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<head><title>singularLocus -- singular locus</title>
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<div><h1>singularLocus -- singular locus</h1>
<div class="single"><h2>Description</h2>
<div><tt>singularLocus R</tt> -- produce the singular locus of a ring, which is assumed to be integral.<p/>
This function can also be applied to an ideal, in which case the singular locus of the quotient ring is returned, or to a variety.<table class="examples"><tr><td><pre>i1 : singularLocus(QQ[x,y] / (x^2 - y^3))
QQ[x, y]
o1 = ---------------------
3 2 2
(- y + x , 2x, -3y )
o1 : QuotientRing</pre>
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<tr><td><pre>i2 : singularLocus Spec( QQ[x,y,z] / (x^2 - y^3) )
/ QQ[x, y, z] \
o2 = Spec|---------------------|
| 3 2 2 |
\(- y + x , 2x, -3y )/
o2 : AffineVariety</pre>
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<tr><td><pre>i3 : singularLocus Proj( QQ[x,y,z] / (x^2*z - y^3) )
/QQ[x, y, z]\
o3 = Proj|-----------|
| 2 |
\ (x, y ) /
o3 : ProjectiveVariety</pre>
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<p>For rings over <a href="___Z__Z.html" title="the class of all integers">ZZ</a> the locus where the ring is not smooth over <a href="___Z__Z.html" title="the class of all integers">ZZ</a> is computed.</p>
<table class="examples"><tr><td><pre>i4 : singularLocus(ZZ[x,y]/(x^2-x-y^3+y^2))
ZZ[x, y]
o4 = ----------------------------------------
3 2 2 2
(- y + x + y - x, 2x - 1, - 3y + 2y)
o4 : QuotientRing</pre>
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<tr><td><pre>i5 : gens gb ideal oo
o5 = | 11 y+3 x+5 |
1 3
o5 : Matrix (ZZ[x, y]) <--- (ZZ[x, y])</pre>
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<div class="waystouse"><h2>Ways to use <tt>singularLocus</tt> :</h2>
<ul><li>singularLocus(AffineVariety)</li>
<li>singularLocus(Ideal)</li>
<li>singularLocus(ProjectiveVariety)</li>
<li>singularLocus(Ring)</li>
</ul>
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