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<head><title>multVar -- extract the sets of multiplicative variables for each generator (in several contexts)</title>
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<div><h1>multVar -- extract the sets of multiplicative variables for each generator (in several contexts)</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>m = multVar(J) or m = multVar(C,n) or m = multVar(F)</tt></div>
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<li><div class="single">Inputs:<ul><li><span><tt>J</tt>, <span>an object of class <a href="___Involutive__Basis.html" title="the class of all involutive bases">InvolutiveBasis</a></span></span></li>
<li><span><tt>C</tt>, <span>a <a href="../../Macaulay2Doc/html/___Chain__Complex.html">chain complex</a></span></span></li>
<li><span><tt>n</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
<li><span><tt>F</tt>, <span>an object of class <a href="___Factor__Module__Basis.html" title="the class of all factor module bases">FactorModuleBasis</a></span></span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><tt>m</tt>, <span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, list of sets of variables of the polynomial ring</span></li>
</ul>
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<div class="single"><h2>Description</h2>
<div><p>If the argument of multVar is <span>an object of class <a href="___Involutive__Basis.html" title="the class of all involutive bases">InvolutiveBasis</a></span>, then the i-th set in m consists of the multiplicative variables for the i-th generator in J.</p>
<p>If the arguments of multVar are <span>a <a href="../../Macaulay2Doc/html/___Chain__Complex.html">chain complex</a></span> and <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, where C is the result of either <a href="_janet__Resolution.html" title="construct a free resolution for a given ideal or module using Janet bases">janetResolution</a> or <a href="../../Macaulay2Doc/html/_resolution.html" title="projective resolution">resolution</a> called with the optional argument 'Strategy => Involutive', then the i-th set in m consists of the multiplicative variables for the i-th generator in the n-th differential of C.</p>
<p>If the argument of multVar is <span>an object of class <a href="___Factor__Module__Basis.html" title="the class of all factor module bases">FactorModuleBasis</a></span>, then the i-th set in m consists of the multiplicative variables for the i-th monomial cone in F.</p>
<table class="examples"><tr><td><pre>i1 : R = QQ[x,y];</pre>
</td></tr>
<tr><td><pre>i2 : I = ideal(x^3,y^2);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : J = janetBasis I;</pre>
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<tr><td><pre>i4 : multVar J
o4 = {set {y}, set {y}, set {x, y}, set {y}}
o4 : List</pre>
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<table class="examples"><tr><td><pre>i5 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i6 : I = ideal(x,y,z);
o6 : Ideal of R</pre>
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<tr><td><pre>i7 : C = res(I, Strategy => Involutive)
1 3 3 1
o7 = R <-- R <-- R <-- R <-- 0
0 1 2 3 4
o7 : ChainComplex</pre>
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<tr><td><pre>i8 : multVar(C, 2)
o8 = {set {x, y, z}, set {x, y, z}, set {y, z}}
o8 : List</pre>
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<table class="examples"><tr><td><pre>i9 : R = QQ[x,y,z];</pre>
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<tr><td><pre>i10 : M = matrix {{x*y,x^3*z}};
1 2
o10 : Matrix R <--- R</pre>
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<tr><td><pre>i11 : J = janetBasis M
+---+---------+
o11 = |x*y|{z, y} |
+---+---------+
| 2 | |
|x y|{z, y} |
+---+---------+
| 3 | |
|x z|{z, x} |
+---+---------+
| 3 | |
|x y|{z, y, x}|
+---+---------+
o11 : InvolutiveBasis</pre>
</td></tr>
<tr><td><pre>i12 : F = factorModuleBasis J
+--+------+
o12 = |1 |{z, y}|
+--+------+
|x |{z} |
+--+------+
| 2| |
|x |{z} |
+--+------+
| 3| |
|x |{x} |
+--+------+
o12 : FactorModuleBasis</pre>
</td></tr>
<tr><td><pre>i13 : basisElements F
o13 = | 1 x x2 x3 |
1 4
o13 : Matrix R <--- R</pre>
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<tr><td><pre>i14 : multVar F
o14 = {set {y, z}, set {z}, set {z}, set {x}}
o14 : List</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_janet__Basis.html" title="compute Janet basis for an ideal or a submodule of a free module">janetBasis</a> -- compute Janet basis for an ideal or a submodule of a free module</span></li>
<li><span><a href="_janet__Mult__Var.html" title="return table of multiplicative variables for given module elements as determined by Janet division">janetMultVar</a> -- return table of multiplicative variables for given module elements as determined by Janet division</span></li>
<li><span><a href="_pommaret__Mult__Var.html" title="return table of multiplicative variables for given module elements as determined by Pommaret division">pommaretMultVar</a> -- return table of multiplicative variables for given module elements as determined by Pommaret division</span></li>
<li><span><a href="_basis__Elements.html" title="extract the matrix of generators from an involutive basis or factor module basis">basisElements</a> -- extract the matrix of generators from an involutive basis or factor module basis</span></li>
<li><span><a href="_janet__Resolution.html" title="construct a free resolution for a given ideal or module using Janet bases">janetResolution</a> -- construct a free resolution for a given ideal or module using Janet bases</span></li>
<li><span><a href="___Involutive.html" title="compute a (usually non-minimal) resolution using involutive bases">Involutive</a> -- compute a (usually non-minimal) resolution using involutive bases</span></li>
<li><span><a href="_factor__Module__Basis.html" title="enumerate standard monomials">factorModuleBasis</a> -- enumerate standard monomials</span></li>
</ul>
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<div class="waystouse"><h2>Ways to use <tt>multVar</tt> :</h2>
<ul><li>multVar(ChainComplex,ZZ)</li>
<li>multVar(FactorModuleBasis)</li>
<li>multVar(InvolutiveBasis)</li>
</ul>
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