>i2 : S = ZZ/101[x,y,z,Degrees => {{1,2},{1,3},{1,3}}]/ideal(x+z^3);</pre>
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<tr><td><pre>i3 : F = map(S,R,{x,y^2,z^3})
2
o3 = map(S,R,{x, y , -x})
o3 : RingMap S <--- R</pre>
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<tr><td><pre>i4 : use R; F(107*x+y+z)
2
o5 = y + 5x
o5 : S</pre>
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<h2>composition of ring maps</h2>
The function <a href="__st.html" title="a binary operator, usually used for multiplication">RingMap * RingMap</a>performs a composition of ring maps. Evaluation of elements in the source of a ring map <tt>G</tt> can also be done using<tt>F(G(m))</tt>.<table class="examples"><tr><td><pre>i6 : T = ZZ/5[x,y];</pre>
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<tr><td><pre>i7 : G = map(T,S);
o7 : RingMap T <--- S</pre>
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<tr><td><pre>i8 : G*F
2
o8 = map(T,R,{x, y , -x})
o8 : RingMap T <--- R</pre>
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<tr><td><pre>i9 : use R; G(F(107*x+y+z))
2
o10 = y
o10 : T</pre>
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