We provide a list of MM-cones for all the planar graphs of genus at most 7.

For each graph, we provide the input and output of our code, as explained at
https://mathrepo.mis.mpg.de/mmcurves/

The names of the graphs in this list are taken from
https://mathrepo.mis.mpg.de/selfdual/#graph-curves

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K4 = complete graph on 4 vertices

Edges = {{0,1}, {1,2}, {2,0}, {2,3}, {3,1}, {0,3}};
EdgePairing = {{1,2}, {0,2}, {0,1}, {1,4}, {0,5}, {2,3}};


Generators of graph curve ideal:
{x_0^2*x_1^2-2*x_0*x_1^3+x_1^4+x_0^2*x_1*x_2-3*x_0*x_1^2*x_2+2*x_1^3*x_2-x_0*x_1*x_2^2+x_1^2*x_2^2}


Tangent vectors:
matrix {{x_1^4+2*x_1^3*x_2+x_1^2*x_2^2},
        {x_0^2*x_1*x_2-x_0*x_1^2*x_2+x_0^2*x_2^2-x_0*x_1*x_2^2},
        {x_0^2*x_1*x_2-3*x_0*x_1^2*x_2+2*x_1^3*x_2+x_0^2*x_2^2-5*x_0*x_1*x_2^2+5*x_1^2*x_2^2-2*x_0*x_2^3+4*x_1*x_2^3+x_2^4},
        {x_0^4-4*x_0^3*x_1+8*x_0*x_1^3-5*x_1^4-2*x_0^3*x_2+12*x_0*x_1^2*x_2-10*x_1^3*x_2+x_0^2*x_2^2+4*x_0*x_1*x_2^2-5*x_1^2*x_2^2},
        {-x_0^2*x_1*x_2+3*x_0*x_1^2*x_2-2*x_1^3*x_2+x_0*x_1*x_2^2-x_1^2*x_2^2},
        {-x_0^2*x_1*x_2+x_0*x_1^2*x_2+x_0*x_1*x_2^2}}


Sum of tangent vectors:
{x_0^4-4*x_0^3*x_1+8*x_0*x_1^3-4*x_1^4-2*x_0^3*x_2+12*x_0*x_1^2*x_2-8*x_1^3*x_2+3*x_0^2*x_2^2-2*x_0*x_2^3+4*x_1*x_2^3+x_2^4}


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Graph61

Edges = {{0, 1}, {1, 2}, {2, 0}, {3, 4}, {4, 5}, {5, 3}, {0, 3}, {1, 4}, {2, 5}};
EdgePairing = {{1,2}, {0,2}, {0,1}, {4,5}, {3,5}, {3,4}, {2,5}, {1,4}, {1,4}};


Generators of graph curve ideal:
{x_0^2+x_0*x_1+x_0*x_2+x_0*x_3, x_1*x_2*x_3}


Tangent vectors:
matrix {{0, x_0*x_1^2},
        {0, x_0*x_2^2},
        {0, x_0*x_3^2},
        {0, -x_0*x_1^2-x_1^3-x_1^2*x_2-x_1^2*x_3},
        {0, -x_0*x_2^2-x_1*x_2^2-x_2^3-x_2^2*x_3},
        {0, -x_0*x_3^2-x_1*x_3^2-x_2*x_3^2-x_3^3},
        {-x_1*x_3, 0},
        {-x_1*x_2, 0},
        {-x_2*x_3, 0}}


Sum of tangent vectors:
{-x_1*x_2-x_1*x_3-x_2*x_3,
 -x_1^3-x_1^2*x_2-x_1*x_2^2-x_2^3-x_1^2*x_3-x_2^2*x_3-x_1*x_3^2-x_2*x_3^2-x_3^3}


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Graph81

Edges = {{0,1}, {1,2}, {2,0}, {2,3}, {3,4}, {4,1}, {4,5}, {5,6}, {6,3}, {6,7}, {7,5}, {0,7}};
EdgePairing = {{1,2}, {0,2}, {0,1}, {1,4}, {3,5}, {1,4}, {4,7}, {6,8}, {4,7}, {7,10}, {7,9}, {0,10}};


Generators of graph curve ideal:
{x_2^2+2*x_2*x_3+x_3^2-x_2*x_4-x_3*x_4,
 x_0*x_2+x_0*x_3-x_0*x_4,
 x_0*x_1+x_0*x_3,
 x_1*x_2*x_3+x_1*x_3^2-x_1*x_2*x_4+x_0*x_3*x_4-x_1*x_3*x_4-x_0*x_4^2,
 x_1^2*x_3+x_1*x_3^2-x_1^2*x_4-x_1*x_3*x_4}


Tangent vectors:
matrix {{0, 0, 0, -x_0^3+2*x_0^2*x_3-x_0*x_3^2, 0},
        {0, 0, 0, -x_0*x_4^2, 0},
        {0, 0, 0, -x_0*x_3^2+2*x_0*x_3*x_4-x_0*x_4^2, 0},
        {0, 0, x_2*x_3+x_3^2-x_2*x_4-x_3*x_4, 0, -x_2*x_3^2-x_3^3+2*x_2*x_3*x_4+2*x_3^2*x_4-x_2*x_4^2-x_3*x_4^2},
        {0, 0, 0, -x_1*x_2*x_4-x_1*x_3*x_4-x_2*x_3*x_4-x_3^2*x_4, -x_1^2*x_2+x_1*x_3^2-x_2*x_3^2-x_3^3-x_1^2*x_4-2*x_1*x_2*x_4+2*x_0*x_3*x_4-3*x_1*x_3*x_4-2*x_0*x_4^2},
        {0, 0, x_1*x_2+x_1*x_3+x_0*x_4, 0, 0},
        {x_1^2+x_1*x_3, 0, 0, 0, 0},
        {0, 0, 0, 0, x_1^2*x_2-x_1*x_3^2+x_2*x_3^2+x_3^3+2*x_1*x_2*x_4-2*x_0*x_3*x_4+x_1*x_3*x_4-x_3^2*x_4+2*x_0*x_4^2},
        {x_1*x_3+x_3^2-x_1*x_4-x_3*x_4, 0, 0, 0, 0},
        {0, 0, 0, 0, x_2*x_3^2+x_3^3-2*x_2*x_3*x_4-3*x_3^2*x_4+x_2*x_4^2+3*x_3*x_4^2-x_4^3},
        {0, 0, 0, 0, x_1^2*x_2-x_1*x_3^2+x_1*x_3*x_4},
        {0, x_0*x_3+x_1*x_3-x_0*x_4-x_1*x_4, 0, -x_0*x_3^2-x_1*x_3^2+2*x_0*x_3*x_4+2*x_1*x_3*x_4-x_0*x_4^2-x_1*x_4^2, 0}}


Sum of tangent vectors:
{x_1^2+2*x_1*x_3+x_3^2-x_1*x_4-x_3*x_4,
 x_0*x_3+x_1*x_3-x_0*x_4-x_1*x_4,
 x_1*x_2+x_1*x_3+x_2*x_3+x_3^2+x_0*x_4-x_2*x_4-x_3*x_4,
 -x_0^3+2*x_0^2*x_3-3*x_0*x_3^2-x_1*x_3^2-x_1*x_2*x_4+4*x_0*x_3*x_4+x_1*x_3*x_4-x_2*x_3*x_4-x_3^2*x_4-3*x_0*x_4^2-x_1*x_4^2,
 x_1^2*x_2-x_1*x_3^2-x_1^2*x_4-x_1*x_3*x_4-2*x_3^2*x_4+2*x_3*x_4^2-x_4^3}


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Graph83

Edges = {{0,1}, {1,2}, {2,3}, {3,0}, {4,5}, {5,6}, {6,7}, {7,4}, {0,4}, {1,5}, {2,6}, {3,7}};
EdgePairing = {{1,3}, {0,2}, {1,3}, {0,2}, {5,7}, {4,6}, {5,7}, {4,6}, {0,4}, {0,4}, {2,6}, {2,6}};


Generators of graph curve ideal:
{x_2*x_4, x_1*x_3, x_0^2+x_0*x_1+x_0*x_2+x_0*x_3+x_0*x_4}


Tangent vectors:
matrix {{x_0*x_1, 0, 0},
        {0, x_0*x_2, 0},
        {x_0*x_3, 0, 0},
        {0, x_0*x_4, 0},
        {-x_0*x_1-x_1^2-x_1*x_2-x_1*x_4, 0, 0},
        {0, -x_0*x_2-x_1*x_2-x_2^2-x_2*x_3, 0},
        {-x_0*x_3-x_2*x_3-x_3^2-x_3*x_4, 0, 0},
        {0, -x_0*x_4-x_1*x_4-x_3*x_4-x_4^2, 0},
        {0, 0, -x_1*x_4},
        {0, 0, -x_1*x_2},
        {0, 0, -x_2*x_3},
        {0, 0, -x_3*x_4}}


Sum of tangent vectors:
{-x_1^2-x_1*x_2-x_2*x_3-x_3^2-x_1*x_4-x_3*x_4,
 -x_1*x_2-x_2^2-x_2*x_3-x_1*x_4-x_3*x_4-x_4^2,
 -x_1*x_2-x_2*x_3-x_1*x_4-x_3*x_4}


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Graph101

Edges = {{0,1}, {1,2}, {2,3}, {3,0}, {1,4}, {4,0}, {5,6}, {6,7}, {7,5}, {6,8}, {8,9}, {9,5}, {2,7}, {3,8}, {4,9}};
EdgePairing = {{4,5}, {0,2}, {1,3}, {0,2}, {0,5}, {0,4}, {7,8}, {6,8}, {6,7}, {7,13}, {13,14}, {6,10}, {2,7}, {2,9}, {5,10}};


Generators of graph curve ideal:
{x_2*x_5+x_4*x_5,
 x_1*x_4+x_2*x_4-x_1*x_5+2*x_4*x_5-x_5^2,
 x_1*x_3+x_2*x_3+x_1*x_5+x_3*x_5-x_4*x_5+x_5^2,
 x_0*x_3+x_0*x_5+x_3*x_5+x_5^2,
 x_1*x_2+x_2^2+x_1*x_5-2*x_4*x_5+x_5^2,
 x_0*x_2+x_0*x_4,
 x_0*x_4^2-x_0*x_4*x_5+x_3*x_4*x_5-x_3*x_5^2+x_4*x_5^2-x_5^3, x_0^2*x_4-x_0*x_1*x_5+2*x_0*x_4*x_5-x_0*x_5^2-x_1*x_5^2+x_4*x_5^2-x_5^3, x_2*x_3^2-x_2*x_3*x_4+x_3^2*x_5-3*x_3*x_4*x_5+x_4^2*x_5+2*x_3*x_5^2-2*x_4*x_5^2+x_5^3}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, x_2*x_3*x_4+x_3^2*x_4-x_3^2*x_5+3*x_3*x_4*x_5-x_4^2*x_5-2*x_3*x_5^2+2*x_4*x_5^2-x_5^3},
        {-x_3^2+x_3*x_4-2*x_3*x_5+x_4*x_5-x_5^2, -x_3^2+x_3*x_4-2*x_3*x_5+x_4*x_5-x_5^2, x_3^2-x_3*x_4+2*x_3*x_5-x_4*x_5+x_5^2, 0, 2*x_3^2-2*x_3*x_4+4*x_3*x_5-2*x_4*x_5+2*x_5^2, x_3^2-x_3*x_4+2*x_3*x_5-x_4*x_5+x_5^2, -x_3^3+2*x_3^2*x_4-x_3*x_4^2-3*x_3^2*x_5+4*x_3*x_4*x_5-x_4^2*x_5-3*x_3*x_5^2+2*x_4*x_5^2-x_5^3, 0, 2*x_3^3-3*x_3^2*x_4+x_3*x_4^2+5*x_3^2*x_5-5*x_3*x_4*x_5+x_4^2*x_5+4*x_3*x_5^2-2*x_4*x_5^2+x_5^3},
        {0, 0, 0, 0, 0, 0, -x_3*x_5^2-x_5^3, 0, x_3^2*x_5+2*x_3*x_5^2+x_5^3},
        {x_2*x_3+x_3*x_5-x_4*x_5+x_5^2, x_2*x_3+x_3*x_5-x_4*x_5+x_5^2, -x_2*x_3-x_3*x_5+x_4*x_5-x_5^2, 0, -2*x_2*x_3-2*x_3*x_5+2*x_4*x_5-2*x_5^2, -x_2*x_3-x_3*x_5+x_4*x_5-x_5^2, 0, 0, -x_2*x_3*x_4-2*x_3*x_4*x_5+x_4^2*x_5+x_3*x_5^2-2*x_4*x_5^2+x_5^3},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3*x_4+x_3^2*x_4+x_2*x_4^2-2*x_3*x_4^2+x_4^3-x_3^2*x_5+3*x_3*x_4*x_5-x_4^2*x_5-2*x_3*x_5^2+2*x_4*x_5^2-x_5^3},
        {0, 0, 0, 0, 0, 0, 0, 0, x_2^3+x_2^2*x_4},
        {0, 0, 0, 0, 0, 0, 0, -x_0^2*x_1-x_0^2*x_5-x_0*x_1*x_5-x_0*x_5^2, 0},
        {0, 0, 0, 0, 0, 0, 0, -x_0^2*x_1+2*x_0*x_1^2-x_1^3-x_2^3-x_0^2*x_5+x_0*x_1*x_5+2*x_3*x_4*x_5-3*x_4^2*x_5-x_0*x_5^2+x_1*x_5^2-2*x_3*x_5^2+4*x_4*x_5^2-2*x_5^3, 0},
        {0, 0, 0, 0, 0, 0, 0, -x_1*x_5^2+x_4*x_5^2-x_5^3, 0},
        {0, x_0^2-x_0*x_1+x_0*x_4-x_1*x_5+x_4*x_5-x_5^2, 0, 0, -x_0^2+x_0*x_1-x_0*x_4+x_1*x_5-x_4*x_5+x_5^2,0, 0, x_0^3-x_0^2*x_1+x_0^2*x_5-x_0*x_1*x_5, 0},
        {0, 0, 0, 0, 0, 0, -x_0*x_4*x_5-x_3*x_4*x_5+x_4^2*x_5+x_0*x_5^2+x_3*x_5^2-3*x_4*x_5^2+2*x_5^3, -x_0^2*x_5+x_0*x_1*x_5-x_0*x_5^2+x_1*x_5^2, 0},
        {0, x_0*x_4+x_4*x_5, 0, 0, -x_0*x_4-x_4*x_5, 0, x_0*x_4*x_5-x_3*x_4*x_5+x_4^2*x_5+x_3*x_5^2-x_4*x_5^2+x_5^3, x_0*x_1*x_5+x_0*x_5^2+x_1*x_5^2+x_5^3, 0},
        {0, 0, x_0*x_4-x_1*x_5+x_3*x_5+x_4*x_5, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, x_0*x_4-x_0*x_5, 0, 0, -x_0*x_4*x_5-x_3*x_4*x_5+x_0*x_5^2+x_3*x_5^2-x_4*x_5^2+x_5^3,-x_0^2*x_5+x_0*x_1*x_5-2*x_0*x_4*x_5+x_0*x_5^2+x_1*x_5^2-x_4*x_5^2+x_5^3, 0},
        {-x_2*x_3+x_2*x_4-x_3*x_5+2*x_4*x_5-x_5^2, -x_2*x_3+x_2*x_4-x_3*x_5+2*x_4*x_5-x_5^2, x_2*x_3-x_2*x_4+x_3*x_5-2*x_4*x_5+x_5^2, 0, 2*x_2*x_3-2*x_2*x_4+2*x_3*x_5-4*x_4*x_5+2*x_5^2, 0, 0, x_3*x_4*x_5-x_4^2*x_5-x_3*x_5^2+2*x_4*x_5^2-x_5^3, -x_2*x_3*x_4+x_2*x_4^2+x_4^2*x_5-x_3*x_5^2+x_4*x_5^2-x_5^3}}


Sum of tangent vectors:
{-x_3^2+x_2*x_4+x_3*x_4-2*x_3*x_5+2*x_4*x_5-x_5^2,
 x_0^2-x_0*x_1-x_3^2+2*x_0*x_4+x_2*x_4+x_3*x_4-x_1*x_5-2*x_3*x_5+4*x_4*x_5-2*x_5^2,
 x_3^2+x_0*x_4-x_2*x_4-x_3*x_4-x_1*x_5+3*x_3*x_5-x_4*x_5+x_5^2, x_0*x_4-x_0*x_5,
 -x_0^2+x_0*x_1+2*x_3^2-2*x_0*x_4-2*x_2*x_4-2*x_3*x_4+x_1*x_5+4*x_3*x_5-6*x_4*x_5+3*x_5^2,
 -x_2*x_3+x_3^2-x_3*x_4+x_3*x_5,
 -x_3^3+2*x_3^2*x_4-x_3*x_4^2-3*x_3^2*x_5-x_0*x_4*x_5+x_3*x_4*x_5+x_4^2*x_5+2*x_0*x_5^2-x_3*x_5^2-3*x_4*x_5^2+2*x_5^3,
 x_0^3-3*x_0^2*x_1+2*x_0*x_1^2-x_1^3-x_2^3-3*x_0^2*x_5+2*x_0*x_1*x_5-2*x_0*x_4*x_5+3*x_3*x_4*x_5-4*x_4^2*x_5-x_0*x_5^2+3*x_1*x_5^2-3*x_3*x_5^2+6*x_4*x_5^2-2*x_5^3,
 x_2^3+2*x_3^3+x_2^2*x_4-2*x_2*x_3*x_4-x_3^2*x_4+2*x_2*x_4^2-x_3*x_4^2+x_4^3+4*x_3^2*x_5-x_3*x_4*x_5+x_4^2*x_5+2*x_3*x_5^2+x_4*x_5^2}


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Graph105

Edges = {{0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {5,6}, {6,7}, {7,8}, {8,5}, {0,5}, {1,6}, {4,8}, {2,9}, {3,9}, {9,7}};
EdgePairing = {{1,4}, {0,2}, {1,3}, {2,4}, {0,3}, {6,8}, {5,7}, {6,8}, {5,7}, {0,5}, {0,5}, {4,8}, {2,13}, {2,12}, {6,12}};


Generators of graph curve ideal:
{x_0*x_4+x_0*x_5,
 x_2*x_3-x_3^2-x_1*x_4-2*x_2*x_4+x_3*x_4-x_4^2-x_1*x_5-x_4*x_5,
 x_0*x_3+x_0*x_5,
 x_2^2-x_3^2-x_1*x_4-2*x_2*x_4+x_3*x_4-x_4^2-x_1*x_5-x_4*x_5,
 x_1*x_2-x_1*x_3+x_1*x_4+2*x_2*x_4-x_3*x_4+x_4^2+x_2*x_5-x_3*x_5+x_4*x_5, x_0*x_2,
 x_0*x_1*x_5-x_1^2*x_5-2*x_1*x_4*x_5-x_2*x_4*x_5-x_4^2*x_5-x_1*x_5^2-x_4*x_5^2}


