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 |
i2 : I = ideal(x * y - z^2 ) 2 o2 = ideal(x*y - z ) o2 : Ideal of R |
i3 : isRegular( I ) o3 = false |
i4 : R = QQ[x, y, u, v] o4 = R o4 : PolynomialRing |
i5 : I = ideal(x * y - u * v) o5 = ideal(x*y - u*v) o5 : Ideal of R |
i6 : isRegular( I ) o6 = false |
i7 : R = QQ[x, y, z] o7 = R o7 : PolynomialRing |
i8 : J = ideal( x ) o8 = ideal x o8 : Ideal of R |
i9 : isRegular( J ) o9 = true |
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 |
i13 : R = QQ[x, y, u, v] o13 = R o13 : PolynomialRing |
i14 : I = ideal(x * y - u * v) o14 = ideal(x*y - u*v) o14 : Ideal of R |
i15 : isRegular(I, IsGraded => true) o15 = true |