i1 : R = QQ[x,y,z]/ideal(x^8-z^6-y^2*z^4-z^3); |
i2 : time R' = integralClosure(R, Verbosity => 2) [jacobian time .00089522 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .00727942 seconds idlizer1: .0136477 seconds idlizer2: .0272833 seconds minpres: .0190377 seconds time .0925924 sec #fractions 4] [step 1: radical (use decompose) .00777748 seconds idlizer1: .0159556 seconds idlizer2: .0470819 seconds minpres: .0290797 seconds time .175169 sec #fractions 4] [step 2: radical (use decompose) .00788954 seconds idlizer1: .0223539 seconds idlizer2: .0562836 seconds minpres: .0246314 seconds time .141856 sec #fractions 5] [step 3: radical (use decompose) .008404 seconds idlizer1: .019456 seconds idlizer2: .0847521 seconds minpres: .0617075 seconds time .220179 sec #fractions 5] [step 4: radical (use decompose) .0083318 seconds idlizer1: .0358156 seconds idlizer2: .171138 seconds minpres: .0302289 seconds time .338847 sec #fractions 5] [step 5: radical (use decompose) .0079767 seconds idlizer1: .0225081 seconds time .0445912 sec #fractions 5] -- used 1.02046 seconds o2 = R' o2 : QuotientRing |
i3 : trim ideal R' 3 2 2 2 4 4 o3 = ideal (w z - x , w x - w , w x - y z - z - z, w x - w z, 4,0 4,0 1,1 1,1 4,0 1,1 ------------------------------------------------------------------------ 2 2 2 3 2 3 2 3 2 4 2 2 4 2 w w - x y z - x z - x , w + w x y - x*y z - x*y z - 2x*y z 4,0 1,1 4,0 4,0 ------------------------------------------------------------------------ 3 3 2 6 2 6 2 - x*z - x, w x - w + x y + x z ) 4,0 1,1 o3 : Ideal of QQ[w , w , x, y, z] 4,0 1,1 |
i4 : icFractions R 3 2 2 4 x y z + z + z o4 = {--, -------------, x, y, z} z x o4 : List |