Tangent vectors:
matrix {{0, -2*x_1*x_4-2*x_2*x_4-2*x_4^2-2*x_1*x_5-2*x_2*x_5-4*x_4*x_5-2*x_5^2, 0,  -3*x_1*x_4-3*x_2*x_4-3*x_4^2-3*x_1*x_5-3*x_2*x_5-6*x_4*x_5-3*x_5^2, x_1*x_4+x_2*x_4+x_4^2+x_1*x_5+x_2*x_5+2*x_4*x_5+x_5^2, 0, -x_1*x_4*x_5-x_2*x_4*x_5-x_4^2*x_5-x_1*x_5^2-x_2*x_5^2-2*x_4*x_5^2-x_5^3},
        {x_1*x_4+x_2*x_4+x_4^2+x_4*x_5, -x_1*x_4-x_2*x_4-x_4^2-x_4*x_5, x_1*x_4+x_2*x_4+x_4^2+x_4*x_5, -x_1*x_4-x_2*x_4-x_4^2-x_4*x_5, 0, 0, -x_1*x_4*x_5-x_2*x_4*x_5-x_4^2*x_5-x_4*x_5^2},
        {0, 0, 0, 0, 0, 0, x_0*x_1^2},
        {0, 0, x_0*x_1-x_1^2-x_1*x_3-x_1*x_4+x_2*x_4-x_3*x_4-x_1*x_5+x_2*x_5-x_3*x_5, 0, 0, x_0*x_1-x_1^2-x_1*x_3-x_1*x_4+x_2*x_4-x_3*x_4-x_1*x_5+x_2*x_5-x_3*x_5, 0},
        {0, x_1*x_3+x_3^2+x_2*x_4+x_1*x_5+x_3*x_5, 0, x_1*x_3+x_3^2+x_2*x_4+x_1*x_5+x_3*x_5, 0, 0, x_1^2*x_3+x_1*x_3^2-x_3^2*x_4-x_1*x_4^2-3*x_2*x_4^2+x_3*x_4^2-x_4^3+x_1^2*x_5+x_3^2*x_5+x_1*x_4*x_5+4*x_2*x_4*x_5-2*x_3*x_4*x_5+x_4^2*x_5+x_1*x_5^2+2*x_2*x_5^2-x_3*x_5^2+2*x_4*x_5^2},
        {0, (1/2)*x_1*x_4+(1/2)*x_2*x_4+(1/2)*x_4^2+(1/2)*x_1*x_5+(1/2)*x_2*x_5-(1/2)*x_3*x_5+x_4*x_5, 0, (3/4)*x_1*x_4+(3/4)*x_2*x_4+(3/4)*x_4^2+(3/4)*x_1*x_5+(3/4)*x_2*x_5-(3/4)*x_3*x_5+(3/2)*x_4*x_5, -(1/4)*x_1*x_4-(1/4)*x_2*x_4-(1/4)*x_4^2-(1/4)*x_1*x_5-(1/4)*x_2*x_5+(1/4)*x_3*x_5-(1/2)*x_4*x_5, 0, (1/4)*x_1*x_4*x_5+(1/4)*x_2*x_4*x_5+(1/4)*x_4^2*x_5+(1/4)*x_1*x_5^2+(1/4)*x_2*x_5^2-(1/4)*x_3*x_5^2+(1/2)*x_4*x_5^2},
        {0, x_1*x_4+x_2*x_4+x_4^2+x_1*x_5+x_4*x_5, 0, x_1*x_4+x_2*x_4+x_4^2+x_1*x_5+x_4*x_5, 0, 0, 0},
        {0, 2*x_1*x_4-2*x_2*x_4+2*x_3*x_4+2*x_1*x_5-2*x_2*x_5+2*x_3*x_5, 0, 3*x_1*x_4-3*x_2*x_4+3*x_3*x_4+3*x_1*x_5-3*x_2*x_5+3*x_3*x_5, -x_1*x_4+x_2*x_4-x_3*x_4-x_1*x_5+x_2*x_5-x_3*x_5, 0, x_3^2*x_4+4*x_2*x_4^2-2*x_3*x_4^2+x_4^3-x_1*x_4*x_5+3*x_2*x_4*x_5-2*x_3*x_4*x_5+x_4^2*x_5-x_1*x_5^2+x_2*x_5^2-x_3*x_5^2},
        {0, -x_2*x_4, 0, -x_2*x_4, 0, 0, x_3^2*x_4+x_1*x_4^2+2*x_2*x_4^2-x_3*x_4^2+x_4^3+x_1*x_4*x_5+x_4^2*x_5},
        {0, x_2*x_5, 0, x_2*x_5, -x_2*x_5, 0, x_2*x_5^2},
        {0, x_1*x_4+2*x_2*x_4-x_3*x_4+x_4^2+x_1*x_5+x_2*x_5-x_3*x_5+x_4*x_5, 0, x_1*x_4+2*x_2*x_4-x_3*x_4+x_4^2+x_1*x_5+x_2*x_5-x_3*x_5+x_4*x_5, -x_1*x_4-2*x_2*x_4+x_3*x_4-x_4^2-x_1*x_5-x_2*x_5+x_3*x_5-x_4*x_5, 0, x_1*x_4*x_5+2*x_2*x_4*x_5-x_3*x_4*x_5+x_4^2*x_5+x_1*x_5^2+x_2*x_5^2-x_3*x_5^2+x_4*x_5^2},
        {0, x_1*x_3-x_1*x_4-2*x_2*x_4+x_3*x_4-x_4^2-x_2*x_5+x_3*x_5-x_4*x_5, 0, x_1*x_3-x_1*x_4-2*x_2*x_4+x_3*x_4-x_4^2-x_2*x_5+x_3*x_5-x_4*x_5, -x_1*x_3+x_1*x_4+2*x_2*x_4-x_3*x_4+x_4^2+x_2*x_5-x_3*x_5+x_4*x_5, 0, 0},
        {0, 0, 0, 0, 0, 0, x_0*x_5^2},
        {0, 0, 0, 0, 0, 0, x_0^3-2*x_0^2*x_1+x_0*x_1^2+2*x_0^2*x_5-2*x_1^2*x_5-4*x_1*x_4*x_5-2*x_2*x_4*x_5-2*x_4^2*x_5+x_0*x_5^2-2*x_1*x_5^2-2*x_4*x_5^2},
        {-x_0*x_5+x_1*x_5-x_2*x_5+x_3*x_5, 0, 0, 0, 0, 0, x_0*x_5^2-x_1*x_5^2+x_2*x_5^2-x_3*x_5^2}}


Sum of tangent vectors:
{x_1*x_4+x_2*x_4+x_4^2-x_0*x_5+x_1*x_5-x_2*x_5+x_3*x_5+x_4*x_5,
 2*x_1*x_3+x_3^2+(1/2)*x_1*x_4-(7/2)*x_2*x_4+2*x_3*x_4-(3/2)*x_4^2+(7/2)*x_1*x_5-(5/2)*x_2*x_5+(5/2)*x_3*x_5-3*x_4*x_5-2*x_5^2,
 x_0*x_1-x_1^2-x_1*x_3+2*x_2*x_4-x_3*x_4+x_4^2-x_1*x_5+x_2*x_5-x_3*x_5+x_4*x_5, 2*x_1*x_3+x_3^2+(3/4)*x_1*x_4-(21/4)*x_2*x_4+3*x_3*x_4-(9/4)*x_4^2+(15/4)*x_1*x_5-(17/4)*x_2*x_5+(13/4)*x_3*x_5-(9/2)*x_4*x_5-3*x_5^2,
 -x_1*x_3-(1/4)*x_1*x_4+(7/4)*x_2*x_4-x_3*x_4+(3/4)*x_4^2-(5/4)*x_1*x_5+(3/4)*x_2*x_5-(3/4)*x_3*x_5+(3/2)*x_4*x_5+x_5^2,
 x_0*x_1-x_1^2-x_1*x_3-x_1*x_4+x_2*x_4-x_3*x_4-x_1*x_5+x_2*x_5-x_3*x_5,
 x_0^3-2*x_0^2*x_1+2*x_0*x_1^2+x_1^2*x_3+x_1*x_3^2+x_3^2*x_4+3*x_2*x_4^2-2*x_3*x_4^2+x_4^3+2*x_0^2*x_5-x_1^2*x_5+x_3^2*x_5-(15/4)*x_1*x_4*x_5+(21/4)*x_2*x_4*x_5-5*x_3*x_4*x_5+(1/4)*x_4^2*x_5+3*x_0*x_5^2-(11/4)*x_1*x_5^2+(21/4)*x_2*x_5^2-(17/4)*x_3*x_5^2-(3/2)*x_4*x_5^2-x_5^3}


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Graph106

Edges = {{0,1}, {1,4}, {4,0}, {4,2}, {2,3}, {3,1}, {3,8}, {8,9}, {9,2}, {9,7}, {7,5}, {5,8}, {5,6}, {6,7}, {0,6}};
EdgePairing = {{1,2}, {0,2}, {0,1}, {1,4}, {3,5}, {1,4}, {4,7}, {6,8}, {4,7}, {7,10}, {9,11}, {7,10}, {10,13}, {10,12}, {0,12}};


Generators of graph curve ideal:
{x_2*x_3-x_3^2+x_2*x_4-x_3*x_4-x_3*x_5-x_4*x_5,
 x_1*x_3+x_1*x_4,
 x_0*x_3+x_0*x_4,
 x_2^2-x_3^2+2*x_2*x_4-2*x_3*x_4-x_2*x_5-x_3*x_5-2*x_4*x_5,
 x_0*x_2+x_0*x_4-x_0*x_5,
 x_0*x_1+x_1*x_2+x_1*x_4,
 x_0*x_4^2+x_2*x_4^2-x_3*x_4^2-x_0*x_4*x_5-x_2*x_4*x_5-x_4^2*x_5+x_3*x_5^2+x_4*x_5^2,
 x_1*x_2*x_4+x_1*x_4^2+x_2*x_4^2-x_3*x_4^2-x_1*x_2*x_5-x_1*x_4*x_5-x_2*x_4*x_5-x_4^2*x_5+x_3*x_5^2+x_4*x_5^2,
 x_1^2*x_2-x_1*x_4^2+x_1*x_4*x_5}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, x_3*x_4^2+x_4^3-2*x_3*x_4*x_5-2*x_4^2*x_5+x_3*x_5^2+x_4*x_5^2, x_3*x_4^2+x_4^3-2*x_3*x_4*x_5-2*x_4^2*x_5+x_3*x_5^2+x_4*x_5^2, 0},
        {0, 0, 0, 0, 0, 0, x_3*x_5^2+x_4*x_5^2, x_3*x_5^2+x_4*x_5^2, 0},
        {0, 0, 0, 0, 0, 0, x_3^3+x_3^2*x_4, x_3^3+x_3^2*x_4, 0},
        {0, 0, -x_0*x_4-x_2*x_4+x_3*x_4+x_3*x_5+x_4*x_5, 0, -x_0*x_4-x_2*x_4+x_3*x_4+x_3*x_5+x_4*x_5, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, x_0^3+2*x_0^2*x_5+x_0*x_5^2, x_0^2*x_5+x_0*x_5^2, 0},
        {0, 0, x_0*x_4+x_2*x_4-x_3*x_4-x_0*x_5-x_2*x_5+x_3*x_5, 0, x_0*x_4+x_2*x_4-x_3*x_4-x_0*x_5-x_2*x_5+x_3*x_5, 0, -x_0*x_4*x_5-x_2*x_4*x_5+2*x_3*x_4*x_5+x_4^2*x_5+x_0*x_5^2+x_2*x_5^2-2*x_3*x_5^2-x_4*x_5^2, 0, 0},
        {0, 0, 0, 0, 0, -x_0*x_4+x_0*x_5, -x_2*x_4^2+x_3*x_4^2-x_0*x_4*x_5+x_2*x_4*x_5+x_4^2*x_5+x_0*x_5^2-x_3*x_5^2-x_4*x_5^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, -x_1*x_2*x_5-x_1*x_4*x_5, x_1^2*x_4+x_1*x_4^2-x_1*x_4*x_5},
        {0, 0, 0, 0, 0, -x_1*x_2+x_0*x_4-x_1*x_4, 0, 0, 0},
        {0, 0, 0, -x_1^2-x_1*x_2-2*x_1*x_4+x_1*x_5, x_1^2+x_1*x_2+2*x_1*x_4-x_1*x_5, 0, 0, -x_1^3-3*x_1^2*x_4-2*x_1*x_4^2+x_2*x_4^2-x_3*x_4^2+x_1^2*x_5-x_1*x_2*x_5+x_1*x_4*x_5-x_2*x_4*x_5-x_4^2*x_5+x_3*x_5^2+x_4*x_5^2, x_1^3+2*x_1^2*x_4+x_1*x_4^2-x_1^2*x_5-x_1*x_4*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, x_1^2*x_4+x_1*x_4^2-x_1^2*x_5-x_1*x_4*x_5},
        {0, 0, 0, -x_1*x_2, x_1*x_2, 0, 0, -x_1*x_4^2-x_2*x_4^2+x_3*x_4^2+x_1*x_4*x_5+x_2*x_4*x_5+x_4^2*x_5-x_3*x_5^2-x_4*x_5^2, x_1*x_4^2-x_1*x_4*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, x_2*x_4^2-x_3*x_4^2-x_4^2*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, x_1^2*x_4+x_1*x_4^2-x_2*x_4^2+x_3*x_4^2-x_1^2*x_5-3*x_1*x_4*x_5+2*x_3*x_4*x_5+x_4^2*x_5+2*x_1*x_5^2+x_2*x_5^2-3*x_3*x_5^2-x_5^3},
        {-x_1*x_2-x_3*x_4+x_3*x_5, 0, 0, -2*x_1*x_2-2*x_3*x_4+2*x_3*x_5, 0, 0, x_1*x_4^2+x_2*x_4^2-2*x_3*x_4^2-x_1*x_4*x_5-x_2*x_4*x_5+2*x_3*x_4*x_5-x_4^2*x_5+x_4*x_5^2, x_1*x_4^2+x_2*x_4^2-2*x_3*x_4^2-x_1*x_4*x_5-x_2*x_4*x_5+2*x_3*x_4*x_5-x_4^2*x_5+x_4*x_5^2, 0}}


Sum of tangent vectors:
{-x_1*x_2-x_3*x_4+x_3*x_5,
 0,
 -x_0*x_5-x_2*x_5+2*x_3*x_5+x_4*x_5,
 -x_1^2-4*x_1*x_2-2*x_1*x_4-2*x_3*x_4+x_1*x_5+2*x_3*x_5,
 x_1^2+2*x_1*x_2+2*x_1*x_4-x_0*x_5-x_1*x_5-x_2*x_5+2*x_3*x_5+x_4*x_5,
 -x_1*x_2-x_1*x_4+x_0*x_5,
 x_0^3+x_3^3+x_3^2*x_4+x_1*x_4^2+x_4^3+2*x_0^2*x_5-2*x_0*x_4*x_5-x_1*x_4*x_5-x_2*x_4*x_5+2*x_3*x_4*x_5-x_4^2*x_5+3*x_0*x_5^2+x_2*x_5^2-x_3*x_5^2+x_4*x_5^2,
 -x_1^3+x_3^3-3*x_1^2*x_4+x_3^2*x_4-2*x_1*x_4^2+x_2*x_4^2-x_3*x_4^2+x_4^3+x_0^2*x_5+x_1^2*x_5-2*x_1*x_2*x_5-x_2*x_4*x_5-3*x_4^2*x_5+x_0*x_5^2+2*x_3*x_5^2+3*x_4*x_5^2,
 x_1^3+5*x_1^2*x_4+5*x_1*x_4^2-3*x_1^2*x_5-7*x_1*x_4*x_5+2*x_3*x_4*x_5+2*x_1*x_5^2+x_2*x_5^2-3*x_3*x_5^2-x_5^3}


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--------------------------------------------------------------------------------

Graph107

Edges = {{0,1}, {1,2}, {2,3}, {3,4}, {4,5}, {5,0}, {3,6}, {6,7}, {7,8}, {8,2}, {0,9}, {5,9}, {7,9}, {1,8}, {4,6}};
EdgePairing = {{1,5}, {0,2}, {1,3}, {2,4}, {3,5}, {0,4}, {3,14}, {6,8}, {7,9}, {2,8}, {5,11}, {5,10}, {8,10}, {0,8}, {4,7}};


Generators of graph curve ideal:
{x_2*x_5+x_3*x_5,
 x_3*x_4,
 x_2*x_4,
 x_0*x_4-x_1*x_4-x_4^2-x_4*x_5,
 x_0*x_2-x_1*x_2+x_0*x_3-x_1*x_3,
 x_0*x_1-x_1^2+x_0*x_3-x_1*x_3-x_1*x_4-x_1*x_5-x_3*x_5,
 x_0*x_3*x_5,
 x_1^2*x_5+x_1*x_3*x_5+x_1*x_4*x_5+x_1*x_5^2+x_3*x_5^2,
 x_1^2*x_2+x_1*x_2*x_3-x_1*x_3*x_5-x_3^2*x_5}


Tangent vectors:
matrix {{0, x_1^2+x_1*x_3+x_1*x_4+x_1*x_5+x_3*x_5, 0, 0, x_1^2+x_1*x_3+x_1*x_4+x_1*x_5+x_3*x_5, x_1^2+x_1*x_3+x_1*x_4+x_1*x_5+x_3*x_5, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, -x_1^2*x_4-2*x_1*x_4^2-x_4^3-2*x_1*x_4*x_5-2*x_4^2*x_5-x_4*x_5^2, 0},
        {0, 0, 0, -x_0*x_5, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, x_0^3-x_1^3+x_0^2*x_3-x_1^2*x_3-3*x_1^2*x_4-3*x_1*x_4^2-x_4^3-x_0^2*x_5-2*x_1*x_4*x_5-2*x_4^2*x_5+x_1*x_5^2+x_3*x_5^2-x_4*x_5^2, 0, 0},
        {0, 0, 0, 0, x_1*x_2-x_0*x_3+x_1*x_3, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, x_1^2*x_3-x_1*x_2*x_3+x_1*x_3*x_5+x_3^2*x_5},
        {0, 0, 0, 0, 0, 0, x_0*x_5^2-x_1*x_5^2-x_4*x_5^2-x_5^3, 0, 0},
        {0, 0, 0, 0, 0, -x_3*x_5, 0, x_3*x_5^2, -x_3^2*x_5},
        {0, -x_1*x_5-x_3*x_5, x_1*x_5+x_3*x_5, 0, 0, -x_1*x_5-x_3*x_5, 0, x_1*x_5^2+x_3*x_5^2, -x_1*x_3*x_5-x_3^2*x_5+x_1*x_4*x_5+x_1*x_5^2+x_3*x_5^2},
        {0, 0, 0, 0, 0, 0, 0, -x_4*x_5^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, x_1^2*x_3+x_1*x_2*x_3+2*x_1*x_3^2+x_2*x_3^2+x_3^3+x_1*x_3*x_5+x_3^2*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, x_2^3+x_2^2*x_3},
        {-x_1*x_2-x_2*x_3, 0, 0, 0, -x_1*x_2-x_2*x_3, 0, 0, 0, x_1*x_2*x_3+x_2*x_3^2+x_1*x_3*x_5+x_3^2*x_5},
        {0, 0, 0, 0, 0, 0, 0, -x_1^2*x_4, 0},
        {0, 0, 0, 0, 0, 0, x_0*x_3^2-x_1*x_3^2-x_3^2*x_5, 0, 0}}


Sum of tangent vectors:
{-x_1*x_2-x_2*x_3,
 x_1^2+x_1*x_3+x_1*x_4,
 x_1*x_5+x_3*x_5,
 -x_0*x_5,
 x_1^2-x_0*x_3+2*x_1*x_3-x_2*x_3+x_1*x_4+x_1*x_5+x_3*x_5,
 x_1^2+x_1*x_3+x_1*x_4-x_3*x_5,
 x_0^3-x_1^3+x_0^2*x_3-x_1^2*x_3+x_0*x_3^2-x_1*x_3^2-3*x_1^2*x_4-3*x_1*x_4^2-x_4^3-x_0^2*x_5-x_3^2*x_5-2*x_1*x_4*x_5-2*x_4^2*x_5+x_0*x_5^2+x_3*x_5^2-2*x_4*x_5^2-x_5^3,
 -2*x_1^2*x_4-2*x_1*x_4^2-x_4^3-2*x_1*x_4*x_5-2*x_4^2*x_5+x_1*x_5^2+2*x_3*x_5^2-2*x_4*x_5^2,
 x_2^3+2*x_1^2*x_3+x_1*x_2*x_3+x_2^2*x_3+2*x_1*x_3^2+2*x_2*x_3^2+x_3^3+2*x_1*x_3*x_5+x_3^2*x_5+x_1*x_4*x_5+x_1*x_5^2+x_3*x_5^2}


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Graph1013

Edges = {{0,1}, {1,2}, {2,3}, {3,4}, {4,0}, {5,6}, {6,7}, {7,8}, {8,9}, {9,5}, {0,5}, {1,6}, {2,7}, {3,8}, {4,9}};
EdgePairing = {{1,4}, {0,2}, {1,3}, {2,4}, {0,3}, {6,9}, {5,7}, {6,8}, {7,9}, {5,8}, {0,5}, {0,5}, {2,7}, {2,7}, {3,8}};


Generators of graph curve ideal:
{x_3*x_5, x_2*x_5, x_2*x_4, x_1*x_4, x_1*x_3, x_0^2+x_0*x_1+x_0*x_2+x_0*x_3+x_0*x_4+x_0*x_5}


Tangent vectors:
matrix {{0, x_0*x_1, 0, 0, 0, 0},
        {0, 0, 0, 0, x_0*x_2, 0},
        {0, 0, x_0*x_3, 0, 0, 0},
        {x_0*x_4, 0, 0, 0, 0, 0},
        {0, 0, 0, x_0*x_5, 0, 0},
        {0, -x_0*x_1-x_1^2-x_1*x_2-x_1*x_5, 0, 0, 0, 0},
        {0, 0, 0, 0, -x_0*x_2-x_1*x_2-x_2^2-x_2*x_3, 0},
        {0, 0, -x_0*x_3-x_2*x_3-x_3^2-x_3*x_4, 0, 0, 0},
        {-x_0*x_4-x_3*x_4-x_4^2-x_4*x_5, 0, 0, 0, 0, 0},
        {0, 0, 0, -x_0*x_5-x_1*x_5-x_4*x_5-x_5^2, 0, 0},
        {0, 0, 0, 0, 0, -x_1*x_5},
        {0, 0, 0, 0, 0, -x_1*x_2},
        {0, 0, 0, 0, 0, -x_2*x_3},
        {0, 0, 0, 0, 0, -x_3*x_4},
        {0, 0, 0, 0, 0, -x_4*x_5}}


