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<head><title>toBinomial -- creates a toric ideal from a given set of exponents of its generators; equivalent to "4ti2-output --binomials" in 4ti2</title>
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<div><h1>toBinomial -- creates a toric ideal from a given set of exponents of its generators; equivalent to "4ti2-output --binomials" in 4ti2</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>toBinomial(M,R)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
<li><span><tt>R</tt>, <span>a <a href="../../Macaulay2Doc/html/___Ring.html">ring</a></span>, ring with as least as many generators as the columns of <tt>M</tt></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>I</tt>, <span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span></span></li>
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<div class="single"><h2>Description</h2>
<div><div>Returns the ideal in the ring <tt>R</tt> generated by the binomials corresponding to rows of <tt>M</tt></div>
<table class="examples"><tr><td><pre>i1 : A = matrix "1,1,1,1; 1,2,3,4"
o1 = | 1 1 1 1 |
| 1 2 3 4 |
2 4
o1 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i2 : B = syz A
o2 = | 1 2 |
| -2 -3 |
| 1 0 |
| 0 1 |
4 2
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : R = QQ[a..d]
o3 = R
o3 : PolynomialRing</pre>
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<tr><td><pre>i4 : toBinomial(transpose B,R)
2 3 2
o4 = ideal (- b + a*c, - b + a d)
o4 : Ideal of R</pre>
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<div class="waystouse"><h2>Ways to use <tt>toBinomial</tt> :</h2>
<ul><li>toBinomial(Matrix,Ring)</li>
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