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<head><title>isPommaretBasis -- check whether or not a given Janet basis is also a Pommaret basis</title>
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<div><h1>isPommaretBasis -- check whether or not a given Janet basis is also a Pommaret basis</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>P = isPommaretBasis J</tt></div>
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<li><div class="single">Inputs:<ul><li><span>J, <span>an object of class <a href="___Involutive__Basis.html" title="the class of all involutive bases">InvolutiveBasis</a></span>, a Janet basis as returned by <a href="_janet__Basis.html" title="compute Janet basis for an ideal or a submodule of a free module">janetBasis</a></span></li>
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<li><div class="single">Outputs:<ul><li><span><tt>P</tt>, <span>a <a href="../../Macaulay2Doc/html/___Boolean.html">Boolean value</a></span>, the result equals true if and only if J is a Pommaret basis</span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = QQ[x,y];</pre>
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<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
+----+------+
| 2 | |
o3 = |y |{y} |
+----+------+
| 2| |
|x*y |{y} |
+----+------+
| 3 | |
|x |{y, x}|
+----+------+
| 2 2| |
|x y |{y} |
+----+------+
o3 : InvolutiveBasis</pre>
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<tr><td><pre>i4 : isPommaretBasis J
o4 = true</pre>
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<table class="examples"><tr><td><pre>i5 : R = QQ[x,y];</pre>
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<tr><td><pre>i6 : I = ideal(x*y,y^2);
o6 : Ideal of R</pre>
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<tr><td><pre>i7 : J = janetBasis I
+---+------+
| 2 | |
o7 = |y |{y} |
+---+------+
|x*y|{y, x}|
+---+------+
o7 : InvolutiveBasis</pre>
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<tr><td><pre>i8 : isPommaretBasis J
o8 = false</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="_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="_mult__Var.html" title="extract the sets of multiplicative variables for each generator (in several contexts)">multVar</a> -- extract the sets of multiplicative variables for each generator (in several contexts)</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>
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<div class="waystouse"><h2>Ways to use <tt>isPommaretBasis</tt> :</h2>
<ul><li>isPommaretBasis(InvolutiveBasis)</li>
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