Sum of tangent vectors:
{-x_3*x_4-x_4^2-x_4*x_5,
 -x_1^2-x_1*x_2-x_1*x_5,
 -x_2*x_3-x_3^2-x_3*x_4,
 -x_1*x_5-x_4*x_5-x_5^2,
 -x_1*x_2-x_2^2-x_2*x_3,
 -x_1*x_2-x_2*x_3-x_3*x_4-x_1*x_5-x_4*x_5}


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Graph121

Edges = {{0,1},{1,2},{2,0},{2,3},{3,4},{4,1},{4,5},{5,6},{6,3},{6,7},{7,8},{8,5},{8,9},{9,10},{10,7},{10,11},{11,9},{0,11}};
EdgePairing = {{1,2},{0,2},{0,1},{1,4},{3,5},{1,4},{4,7},{6,8},{4,7},{7,10},{9,11},{7,10},{10,13},{12,14},{10,13},{13,16},{13,15},{0,16}};


Generators of graph curve ideal:
{x_4*x_6+x_5*x_6,
 x_0*x_6,
 x_3*x_4-x_4^2+x_3*x_5-x_4*x_5,
 x_2*x_4+x_2*x_5,
 x_1*x_4+x_1*x_5, x_3^2-x_4^2+2*x_3*x_5-2*x_4*x_5-x_3*x_6-x_5*x_6,
 x_1*x_3+x_1*x_5-x_1*x_6,
 x_0*x_3-x_0*x_4,
 x_1*x_2+x_1*x_6,
 x_0*x_2,
 x_2*x_3*x_5+x_2*x_5^2-x_3*x_5^2+x_4*x_5^2-x_2*x_3*x_6+x_1*x_5*x_6-x_2*x_5*x_6+2*x_3*x_5*x_6+2*x_5^2*x_6-x_1*x_6^2-x_3*x_6^2-x_5*x_6^2,
 x_2^2*x_5-x_2*x_5^2+x_3*x_5^2-x_4*x_5^2-x_2^2*x_6-2*x_1*x_5*x_6+x_2*x_5*x_6-2*x_3*x_5*x_6-2*x_5^2*x_6+2*x_1*x_6^2+x_3*x_6^2+x_5*x_6^2,
 x_0*x_1^2-x_0*x_1*x_5-x_1^2*x_5+x_1*x_5^2+x_1^2*x_6-x_1*x_5*x_6,
 x_0^2*x_1+x_0^2*x_4-x_0*x_1*x_5-x_0*x_4*x_5}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_4^3+x_4^2*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0^2*x_4+x_0^2*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0^2*x_4+x_0^2*x_5-2*x_0*x_4*x_5-2*x_0*x_5^2+x_4*x_5^2+x_5^3},
        {0, 0, 0, 0, -x_0^2+x_0*x_5, 0, -x_0^2+x_0*x_5, 0, 0, 0, 0, 0, x_0^3-2*x_0^2*x_5+x_0*x_5^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0*x_1*x_5+x_1^2*x_5-x_1*x_5^2-x_1^2*x_6+x_1*x_5*x_6, -x_0^2*x_4+x_0*x_1*x_5+x_0*x_4*x_5},
        {0, 0, 0, 0, x_0*x_1+x_0*x_4, 0, x_0*x_1+x_0*x_4, 0, 0, 0, 0, 0, 0, 0},
        {0, -x_1^2+x_1*x_5, 0, 0, 0, 0, 0, -x_1^2+x_1*x_5, 0, x_1^2-x_1*x_5, -x_1^3+2*x_1^2*x_5-x_1*x_5^2, 2*x_1^3-4*x_1^2*x_5+2*x_1*x_5^2, 0, x_1^3-2*x_1^2*x_5+x_1*x_5^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_1*x_6^2, 2*x_1*x_6^2, x_1^2*x_6, 0},
        {0, x_0*x_1-x_1*x_5+x_1*x_6, 0, 0, 0, 0, 0, x_0*x_1-x_1*x_5+x_1*x_6, 0, -x_0*x_1+x_1*x_5-x_1*x_6, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, x_3*x_5-x_4*x_5-x_3*x_6-x_5*x_6, 0, 0, -x_3*x_5^2+x_4*x_5^2+2*x_3*x_5*x_6+2*x_5^2*x_6-x_3*x_6^2-x_5*x_6^2, x_3*x_5^2-x_4*x_5^2-2*x_3*x_5*x_6-2*x_5^2*x_6+x_3*x_6^2+x_5*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3*x_6-x_2*x_5*x_6-x_3*x_6^2-x_5*x_6^2, -x_2^2*x_3-x_2*x_5^2+x_3*x_5^2-x_4*x_5^2-x_2^2*x_6-2*x_1*x_5*x_6+x_2*x_5*x_6-2*x_3*x_5*x_6-2*x_5^2*x_6+2*x_1*x_6^2+2*x_3*x_6^2+2*x_5*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, x_2*x_3+x_2*x_5-x_3*x_5+x_4*x_5+x_1*x_6+x_3*x_6+x_5*x_6, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, x_2^2+2*x_2*x_3+x_2*x_5-x_3*x_5+x_4*x_5+x_3*x_6+x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_2^2*x_3+x_2*x_5^2-x_3*x_5^2+x_4*x_5^2+2*x_1*x_5*x_6-x_2*x_5*x_6+2*x_3*x_5*x_6+2*x_5^2*x_6-2*x_1*x_6^2-x_3*x_6^2-x_5*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, x_2*x_5+x_3*x_5-x_4*x_5-x_2*x_6-x_3*x_6-x_5*x_6, 0, 0, 0, 0, -x_2*x_5^2-x_3*x_5^2+x_4*x_5^2+2*x_2*x_5*x_6+2*x_3*x_5*x_6+2*x_5^2*x_6-x_2*x_6^2-x_3*x_6^2-x_5*x_6^2, x_2*x_5^2+x_3*x_5^2-x_4*x_5^2-2*x_2*x_5*x_6-2*x_3*x_5*x_6-2*x_5^2*x_6+x_2*x_6^2+x_3*x_6^2+x_5*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_3*x_5^2-x_4*x_5^2-2*x_3*x_5*x_6-3*x_5^2*x_6+x_3*x_6^2+3*x_5*x_6^2-x_6^3, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_2^2*x_3+x_2*x_5^2-2*x_3*x_5^2+2*x_4*x_5^2-2*x_2*x_3*x_6+4*x_1*x_5*x_6-x_2*x_5*x_6+6*x_3*x_5*x_6+5*x_5^2*x_6-4*x_1*x_6^2-3*x_3*x_6^2-3*x_5*x_6^2, 0, 0},
        {x_0*x_1+x_0*x_4-x_1*x_5-x_2*x_5-x_3*x_5+x_1*x_6+x_2*x_6+x_3*x_6, 0, 0, 0, 0, -x_0*x_1-x_0*x_4+x_1*x_5+x_2*x_5+x_3*x_5-x_1*x_6-x_2*x_6-x_3*x_6, 0, 0, 0, 0, 2*x_0*x_1*x_5+2*x_0*x_4*x_5-2*x_1*x_5^2-2*x_2*x_5^2-2*x_3*x_5^2+3*x_1*x_5*x_6+3*x_2*x_5*x_6+3*x_3*x_5*x_6-x_1*x_6^2-x_2*x_6^2-x_3*x_6^2, -2*x_0*x_1*x_5-2*x_0*x_4*x_5+2*x_1*x_5^2+2*x_2*x_5^2+2*x_3*x_5^2-3*x_1*x_5*x_6-3*x_2*x_5*x_6-3*x_3*x_5*x_6+x_1*x_6^2+x_2*x_6^2+x_3*x_6^2, 0, 0}}


Sum of tangent vectors:
{x_0*x_1+x_0*x_4-x_1*x_5-x_2*x_5-x_3*x_5+x_1*x_6+x_2*x_6+x_3*x_6,
 x_0*x_1-x_1^2+x_1*x_6,
 0,
 0,
 -x_0^2+x_0*x_1+x_0*x_4+x_0*x_5,
 -x_0*x_1+x_2^2+2*x_2*x_3-x_0*x_4+x_1*x_5+3*x_2*x_5+x_3*x_5-x_1*x_6-2*x_2*x_6-x_3*x_6,
 -x_0^2+x_0*x_1+x_0*x_4+x_0*x_5,
 x_0*x_1-x_1^2+x_1*x_6,
 x_2*x_3+x_2*x_5+x_1*x_6,
 -x_0*x_1+x_1^2-x_1*x_6,
 -x_1^3+2*x_0*x_1*x_5+2*x_1^2*x_5+2*x_0*x_4*x_5-3*x_1*x_5^2-3*x_2*x_5^2-3*x_3*x_5^2+x_4*x_5^2-x_2*x_3*x_6+3*x_1*x_5*x_6+4*x_2*x_5*x_6+5*x_3*x_5*x_6+2*x_5^2*x_6-2*x_1*x_6^2-2*x_2*x_6^2-3*x_3*x_6^2-2*x_5*x_6^2,
 2*x_1^3+x_2^2*x_3-2*x_0*x_1*x_5-4*x_1^2*x_5-2*x_0*x_4*x_5+4*x_1*x_5^2+4*x_2*x_5^2+x_3*x_5^2+x_4*x_5^2-x_2^2*x_6-2*x_2*x_3*x_6+x_1*x_5*x_6-6*x_2*x_5*x_6+x_3*x_5*x_6+2*x_5^2*x_6-x_1*x_6^2+2*x_2*x_6^2+x_5*x_6^2-x_6^3,
 x_0^3-2*x_0^2*x_5+x_0*x_1*x_5+x_1^2*x_5+x_0*x_5^2-x_1*x_5^2+x_3*x_5^2-x_4*x_5^2+x_1*x_5*x_6-2*x_3*x_5*x_6-2*x_5^2*x_6+x_3*x_6^2+x_5*x_6^2,
 x_1^3+x_0^2*x_4+x_4^3+2*x_0^2*x_5+x_0*x_1*x_5-2*x_1^2*x_5-x_0*x_4*x_5+x_4^2*x_5-2*x_0*x_5^2+x_1*x_5^2+x_4*x_5^2+x_5^3}


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Graph123

Edges = {{0,1},{1,2},{2,0},{2,3},{3,4},{4,1},{4,5},{5,6},{6,3},{6,7},{5,8},{7,9},{8,9},{8,10},{9,10},{10,11},{11,7},{0,11}};
EdgePairing = {{1,2},{0,2},{0,1},{1,4},{3,5},{1,4},{4,7},{6,8},{4,7},{7,11},{7,12},{9,12},{10,11},{12,14},{12,13},{14,16},{11,15},{2,16}};


Generators of graph curve ideal:
{x_4*x_6+x_5*x_6,
 x_0*x_6,
 x_3*x_4-x_4^2+x_3*x_5-x_4*x_5,
 x_2*x_4+x_2*x_5,
 x_1*x_4+x_1*x_5,
 x_2*x_3+x_3^2-x_4^2+x_3*x_5-x_4*x_5,
 x_1*x_3+x_1*x_5+x_1*x_6,
 x_0*x_3-x_0*x_4,
 x_1*x_2-x_1*x_6,
 x_0*x_2,
 x_3^2*x_5-x_4^2*x_5+x_3*x_5^2-x_4*x_5^2+x_3^2*x_6-x_1*x_5*x_6-x_2*x_5*x_6+x_3*x_5*x_6-x_1*x_6^2-x_2*x_6^2,
 x_3^3-x_4^3-x_3*x_5^2+x_4*x_5^2+2*x_1*x_5*x_6+x_2*x_5*x_6+2*x_1*x_6^2+x_2*x_6^2,
 x_0*x_1^2-x_0*x_1*x_5-x_1^2*x_5+x_1*x_5^2-x_1^2*x_6+x_1*x_5*x_6,
 x_0^2*x_1+x_0^2*x_4-x_0*x_1*x_5-x_0*x_4*x_5}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_4^3+x_4^2*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0^2*x_4+x_0^2*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0^2*x_4+x_0^2*x_5-2*x_0*x_4*x_5-2*x_0*x_5^2+x_4*x_5^2+x_5^3},
        {0, 0, 0, 0, -x_0^2+x_0*x_5, 0, -x_0^2+x_0*x_5, 0, 0, 0, 0, 0, x_0^3-2*x_0^2*x_5+x_0*x_5^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0*x_1*x_5+x_1^2*x_5-x_1*x_5^2+x_1^2*x_6-x_1*x_5*x_6, -x_0^2*x_4+x_0*x_1*x_5+x_0*x_4*x_5},
        {0, 0, 0, 0, x_0*x_1+x_0*x_4, 0, x_0*x_1+x_0*x_4, 0, 0, 0, 0, 0, 0, 0},
        {0, x_1^2-x_1*x_5, 0, 0, 0, 0, 0, -x_1^2+x_1*x_5, 0, x_1^2-x_1*x_5, -x_1^3+2*x_1^2*x_5-x_1*x_5^2, 2*x_1^3-4*x_1^2*x_5+2*x_1*x_5^2, 0, x_1^3-2*x_1^2*x_5+x_1*x_5^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_1*x_6^2, 2*x_1*x_6^2, -x_1^2*x_6, 0},
        {0, -x_0*x_1+x_1*x_5+x_1*x_6, 0, 0, 0, 0, 0, x_0*x_1-x_1*x_5-x_1*x_6, 0, -x_0*x_1+x_1*x_5+x_1*x_6, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, -x_3^2+x_4^2-x_3*x_5+x_4*x_5, 0, x_3^2-x_4^2+x_3*x_5-x_4*x_5, 0, x_1*x_5*x_6+x_2*x_5*x_6+x_1*x_6^2+x_2*x_6^2, -2*x_3^2*x_6-2*x_1*x_5*x_6-x_2*x_5*x_6-2*x_3*x_5*x_6-2*x_1*x_6^2-x_2*x_6^2, -x_1*x_5*x_6-x_2*x_5*x_6-x_1*x_6^2-x_2*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_3^2+x_4^2-x_3*x_5+x_4*x_5+x_1*x_6+x_2*x_6, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, x_3^2-x_4^2-x_2*x_5+x_3*x_5-x_4*x_5-x_2*x_6, 0, 0, 0, 0, -x_2*x_5^2+x_1*x_5*x_6-x_2*x_5*x_6+x_1*x_6^2, x_2*x_5^2-x_1*x_5*x_6+x_2*x_5*x_6-x_1*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2^3-x_2^2*x_5+2*x_3^2*x_6-x_2*x_5*x_6+2*x_3*x_5*x_6-x_2*x_6^2, x_2^3+x_2^2*x_5-2*x_3^2*x_6+x_2*x_5*x_6-2*x_3*x_5*x_6+x_2*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_6^2-x_3*x_6^2-x_5*x_6^2, x_2*x_6^2+x_3*x_6^2+x_5*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_5^2-x_3*x_5^2+x_4*x_5^2-2*x_2*x_5*x_6-2*x_3*x_5*x_6-2*x_5^2*x_6-x_2*x_6^2-x_3*x_6^2-x_5*x_6^2, x_2*x_5^2+x_3*x_5^2-x_4*x_5^2+2*x_2*x_5*x_6+2*x_3*x_5*x_6+2*x_5^2*x_6+x_2*x_6^2+x_3*x_6^2+x_5*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, x_3^2-x_4^2+x_3*x_5-x_4*x_5+2*x_3*x_6+x_5*x_6+x_6^2, 0, 0, 0, 0, x_1*x_5*x_6+x_2*x_5*x_6+2*x_3*x_5*x_6+x_5^2*x_6+x_1*x_6^2+x_2*x_6^2+2*x_3*x_6^2+2*x_5*x_6^2+x_6^3, 2*x_3^2*x_6-2*x_1*x_5*x_6-x_2*x_5*x_6-x_3*x_5*x_6-x_5^2*x_6-2*x_1*x_6^2-x_2*x_6^2+x_3*x_6^2-x_5*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_1*x_5*x_6+x_2*x_5*x_6+x_3*x_5*x_6+x_1*x_6^2+x_2*x_6^2+x_3*x_6^2, -2*x_1*x_5*x_6-x_2*x_5*x_6-2*x_3*x_5*x_6-2*x_1*x_6^2-x_2*x_6^2-x_3*x_6^2, 0, 0},
        {-x_0*x_1-x_3^2-x_0*x_4+x_4^2+x_1*x_5+x_4*x_5+x_1*x_6-x_3*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_4^2+x_0*x_1*x_5+x_4^2*x_5-x_1*x_5^2-x_3*x_5^2+x_4*x_5^2-x_3^2*x_6+x_2*x_5*x_6+x_1*x_6^2+x_2*x_6^2, 0, 0, 0}}


Sum of tangent vectors:
{-x_0*x_1-x_3^2-x_0*x_4+x_4^2+x_1*x_5+x_4*x_5+x_1*x_6-x_3*x_6,
 -x_0*x_1+x_1^2+x_1*x_6,
 0,
 0,
 -x_0^2+x_0*x_1+x_0*x_4+x_0*x_5,
 2*x_3^2-2*x_4^2-x_2*x_5+2*x_3*x_5-2*x_4*x_5-x_2*x_6+2*x_3*x_6+x_5*x_6+x_6^2,
 -x_0^2+x_0*x_1-x_3^2+x_0*x_4+x_4^2+x_0*x_5-x_3*x_5+x_4*x_5,
 x_0*x_1-x_1^2-x_1*x_6, x_1*x_6+x_2*x_6,
 -x_0*x_1+x_1^2+x_1*x_6,
 -x_1^3-x_2^3-x_0*x_4^2+x_0*x_1*x_5+2*x_1^2*x_5-x_2^2*x_5+x_4^2*x_5-2*x_1*x_5^2-2*x_2*x_5^2-2*x_3*x_5^2+2*x_4*x_5^2+x_3^2*x_6+4*x_1*x_5*x_6+3*x_3*x_5*x_6-x_5^2*x_6+4*x_1*x_6^2+x_2*x_6^2+x_3*x_6^2+x_6^3,
 2*x_1^3+x_2^3-4*x_1^2*x_5+x_2^2*x_5+2*x_1*x_5^2+2*x_2*x_5^2+x_3*x_5^2-x_4*x_5^2-2*x_3^2*x_6-7*x_1*x_5*x_6+x_2*x_5*x_6-5*x_3*x_5*x_6+x_5^2*x_6-5*x_1*x_6^2+2*x_3*x_6^2+x_5*x_6^2,
 x_0^3-2*x_0^2*x_5+x_0*x_1*x_5+x_1^2*x_5+x_0*x_5^2-x_1*x_5^2-2*x_1*x_5*x_6-x_2*x_5*x_6-x_1*x_6^2-x_2*x_6^2,
 x_1^3+x_0^2*x_4+x_4^3+2*x_0^2*x_5+x_0*x_1*x_5-2*x_1^2*x_5-x_0*x_4*x_5+x_4^2*x_5-2*x_0*x_5^2+x_1*x_5^2+x_4*x_5^2+x_5^3}


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Graph128

Edges = {{0,1},{1,2},{2,3},{3,4},{4,0},{4,5},{5,6},{6,3},{6,7},{7,5},{2,8},{8,9},{9,1},{9,10},{10,8},{0,11},{7,11},{10,11}};
EdgePairing = {{1,4},{0,2},{1,3},{2,4},{0,3},{4,9},{5,7},{3,6},{6,9},{6,8},{1,11},{10,12},{1,11},{11,14},{11,13},{0,17},{9,15},{13,15}};


Generators of graph curve ideal:
{x_4*x_5+x_4*x_6,
 x_2*x_5+x_3*x_5+x_2*x_6+x_3*x_6,
 x_2*x_4,
 x_1*x_4,
 x_0*x_4,
 x_1*x_3-x_1*x_6,
 x_0*x_3-x_0*x_6,
 x_1*x_2+x_1*x_6,
 x_0*x_2+x_0*x_6,
 x_0*x_1-x_1*x_6,
 x_3^2*x_5+x_2*x_3*x_6+x_3^2*x_6-x_3*x_5*x_6-x_2*x_6^2-x_3*x_6^2,
 x_3^2*x_4+2*x_3*x_4^2+x_4^3-x_2*x_3*x_6-x_3^2*x_6-3*x_3*x_4*x_6-2*x_4^2*x_6+x_2*x_6^2+x_3*x_6^2+x_4*x_6^2,
 x_1^3-2*x_1^2*x_5+x_1*x_5^2+x_3*x_5^2+x_0^2*x_6+2*x_1^2*x_6-2*x_0*x_5*x_6-3*x_1*x_5*x_6+x_3*x_5*x_6-x_0*x_6^2+x_1*x_6^2,
 x_0^3-2*x_0^2*x_5+x_0*x_5^2-x_3*x_5^2-2*x_0^2*x_6+3*x_0*x_5*x_6-x_3*x_5*x_6+x_0*x_6^2}


