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 .000924762 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .00731627 seconds idlizer1: .0137607 seconds idlizer2: .0276219 seconds minpres: .0189735 seconds time .0947639 sec #fractions 4] [step 1: radical (use decompose) .00780457 seconds idlizer1: .0152003 seconds idlizer2: .0517075 seconds minpres: .0306378 seconds time .136641 sec #fractions 4] [step 2: radical (use decompose) .0080006 seconds idlizer1: .0226453 seconds idlizer2: .118591 seconds minpres: .0125984 seconds time .184629 sec #fractions 5] [step 3: radical (use decompose) .00434046 seconds idlizer1: .00970436 seconds idlizer2: .0437013 seconds minpres: .0338261 seconds time .11737 sec #fractions 5] [step 4: radical (use decompose) .0045304 seconds idlizer1: .0194735 seconds idlizer2: .0927873 seconds minpres: .0155485 seconds time .15676 sec #fractions 5] [step 5: radical (use decompose) .00443167 seconds idlizer1: .0119746 seconds time .0251753 sec #fractions 5] -- used 0.722665 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 |