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output-example.txt
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output-example.txt
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ii15 : load "code.m2"
[computed a random nodal curve of degree 5,
f =
5 4 3 2 2 3 4 5 4 3 2 2 4 3 2 2 2 2 2 3 2 2 3 3 2 3
6a - a b + 2a b + 4a b - 3a*b + 5b + 4a c - 3a b*c - 6a b c - 2b c - 5a c + 6a b*c + 3a*b c + 3b c + 3a c - 3a*b*c - 3b c
need to check that it has a node at the point p (and not some higher singularity),
and that it has no singularities at any other points
[sanity check: if we are unlucky, f can land in m^3! ]
-> [OK; f is not in m^3]
[sanity check: if we are unlucky, quadratic part of f at p could be degenerate; ]
[that is, the tangent cone can be a double line ]
quadratic part of f at p:
2 2
3a - 3a*b - 3b
Discriminant of q:
-6
-> [OK; lucky; point p is just a node ]
singularities of the curve Gamma:
ideal (b, a)
-> [OK; point p is the only singularity ]
[computed the canonical map on the resolution C, i.e., |2l - p|; canonicalSeries =
| a2 ab ac b2 bc |
[constructing P^4 with coordinates x_i]
[ S = k[P^2], homogeneous ]
[T = k[C], homogeneous ]
[constructing the map f: C -> P^4, or phi: T <- S ]
[computing kernel of the map phi: k[P^4] -> k[C] ]
[that is, the equations of the canonical model of C ]
[computed IdealC, ideal of the canonical model of C]
| x_2x_3-x_1x_4 x_1x_2-x_0x_4 x_1^2-x_0x_3 x_0^2x_1+2x_0^2x_3-4x_0x_1x_3+5x_0x_3^2+6x_1x_3^2+3x_3^3+5x_0^2x_4+6x_0x_1x_4-3x_0x_2x_4-6x_2^2x_4-x_0x_3x_4+4x_3^2x_4+x_0x_4^2-6x_1x_4^2+6x_2x_4^2-6x_3x_4^2+6x_4^3 x_0^3+5x_0^2x_2-3x_0x_2^2-6x_2^3+5x_0^2x_3-4x_0x_3^2+4x_1x_3^2-6x_3^3-4x_0^2x_4-6x_0x_2x_4+5x_2^2x_4+2x_0x_3x_4+4x_1x_3x_4+5x_3^2x_4+5x_0x_4^2+6x_1x_4^2-6x_2x_4^2-x_3x_4^2+x_4^3 |
[number of generators of the IdealC: ]
5
[degrees of the generators of the IdealC: ]
{2}
{2}
{2}
{3}
{3}
[the generators of the IdealC: ]
| x_2x_3-x_1x_4 |
| x_1x_2-x_0x_4 |
| x_1^2-x_0x_3 |
| x_0^2x_1+2x_0^2x_3-4x_0x_1x_3+5x_0x_3^2+6x_1x_3^2+3x_3^3+5x_0^2x_4+6x_0x_1x_4-3x_0x_2x_4-6x_2^2x_4-x_0x_3x_4+4x_3^2x_4+x_0x_4^2-6x_1x_4^2+6x_2x_4^2-6x_3x_4^2+6x_4^3 |
| x_0^3+5x_0^2x_2-3x_0x_2^2-6x_2^3+5x_0^2x_3-4x_0x_3^2+4x_1x_3^2-6x_3^3-4x_0^2x_4-6x_0x_2x_4+5x_2^2x_4+2x_0x_3x_4+4x_1x_3x_4+5x_3^2x_4+5x_0x_4^2+6x_1x_4^2-6x_2x_4^2-x_3x_4^2+x_4^3 |