Tangent vectors:
matrix {{0, -x_2*x_3+x_2*x_6, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3^2+2*x_2*x_3*x_6-x_2*x_6^2, x_2*x_3^2-2*x_2*x_3*x_6+x_2*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2^3-x_2^2*x_3, x_2^3+2*x_2^2*x_3+x_2*x_3^2, 0, 0},
        {0, x_0^2-x_0*x_5+x_3*x_5-x_0*x_6+x_2*x_6+x_3*x_6, 0, 0, 0, 0, 0, 0, x_0^2-x_0*x_5+x_3*x_5-x_0*x_6+x_2*x_6+x_3*x_6, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0^2*x_6-x_0*x_6^2, 2*x_0^2*x_5-x_0*x_5^2+x_3*x_5^2-3*x_0*x_5*x_6+x_3*x_5*x_6},
        {0, 0, 0, 0, 0, 0, x_0^2-x_0*x_5+x_3*x_5-2*x_0*x_6+x_3*x_6, 0, -x_0^2+x_0*x_5-x_3*x_5+2*x_0*x_6-x_3*x_6, 0, x_0^2*x_6-x_2*x_3*x_6-x_0*x_5*x_6+x_3*x_5*x_6-2*x_0*x_6^2+x_2*x_6^2+x_3*x_6^2, 0, x_0^2*x_5-x_0*x_5^2+x_3*x_5^2+x_0^2*x_6-3*x_0*x_5*x_6+2*x_3*x_5*x_6-2*x_0*x_6^2+x_3*x_6^2, -x_0^2*x_5+x_0*x_5^2-x_3*x_5^2-x_0^2*x_6+3*x_0*x_5*x_6-2*x_3*x_5*x_6+2*x_0*x_6^2-x_3*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, x_0^2+x_1^2-x_0*x_5-x_1*x_5-x_0*x_6+x_1*x_6, 0, 0, x_0^2*x_5-x_0*x_5^2+x_3*x_5^2-x_0^2*x_6-x_1^2*x_6-x_0*x_5*x_6+x_1*x_5*x_6+x_3*x_5*x_6+x_0*x_6^2-x_1*x_6^2, x_1^2*x_5-x_1*x_5^2-x_3*x_5^2+x_0*x_5*x_6+x_1*x_5*x_6-x_3*x_5*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*x_1^2*x_5-x_1*x_5^2-x_3*x_5^2-x_0^2*x_6+2*x_0*x_5*x_6+3*x_1*x_5*x_6-x_3*x_5*x_6+x_0*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0^2-x_1^2+x_0*x_5+x_1*x_5-2*x_1*x_6, 0, 0, -x_0^2*x_5+x_0*x_5^2-x_3*x_5^2+2*x_0^2*x_6+3*x_1^2*x_6-x_0*x_5*x_6-3*x_1*x_5*x_6-x_3*x_5*x_6+x_0*x_6^2+6*x_1*x_6^2, -x_1^2*x_5+x_1*x_5^2+x_3*x_5^2+2*x_0^2*x_6+x_1^2*x_6-3*x_0*x_5*x_6-3*x_1*x_5*x_6+x_3*x_5*x_6-x_0*x_6^2+2*x_1*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_3*x_5^2-x_0^2*x_6+2*x_0*x_5*x_6+x_1*x_5*x_6-x_3*x_5*x_6+x_0*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_3*x_5^2-x_0^2*x_6-2*x_1^2*x_6+2*x_0*x_5*x_6+3*x_1*x_5*x_6-x_3*x_5*x_6+x_0*x_6^2-x_1*x_6^2, 0},
        {0, 0, x_3*x_4+x_4^2-x_2*x_6-x_3*x_6-x_4*x_6, 0, 0, 0, 0, 0, 0, 0, -x_3*x_4*x_6-x_4^2*x_6+x_2*x_6^2+x_3*x_6^2+x_4*x_6^2, x_3*x_4*x_6+x_4^2*x_6-x_2*x_6^2-x_3*x_6^2-x_4*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_2*x_3*x_6+x_3^2*x_6+3*x_3*x_4*x_6+2*x_4^2*x_6-x_2*x_6^2-x_3*x_6^2-x_4*x_6^2, 0, 0},
        {0, 0, -x_2*x_3-x_3^2-2*x_3*x_4-x_4^2+x_2*x_6+x_3*x_6+x_4*x_6, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3^2-x_3^3+3*x_3*x_4^2+2*x_4^3-3*x_3*x_4*x_6-3*x_4^2*x_6+x_2*x_6^2+x_3*x_6^2+x_4*x_6^2, x_2*x_3^2+x_3^3-3*x_3*x_4^2-2*x_4^3+3*x_3*x_4*x_6+3*x_4^2*x_6-x_2*x_6^2-x_3*x_6^2-x_4*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_2*x_3*x_6+x_3^2*x_6+x_3*x_4*x_6-x_2*x_6^2-x_3*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_4^3-2*x_4^2*x_6+x_4*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3*x_6-x_3*x_5*x_6+x_2*x_6^2-x_3*x_6^2+x_5*x_6^2+x_6^3, 0, x_3*x_5^2+2*x_3*x_5*x_6-x_5^2*x_6+x_3*x_6^2-2*x_5*x_6^2-x_6^3, -x_3*x_5^2-2*x_3*x_5*x_6+x_5^2*x_6-x_3*x_6^2+2*x_5*x_6^2+x_6^3},
        {0, 0, 0, 0, 0, -x_0^2-x_1^2+2*x_0*x_5+2*x_1*x_5-x_5^2+x_0*x_6-x_1*x_6-x_5*x_6, x_0^2+x_1^2-2*x_0*x_5-2*x_1*x_5+x_5^2-x_0*x_6+x_1*x_6+x_5*x_6, x_0^2+x_1^2-2*x_0*x_5-2*x_1*x_5+x_5^2-x_0*x_6+x_1*x_6+x_5*x_6, -x_0^2-x_1^2+2*x_0*x_5+2*x_1*x_5-x_5^2+x_0*x_6-x_1*x_6-x_5*x_6, -x_0^2-x_1^2+2*x_0*x_5+2*x_1*x_5-x_5^2+x_0*x_6-x_1*x_6-x_5*x_6, x_0^2*x_5+x_1^2*x_5-2*x_0*x_5^2-2*x_1*x_5^2+x_5^3-x_0*x_5*x_6+x_1*x_5*x_6+x_5^2*x_6, 0, -2*x_0^2*x_5-2*x_1^2*x_5+4*x_0*x_5^2+4*x_1*x_5^2-x_3*x_5^2-2*x_5^3+x_0^2*x_6+x_1^2*x_6-4*x_1*x_5*x_6-x_3*x_5*x_6-x_0*x_6^2+x_1*x_6^2+2*x_5*x_6^2, -2*x_0^2*x_5-2*x_1^2*x_5+4*x_0*x_5^2+4*x_1*x_5^2+x_3*x_5^2-2*x_5^3+2*x_0*x_5*x_6-2*x_1*x_5*x_6+x_3*x_5*x_6-3*x_5^2*x_6-x_5*x_6^2},
        {-x_3*x_4-x_4^2-x_3*x_5+2*x_4*x_6+x_5*x_6, x_3*x_4+x_4^2+x_3*x_5-2*x_4*x_6-x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0, -x_3*x_4^2-x_4^3+x_4^2*x_6-x_3*x_5*x_6+x_4*x_6^2+x_5*x_6^2, 0, x_3*x_5^2-x_3*x_4*x_6-x_4^2*x_6-x_5^2*x_6+2*x_4*x_6^2, -x_3*x_5^2+x_3*x_4*x_6+x_4^2*x_6+x_5^2*x_6-2*x_4*x_6^2}}


Sum of tangent vectors:
{-x_3*x_4-x_4^2-x_3*x_5+2*x_4*x_6+x_5*x_6,
 x_0^2-x_2*x_3+x_3*x_4+x_4^2-x_0*x_5+2*x_3*x_5-x_0*x_6+2*x_2*x_6+x_3*x_6-2*x_4*x_6-x_5*x_6,
 -x_2*x_3-x_3^2-x_3*x_4,
 0,
 0,
 -x_0^2-x_1^2+2*x_0*x_5+2*x_1*x_5-x_5^2+x_0*x_6-x_1*x_6-x_5*x_6,
 2*x_0^2+x_1^2-3*x_0*x_5-2*x_1*x_5+x_3*x_5+x_5^2-3*x_0*x_6+x_1*x_6+x_3*x_6+x_5*x_6,
 x_0^2+x_1^2-2*x_0*x_5-2*x_1*x_5+x_5^2-x_0*x_6+x_1*x_6+x_5*x_6,
 -x_0^2-x_1^2+2*x_0*x_5+2*x_1*x_5-x_5^2+2*x_0*x_6-x_1*x_6+x_2*x_6-x_5*x_6,
 -x_0^2-x_1^2+2*x_0*x_5+2*x_1*x_5-x_5^2-2*x_1*x_6-x_5*x_6,
 -x_2^3-x_2^2*x_3-2*x_2*x_3^2-x_3^3+2*x_3*x_4^2+x_4^3+x_0^2*x_5+x_1^2*x_5-2*x_0*x_5^2-2*x_1*x_5^2+x_5^3+x_0^2*x_6-4*x_3*x_4*x_6-3*x_4^2*x_6-2*x_0*x_5*x_6+x_1*x_5*x_6-x_3*x_5*x_6+x_5^2*x_6-2*x_0*x_6^2+3*x_2*x_6^2+2*x_3*x_6^2+3*x_4*x_6^2+2*x_5*x_6^2+x_6^3,
 x_2^3+2*x_2^2*x_3+3*x_2*x_3^2+x_3^3-3*x_3*x_4^2-x_4^3+2*x_3^2*x_6+8*x_3*x_4*x_6+4*x_4^2*x_6-3*x_2*x_6^2-4*x_3*x_6^2-2*x_4*x_6^2,
 -x_0^2*x_5+3*x_0*x_5^2+3*x_1*x_5^2-x_3*x_5^2-2*x_5^3+x_0^2*x_6+x_1^2*x_6-x_3*x_4*x_6-x_4^2*x_6+x_0*x_5*x_6+x_1*x_5*x_6-2*x_5^2*x_6+x_0*x_6^2+5*x_1*x_6^2+2*x_3*x_6^2+2*x_4*x_6^2-x_6^3,
 -x_0^2*x_5-2*x_1^2*x_5+4*x_0*x_5^2+4*x_1*x_5^2-x_3*x_5^2-2*x_5^3+x_0^2*x_6+x_1^2*x_6+x_3*x_4*x_6+x_4^2*x_6-4*x_1*x_5*x_6-2*x_3*x_5*x_6-x_5^2*x_6+x_0*x_6^2+2*x_1*x_6^2-2*x_3*x_6^2-2*x_4*x_6^2+x_5*x_6^2+x_6^3}


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Graph1212

Edges = {{0,1},{1,2},{2,3},{3,4},{4,5},{5,6},{6,0},{0,7},{7,1},{2,10},{10,8},{8,7},{3,10},{8,9},{9,11},{11,4},{5,11},{9,6}};
EdgePairing = {{7,8},{0,2},{1,3},{2,4},{3,5},{4,6},{0,5},{0,8},{0,7},{1,10},{9,11},{8,10},{2,9},{10,14},{13,15},{4,16},{4,15},{5,14}};


Generators of graph curve ideal:
{x_2*x_6,
 x_3*x_5,
 x_2*x_5,
 x_1*x_5-x_5^2+x_5*x_6,
 x_0*x_5,
 x_0*x_4,
 x_0*x_3+x_1*x_3+x_2*x_3-x_3^2-x_3*x_4+x_3*x_6,
 x_1*x_2+x_2^2-x_2*x_3-x_2*x_4,
 x_0*x_2,
 x_0^2+x_0*x_1+x_1*x_3+x_2*x_3-x_3^2-x_3*x_4+x_0*x_6+x_3*x_6,
 x_2*x_3*x_4-x_3^2*x_4-x_3*x_4^2+x_3*x_4*x_6,
 x_1^2*x_4-x_2^2*x_4+x_3^2*x_4-x_1*x_4^2+x_2*x_4^2+x_3*x_4^2-x_4*x_5^2-x_3*x_4*x_6+x_4*x_5*x_6,
 x_1*x_3^2+x_2*x_3^2-x_3^3-x_3^2*x_4-x_1*x_3*x_6+x_3^2*x_6,
 x_0*x_1^2+x_1^3+x_2^3-x_1^2*x_3-2*x_2^2*x_3+x_2*x_3^2-3*x_2^2*x_4+3*x_3^2*x_4-x_1*x_4^2+2*x_2*x_4^2+3*x_3*x_4^2-x_5^3+x_1^2*x_6-x_1*x_4*x_6-3*x_3*x_4*x_6+2*x_5^2*x_6-x_5*x_6^2}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2^3+2*x_2^2*x_3-x_2*x_3^2+2*x_2^2*x_4-2*x_3^2*x_4-x_2*x_4^2-2*x_3*x_4^2+2*x_3*x_4*x_6, 2*x_2^3-4*x_2^2*x_3+2*x_2*x_3^2-4*x_2^2*x_4+4*x_3^2*x_4+2*x_2*x_4^2+4*x_3*x_4^2-4*x_3*x_4*x_6, 0, 4*x_2^3-8*x_2^2*x_3+4*x_2*x_3^2-8*x_2^2*x_4+8*x_3^2*x_4+4*x_2*x_4^2+8*x_3*x_4^2-8*x_3*x_4*x_6},
        {x_2*x_3-x_3^2-x_3*x_4+x_3*x_6, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3+x_3^2+x_3*x_4-x_3*x_6, x_2*x_3-x_3^2-x_3*x_4+x_3*x_6, 0, 0, x_2*x_3^2-x_3^3-x_3^2*x_4+x_3^2*x_6, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_1*x_3*x_6+2*x_3^2*x_6+2*x_3*x_4*x_6-x_0*x_6^2-2*x_3*x_6^2, 0},
        {0, 0, 0, x_0*x_1+x_1^2-x_2^2+2*x_2*x_3-x_3^2-x_1*x_4+x_2*x_4-x_3*x_4-x_5^2+x_3*x_6+x_5*x_6, -x_0*x_1-x_1^2+x_2^2-2*x_2*x_3+x_3^2+x_1*x_4-x_2*x_4+x_3*x_4+x_5^2-x_3*x_6-x_5*x_6, 0, 0, 0, 0, -x_0*x_1-x_1^2+x_2^2-2*x_2*x_3+x_3^2+x_1*x_4-x_2*x_4+x_3*x_4+x_5^2-x_3*x_6-x_5*x_6, 0, 0, 0, x_1^2*x_3-x_2^2*x_3+2*x_2*x_3^2-x_3^3+x_3*x_4^2-2*x_4*x_5^2-x_0*x_1*x_6-2*x_1^2*x_6+2*x_3^2*x_6+2*x_1*x_4*x_6+2*x_4*x_5*x_6-x_3*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_5^3+2*x_5^2*x_6-x_5*x_6^2, 0, -x_5^3+2*x_5^2*x_6-x_5*x_6^2},
        {0, 0, 0, x_0*x_1+x_1^2-x_2^2-x_1*x_3+x_2*x_3-x_1*x_4+x_2*x_4-x_5^2+x_1*x_6+x_5*x_6, 0, 0, 0, 0, 0, 0, 0, x_1*x_4*x_6, 0, -3*x_4*x_5^2-x_0*x_1*x_6-x_1^2*x_6+x_1*x_3*x_6+3*x_1*x_4*x_6+3*x_4*x_5*x_6+x_5^2*x_6-x_1*x_6^2-x_5*x_6^2},
        {-x_0*x_1-x_1^2+x_2^2+x_1*x_3-x_2*x_3-x_2*x_4+x_5^2-x_1*x_6-x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_2^2*x_4-x_3^2*x_4+x_1*x_4^2-x_2*x_4^2-x_3*x_4^2+x_1*x_4*x_6+x_3*x_4*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_4^2, 2*x_2*x_4^2, 0, 4*x_2*x_4^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3^2, 2*x_2*x_3^2, 0, 4*x_2*x_3^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_1*x_3*x_6, 0},
        {0, 0, 0, 0, 0, x_1*x_3+x_2*x_3-x_3^2-x_3*x_4, 0, 0, 0, x_1*x_3+x_2*x_3-x_3^2-x_3*x_4, 0, -x_1^2*x_3+x_2^2*x_3-2*x_2*x_3^2+x_3^3-x_3*x_4^2+x_1*x_3*x_6-x_3^2*x_6, x_1*x_3*x_6-x_3^2*x_6, -x_1^2*x_3+x_2^2*x_3-2*x_2*x_3^2+x_3^3-x_3*x_4^2+2*x_1*x_3*x_6-2*x_3^2*x_6-x_3*x_4*x_6},
        {x_3*x_4, 0, 0, 0, 0, 0, 0, -x_3*x_4, 0, 0, 0, x_3*x_4^2, 0, x_3*x_4^2+x_3*x_4*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_1^3+x_2^3-3*x_1^2*x_3-3*x_2*x_3^2+2*x_3^3-3*x_2^2*x_4+3*x_3^2*x_4-x_1*x_4^2+2*x_2*x_4^2+x_3*x_4^2-x_5^3+x_1^2*x_6+x_1*x_3*x_6-2*x_3^2*x_6-x_1*x_4*x_6-x_3*x_4*x_6+2*x_5^2*x_6-x_5*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, -x_0*x_1-x_1^2+x_2^2+x_1*x_3-x_2*x_3+x_1*x_4-x_2*x_4-x_4*x_5+x_5^2-x_1*x_6+x_4*x_6-x_5*x_6, 0, 0, -x_0*x_1-x_1^2+x_2^2+x_1*x_3-x_2*x_3+x_1*x_4-x_2*x_4-x_4*x_5+x_5^2-x_1*x_6+x_4*x_6-x_5*x_6, -x_4^2*x_5-x_1*x_4*x_6+x_4^2*x_6, x_4^2*x_5+x_1*x_4*x_6-x_4^2*x_6, x_3*x_4*x_6, 3*x_4^2*x_5+3*x_1*x_4*x_6-3*x_4^2*x_6},
        {0, 0, 0, -x_0*x_1-x_1^2+x_2^2+x_1*x_3-x_2*x_3+2*x_1*x_4-x_3*x_4-x_4^2-2*x_4*x_5+x_5^2-x_1*x_6+x_4*x_6-x_5*x_6, 0, 0, 0, 0, 0, 0, 0, x_1*x_4^2+x_2*x_4^2-x_3*x_4^2-x_4^3-2*x_4^2*x_5-x_1*x_4*x_6+x_4^2*x_6, 0, -x_4^2*x_5+x_0*x_1*x_6+x_1^2*x_6-x_1*x_3*x_6-2*x_1*x_4*x_6+x_3*x_4*x_6+x_4^2*x_6+x_4*x_5*x_6-x_5^2*x_6+x_1*x_6^2-x_4*x_6^2+x_5*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_4^2*x_5-2*x_4*x_5*x_6-x_5*x_6^2, 0, -x_4^2*x_5-2*x_4*x_5*x_6-x_5*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_4^2*x_5, 0, -x_4^2*x_5},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_4^2*x_5+2*x_1*x_4*x_6-x_3*x_4*x_6-x_4^2*x_6-x_4*x_5*x_6+x_4*x_6^2, 0, x_4^2*x_5+2*x_0*x_1*x_6+2*x_1^2*x_6-2*x_1*x_3*x_6+x_1*x_4*x_6-x_3*x_4*x_6-x_4^2*x_6-2*x_5^2*x_6+x_0*x_6^2+3*x_1*x_6^2-x_3*x_6^2+x_5*x_6^2+x_6^3}}


