-- -*- M2-comint -*- {* hash: 465178623 *}
i1 : S = QQ[x_0..x_4]
o1 = S
o1 : PolynomialRing
i2 : i = monomialCurveIdeal(S,{2,3,5,6})
2 3 2 2 2 2
o2 = ideal (x x - x x , x - x x , x x - x x , x - x x , x x - x x , x x
2 3 1 4 2 0 4 1 2 0 3 3 2 4 1 3 0 4 0 3
------------------------------------------------------------------------
2 2 3 2
- x x , x x - x x x , x - x x )
1 4 1 3 0 2 4 1 0 4
o2 : Ideal of S
i3 : time I = reesIdeal i;
-- used 0.081987 seconds
o3 : Ideal of S[w , w , w , w , w , w , w , w ]
0 1 2 3 4 5 6 7
i4 : reesIdeal(i, Variable=>v)
o4 = ideal (x v - x v + x v , x v - x v - v , x v - x v + x v , x v -
2 0 3 1 4 2 1 0 3 2 5 0 0 1 1 2 2 0 4
------------------------------------------------------------------------
2
x v - x v , x v - x v - x v , x v + x v - x v , x x v + x v -
1 5 4 7 0 3 3 5 4 6 4 2 1 3 3 4 0 4 2 1 6
------------------------------------------------------------------------
2 2
x v , x v - x v + x v + x v , x v + x v - x v , x x v - x x v -
3 7 3 2 2 4 3 5 4 6 1 2 0 6 2 7 1 4 1 2 4 2
------------------------------------------------------------------------
2 2
x v + x v , x x v - x x v - x v + x v - x v , x v - x v - x v +
1 4 3 6 0 4 1 1 3 2 1 5 2 6 4 7 3 0 4 1 2 3
------------------------------------------------------------------------
2 2
x v , x v v + v v - v v , x x v - v - x v v + v v , x x v v -
4 4 4 2 5 4 6 3 7 1 4 2 6 4 1 7 4 7 3 4 0 2
------------------------------------------------------------------------
2
x v v + v - v v )
4 1 4 4 3 6
o4 : Ideal of S[v , v , v , v , v , v , v , v ]
0 1 2 3 4 5 6 7
i5 : time I=reesIdeal(i,i_0);
-- used 0.405939 seconds
o5 : Ideal of S[w , w , w , w , w , w , w , w ]
0 1 2 3 4 5 6 7
i6 : time (J=symmetricKernel gens i);
-- used 0. seconds
o6 : Ideal of S[w , w , w , w , w , w , w , w ]
0 1 2 3 4 5 6 7
i7 : isLinearType(i,i_0)
o7 = false
i8 : isLinearType i
o8 = false
i9 : reesAlgebra (i,i_0)
S[w , w , w , w , w , w , w , w ]
0 1 2 3 4 5 6 7
o9 = -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2 2 2 2 2
(x w - x w + x w , x w - x w - w , x w - x w + x w , x w - x w - x w , x w - x w - x w , x w + x w - x w , x x w + x w - x w , x w - x w + x w + x w , x w + x w - x w , x x w - x x w - x w + x w , x x w - x x w - x w + x w - x w , x w - x w - x w + x w , x w w + w w - w w , x x w - w - x w w + w w , x x w w - x w w + w - w w )
2 0 3 1 4 2 1 0 3 2 5 0 0 1 1 2 2 0 4 1 5 4 7 0 3 3 5 4 6 4 2 1 3 3 4 0 4 2 1 6 3 7 3 2 2 4 3 5 4 6 1 2 0 6 2 7 1 4 1 2 4 2 1 4 3 6 0 4 1 1 3 2 1 5 2 6 4 7 3 0 4 1 2 3 4 4 4 2 5 4 6 3 7 1 4 2 6 4 1 7 4 7 3 4 0 2 4 1 4 4 3 6
o9 : QuotientRing
i10 : trim ideal normalCone (i, i_0)
2 3 2 2 2
o10 = ideal (x x - x x , x - x x , x x - x x , x - x x , x x - x x ,
2 3 1 4 2 0 4 1 2 0 3 3 2 4 1 3 0 4
-----------------------------------------------------------------------
2 3 2
x x - x x x , x - x x )
1 3 0 2 4 1 0 4
S[w , w , w , w , w , w , w , w ]
0 1 2 3 4 5 6 7
o10 : Ideal of -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2 2 2 2 2
(x w - x w + x w , x w - x w - w , x w - x w + x w , x w - x w - x w , x w - x w - x w , x w + x w - x w , x x w + x w - x w , x w - x w + x w + x w , x w + x w - x w , x x w - x x w - x w + x w , x x w - x x w - x w + x w - x w , x w - x w - x w + x w , x w w + w w - w w , x x w - w - x w w + w w , x x w w - x w w + w - w w )
2 0 3 1 4 2 1 0 3 2 5 0 0 1 1 2 2 0 4 1 5 4 7 0 3 3 5 4 6 4 2 1 3 3 4 0 4 2 1 6 3 7 3 2 2 4 3 5 4 6 1 2 0 6 2 7 1 4 1 2 4 2 1 4 3 6 0 4 1 1 3 2 1 5 2 6 4 7 3 0 4 1 2 3 4 4 4 2 5 4 6 3 7 1 4 2 6 4 1 7 4 7 3 4 0 2 4 1 4 4 3 6
i11 : trim ideal associatedGradedRing (i,i_0)
2 3 2 2 2
o11 = ideal (x x - x x , x - x x , x x - x x , x - x x , x x - x x ,
2 3 1 4 2 0 4 1 2 0 3 3 2 4 1 3 0 4
-----------------------------------------------------------------------
2 3 2
x x - x x x , x - x x )
1 3 0 2 4 1 0 4
S[w , w , w , w , w , w , w , w ]
0 1 2 3 4 5 6 7
o11 : Ideal of -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 2 2 2 2 2 2 2
(x w - x w + x w , x w - x w - w , x w - x w + x w , x w - x w - x w , x w - x w - x w , x w + x w - x w , x x w + x w - x w , x w - x w + x w + x w , x w + x w - x w , x x w - x x w - x w + x w , x x w - x x w - x w + x w - x w , x w - x w - x w + x w , x w w + w w - w w , x x w - w - x w w + w w , x x w w - x w w + w - w w )
2 0 3 1 4 2 1 0 3 2 5 0 0 1 1 2 2 0 4 1 5 4 7 0 3 3 5 4 6 4 2 1 3 3 4 0 4 2 1 6 3 7 3 2 2 4 3 5 4 6 1 2 0 6 2 7 1 4 1 2 4 2 1 4 3 6 0 4 1 1 3 2 1 5 2 6 4 7 3 0 4 1 2 3 4 4 4 2 5 4 6 3 7 1 4 2 6 4 1 7 4 7 3 4 0 2 4 1 4 4 3 6
i12 : trim specialFiberIdeal (i,i_0)
2 2
o12 = ideal (x , x , x , x , x , w , w - w w , w w - w w , w - w w )
4 3 2 1 0 5 6 4 7 4 6 3 7 4 3 6
o12 : Ideal of S[w , w , w , w , w , w , w , w ]
0 1 2 3 4 5 6 7
i13 :
