-- -*- M2-comint -*- {* hash: -1918198547 *}
i1 : R = ZZ/32003[symbol a..symbol d]
o1 = R
o1 : PolynomialRing
i2 : inL = {c^4, b*d^2, b*c, b^2*d, b^3}
4 2 2 3
o2 = {c , b*d , b*c, b d, b }
o2 : List
i3 : L = {c^4-a*d^3, -c^3+b*d^2, b*c-a*d, -a*c^2+b^2*d, b^3-a^2*c}
4 3 3 2 2 2 3 2
o3 = {c - a*d , - c + b*d , b*c - a*d, - a*c + b d, b - a c}
o3 : List
i4 : weightVector(inL,L)
o4 = {8, 8, 3, 1}
o4 : List
i5 : groebnerCone(inL,L)
o5 = (| 0 0 |, | 1 0 |)
| 0 0 | | 0 1 |
| -2 -3 | | -2 3 |
| -3 -4 | | -3 4 |
o5 : Sequence
i6 : I = monomialCurveIdeal(R,{1,3,4})
3 2 2 2 3 2
o6 = ideal (b*c - a*d, c - b*d , a*c - b d, b - a c)
o6 : Ideal of R
i7 : time (inLs,Ls) = gfan I
LP algorithm being used: "cddgmp".
-- used 0.002521 seconds
2 2 2 3 2 2 3 2 2
o7 = ({{b*d , a*d, a*c , a c}, {c , a*d, a*c , a c}, {c , b*c, a*c , a c,
------------------------------------------------------------------------
3 3 4 2 2 3 3 2 3 2 3
a d}, {c , b*c, b , a*c , a c}, {c , b*c, b , a*c }, {c , b*c, b d, b },
------------------------------------------------------------------------
2 2 2 2 2 3 2 2 3 3
{b*d , b d, a*d, a c}, {b*d , b d, b , a*d}, {b*d , b*c, b d, b , a*d },
------------------------------------------------------------------------
4 2 2 3 3 2 2 2 3
{c , b*d , b*c, b d, b }}, {{- c + b*d , - b*c + a*d, a*c - b d, - b
------------------------------------------------------------------------
2 3 2 2 2 3 2 3 2
+ a c}, {c - b*d , - b*c + a*d, a*c - b d, - b + a c}, {c - b*d ,
------------------------------------------------------------------------
2 2 3 2 4 3 3 2
b*c - a*d, a*c - b d, - b + a c, - b + a d}, {c - b*d , b*c - a*d,
------------------------------------------------------------------------
4 3 2 2 3 2 3 2 3 2 2
b - a d, a*c - b d, - b + a c}, {c - b*d , b*c - a*d, b - a c, a*c
------------------------------------------------------------------------
2 3 2 2 2 3 2 3 2
- b d}, {c - b*d , b*c - a*d, - a*c + b d, b - a c}, {- c + b*d , -
------------------------------------------------------------------------
2 2 3 2 3 2 2 2 3
a*c + b d, - b*c + a*d, - b + a c}, {- c + b*d , - a*c + b d, b -
------------------------------------------------------------------------
2 3 2 2 2 3 2 4
a c, - b*c + a*d}, {- c + b*d , b*c - a*d, - a*c + b d, b - a c, - c
------------------------------------------------------------------------
3 4 3 3 2 2 2 3 2
+ a*d }, {c - a*d , - c + b*d , b*c - a*d, - a*c + b d, b - a c}})
o7 : Sequence
i8 : wtvecs = apply(#inLs, i -> weightVector(inLs#i, Ls#i));
i9 : wtvecs/print;
{1, 1, 4, 6}
{1, 1, 4, 5}
{1, 1, 3, 2}
{2, 2, 3, 1}
{4, 4, 3, 1}
{6, 6, 3, 1}
{1, 1, 2, 4}
{2, 2, 1, 2}
{6, 6, 2, 1}
{8, 8, 3, 1}
i10 : inL1 = wtvecs/(w -> initialIdeal(w,I));
i11 : inL1/toString/print;
ideal(a^2*c,a*d,a*c^2,b*d^2)
ideal(a*d,a^2*c,a*c^2,c^3)
ideal(b*c,a^2*c,a^3*d,a*c^2,c^3)
ideal(b*c,a^2*c,a*c^2,b^4,c^3)
ideal(b*c,c^3,a*c^2,b^3)
ideal(b*c,c^3,b^2*d,b^3)
ideal(a^2*c,a*d,b^2*d,b*d^2)
ideal(a*d,b*d^2,b^2*d,b^3)
ideal(b*c,b*d^2,a*d^3,b^2*d,b^3)
ideal(b*d^2,b*c,c^4,b^2*d,b^3)
i12 : assert(inL1 == inLs/ideal)
i13 :