Sum of tangent vectors:
{-x_0*x_1-x_1^2+x_2^2+x_1*x_3-x_3^2-x_2*x_4+x_5^2-x_1*x_6+x_3*x_6-x_5*x_6,
 0,
 0,
 x_0*x_1+x_1^2-x_2^2+2*x_2*x_3-x_3^2+2*x_2*x_4-2*x_3*x_4-x_4^2-2*x_4*x_5-x_5^2+x_3*x_6+x_4*x_6+x_5*x_6,
 -x_0*x_1-x_1^2+x_2^2-2*x_2*x_3+x_3^2+x_1*x_4-x_2*x_4+x_3*x_4+x_5^2-x_3*x_6-x_5*x_6,
 x_1*x_3+x_2*x_3-x_3^2-x_3*x_4,
 -x_0*x_1-x_1^2+x_2^2+x_1*x_3-x_2*x_3+x_1*x_4-x_2*x_4-x_4*x_5+x_5^2-x_1*x_6+x_4*x_6-x_5*x_6,
 -x_3*x_4,
 -x_2*x_3+x_3^2+x_3*x_4-x_3*x_6,
 -2*x_0*x_1-2*x_1^2+2*x_2^2+2*x_1*x_3-x_2*x_3-x_3^2+2*x_1*x_4-2*x_2*x_4-x_3*x_4-x_4*x_5+2*x_5^2-x_1*x_6+x_4*x_6-2*x_5*x_6,
 -x_2^3+2*x_2^2*x_3-2*x_2*x_3^2+2*x_2^2*x_4-2*x_3^2*x_4-2*x_2*x_4^2-2*x_3*x_4^2-x_4^2*x_5-x_1*x_4*x_6+2*x_3*x_4*x_6+x_4^2*x_6,
 2*x_2^3-x_1^2*x_3-3*x_2^2*x_3+2*x_2*x_3^2+x_3^3-4*x_2^2*x_4+4*x_3^2*x_4+x_1*x_4^2+5*x_2*x_4^2+3*x_3*x_4^2-x_4^3-2*x_4^2*x_5-x_5^3+x_1*x_3*x_6-x_3^2*x_6+3*x_1*x_4*x_6-5*x_3*x_4*x_6-x_4^2*x_6-3*x_4*x_5*x_6+2*x_5^2*x_6+x_4*x_6^2-2*x_5*x_6^2,
 x_1^3+x_2^3-3*x_1^2*x_3-2*x_2*x_3^2+x_3^3-3*x_2^2*x_4+2*x_3^2*x_4-x_1*x_4^2+2*x_2*x_4^2+x_3*x_4^2-x_5^3+x_1^2*x_6+2*x_1*x_3*x_6-x_1*x_4*x_6+2*x_3*x_4*x_6+2*x_5^2*x_6-x_0*x_6^2-2*x_3*x_6^2-x_5*x_6^2,
 4*x_2^3-8*x_2^2*x_3+8*x_2*x_3^2-7*x_2^2*x_4+7*x_3^2*x_4+x_1*x_4^2+7*x_2*x_4^2+8*x_3*x_4^2+x_4^2*x_5-5*x_4*x_5^2-x_5^3+x_0*x_1*x_6+8*x_1*x_4*x_6-7*x_3*x_4*x_6-3*x_4^2*x_6+4*x_4*x_5*x_6+x_0*x_6^2+3*x_1*x_6^2-2*x_3*x_6^2-x_4*x_6^2-x_5*x_6^2+x_6^3}


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Graph1214

Edges = {{0,1},{1,2},{2,0},{2,3},{3,4},{4,1},{4,5},{5,6},{6,7},{7,8},{8,3},{6,11},{11,10},{9,10},{9,7},{8,9},{11,5},{0,10}};
EdgePairing = {{1,2},{0,2},{0,1},{1,4},{3,5},{1,4},{4,7},{6,8},{7,9},{8,10},{4,9},{7,16},{16,17},{12,14},{8,13},{9,14},{7,11},{0,12}};


Generators of graph curve ideal:
{x_0*x_6,
 x_3*x_4+x_4*x_5,
 x_2*x_4,
 x_1*x_4,
 x_0*x_4,
 x_1*x_3-x_1*x_6,
 x_0*x_3,
 x_2^2-x_2*x_3+x_2*x_5+x_2*x_6,
 x_1*x_2,
 x_0*x_2,
 x_2*x_3*x_5-x_3^2*x_5-x_3*x_5^2-x_1*x_5*x_6-x_1*x_6^2,
 x_0*x_1*x_5-x_1^2*x_5-x_1*x_5^2-x_1^2*x_6-x_1*x_5*x_6,
 x_4^3-4*x_4^2*x_5+2*x_3*x_5^2+5*x_4*x_5^2+x_2*x_3*x_6-x_3^2*x_6-2*x_4^2*x_6+2*x_1*x_5*x_6+2*x_3*x_5*x_6+5*x_4*x_5*x_6+2*x_1*x_6^2+x_3*x_6^2+x_4*x_6^2,
 x_2*x_3^2-x_3^3+x_3^2*x_5+2*x_3*x_5^2+x_3^2*x_6+2*x_1*x_5*x_6+x_3*x_5*x_6+2*x_1*x_6^2}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_5^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_1^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0^3+2*x_0^2*x_1-x_0*x_1^2+2*x_0^2*x_5-2*x_1^2*x_5-x_0*x_5^2-2*x_1*x_5^2-2*x_1^2*x_6-2*x_1*x_5*x_6, 0, 0},
        {x_0*x_1-x_1^2-x_1*x_5, 0, 0, 0, 0, 0, x_0*x_1-x_1^2-x_1*x_5, 0, 0, 0, 0, -x_0*x_1^2+x_1^3+x_1^2*x_5, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_1*x_6^2, -x_1^2*x_6, 2*x_1*x_6^2, 2*x_1*x_6^2},
        {x_1*x_5+x_1*x_6, 0, 0, 0, 0, 0, x_1*x_5+x_1*x_6, 0, 0, 0, -x_1*x_5^2-2*x_1*x_5*x_6-x_1*x_6^2, -x_1^2*x_5-x_1^2*x_6, 2*x_1*x_5^2+4*x_1*x_5*x_6+2*x_1*x_6^2, 2*x_1*x_5^2+4*x_1*x_5*x_6+2*x_1*x_6^2},
        {0, 0, 0, 0, 0, x_2*x_3-x_3^2-x_3*x_5, 0, -x_2*x_3+x_3^2+x_3*x_5, x_2*x_3-x_3^2-x_3*x_5, 0, x_2*x_3*x_6-x_3^2*x_6+x_1*x_5*x_6-x_3*x_5*x_6+x_1*x_6^2, 0, -2*x_2*x_3*x_6+2*x_3^2*x_6-2*x_1*x_5*x_6+2*x_3*x_5*x_6-2*x_1*x_6^2, 2*x_3^2*x_5+2*x_3*x_5^2-2*x_2*x_3*x_6+3*x_3^2*x_6+3*x_3*x_5*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_3^3+x_3^2*x_5+2*x_3*x_5^2+x_3^2*x_6+2*x_1*x_5*x_6+x_3*x_5*x_6+2*x_1*x_6^2, 0, x_3^3-x_3^2*x_5-2*x_3*x_5^2-x_3^2*x_6-2*x_1*x_5*x_6-x_3*x_5*x_6-2*x_1*x_6^2, x_3^3-x_3^2*x_5-2*x_3*x_5^2-x_3^2*x_6-2*x_1*x_5*x_6-x_3*x_5*x_6-2*x_1*x_6^2},
        {0, -x_2*x_3+x_3^2+x_4^2-2*x_4*x_5-x_3*x_6-x_4*x_6, -x_2*x_3+x_3^2+x_4^2-2*x_4*x_5-x_3*x_6-x_4*x_6, 0, 0, 0, 0, -x_2*x_3+x_3^2+x_4^2-2*x_4*x_5-x_3*x_6-x_4*x_6, 0, 0, 0, 0, x_4^2*x_5-x_3*x_5^2-2*x_4*x_5^2-x_2*x_3*x_6+x_3^2*x_6+x_4^2*x_6-x_1*x_5*x_6-x_3*x_5*x_6-3*x_4*x_5*x_6-x_1*x_6^2-x_3*x_6^2-x_4*x_6^2, x_3^2*x_5-x_4^2*x_5+2*x_3*x_5^2+2*x_4*x_5^2+2*x_1*x_5*x_6+x_3*x_5*x_6+x_4*x_5*x_6+2*x_1*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*x_4^2*x_5-2*x_3*x_5^2-4*x_4*x_5^2-x_2*x_3*x_6+x_3^2*x_6+2*x_4^2*x_6-2*x_1*x_5*x_6-2*x_3*x_5*x_6-5*x_4*x_5*x_6-2*x_1*x_6^2-x_3*x_6^2-x_4*x_6^2, 0},
        {0, 0, 0, x_2*x_3-x_3^2-x_4^2+x_3*x_5+3*x_4*x_5+x_1*x_6+x_3*x_6+x_4*x_6, 0, -x_2*x_3+x_3^2+x_4^2-x_3*x_5-3*x_4*x_5-x_1*x_6-x_3*x_6-x_4*x_6, 0, 0, 0, 0, -x_2*x_3*x_6+x_3^2*x_6+x_4^2*x_6-x_3*x_5*x_6-3*x_4*x_5*x_6-x_1*x_6^2-x_3*x_6^2-x_4*x_6^2, x_4^2*x_5-2*x_3*x_5^2-3*x_4*x_5^2-x_1^2*x_6-3*x_1*x_5*x_6-x_3*x_5*x_6-x_4*x_5*x_6-x_1*x_6^2, 2*x_2*x_3*x_6-2*x_3^2*x_6-2*x_4^2*x_6+2*x_3*x_5*x_6+6*x_4*x_5*x_6+2*x_1*x_6^2+2*x_3*x_6^2+2*x_4*x_6^2, 2*x_2*x_3*x_6-2*x_3^2*x_6-2*x_4^2*x_6+2*x_3*x_5*x_6+6*x_4*x_5*x_6+2*x_1*x_6^2+2*x_3*x_6^2+2*x_4*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_5^2, 0, x_2*x_5^2, x_2*x_5^2},
        {0, 0, 0, 0, 0, 0, 0, -x_2*x_3+x_3^2-2*x_2*x_5+x_3*x_5-x_3*x_6-x_5*x_6, 0, 0, 0, 0, 0, 0},
        {0, x_2*x_3-x_3^2-x_4^2+x_3*x_5+3*x_4*x_5-x_2*x_6+2*x_3*x_6+2*x_4*x_6-x_5*x_6-x_6^2, 0, 0, 0, 0, 0, 0, 0, 0, -x_4^2*x_5+2*x_3*x_5^2+3*x_4*x_5^2+x_1*x_5*x_6-x_2*x_5*x_6+2*x_3*x_5*x_6+2*x_4*x_5*x_6-x_5^2*x_6+x_1*x_6^2-x_5*x_6^2, 0, -2*x_4^2*x_5+4*x_3*x_5^2+6*x_4*x_5^2+2*x_2*x_3*x_6-2*x_3^2*x_6-3*x_4^2*x_6+x_1*x_5*x_6-3*x_2*x_5*x_6+7*x_3*x_5*x_6+13*x_4*x_5*x_6-3*x_5^2*x_6+x_1*x_6^2-3*x_2*x_6^2+5*x_3*x_6^2+6*x_4*x_6^2-6*x_5*x_6^2-3*x_6^3, 3*x_4^2*x_5-6*x_3*x_5^2-9*x_4*x_5^2-2*x_2*x_3*x_6+2*x_3^2*x_6+x_4^2*x_6-4*x_1*x_5*x_6+2*x_2*x_5*x_6-7*x_3*x_5*x_6-9*x_4*x_5*x_6+2*x_5^2*x_6-4*x_1*x_6^2+x_2*x_6^2-3*x_3*x_6^2-2*x_4*x_6^2+3*x_5*x_6^2+x_6^3},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2*x_4^2*x_5-2*x_3*x_5^2-4*x_4*x_5^2-x_2*x_3*x_6+x_3^2*x_6-2*x_1*x_5*x_6-2*x_3*x_5*x_6-3*x_4*x_5*x_6-2*x_1*x_6^2-x_3*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*x_3*x_5^2-x_4*x_5^2-x_2*x_3*x_6+x_3^2*x_6-2*x_1*x_5*x_6-2*x_3*x_5*x_6-x_4*x_5*x_6-2*x_1*x_6^2-x_3*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4*x_2*x_5^2-4*x_2*x_5*x_6-x_2*x_6^2, 0, 4*x_2*x_5^2+4*x_2*x_5*x_6+x_2*x_6^2, 4*x_2*x_5^2+4*x_2*x_5*x_6+x_2*x_6^2},
        {x_2*x_3-x_3^2-x_0*x_5+x_1*x_5+x_2*x_5+x_5^2+x_1*x_6+x_3*x_6+x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}


Sum of tangent vectors:
{x_0*x_1-x_1^2+x_2*x_3-x_3^2-x_0*x_5+x_1*x_5+x_2*x_5+x_5^2+2*x_1*x_6+x_3*x_6+x_5*x_6,
 x_3*x_5+x_4*x_5-x_2*x_6+x_3*x_6+x_4*x_6-x_5*x_6-x_6^2,
 -x_2*x_3+x_3^2+x_4^2-2*x_4*x_5-x_3*x_6-x_4*x_6,
 x_2*x_3-x_3^2-x_4^2+x_3*x_5+3*x_4*x_5+x_1*x_6+x_3*x_6+x_4*x_6,
 0,
 x_4^2-2*x_3*x_5-3*x_4*x_5-x_1*x_6-x_3*x_6-x_4*x_6,
 x_0*x_1-x_1^2+x_1*x_6,
 -3*x_2*x_3+3*x_3^2+x_4^2-2*x_2*x_5+2*x_3*x_5-2*x_4*x_5-2*x_3*x_6-x_4*x_6-x_5*x_6,
 x_2*x_3-x_3^2-x_3*x_5,
 0,
 -x_3^3+x_3^2*x_5-x_4^2*x_5-x_1*x_5^2-5*x_2*x_5^2+4*x_3*x_5^2+3*x_4*x_5^2+x_3^2*x_6+x_4^2*x_6+2*x_1*x_5*x_6-5*x_2*x_5*x_6+x_3*x_5*x_6-x_4*x_5*x_6-x_5^2*x_6+x_1*x_6^2-x_2*x_6^2-x_3*x_6^2-x_4*x_6^2-x_5*x_6^2,
 -x_0^3+2*x_0^2*x_1-3*x_0*x_1^2+x_1^3+2*x_0^2*x_5-2*x_1^2*x_5+x_4^2*x_5-2*x_0*x_5^2-2*x_1*x_5^2-2*x_3*x_5^2-3*x_4*x_5^2-5*x_1^2*x_6-5*x_1*x_5*x_6-x_3*x_5*x_6-x_4*x_5*x_6-x_1*x_6^2,
 x_3^3-x_3^2*x_5+3*x_4^2*x_5+2*x_1*x_5^2+5*x_2*x_5^2-5*x_3*x_5^2-5*x_4*x_5^2-2*x_2*x_3*x_6+x_3^2*x_6-2*x_4^2*x_6-6*x_1*x_5*x_6+x_2*x_5*x_6+3*x_3*x_5*x_6+7*x_4*x_5*x_6-3*x_5^2*x_6-4*x_1*x_6^2-2*x_2*x_6^2+3*x_3*x_6^2+6*x_4*x_6^2-6*x_5*x_6^2-3*x_6^3,
 x_3^3+2*x_3^2*x_5+2*x_4^2*x_5+2*x_1*x_5^2+5*x_2*x_5^2-4*x_3*x_5^2-7*x_4*x_5^2-2*x_2*x_3*x_6+2*x_3^2*x_6-x_4^2*x_6+6*x_2*x_5*x_6-2*x_3*x_5*x_6-2*x_4*x_5*x_6+2*x_5^2*x_6+2*x_1*x_6^2+2*x_2*x_6^2-x_3*x_6^2+3*x_5*x_6^2+x_6^3}


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

Graph1215

Edges = {{0,1},{1,2},{2,3},{3,4},{4,0},{5,6},{6,7},{7,8},{8,5},{0,5},{1,6},{4,8},{7,9},{9,10},{10,11},{11,9},{10,2},{11,3}};
EdgePairing = {{1,4},{0,2},{1,3},{2,4},{0,3},{6,8},{5,7},{6,8},{5,7},{0,5},{0,5},{4,8},{6,13},{12,16},{13,15},{13,14},{1,13},{2,14}};


Generators of graph curve ideal:
{x_3*x_6-x_4*x_6,
 x_2*x_6+x_4*x_6,
 x_1*x_6,
 x_0*x_6,
 x_3*x_5-x_4*x_5,
 x_2*x_5+x_4*x_5,
 x_1*x_5,
 x_0*x_2-x_1*x_3+x_3^2+x_0*x_4+2*x_1*x_4+x_2*x_4-x_3*x_4+x_4^2,
 x_1^2-x_1*x_3,
 x_0*x_1+x_1*x_2-x_0*x_3-x_2*x_3+x_0*x_4+2*x_1*x_4+x_2*x_4-x_3*x_4+x_4^2,
 x_0*x_4*x_5+x_4^2*x_5+x_4*x_5^2-x_4*x_5*x_6,
 x_0^2*x_4-x_1*x_2*x_4-x_3^2*x_4+x_0*x_4^2-2*x_1*x_4^2+x_3*x_4^2-x_4^2*x_5-x_4*x_5^2+x_4*x_5*x_6}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 2*x_1*x_2+2*x_2^2+2*x_1*x_3-2*x_3^2-2*x_1*x_4+2*x_2*x_4+2*x_3*x_4, -x_1*x_2-x_2^2-x_1*x_3+x_3^2+x_1*x_4-x_2*x_4-x_3*x_4, x_1*x_2+x_2^2+x_1*x_3-x_3^2-x_1*x_4+x_2*x_4+x_3*x_4, 0, -x_2^3-2*x_1*x_2*x_3-2*x_2^2*x_3-2*x_1*x_3^2+x_2*x_3^2+2*x_3^3+x_1*x_2*x_4-2*x_2^2*x_4+x_1*x_3*x_4-3*x_2*x_3*x_4-x_3^2*x_4+x_1*x_4^2-x_2*x_4^2-x_3*x_4^2},
        {0, 0, 0, 0, 0, -x_0*x_4-x_1*x_4-x_2*x_4-x_4^2, 0, x_0*x_4+x_1*x_4+x_2*x_4+x_4^2, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_5^2, -x_0^2*x_5+x_0*x_5^2},
        {0, 0, 0, 0, x_0^2-x_1*x_2+x_0*x_3+x_1*x_3+x_2*x_3-x_3^2-3*x_1*x_4-x_2*x_4+2*x_3*x_4-x_4^2+x_0*x_5, 0, x_0^2-x_1*x_2+x_0*x_3+x_1*x_3+x_2*x_3-x_3^2-3*x_1*x_4-x_2*x_4+2*x_3*x_4-x_4^2+x_0*x_5, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, -x_0*x_3-x_1*x_3-x_2*x_3+x_0*x_4+x_1*x_4+x_2*x_4-x_3*x_4+x_4^2, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, -(1/2)*x_1*x_2-(1/2)*x_1*x_3+(1/2)*x_2*x_3+(1/2)*x_3^2+(1/2)*x_1*x_4-(1/2)*x_2*x_4-(1/2)*x_3*x_4, (1/4)*x_1*x_2+(1/4)*x_1*x_3-(1/4)*x_2*x_3-(1/4)*x_3^2-(1/4)*x_1*x_4+(1/4)*x_2*x_4+(1/4)*x_3*x_4, -(1/4)*x_1*x_2-(1/4)*x_1*x_3+(1/4)*x_2*x_3+(1/4)*x_3^2+(1/4)*x_1*x_4-(1/4)*x_2*x_4-(1/4)*x_3*x_4, 0, (3/4)*x_1*x_2*x_4+(3/4)*x_1*x_3*x_4-(3/4)*x_2*x_3*x_4-(3/4)*x_3^2*x_4-(3/4)*x_1*x_4^2+(3/4)*x_2*x_4^2+(3/4)*x_3*x_4^2},
        {0, 0, 0, 0, 0, 0, 0, -x_1*x_3+x_3^2+x_1*x_4-x_3*x_4, 0, 0, 0, x_1*x_3*x_4-x_3^2*x_4-x_1*x_4^2+x_3*x_4^2},
        {0, 0, 0, 0, 0, 0, 0, 8*x_1*x_2-8*x_1*x_3-8*x_2*x_3+8*x_3^2+24*x_1*x_4+8*x_2*x_4-16*x_3*x_4+8*x_4^2, -4*x_1*x_2+4*x_1*x_3+4*x_2*x_3-4*x_3^2-12*x_1*x_4-4*x_2*x_4+8*x_3*x_4-4*x_4^2, 4*x_1*x_2-4*x_1*x_3-4*x_2*x_3+4*x_3^2+12*x_1*x_4+4*x_2*x_4-8*x_3*x_4+4*x_4^2, 0, -12*x_1*x_2*x_4+12*x_1*x_3*x_4+12*x_2*x_3*x_4-12*x_3^2*x_4-36*x_1*x_4^2-12*x_2*x_4^2+24*x_3*x_4^2-12*x_4^3},
        {0, 0, 0, 0, 0, 0, 0, x_1*x_4, 0, 0, 0, -x_1*x_4^2},
        {0, 0, 0, 0, 0, 0, 0, -x_1*x_2, 0, -x_1*x_2, 0, x_1*x_2*x_3},
        {0, 0, 0, 0, 0, 0, 0, -x_1*x_2-x_1*x_3+x_2*x_3+x_3^2, 0, -x_1*x_2-x_1*x_3+x_2*x_3+x_3^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, x_1*x_2-x_0*x_3-x_2*x_3+x_0*x_4+2*x_1*x_4+x_2*x_4-x_3*x_4+x_4^2, 0, x_1*x_2-x_0*x_3-x_2*x_3+x_0*x_4+2*x_1*x_4+x_2*x_4-x_3*x_4+x_4^2, 0, -x_0^2*x_3-x_1*x_2*x_3+x_0*x_3^2-x_1*x_3^2+x_2*x_3^2+x_3^3-x_1*x_2*x_4+x_2*x_3*x_4-2*x_0*x_4^2-3*x_1*x_4^2-2*x_2*x_4^2+x_3*x_4^2-2*x_4^3+x_4^2*x_5+x_4*x_5^2-x_4*x_5*x_6},
        {x_1*x_2-x_1*x_3-x_2*x_3+x_3^2+x_0*x_4+2*x_1*x_4+x_2*x_4-x_3*x_4+x_4^2+x_4*x_5-x_4*x_6, -x_1*x_2+x_1*x_3+x_2*x_3-x_3^2-x_0*x_4-2*x_1*x_4-x_2*x_4+x_3*x_4-x_4^2-x_4*x_5+x_4*x_6, 0, x_1*x_2-x_1*x_3-x_2*x_3+x_3^2+x_0*x_4+2*x_1*x_4+x_2*x_4-x_3*x_4+x_4^2+x_4*x_5-x_4*x_6, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_4^2*x_6, -x_4^2*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_5^2*x_6, -x_5^2*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_4^2*x_6+2*x_4*x_5*x_6+x_5^2*x_6-2*x_4*x_6^2-2*x_5*x_6^2+x_6^3, -x_4^2*x_6-2*x_4*x_5*x_6-x_5^2*x_6+2*x_4*x_6^2+2*x_5*x_6^2-x_6^3},
        {0, 0, 0, -x_4*x_5, 0, 0, 0, 0, 0, 0, 0, -x_4^2*x_5},
        {0, 0, 0, x_0*x_5+x_4*x_5+x_5^2-x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0}}


