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 .000335829 sec #minors 3] integral closure nvars 3 numgens 1 is S2 codim 1 codimJ 2 [step 0: radical (use decompose) .00272187 seconds idlizer1: .00494448 seconds idlizer2: .0101371 seconds minpres: .00710922 seconds time .0350328 sec #fractions 4] [step 1: radical (use decompose) .00286606 seconds idlizer1: .0058595 seconds idlizer2: .0174299 seconds minpres: .0107582 seconds time .0484446 sec #fractions 4] [step 2: radical (use decompose) .00286193 seconds idlizer1: .00808713 seconds idlizer2: .0486913 seconds minpres: .0085886 seconds time .0796382 sec #fractions 5] [step 3: radical (use decompose) .00298289 seconds idlizer1: .00677816 seconds idlizer2: .0300939 seconds minpres: .0233297 seconds time .0808939 sec #fractions 5] [step 4: radical (use decompose) .00307365 seconds idlizer1: .0127823 seconds idlizer2: .0881699 seconds minpres: .0112507 seconds time .132643 sec #fractions 5] [step 5: radical (use decompose) .00304623 seconds idlizer1: .00850219 seconds time .0170324 sec #fractions 5] -- used 0.396589 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 |