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<head><title>monomialIdeal(Ideal) -- monomial ideal of lead monomials of a Gröbner basis</title>
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<div><h1>monomialIdeal(Ideal) -- monomial ideal of lead monomials of a Gröbner 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>monomialIdeal J</tt></div>
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<li><span>Function: <a href="_monomial__Ideal.html" title="make a monomial ideal">monomialIdeal</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>J</tt>, <span>an <a href="___Ideal.html">ideal</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Monomial__Ideal.html">monomial ideal</a></span>, the monomial ideal generated by the lead monomials of a Gröbner basis of <tt>J</tt></span></li>
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<div class="single"><h2>Description</h2>
<div>J may also be a submodule of R^1, for R the ring of J.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a,b,c];</pre>
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<tr><td><pre>i2 : I = ideal(a^3,b^3,c^3, a^2-b^2)
3 3 3 2 2
o2 = ideal (a , b , c , a - b )
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : monomialIdeal I
2 2 3 3
o3 = monomialIdeal (a , a*b , b , c )
o3 : MonomialIdeal of R</pre>
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<tr><td><pre>i4 : monomialSubideal I
3 2 2 3 3
o4 = monomialIdeal (a , a b, a*b , b , c )
o4 : MonomialIdeal of R</pre>
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If the coefficient ring is ZZ, lead coefficients of the monomials are ignored.<table class="examples"><tr><td><pre>i5 : R = ZZ[x,y]
o5 = R
o5 : PolynomialRing</pre>
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<tr><td><pre>i6 : monomialIdeal ideal(2*x,3*y)
o6 = monomialIdeal (x, y)
o6 : MonomialIdeal of R</pre>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="___Monomial__Ideal.html" title="the class of all monomial ideals handled by the engine">MonomialIdeal</a> -- the class of all monomial ideals handled by the engine</span></li>
<li><span><a href="_monomial__Subideal.html" title="find the largest monomial ideal in an ideal">monomialSubideal</a> -- find the largest monomial ideal in an ideal</span></li>
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