Sum of tangent vectors:
{x_1*x_2-x_1*x_3-x_2*x_3+x_3^2+x_0*x_4+2*x_1*x_4+x_2*x_4-x_3*x_4+x_4^2+x_4*x_5-x_4*x_6,
 -x_1*x_2+x_1*x_3+x_2*x_3-x_3^2-x_0*x_4-2*x_1*x_4-x_2*x_4+x_3*x_4-x_4^2-x_4*x_5+x_4*x_6,
 0,
 x_1*x_2-x_1*x_3-x_2*x_3+x_3^2+x_0*x_4+2*x_1*x_4+x_2*x_4-x_3*x_4+x_4^2+x_0*x_5+x_4*x_5+x_5^2-x_4*x_6-x_5*x_6,
 x_0^2-x_1*x_2+x_0*x_3+x_1*x_3+x_2*x_3-x_3^2-3*x_1*x_4-x_2*x_4+2*x_3*x_4-x_4^2+x_0*x_5,
 -x_0*x_4-x_1*x_4-x_2*x_4-x_4^2,
 x_0^2-x_1*x_2+x_0*x_3+x_1*x_3+x_2*x_3-x_3^2-3*x_1*x_4-x_2*x_4+2*x_3*x_4-x_4^2+x_0*x_5,
 (17/2)*x_1*x_2+2*x_2^2-2*x_0*x_3-(19/2)*x_1*x_3-(17/2)*x_2*x_3+(17/2)*x_3^2+3*x_0*x_4+(57/2)*x_1*x_4+(25/2)*x_2*x_4-(35/2)*x_3*x_4+11*x_4^2,
 -(19/4)*x_1*x_2-x_2^2+(13/4)*x_1*x_3+(15/4)*x_2*x_3-(13/4)*x_3^2-(45/4)*x_1*x_4-(19/4)*x_2*x_4+(29/4)*x_3*x_4-4*x_4^2,
 (15/4)*x_1*x_2+x_2^2-x_0*x_3-(17/4)*x_1*x_3-(15/4)*x_2*x_3+(17/4)*x_3^2+x_0*x_4+(53/4)*x_1*x_4+(23/4)*x_2*x_4-(33/4)*x_3*x_4+5*x_4^2,
 -x_0*x_5^2+2*x_4^2*x_6+2*x_4*x_5*x_6+2*x_5^2*x_6-2*x_4*x_6^2-2*x_5*x_6^2+x_6^3,
 -x_2^3-x_0^2*x_3-2*x_1*x_2*x_3-2*x_2^2*x_3+x_0*x_3^2-3*x_1*x_3^2+2*x_2*x_3^2+3*x_3^3-(45/4)*x_1*x_2*x_4-2*x_2^2*x_4+(59/4)*x_1*x_3*x_4+(37/4)*x_2*x_3*x_4-(59/4)*x_3^2*x_4-2*x_0*x_4^2-(163/4)*x_1*x_4^2-(57/4)*x_2*x_4^2+(103/4)*x_3*x_4^2-14*x_4^3-x_0^2*x_5+x_0*x_5^2+x_4*x_5^2-2*x_4^2*x_6-3*x_4*x_5*x_6-2*x_5^2*x_6+2*x_4*x_6^2+2*x_5*x_6^2-x_6^3}


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

Graph1217

Edges = {{0,1},{1,2},{2,3},{3,4},{4,0},{4,5},{5,6},{6,7},{7,3},{1,8},{8,2},{8,9},{9,10},{7,10},{11,6},{10,11},{5,11},{0,9}};
EdgePairing = {{1,4},{0,2},{1,3},{2,4},{0,3},{3,6},{5,7},{6,8},{3,7},{1,10},{1,9},{9,17},{11,13},{8,12},{6,16},{13,14},{6,14},{0,11}};


Generators of graph curve ideal:
{x_2*x_6,
 x_0*x_6,
 x_3*x_5,
 x_2*x_5,
 x_1*x_5,
 x_0*x_5,
 x_2*x_4,
 x_1*x_4,
 x_0*x_4,
 x_0^2-x_0*x_1-x_0*x_2-x_0*x_3,
 x_1*x_3*x_6+x_3^2*x_6+x_3*x_4*x_6-x_3*x_6^2,
 x_4^2*x_5-2*x_4*x_5^2+x_5^3+x_3*x_4*x_6+x_4^2*x_6-3*x_4*x_5*x_6+2*x_5^2*x_6-x_4*x_6^2+x_5*x_6^2,
 x_1*x_2^2+x_2^3+x_1*x_2*x_3+x_2^2*x_3,
 x_0*x_1*x_2-x_1^2*x_2+x_0*x_2^2+x_2^3+x_0*x_1*x_3-x_1^2*x_3+x_0*x_2*x_3-x_1*x_2*x_3-x_1*x_3^2-x_2*x_3^2-x_3^2*x_6-x_3*x_4*x_6+x_3*x_6^2}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, x_1*x_2+x_2^2, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0*x_1^2+2*x_1^2*x_2-x_0*x_2^2-2*x_2^3-2*x_0*x_1*x_3+2*x_1^2*x_3-2*x_0*x_2*x_3+2*x_1*x_2*x_3+2*x_1*x_3^2+2*x_2*x_3^2+2*x_3^2*x_6+2*x_3*x_4*x_6-2*x_3*x_6^2, 2*x_0*x_1^2+4*x_1^2*x_2-2*x_0*x_2^2-4*x_2^3-4*x_0*x_1*x_3+4*x_1^2*x_3-4*x_0*x_2*x_3+4*x_1*x_2*x_3+4*x_1*x_3^2+4*x_2*x_3^2+4*x_3^2*x_6+4*x_3*x_4*x_6-4*x_3*x_6^2},
        {0, x_1*x_2+x_2^2+x_1*x_3+x_2*x_3, 0, 0, 0, 0, 0, 0, 0, -x_1*x_2-x_2^2-x_1*x_3-x_2*x_3, x_1*x_2*x_3+x_2^2*x_3+x_1*x_3^2+x_2*x_3^2, 0, 0, -x_1*x_2*x_3-x_2^2*x_3-x_1*x_3^2-x_2*x_3^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_1*x_6^2, 0, 0, -x_1^2*x_6-x_1*x_6^2},
        {x_0*x_1-x_1^2+x_0*x_2-2*x_1*x_2-x_2^2-x_1*x_3-x_2*x_3+x_1*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_1^2+x_1^3+x_1^2*x_2+x_0*x_2^2+x_1^2*x_3+x_1*x_2*x_3-2*x_1^2*x_6+x_3^2*x_6+x_3*x_4*x_6+x_1*x_6^2-x_3*x_6^2, 0, 0, x_0*x_1*x_3-x_1^2*x_3+x_0*x_2*x_3-2*x_1*x_2*x_3-x_2^2*x_3-x_1*x_3^2-x_2*x_3^2+x_1^2*x_6-2*x_3^2*x_6-2*x_3*x_4*x_6-x_1*x_6^2+2*x_3*x_6^2},
        {0, 0, 0, 0, x_4*x_5-x_5^2+x_1*x_6+x_3*x_6+x_4*x_6-2*x_5*x_6-x_6^2, 0, 0, x_4*x_5-x_5^2+x_1*x_6+x_3*x_6+x_4*x_6-2*x_5*x_6-x_6^2, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_5^3+2*x_5^2*x_6+x_5*x_6^2, 0, 0},
        {0, 0, -x_4*x_5+x_5^2-x_4*x_6+x_5*x_6, 0, 0, 0, 0, 0, 0, 0, -x_4*x_5*x_6+x_5^2*x_6-x_4*x_6^2+x_5*x_6^2, -x_3*x_4*x_6, 0, x_4*x_5*x_6-x_5^2*x_6+x_4*x_6^2-x_5*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, -x_3*x_6, 0, 0, 0, x_3*x_6^2, 0, -x_3^2*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0*x_2^2, 2*x_0*x_2^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0*x_2^2+2*x_0*x_2*x_3+x_0*x_3^2, 2*x_0*x_2^2+4*x_0*x_2*x_3+2*x_0*x_3^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, x_2^2+x_2*x_3, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, -x_0*x_2+x_1*x_2+x_2^2-x_0*x_3+x_1*x_3+2*x_2*x_3+x_3^2+x_3*x_4-x_3*x_6, x_0*x_2-x_1*x_2-x_2^2+x_0*x_3-x_1*x_3-2*x_2*x_3-x_3^2-x_3*x_4+x_3*x_6, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_3^2*x_4, x_3*x_4^2, 0, -x_3^2*x_4},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_3*x_4*x_6-x_4^2*x_6+3*x_4*x_5*x_6-2*x_5^2*x_6+x_4*x_6^2-x_5*x_6^2, 0, 0},
        {0, 0, -x_3*x_4-x_4^2+2*x_4*x_5-x_5^2+x_4*x_6-x_5*x_6, 0, 0, 0, 0, 0, 0, 0, x_3^2*x_4+2*x_3*x_4^2+x_4^3-3*x_4*x_5^2+2*x_5^3-3*x_4*x_5*x_6+3*x_5^2*x_6-x_4*x_6^2+x_5*x_6^2, x_3*x_4^2+x_4^3-3*x_4*x_5^2+2*x_5^3+2*x_3*x_4*x_6+x_4^2*x_6-5*x_4*x_5*x_6+4*x_5^2*x_6-2*x_4*x_6^2+2*x_5*x_6^2, 0, -x_3^2*x_4-2*x_3*x_4^2-x_4^3+3*x_4*x_5^2-2*x_5^3+3*x_4*x_5*x_6-3*x_5^2*x_6+x_4*x_6^2-x_5*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_3*x_4*x_6-x_4^2*x_6+x_4*x_5*x_6+x_4*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_2^2-x_1*x_2*x_3, -2*x_0*x_2^2-x_0*x_1*x_3+x_1^2*x_3-x_1*x_2*x_3+x_1*x_3^2+x_3^2*x_6+x_3*x_4*x_6-x_3*x_6^2}}

Sum of tangent vectors:
{x_0*x_1-x_1^2+x_0*x_2-2*x_1*x_2-x_2^2-x_1*x_3-x_2*x_3+x_1*x_6,
 x_1*x_2+x_2^2+x_1*x_3+x_2*x_3,
 -x_3*x_4-x_4^2+x_4*x_5,
 0,
 x_4*x_5-x_5^2+x_1*x_6+x_3*x_6+x_4*x_6-2*x_5*x_6-x_6^2,
 0,
 -x_0*x_2+x_1*x_2+x_2^2-x_0*x_3+x_1*x_3+2*x_2*x_3+x_3^2+x_3*x_4-x_3*x_6,
 x_0*x_2-x_1*x_2-x_2^2+x_0*x_3-x_1*x_3-2*x_2*x_3-x_3^2-x_3*x_4+x_4*x_5-x_5^2+x_1*x_6+x_3*x_6+x_4*x_6-2*x_5*x_6-x_6^2,
 0,
 x_2^2-x_1*x_3,
 -x_0*x_1^2+x_1^3+x_1^2*x_2+x_0*x_2^2+x_1^2*x_3+2*x_1*x_2*x_3+x_2^2*x_3+x_1*x_3^2+x_2*x_3^2+2*x_3^2*x_4+2*x_3*x_4^2+x_4^3-3*x_4*x_5^2+2*x_5^3-2*x_1^2*x_6+x_3^2*x_6+x_3*x_4*x_6-4*x_4*x_5*x_6+4*x_5^2*x_6+2*x_1*x_6^2-x_3*x_6^2-2*x_4*x_6^2+2*x_5*x_6^2,
 2*x_3*x_4^2+x_4^3-3*x_4*x_5^2+3*x_5^3-x_3*x_4*x_6-x_4^2*x_6-x_4*x_5*x_6+4*x_5^2*x_6+x_3*x_6^2+2*x_5*x_6^2,
 x_0*x_1^2+2*x_1^2*x_2-2*x_2^3-2*x_0*x_1*x_3+2*x_1^2*x_3+x_1*x_2*x_3+x_0*x_3^2+2*x_1*x_3^2+2*x_2*x_3^2+2*x_3^2*x_6+2*x_3*x_4*x_6-2*x_3*x_6^2,
 2*x_0*x_1^2+4*x_1^2*x_2-4*x_2^3-4*x_0*x_1*x_3+4*x_1^2*x_3+x_0*x_2*x_3-2*x_2^2*x_3+2*x_0*x_3^2+3*x_1*x_3^2+2*x_2*x_3^2-2*x_3^2*x_4-2*x_3*x_4^2-x_4^3+3*x_4*x_5^2-2*x_5^3+2*x_3^2*x_6+3*x_3*x_4*x_6+4*x_4*x_5*x_6-4*x_5^2*x_6-2*x_1*x_6^2-3*x_3*x_6^2+2*x_4*x_6^2-2*x_5*x_6^2}


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--------------------------------------------------------------------------------

Graph1218

Edges = {{0,1},{1,6},{6,0},{1,2},{2,3},{3,4},{4,5},{5,6},{4,11},{7,11},{3,7},{5,10},{8,2},{7,8},{8,9},{10,9},{10,11},{0,9}};
EdgePairing = {{1,2},{0,2},{0,1},{1,4},{3,5},{4,6},{5,7},{1,6},{5,9},{8,10},{5,9},{6,16},{4,13},{10,12},{13,15},{14,16},{9,15},{0,14}};


Generators of graph curve ideal:
{x_4*x_6+x_5*x_6,
 x_3*x_5-x_3*x_6+x_5*x_6-x_6^2,
 x_3*x_4+x_3*x_6-x_5*x_6+x_6^2,
 x_2*x_4+x_4^2+x_2*x_5+x_4*x_5,
 x_0*x_4+x_0*x_5,
 x_0*x_3+x_0*x_6,
 x_1*x_2-x_1*x_3-x_2*x_3+x_3^2+x_1*x_4+x_2*x_5+x_4*x_5-x_2*x_6+x_3*x_6+x_5*x_6,
 x_0*x_2-x_0*x_5-x_2*x_5-x_4*x_5+x_0*x_6+x_2*x_6-2*x_5*x_6+x_6^2,
 x_0*x_1+x_0*x_5,
 x_0^2-x_1*x_3-x_2*x_3-x_0*x_5+x_2*x_5+x_4*x_5+x_0*x_6-x_2*x_6+x_5*x_6,
 x_1^2*x_4+x_1*x_4*x_5+x_1^2*x_6+x_1*x_5*x_6}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_1^2*x_5+x_1*x_4*x_5+2*x_1*x_5^2+x_4*x_5^2+x_5^3-x_1^2*x_6-x_1*x_5*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_1^2*x_5-x_1*x_4*x_5-x_1^2*x_6-x_1*x_5*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_4^3+x_4^2*x_5},
        {x_1^2-x_3^2+x_1*x_5-x_3*x_6, x_1^2-x_3^2+x_1*x_5-x_3*x_6, -x_1^2+x_3^2-x_1*x_5+x_3*x_6, 0, 0, 0, x_1^2-x_3^2+x_1*x_5-x_3*x_6, -2*x_1^2+2*x_3^2-2*x_1*x_5+2*x_3*x_6, 0, x_1^2-x_3^2+x_1*x_5-x_3*x_6, 0},
        {0, 0, 0, 0, 0, 0, -x_1*x_3-x_2*x_3-x_1*x_6-x_2*x_6, 0, 0, 0, 0},
        {0, -x_2^2+x_3^2+x_4^2+2*x_2*x_5+2*x_4*x_5-x_2*x_6+x_3*x_6+x_5*x_6, x_2^2-x_3^2-x_4^2-2*x_2*x_5-2*x_4*x_5+x_2*x_6-x_3*x_6-x_5*x_6, 0, 0, -x_2^2+x_3^2+x_4^2+2*x_2*x_5+2*x_4*x_5-x_2*x_6+x_3*x_6+x_5*x_6, 0, 0, -x_2^2+x_3^2+x_4^2+2*x_2*x_5+2*x_4*x_5-x_2*x_6+x_3*x_6+x_5*x_6, x_2^2-x_3^2-x_4^2-2*x_2*x_5-2*x_4*x_5+x_2*x_6-x_3*x_6-x_5*x_6, 0},
        {0, 0, 0, 0, 0, 0, 0, -x_1*x_3-x_2*x_3+x_0*x_6-x_5*x_6+x_6^2, 0, x_1*x_3+x_2*x_3-x_0*x_6+x_5*x_6-x_6^2, 0},
        {-x_1*x_3-x_2*x_3-x_1*x_4+x_0*x_5+x_2*x_5+x_4*x_5-x_1*x_6-x_2*x_6+x_5*x_6, 0, x_1*x_3+x_2*x_3+x_1*x_4-x_0*x_5-x_2*x_5-x_4*x_5+x_1*x_6+x_2*x_6-x_5*x_6, x_1*x_3+x_2*x_3+x_1*x_4-x_0*x_5-x_2*x_5-x_4*x_5+x_1*x_6+x_2*x_6-x_5*x_6, x_1*x_3+x_2*x_3+x_1*x_4-x_0*x_5-x_2*x_5-x_4*x_5+x_1*x_6+x_2*x_6-x_5*x_6, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, x_2*x_5+x_4*x_5-x_2*x_6+2*x_5*x_6-x_6^2, 0},
        {0, x_2*x_3-x_3^2-x_2*x_5-x_4*x_5+x_2*x_6-x_3*x_6-x_5*x_6, -x_2*x_3+x_3^2+x_2*x_5+x_4*x_5-x_2*x_6+x_3*x_6+x_5*x_6, 0, 0, x_2*x_3-x_3^2-x_2*x_5-x_4*x_5+x_2*x_6-x_3*x_6-x_5*x_6, 0, 0, x_2*x_3-x_3^2-x_2*x_5-x_4*x_5+x_2*x_6-x_3*x_6-x_5*x_6, -x_2*x_3+x_3^2+x_2*x_5+x_4*x_5-x_2*x_6+x_3*x_6+x_5*x_6, -x_2*x_3^2+x_3^3-x_2*x_5^2-x_4*x_5^2+x_3^2*x_6-x_5^2*x_6+x_2*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, x_2*x_3-x_3^2+x_2*x_6-2*x_3*x_6-x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, x_1*x_3+x_2*x_3-x_2*x_5-x_4*x_5+x_2*x_6-x_5*x_6, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, x_1*x_3-x_3^2+x_1*x_6-x_3*x_6, 0},
        {0, 0, 0, 0, 0, 0, x_3^2+x_3*x_6, 0, 0, 0, 0},
        {0, -x_1*x_3+x_3^2+x_5*x_6-x_6^2, x_1*x_3-x_3^2-x_5*x_6+x_6^2, 0, 0, 0, 0, x_1*x_3-x_3^2-x_5*x_6+x_6^2, 0, 0, -x_2*x_3^2-x_3^3-x_1*x_3*x_6-x_2*x_3*x_6+x_1*x_5*x_6+x_5^2*x_6-x_1*x_6^2-x_6^3},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_1*x_3-x_2*x_3+x_2*x_5+x_4*x_5-x_0*x_6-x_2*x_6+2*x_5*x_6-x_6^2, x_1*x_3+x_2*x_3-x_2*x_5-x_4*x_5+x_0*x_6+x_2*x_6-2*x_5*x_6+x_6^2, x_2*x_5^2+x_4*x_5^2-x_0*x_5*x_6+x_1*x_5*x_6-x_2*x_5*x_6+3*x_5^2*x_6+x_0*x_6^2-x_1*x_6^2-3*x_5*x_6^2+x_6^3},
        {0, 0, 0, 0, 0, 0, 0, -x_1*x_3-x_2*x_3-x_0*x_5+x_2*x_5+x_4*x_5-x_2*x_6+x_5*x_6, 0, x_1*x_3+x_2*x_3+x_0*x_5-x_2*x_5-x_4*x_5+x_2*x_6-x_5*x_6, 0},
        {x_1*x_4+x_4*x_5+x_1*x_6+x_5*x_6, 0, -x_1*x_4-x_4*x_5-x_1*x_6-x_5*x_6, -x_1*x_4-x_4*x_5-x_1*x_6-x_5*x_6, 0, 0, 0, -x_1*x_4-x_4*x_5-x_1*x_6-x_5*x_6, 0, 0, 0}}


