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<head><title>Singular Book 1.5.10 -- realization of rings</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_sp1.5.10.html" title="realization of rings">Singular Book 1.5.10</a></div>
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<div><h1>Singular Book 1.5.10 -- realization of rings</h1>
<div>We define the rings of example 1.5.3, in the Singular book.<table class="examples"><tr><td><pre>i1 : (n,m) = (2,3);</pre>
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<tr><td><pre>i2 : A1 = QQ[x_1..x_n,y_1..y_m,MonomialOrder=>{n, RevLex=>m},Global=>false];</pre>
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<tr><td><pre>i3 : f = x_1*x_2^2 + 1 + y_1^10 + x_1*y_2^5 + y_3
2 5 10
o3 = x x + x y + 1 + y + y
1 2 1 2 3 1
o3 : A1</pre>
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<tr><td><pre>i4 : 1_A1 > y_1^10
o4 = true</pre>
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The second monomial order has the first block local, and the second block polynomial.<table class="examples"><tr><td><pre>i5 : A2 = QQ[x_1..x_n,y_1..y_m,MonomialOrder=>{RevLex=>n, m},Global=>false];</pre>
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<tr><td><pre>i6 : substitute(f,A2)
10 5 2
o6 = y + y + 1 + x y + x x
1 3 1 2 1 2
o6 : A2</pre>
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<tr><td><pre>i7 : x_1*y_2^5 < 1_A2
o7 = true</pre>
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The third example has three blocks of variables.<table class="examples"><tr><td><pre>i8 : A3 = QQ[x_1..x_n,y_1..y_m,MonomialOrder=>{n, RevLex=>2, m-2},Global=>false];</pre>
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<tr><td><pre>i9 : substitute(f,A3)
2 5 10
o9 = x x + x y + y + 1 + y
1 2 1 2 3 1
o9 : A3</pre>
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