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<head><title>Singular Book 1.1.9 -- computation in polynomial 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_sp1.1.9.html" title="computation in polynomial rings">Singular Book 1.1.9</a></div>
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<div><h1>Singular Book 1.1.9 -- computation in polynomial rings</h1>
<div>Create a polynomial ring using reasonably standard notation.<table class="examples"><tr><td><pre>i1 : A = QQ[x,y,z];</pre>
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<tr><td><pre>i2 : f = x^3+y^2+z^2
3 2 2
o2 = x + y + z
o2 : A</pre>
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<tr><td><pre>i3 : f^2-f
6 3 2 3 2 4 2 2 4 3 2 2
o3 = x + 2x y + 2x z + y + 2y z + z - x - y - z
o3 : A</pre>
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Here are several more examples.<table class="examples"><tr><td><pre>i4 : B = ZZ/32003[x,y,z];</pre>
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<tr><td><pre>i5 : C = GF(8)[x,y,z];</pre>
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<tr><td><pre>i6 : D = ZZ[x,y,z];</pre>
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<tr><td><pre>i7 : E = (frac(ZZ[a,b,c]))[x,y,z];</pre>
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In Macaulay2, there is no concept of current ring. When you assign a ring to a variable, the variables in the ring are made global variables. To get the variables in a previous ring to be available, use <a href="_use_lp__Ring_rp.html" title="install ring variables and ring operations">use(Ring)</a>.<table class="examples"><tr><td><pre>i8 : x
o8 = x
o8 : E</pre>
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<tr><td><pre>i9 : use D
o9 = D
o9 : PolynomialRing</pre>
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<tr><td><pre>i10 : x
o10 = x
o10 : D</pre>
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Now x is an element of the ring D.<table class="examples"><tr><td><pre>i11 : describe D
o11 = ZZ[x..z, Degrees => {3:1}, Heft => {1}, MonomialOrder =>
-----------------------------------------------------------------------
{MonomialSize => 32}, DegreeRank => 1]
{GRevLex => {3:1} }
{Position => Up }</pre>
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