Sum of tangent vectors:
{x_1^2-x_1*x_3-x_2*x_3-x_3^2+x_0*x_5+x_1*x_5+x_2*x_5+2*x_4*x_5-x_2*x_6-x_3*x_6+2*x_5*x_6,
 x_1^2-x_2^2-x_1*x_3+x_2*x_3+x_4^2+x_1*x_5+x_2*x_5+x_4*x_5-x_3*x_6+x_5*x_6-x_6^2,
 -x_1^2+x_2^2+2*x_1*x_3-x_4^2-x_0*x_5-x_1*x_5-2*x_2*x_5-3*x_4*x_5+x_2*x_6+x_3*x_6-3*x_5*x_6+x_6^2,
 x_1*x_3+x_2*x_3-x_0*x_5-x_2*x_5-2*x_4*x_5+x_2*x_6-2*x_5*x_6,
 x_1*x_3+x_2*x_3+x_1*x_4-x_0*x_5-x_2*x_5-x_4*x_5+x_1*x_6+x_2*x_6-x_5*x_6,
 -x_2^2+x_2*x_3+x_4^2+x_2*x_5+x_4*x_5,
 x_1^2-x_1*x_3-x_2*x_3+x_1*x_5-x_1*x_6-x_2*x_6,
 -2*x_1^2-x_1*x_3-2*x_2*x_3+x_3^2-x_1*x_4-x_0*x_5-2*x_1*x_5+x_2*x_5+x_0*x_6-x_1*x_6-x_2*x_6+2*x_3*x_6-2*x_5*x_6+2*x_6^2,
 -x_2^2-x_1*x_3+x_4^2+2*x_2*x_5+2*x_4*x_5-x_0*x_6-x_2*x_6+2*x_5*x_6-x_6^2,
 x_1^2+x_2^2+5*x_1*x_3+4*x_2*x_3-3*x_3^2-x_4^2+x_0*x_5+x_1*x_5-3*x_2*x_5-3*x_4*x_5+x_1*x_6+3*x_2*x_6-4*x_3*x_6-x_5*x_6-2*x_6^2,
 -2*x_2*x_3^2+x_4^3+2*x_1^2*x_5+x_4^2*x_5+2*x_1*x_5^2+x_4*x_5^2+x_5^3-2*x_1^2*x_6-x_1*x_3*x_6-x_2*x_3*x_6+x_3^2*x_6-x_0*x_5*x_6-x_2*x_5*x_6+3*x_5^2*x_6+x_0*x_6^2-2*x_1*x_6^2+x_2*x_6^2-3*x_5*x_6^2}


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

Graph1221

Edges = {{0,1},{1,2},{2,3},{3,4},{4,0},{5,6},{6,7},{7,8},{8,9},{9,5},{0,5},{4,9},{6,10},{1,10},{2,10},{7,11},{11,8},{3,11}};
EdgePairing = {{1,4},{0,2},{1,3},{2,4},{0,3},{6,9},{5,7},{6,8},{7,9},{5,8},{4,9},{4,9},{5,13},{0,12},{1,13},{7,16},{7,15},{3,16}};


Generators of graph curve ideal:
{x_5*x_6,
 x_4*x_6,
 x_1*x_6,
 x_0*x_6,
 x_3*x_4-x_4^2+x_3*x_5-x_4*x_5,
 x_2*x_4,
 x_0*x_4,
 x_0*x_3,
 x_0*x_1-x_1^2-x_1*x_2+x_1*x_3-x_1*x_4-x_1*x_5,
 x_0^2-x_1^2-x_0*x_2-x_1*x_2+x_1*x_3-x_1*x_4-x_0*x_5-x_1*x_5,
 x_1*x_2*x_5,
 x_1*x_2*x_3+x_2^2*x_3-x_2*x_3^2-x_2*x_3*x_6}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, x_1*x_4+x_1*x_5, x_1*x_4+x_1*x_5, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_5^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_5, 0, 0},
        {0, 0, 0, 0, 0, x_1*x_4-x_0*x_5+x_1*x_5+x_2*x_5+x_4*x_5+x_5^2, 0, 0, 0, 0, 0, -x_1*x_4^2-x_0*x_2*x_5+x_2^2*x_5-x_1*x_4*x_5-x_4^2*x_5+x_2*x_5^2-x_4*x_5^2},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_4^2-x_4*x_5, -x_4^2-x_4*x_5, 0, 0},
        {0, 0, 0, 0, 0, x_1*x_3-x_1*x_4, 0, 0, 0, 0, -x_2^2*x_3-x_1*x_3^2+x_2*x_3^2+x_1*x_4^2-x_1*x_3*x_5+x_1*x_4*x_5+x_2*x_3*x_6, 0},
        {0, 0, x_2*x_3, 0, 0, 0, 0, 0, -x_2*x_3, -x_2*x_3, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_3^2*x_6},
        {-x_1*x_3-x_2*x_3+x_3^2+x_1*x_4-x_4^2+x_3*x_5-x_4*x_5+x_3*x_6, x_1*x_3+x_2*x_3-x_3^2-x_1*x_4+x_4^2-x_3*x_5+x_4*x_5-x_3*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_3*x_5+x_4*x_5, -x_3*x_5+x_4*x_5, 0, 0},
        {0, 0, 0, 0, x_1*x_4, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, -x_1*x_4-x_3*x_5, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, x_1*x_2, 0, -x_1*x_2, 0, x_1*x_2^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_1^3-x_1^2*x_2+x_2^2*x_3+x_1*x_3^2-x_2*x_3^2-x_1*x_4^2-x_1^2*x_5+x_1*x_3*x_5-x_1*x_4*x_5-x_2*x_3*x_6, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_2^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2^2*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2^2*x_6+2*x_2*x_3*x_6-x_3^2*x_6+2*x_2*x_6^2-2*x_3*x_6^2-x_6^3},
        {-x_0*x_2+x_1*x_2+x_2^2-x_2*x_3+x_2*x_5-x_2*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}


Sum of tangent vectors:
{-x_0*x_2+x_1*x_2+x_2^2-x_1*x_3-2*x_2*x_3+x_3^2+x_1*x_4-x_4^2+x_2*x_5+x_3*x_5-x_4*x_5-x_2*x_6+x_3*x_6,
 x_1*x_3+x_2*x_3-x_3^2-x_1*x_4+x_4^2-x_3*x_5+x_4*x_5-x_3*x_6,
 x_2*x_3,
 0,
 -x_3*x_5,
 x_1*x_3-x_0*x_5+x_1*x_5+x_2*x_5+x_4*x_5+x_5^2,
 x_1*x_4+x_1*x_5,
 x_1*x_2+x_1*x_4+x_1*x_5,
 -x_2*x_3-x_4^2-x_3*x_5,
 -x_1*x_2-x_2*x_3-x_4^2-x_2*x_5-x_3*x_5,
 -x_1^3-x_1^2*x_2-x_0*x_2^2-x_1^2*x_5-x_0*x_5^2,
 x_1*x_2^2-x_1*x_4^2-x_0*x_2*x_5+x_2^2*x_5-x_1*x_4*x_5-x_4^2*x_5+x_2*x_5^2-x_4*x_5^2-2*x_2^2*x_6+2*x_2*x_3*x_6-2*x_3^2*x_6+2*x_2*x_6^2-2*x_3*x_6^2-x_6^3}


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--------------------------------------------------------------------------------

Graph1228

Edges = {{0,1},{1,2},{2,0},{2,3},{3,4},{4,5},{5,1},{3,8},{4,7},{5,6},{6,7},{7,8},{8,9},{9,10},{10,6},{10,11},{11,9},{0,11}};
EdgePairing = {{1,2},{0,2},{0,1},{1,4},{3,5},{4,6},{1,5},{4,11},{4,11},{5,10},{8,9},{7,8},{11,13},{12,14},{10,13},{13,16},{13,15},{0,15}};


Generators of graph curve ideal:
{x_0*x_6,
 x_1*x_5+x_2*x_5-x_3*x_5+x_5^2-x_1*x_6-x_2*x_6+x_3*x_6-2*x_5*x_6+x_6^2,
 x_4^2-2*x_4*x_5+x_5^2+x_4*x_6-x_5*x_6,
 x_3*x_4-x_3*x_5,
 x_2*x_4-x_2*x_5+x_4*x_5-x_5^2+x_2*x_6-x_3*x_6-x_4*x_6+2*x_5*x_6-x_6^2,
 x_1*x_4+x_2*x_5-x_3*x_5+x_5^2-x_2*x_6+x_3*x_6-2*x_5*x_6+x_6^2,
 x_0*x_4-x_0*x_5,
 x_1*x_2-x_1*x_6,
 x_0*x_2,
 x_0*x_1-x_0*x_3+x_0*x_5,
 x_2*x_3*x_5-x_4*x_5^2+x_5^3-x_3^2*x_6+2*x_3*x_5*x_6+2*x_4*x_5*x_6-3*x_5^2*x_6-2*x_3*x_6^2-x_4*x_6^2+3*x_5*x_6^2-x_6^3,
 x_0*x_3^2-x_0*x_3*x_5+x_3^2*x_5-x_3*x_5^2-x_4*x_5^2+x_5^3-x_3^2*x_6+3*x_3*x_5*x_6+2*x_4*x_5*x_6-3*x_5^2*x_6-2*x_3*x_6^2-x_4*x_6^2+3*x_5*x_6^2-x_6^3}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0^3+2*x_0^2*x_5+x_0*x_5^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_3*x_5-x_3^2*x_5+x_0*x_5^2+x_3*x_5^2+x_4*x_5^2-x_5^3+x_3^2*x_6-3*x_3*x_5*x_6-2*x_4*x_5*x_6+3*x_5^2*x_6+2*x_3*x_6^2+x_4*x_6^2-3*x_5*x_6^2+x_6^3},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0*x_3*x_5-x_3^2*x_5+x_3*x_5^2+x_4*x_5^2-x_5^3+x_3^2*x_6-3*x_3*x_5*x_6-2*x_4*x_5*x_6+3*x_5^2*x_6+2*x_3*x_6^2+x_4*x_6^2-3*x_5*x_6^2+x_6^3},
        {0, x_1*x_3, 0, 0, 0, x_1*x_3, 0, 0, 0, -x_1*x_3, 0, 0},
        {0, 0, 0, -x_1^2+x_1*x_3+x_2*x_5-x_3*x_5+x_5^2-x_1*x_6-x_2*x_6+x_3*x_6-2*x_5*x_6+x_6^2, -x_1^2+x_1*x_3+x_2*x_5-x_3*x_5+x_5^2-x_1*x_6-x_2*x_6+x_3*x_6-2*x_5*x_6+x_6^2, 0, 0, 0, 0, 0, -x_1^2*x_3+x_1*x_3^2-x_3^2*x_5+x_3*x_5^2+x_4*x_5^2-x_5^3+x_1^2*x_6+x_3^2*x_6-x_2*x_5*x_6-2*x_3*x_5*x_6-2*x_4*x_5*x_6+2*x_5^2*x_6+x_1*x_6^2+x_2*x_6^2+x_3*x_6^2+x_4*x_6^2-x_5*x_6^2, 0},
        {0, -x_1*x_6, 0, 0, 0, -x_1*x_6, 0, 0, 0, 0, 0, 0},
        {-x_0*x_3+x_0*x_5+x_2*x_5-x_3*x_5+x_5^2-x_2*x_6+x_3*x_6-2*x_5*x_6+x_6^2, 0, 0, 0, 0, 0, x_0*x_3-x_0*x_5-x_2*x_5+x_3*x_5-x_5^2+x_2*x_6-x_3*x_6+2*x_5*x_6-x_6^2, 0, -x_0*x_3+x_0*x_5+x_2*x_5-x_3*x_5+x_5^2-x_2*x_6+x_3*x_6-2*x_5*x_6+x_6^2, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, x_1*x_3+x_2*x_3-x_3^2+x_3*x_5-x_3*x_6, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, -x_1*x_6-x_2*x_6+x_3*x_6-x_5*x_6+x_6^2, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, -x_4*x_5+x_5^2+x_4*x_6-x_5*x_6, 0, 0, 0, 0},
        {0, -x_4*x_5+x_5^2-x_2*x_6+x_3*x_6-x_5*x_6+x_6^2, 0, 0, 0, -x_4*x_5+x_5^2-x_2*x_6+x_3*x_6-x_5*x_6+x_6^2, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, -x_2^2+x_2*x_3-x_2*x_5+2*x_2*x_6-x_3*x_6+x_5*x_6-x_6^2, -x_2^2+x_2*x_3-x_2*x_5+2*x_2*x_6-x_3*x_6+x_5*x_6-x_6^2, 0, 0, 0, 0, 0, x_2^3-2*x_2^2*x_3+x_2*x_3^2-x_2*x_5^2-x_2^2*x_6+x_3^2*x_6+2*x_2*x_5*x_6-2*x_3*x_5*x_6+x_5^2*x_6-x_2*x_6^2+2*x_3*x_6^2-2*x_5*x_6^2+x_6^3, 0},
        {0, 0, 0, 0, x_2*x_3-x_4*x_5+x_5^2+x_3*x_6+x_4*x_6-2*x_5*x_6+x_6^2, 0, 0, 0, 0, 0, x_2*x_3^2+x_3^2*x_6-x_3*x_5*x_6+x_3*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_4*x_5^2+x_5^3-x_3^2*x_6+2*x_3*x_5*x_6+2*x_4*x_5*x_6-3*x_5^2*x_6-2*x_3*x_6^2-x_4*x_6^2+3*x_5*x_6^2-x_6^3, -x_4*x_5^2+x_5^3-x_3^2*x_6+2*x_3*x_5*x_6+2*x_4*x_5*x_6-3*x_5^2*x_6-2*x_3*x_6^2-x_4*x_6^2+3*x_5*x_6^2-x_6^3},
        {0, 0, -x_2*x_5-x_4*x_5+x_5^2+x_2*x_6+x_4*x_6-x_5*x_6, x_2*x_5+x_4*x_5-x_5^2-x_2*x_6-x_4*x_6+x_5*x_6, x_2*x_5+x_4*x_5-x_5^2-x_2*x_6-x_4*x_6+x_5*x_6, 0, 0, 0, 0, 0, -x_2*x_5^2-x_4*x_5^2+x_5^3+2*x_2*x_5*x_6+2*x_4*x_5*x_6-2*x_5^2*x_6-x_2*x_6^2-x_4*x_6^2+x_5*x_6^2, -x_2*x_5^2-x_4*x_5^2+x_5^3+2*x_2*x_5*x_6+2*x_4*x_5*x_6-2*x_5^2*x_6-x_2*x_6^2-x_4*x_6^2+x_5*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_4*x_5^2+x_5^3+2*x_4*x_5*x_6-3*x_5^2*x_6-x_4*x_6^2+3*x_5*x_6^2-x_6^3, -x_4*x_5^2+x_5^3+2*x_4*x_5*x_6-3*x_5^2*x_6-x_4*x_6^2+3*x_5*x_6^2-x_6^3},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_3^2*x_6-2*x_3*x_6^2-x_4*x_6^2+x_5*x_6^2-x_6^3, -x_3^2*x_6-2*x_3*x_6^2-x_4*x_6^2+x_5*x_6^2-x_6^3},
        {x_0*x_3+x_3*x_5+x_4*x_5-x_5^2-x_3*x_6-x_4*x_6+2*x_5*x_6-x_6^2, 0, 0, 0, 0, 0, 0, 0, 0, x_0*x_3+x_3*x_5+x_4*x_5-x_5^2-x_3*x_6-x_4*x_6+2*x_5*x_6-x_6^2, 0, -x_0*x_3*x_5-x_3*x_5^2-x_4*x_5^2+x_5^3+2*x_3*x_5*x_6+2*x_4*x_5*x_6-3*x_5^2*x_6-x_3*x_6^2-x_4*x_6^2+3*x_5*x_6^2-x_6^3}}


Sum of tangent vectors:
{x_0*x_5+x_2*x_5+x_4*x_5-x_2*x_6-x_4*x_6,
 x_1*x_3-x_4*x_5+x_5^2-x_1*x_6-x_2*x_6+x_3*x_6-x_5*x_6+x_6^2,
 -x_2*x_5-x_4*x_5+x_5^2+x_2*x_6+x_4*x_6-x_5*x_6,
 -x_1^2-x_2^2+x_1*x_3+x_2*x_3+x_2*x_5-x_3*x_5+x_4*x_5-x_1*x_6-x_4*x_6,
 -x_1^2-x_2^2+x_1*x_3+2*x_2*x_3+x_2*x_5-x_3*x_5+x_5^2-x_1*x_6+x_3*x_6-2*x_5*x_6+x_6^2,
 x_1*x_3-x_4*x_5+x_5^2-x_1*x_6-x_2*x_6+x_3*x_6-x_5*x_6+x_6^2,
 x_0*x_3-x_0*x_5-x_2*x_5+x_3*x_5-x_5^2+x_2*x_6-x_3*x_6+2*x_5*x_6-x_6^2,
 x_1*x_3+x_2*x_3-x_3^2+x_3*x_5-x_4*x_5+x_5^2-x_1*x_6-x_2*x_6+x_4*x_6-2*x_5*x_6+x_6^2,
 -x_0*x_3+x_0*x_5+x_2*x_5-x_3*x_5+x_5^2-x_2*x_6+x_3*x_6-2*x_5*x_6+x_6^2,
 x_0*x_3-x_1*x_3+x_3*x_5+x_4*x_5-x_5^2-x_3*x_6-x_4*x_6+2*x_5*x_6-x_6^2,
 x_2^3-x_1^2*x_3-2*x_2^2*x_3+x_1*x_3^2+2*x_2*x_3^2-x_3^2*x_5-2*x_2*x_5^2+x_3*x_5^2-2*x_4*x_5^2+2*x_5^3+x_1^2*x_6-x_2^2*x_6+x_3^2*x_6+3*x_2*x_5*x_6-3*x_3*x_5*x_6+4*x_4*x_5*x_6-5*x_5^2*x_6+x_1*x_6^2-x_2*x_6^2-3*x_4*x_6^2+5*x_5*x_6^2-2*x_6^3,
 x_0^3+2*x_0^2*x_5-x_0*x_3*x_5-2*x_3^2*x_5+2*x_0*x_5^2-x_2*x_5^2+x_3*x_5^2-2*x_4*x_5^2+2*x_5^3+2*x_2*x_5*x_6-2*x_3*x_5*x_6+4*x_4*x_5*x_6-5*x_5^2*x_6-x_2*x_6^2-x_3*x_6^2-3*x_4*x_6^2+5*x_5*x_6^2-2*x_6^3}


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

Graph1233

Edges = {{0,1},{1,2},{2,3},{3,4},{4,5},{5,0},{6,8},{8,10},{10,6},{7,11},{11,9},{9,7},{5,6},{0,7},{1,8},{2,9},{3,10},{4,11}};
EdgePairing = {{1,13},{0,15},{1,16},{2,17},{5,17},{4,13},{7,8},{6,8},{6,7},{10,11},{9,11},{9,10},{5,6},{5,9},{0,6},{1,11},{2,7},{4,9}};


Generators of graph curve ideal:
{2*x_3*x_4-x_1*x_5+2*x_3*x_5+x_4*x_5+x_5^2+2*x_4*x_6+x_5*x_6,
 2*x_2*x_4-x_0*x_5+x_2*x_5-x_3*x_5+x_4*x_5+2*x_4*x_6+x_5*x_6,
 2*x_1*x_4+x_1*x_5+2*x_4*x_6+x_5*x_6,
 2*x_0*x_4+2*x_0*x_5+x_1*x_5-2*x_4*x_6-x_5*x_6,
 2*x_2*x_3+x_2*x_5,
 2*x_0*x_3+2*x_3^2+x_0*x_5+3*x_3*x_5+x_5^2+2*x_3*x_6+x_5*x_6,
 2*x_1*x_2+x_1*x_5-2*x_0*x_6+2*x_1*x_6-2*x_3*x_6-x_5*x_6,
 x_0*x_2,
 2*x_0*x_1+2*x_1*x_3+x_1*x_5+2*x_0*x_6+2*x_3*x_6+x_5*x_6,
 2*x_0^2-2*x_3^2+x_0*x_5-3*x_3*x_5-x_5^2+2*x_0*x_6-2*x_3*x_6-x_5*x_6,
 x_0*x_5*x_6+x_2*x_5*x_6+x_3*x_5*x_6-x_4*x_5*x_6-2*x_4*x_6^2-x_5*x_6^2,
 2*x_1*x_3*x_6-2*x_3^2*x_6+x_1*x_5*x_6+x_2*x_5*x_6-2*x_3*x_5*x_6-x_4*x_5*x_6-x_5^2*x_6-2*x_4*x_6^2-x_5*x_6^2}


