Returns true if R/I is regular where R is the ambient ring of I, otherwise it sets to false.
i1 : R = QQ[x, y, z]
o1 = R
o1 : PolynomialRing
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i2 : I = ideal(x * y - z^2 )
2
o2 = ideal(x*y - z )
o2 : Ideal of R
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i3 : isRegular( I )
o3 = false
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i4 : R = QQ[x, y, u, v]
o4 = R
o4 : PolynomialRing
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i5 : I = ideal(x * y - u * v)
o5 = ideal(x*y - u*v)
o5 : Ideal of R
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i6 : isRegular( I )
o6 = false
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i7 : R = QQ[x, y, z]
o7 = R
o7 : PolynomialRing
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i8 : J = ideal( x )
o8 = ideal x
o8 : Ideal of R
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i9 : isRegular( J )
o9 = true
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If IsGraded is set to true (default false) then it treats I as an ideal on Proj R. In particular, singularities at the origin (corresponding to the irrelevant ideal) are ignored.
i10 : R = QQ[x, y, z]
o10 = R
o10 : PolynomialRing
|
i11 : I = ideal(x * y - z^2 )
2
o11 = ideal(x*y - z )
o11 : Ideal of R
|
i12 : isRegular(I, IsGraded => true)
o12 = true
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i13 : R = QQ[x, y, u, v]
o13 = R
o13 : PolynomialRing
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i14 : I = ideal(x * y - u * v)
o14 = ideal(x*y - u*v)
o14 : Ideal of R
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i15 : isRegular(I, IsGraded => true)
o15 = true
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