Tangent vectors:
matrix {{0, 0, 0, 0, 2*x_1^2-2*x_1*x_3-x_1*x_5+2*x_1*x_6-2*x_3*x_6-x_5*x_6, -2*x_1^2+2*x_1*x_3+x_1*x_5-2*x_1*x_6+2*x_3*x_6+x_5*x_6, 0, -x_1^2+x_1*x_3+(1/2)*x_1*x_5-x_1*x_6+x_3*x_6+(1/2)*x_5*x_6, 0, 4*x_1^2-4*x_1*x_3-2*x_1*x_5+4*x_1*x_6-4*x_3*x_6-2*x_5*x_6, 0, -2*x_1^3+4*x_1^2*x_3-2*x_1*x_3^2-2*x_1^2*x_6+2*x_3^2*x_6-3*x_1*x_5*x_6-2*x_2*x_5*x_6+4*x_3*x_5*x_6+3*x_4*x_5*x_6+3*x_5^2*x_6+6*x_4*x_6^2+3*x_5*x_6^2},
        {-2*x_1*x_3-x_1*x_5-2*x_3*x_6-x_5*x_6, 0, 0, 2*x_1*x_3+x_1*x_5+2*x_3*x_6+x_5*x_6, 0, 0, 0, 0, 0, 0, 0, -2*x_1*x_3^2+2*x_3^2*x_6-x_1*x_5*x_6-2*x_2*x_5*x_6+4*x_3*x_5*x_6+3*x_4*x_5*x_6+3*x_5^2*x_6+4*x_3*x_6^2+6*x_4*x_6^2+5*x_5*x_6^2},
        {x_1*x_5-2*x_4*x_6-x_5*x_6, 0, x_1*x_5-2*x_4*x_6-x_5*x_6, -x_1*x_5+2*x_4*x_6+x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 2*x_4^2+3*x_4*x_5+x_5^2, -2*x_4^2-3*x_4*x_5-x_5^2, 0, -x_4^2-(3/2)*x_4*x_5-(1/2)*x_5^2, 0, 4*x_4^2+6*x_4*x_5+2*x_5^2, -2*x_4^3-5*x_4^2*x_5-4*x_4*x_5^2-x_5^3, -2*x_4^3-5*x_4^2*x_5-4*x_4*x_5^2-x_5^3},
        {-2*x_0*x_5-2*x_3*x_5+2*x_4*x_5+4*x_4*x_6+2*x_5*x_6, 0, 0, 2*x_0*x_5+2*x_3*x_5-2*x_4*x_5-4*x_4*x_6-2*x_5*x_6, 0, 0, 0, 0, 0, 0, x_0*x_5^2+x_3*x_5^2-x_4*x_5^2-2*x_2*x_5*x_6-2*x_4*x_5*x_6-x_5^2*x_6, x_0*x_5^2+x_3*x_5^2-x_4*x_5^2-2*x_2*x_5*x_6-2*x_4*x_5*x_6-x_5^2*x_6},
        {-(1/2)*x_1*x_5+x_0*x_6-x_1*x_6+x_3*x_6+(1/2)*x_5*x_6, 0, -(1/2)*x_1*x_5+x_0*x_6-x_1*x_6+x_3*x_6+(1/2)*x_5*x_6, (1/2)*x_1*x_5-x_0*x_6+x_1*x_6-x_3*x_6-(1/2)*x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*x_3^2*x_5+x_0*x_5^2+x_3*x_5^2+x_5^3-4*x_3^2*x_6+x_5^2*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*x_3^2*x_5+x_0*x_5^2-3*x_3*x_5^2-x_5^3-4*x_3^2*x_6-4*x_2*x_5*x_6-12*x_3*x_5*x_6+4*x_4*x_5*x_6-3*x_5^2*x_6+4*x_0*x_6^2-4*x_3*x_6^2+8*x_4*x_6^2+2*x_5*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4*x_0*x_6^2+4*x_3*x_6^2+2*x_5*x_6^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*x_2^3-x_2^2*x_5-2*x_2^2*x_6, -2*x_2^3-x_2^2*x_5-2*x_2^2*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_5^2-x_2*x_5^2-x_3*x_5^2-x_5^3-x_5^2*x_6, -x_0*x_5^2-x_2*x_5^2-x_3*x_5^2-x_5^3-x_5^2*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2*x_0*x_6^2-2*x_2*x_6^2-2*x_3*x_6^2-2*x_5*x_6^2-2*x_6^3, -2*x_0*x_6^2-2*x_2*x_6^2-2*x_3*x_6^2-2*x_5*x_6^2-2*x_6^3},
        {0, 0, 0, 0, (1/2)*x_1*x_5+x_3*x_6+(1/2)*x_5*x_6, -(1/2)*x_1*x_5-x_3*x_6-(1/2)*x_5*x_6, 0, 0, 0, (1/2)*x_1*x_5+x_3*x_6+(1/2)*x_5*x_6, 0, (1/2)*x_1*x_5*x_6+x_3*x_6^2+(1/2)*x_5*x_6^2},
        {0, 0, 0, 0, 0, 0, -x_1*x_5+2*x_0*x_6-2*x_1*x_6+2*x_2*x_6+2*x_3*x_6+x_5*x_6, 0, 0, 0, 0, 0},
        {-x_1*x_3+x_3^2+(1/2)*x_0*x_5-(1/2)*x_1*x_5+(3/2)*x_3*x_5+(1/2)*x_5^2, 0, -x_1*x_3+x_3^2+(1/2)*x_0*x_5-(1/2)*x_1*x_5+(3/2)*x_3*x_5+(1/2)*x_5^2, x_1*x_3-x_3^2-(1/2)*x_0*x_5+(1/2)*x_1*x_5-(3/2)*x_3*x_5-(1/2)*x_5^2, 0, 0, x_1*x_3-x_3^2-(1/2)*x_0*x_5+(1/2)*x_1*x_5-(3/2)*x_3*x_5-(1/2)*x_5^2, 0, -x_1*x_3+x_3^2+(1/2)*x_0*x_5-(1/2)*x_1*x_5+(3/2)*x_3*x_5+(1/2)*x_5^2, 0, 0, 0},
        {0, 0, 0, 0, 0, (1/4)*x_1*x_5+(1/4)*x_5*x_6, (1/4)*x_1*x_5+(1/4)*x_5*x_6, 0, 0, -(1/2)*x_1*x_5-(1/2)*x_5*x_6, 0, 0},
        {(1/2)*x_1*x_5-x_0*x_6-x_4*x_6-(1/2)*x_5*x_6, (1/2)*x_1*x_5-x_0*x_6-x_4*x_6-(1/2)*x_5*x_6, 0, -x_1*x_5+2*x_0*x_6+2*x_4*x_6+x_5*x_6, 0, 0, 0, 0, 0, 0, -(1/2)*x_1*x_5*x_6+x_0*x_6^2+x_4*x_6^2+(1/2)*x_5*x_6^2, -(1/2)*x_1*x_5*x_6+x_0*x_6^2+x_4*x_6^2+(1/2)*x_5*x_6^2},
        {0, (1/4)*x_0*x_5+(1/4)*x_2*x_5+(1/4)*x_3*x_5-(1/4)*x_4*x_5-(1/2)*x_4*x_6-(1/4)*x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}}


Sum of tangent vectors:
{-3*x_1*x_3+x_3^2-(3/2)*x_0*x_5-(1/2)*x_1*x_5-(1/2)*x_3*x_5+2*x_4*x_5+(1/2)*x_5^2-x_1*x_6-x_3*x_6+x_4*x_6,
 (1/4)*x_0*x_5+(1/2)*x_1*x_5+(1/4)*x_2*x_5+(1/4)*x_3*x_5-(1/4)*x_4*x_5-x_0*x_6-(3/2)*x_4*x_6-(3/4)*x_5*x_6,
 -x_1*x_3+x_3^2+(1/2)*x_0*x_5+(3/2)*x_3*x_5+(1/2)*x_5^2+x_0*x_6-x_1*x_6+x_3*x_6-2*x_4*x_6-(1/2)*x_5*x_6,
 3*x_1*x_3-x_3^2+(3/2)*x_0*x_5+(1/2)*x_3*x_5-2*x_4*x_5-(1/2)*x_5^2+x_0*x_6+x_1*x_6+x_3*x_6+(1/2)*x_5*x_6,
 2*x_1^2-2*x_1*x_3+2*x_4^2-(1/2)*x_1*x_5+3*x_4*x_5+x_5^2+2*x_1*x_6-x_3*x_6-(1/2)*x_5*x_6,
 -2*x_1^2+2*x_1*x_3-2*x_4^2+(3/4)*x_1*x_5-3*x_4*x_5-x_5^2-2*x_1*x_6+x_3*x_6+(3/4)*x_5*x_6,
 x_1*x_3-x_3^2-(1/2)*x_0*x_5-(1/4)*x_1*x_5-(3/2)*x_3*x_5-(1/2)*x_5^2+2*x_0*x_6-2*x_1*x_6+2*x_2*x_6+2*x_3*x_6+(5/4)*x_5*x_6,
 -x_1^2+x_1*x_3-x_4^2+(1/2)*x_1*x_5-(3/2)*x_4*x_5-(1/2)*x_5^2-x_1*x_6+x_3*x_6+(1/2)*x_5*x_6,
 -x_1*x_3+x_3^2+(1/2)*x_0*x_5-(1/2)*x_1*x_5+(3/2)*x_3*x_5+(1/2)*x_5^2,
 4*x_1^2-4*x_1*x_3+4*x_4^2-2*x_1*x_5+6*x_4*x_5+2*x_5^2+4*x_1*x_6-3*x_3*x_6-2*x_5*x_6,
 -2*x_2^3-2*x_4^3-x_2^2*x_5-5*x_4^2*x_5-x_2*x_5^2-5*x_4*x_5^2-2*x_5^3-2*x_2^2*x_6-(1/2)*x_1*x_5*x_6-2*x_2*x_5*x_6-2*x_4*x_5*x_6-2*x_5^2*x_6-x_0*x_6^2-2*x_2*x_6^2-2*x_3*x_6^2+x_4*x_6^2-(3/2)*x_5*x_6^2-2*x_6^3,
 -2*x_1^3-2*x_2^3+4*x_1^2*x_3-4*x_1*x_3^2-2*x_4^3-x_2^2*x_5-4*x_3^2*x_5-5*x_4^2*x_5+2*x_0*x_5^2-x_2*x_5^2-2*x_3*x_5^2-5*x_4*x_5^2-2*x_5^3-2*x_1^2*x_6-2*x_2^2*x_6-4*x_3^2*x_6-4*x_1*x_5*x_6-10*x_2*x_5*x_6-4*x_3*x_5*x_6+8*x_4*x_5*x_6+2*x_5^2*x_6+7*x_0*x_6^2-2*x_2*x_6^2+3*x_3*x_6^2+21*x_4*x_6^2+11*x_5*x_6^2-2*x_6^3}


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

Graph1237

Edges = {{0,1},{1,2},{2,3},{3,4},{4,5},{5,0},{0,8},{8,1},{5,6},{6,4},{3,7},{7,2},{8,9},{9,10},{11,9},{6,10},{11,10},{11,7}};
EdgePairing = {{1,5},{0,2},{1,3},{2,4},{3,5},{0,4},{0,7},{0,6},{4,9},{4,8},{2,11},{2,10},{6,13},{12,15},{13,16},{8,13},{13,14},{10,16}};


Generators of graph curve ideal:
{x_1*x_6,
 x_4*x_5-x_4*x_6,
 x_3*x_5-x_3*x_6,
 x_1*x_5,
 x_0*x_5-x_0*x_6,
 x_1*x_4,
 x_0*x_3+x_2*x_4+x_3*x_4+x_0*x_6+x_4*x_6,
 x_0*x_2,
 x_0*x_1,
 x_0^2+x_0*x_4,
 x_2^2*x_5+x_2*x_3*x_6+x_2*x_5*x_6,
 x_3^2*x_4+x_3^2*x_6+x_3*x_4*x_6+x_3*x_6^2,
 x_2*x_3*x_4+x_2*x_3*x_6,
 x_1*x_2*x_3+x_2^2*x_3+x_2*x_3^2+x_2*x_3*x_6}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2^2*x_6-x_2*x_3*x_6+x_2*x_5*x_6-2*x_2*x_6^2+x_5*x_6^2-x_6^3, 0, 0, 0},
        {-x_1*x_2-x_2^2-x_2*x_3-x_2*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_1^3-2*x_1^2*x_2-x_1*x_2^2-2*x_1^2*x_3+2*x_2^2*x_3-x_1*x_3^2+2*x_2*x_3^2+2*x_2*x_3*x_6},
        {-x_1*x_3-x_2*x_3-x_3^2-x_3*x_6, 0, 0, -x_1*x_3-x_2*x_3-x_3^2-x_3*x_6, 0, x_1*x_3+x_2*x_3+x_3^2+x_3*x_6, 0, 0, -x_1*x_3-x_2*x_3-x_3^2-x_3*x_6, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3*x_6-x_3^2*x_6+x_2*x_4*x_6+x_3*x_4*x_6-x_3*x_6^2+x_4*x_6^2, 0, 0},
        {0, -x_2*x_4-x_3*x_4-x_2*x_5-x_3*x_6-x_4*x_6-x_5*x_6, 0, 0, x_2*x_4+x_3*x_4+x_2*x_5+x_3*x_6+x_4*x_6+x_5*x_6, 0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_5^3-x_5^2*x_6, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2^2*x_6-x_2*x_3*x_6-x_2*x_5*x_6, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_4^2-2*x_0*x_4*x_6-x_0*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3*x_6-x_3^2*x_6-x_2*x_4*x_6-x_3*x_4*x_6-x_0*x_6^2-x_3*x_6^2-x_4*x_6^2, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_1*x_3^2},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -x_1*x_2^2},
        {0, x_2*x_4+x_2*x_5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_0*x_4^2+x_4^3+2*x_0*x_4*x_6+2*x_4^2*x_6+x_0*x_6^2+x_4*x_6^2, -x_0*x_4^2-x_4^3-2*x_0*x_4*x_6-2*x_4^2*x_6-x_0*x_6^2-x_4*x_6^2, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_2*x_3*x_6-x_2*x_4*x_6, -x_2*x_3*x_6+x_2*x_4*x_6, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, -x_3*x_4-x_3*x_6, 0, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, x_2*x_3*x_6+x_2*x_4*x_6+x_0*x_6^2+x_4*x_6^2, -x_2*x_3*x_6-x_2*x_4*x_6-x_0*x_6^2-x_4*x_6^2, 0},
        {x_2*x_3, 0, 0, x_2*x_3, 0, -x_2*x_3, x_2*x_3, 0, 0, 0, -x_2^2*x_3, 0, 0, 0}}


Sum of tangent vectors:
{-x_1*x_2-x_2^2-x_1*x_3-x_2*x_3-x_3^2-x_2*x_6-x_3*x_6,
 -x_3*x_4-x_3*x_6-x_4*x_6-x_5*x_6,
 0,
 -x_1*x_3-x_3^2-x_3*x_6,
 x_2*x_4+x_3*x_4+x_2*x_5+x_3*x_6+x_4*x_6+x_5*x_6,
 x_1*x_3+x_3^2+x_3*x_6,
 x_2*x_3,
 0,
 -x_1*x_3-x_2*x_3-x_3^2-x_3*x_6,
 -x_3*x_4-x_3*x_6,
 -x_2^2*x_3+x_5^3-2*x_2^2*x_6-2*x_2*x_3*x_6-x_5^2*x_6-2*x_2*x_6^2+x_5*x_6^2-x_6^3,
 x_4^3-2*x_3^2*x_6+2*x_4^2*x_6-2*x_3*x_6^2+2*x_4*x_6^2,
 -x_0*x_4^2-x_4^3-2*x_2*x_3*x_6-2*x_0*x_4*x_6-2*x_4^2*x_6-2*x_0*x_6^2-2*x_4*x_6^2,
 -x_1^3-2*x_1^2*x_2-2*x_1*x_2^2-2*x_1^2*x_3+2*x_2^2*x_3-2*x_1*x_3^2+2*x_2*x_3^2+2*x_2*x_3*x_6}


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

Graph1240

Edges = {{0,1},{1,2},{2,3},{3,4},{4,5},{5,0},{6,7},{7,8},{8,9},{9,10},{10,11},{11,6},{0,7},{1,8},{2,9},{3,10},{4,11},{5,6}};
EdgePairing = {{1,5},{0,2},{1,3},{2,4},{3,5},{0,4},{7,11},{6,8},{7,9},{8,10},{9,11},{6,10},{0,7},{0,7},{1,8},{2,9},{3,10},{5,6}};


Generators of graph curve ideal:
{x_3*x_6-x_4*x_6,
 x_1*x_6,
 x_0*x_6,
 x_0*x_5+x_1*x_5+x_2*x_5+x_3*x_5+x_2*x_6+x_4*x_6,
 x_2*x_4-x_2*x_5,
 x_1*x_4-x_1*x_5,
 x_0*x_4+x_1*x_5+x_2*x_5+x_3*x_5+x_2*x_6+x_4*x_6,
 x_2*x_3-x_2*x_5,
 x_1*x_3-x_1*x_5,
 x_0*x_2}


Tangent vectors:
matrix {{0, 0, 0, 0, 0, 0, -x_0*x_3-x_3^2+x_3*x_4-x_1*x_5-x_2*x_5-x_3*x_5-x_2*x_6-x_4*x_6, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_0^2-x_0*x_1-x_0*x_3, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, -x_0*x_1-x_1^2-x_1*x_2-x_1*x_5},
        {0, x_1*x_2+x_2^2+x_2*x_5, 0, -x_1*x_2-x_2^2-x_2*x_5, 0, 0, -x_1*x_2-x_2^2-x_2*x_5, 0, 0, 0},
        {0, 0, 0, 0, x_2*x_6+x_4*x_6, 0, 0, x_2*x_6+x_4*x_6, 0, 0},
        {x_3*x_4-x_3*x_5, 0, 0, -x_3*x_4+x_3*x_5, 0, 0, -x_3*x_4+x_3*x_5, 0, 0, 0},
        {-x_4*x_5+x_5^2-x_4*x_6+x_5*x_6, 0, 0, x_4*x_5-x_5^2+x_4*x_6-x_5*x_6, 0, 0, x_4*x_5-x_5^2+x_4*x_6-x_5*x_6, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, x_3*x_5-x_4*x_5, 0, 0, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_1*x_5-x_2*x_5-x_3*x_5-x_2*x_6-x_4*x_6, 0},
        {0, 0, 0, 0, 0, 0, 0, 0, 0, x_1*x_5},
        {0, -x_2*x_5-x_2*x_6, 0, x_2*x_5+x_2*x_6, 0, 0, x_2*x_5+x_2*x_6, 0, 0, 0},
        {0, 0, 0, 0, -x_5*x_6-x_6^2, 0, 0, -x_5*x_6-x_6^2, 0, 0},
        {0, 0, 0, -x_3*x_4+x_4^2+x_3*x_5-x_4*x_5, 0, 0, -x_3*x_4+x_4^2+x_3*x_5-x_4*x_5, 0, 0, 0},
        {0, 0, 0, -x_0*x_3-x_1*x_5-x_2*x_5-x_3*x_5-x_2*x_6-x_4*x_6, 0, 0, -x_0*x_3-x_1*x_5-x_2*x_5-x_3*x_5-x_2*x_6-x_4*x_6, 0, 0, 0},
        {0, 0, 0, -x_0*x_1, 0, 0, -x_0*x_1, 0, 0, 0},
        {0, 0, 0, -x_1*x_2, 0, 0, -x_1*x_2, 0, 0, 0},
        {0, 0, 0, x_2*x_6, 0, 0, x_2*x_6, 0, 0, 0},
        {0, 0, 0, x_4*x_6-x_5*x_6, 0, 0, x_4*x_6-x_5*x_6, 0, 0, 0}}


Sum of tangent vectors:
{x_3*x_4-x_3*x_5-x_4*x_5+x_5^2-x_4*x_6+x_5*x_6,
 x_1*x_2+x_2^2-x_2*x_6,
 0,
 -x_0*x_1-2*x_1*x_2-x_2^2-x_0*x_3-2*x_3*x_4+x_4^2-x_1*x_5-x_2*x_5+x_3*x_5-x_5^2+x_2*x_6+x_4*x_6-2*x_5*x_6,
 x_2*x_6+x_4*x_6-x_5*x_6-x_6^2,
 0,
 -x_0*x_1-2*x_1*x_2-x_2^2-2*x_0*x_3-x_3^2-x_3*x_4+x_4^2-2*x_1*x_5-2*x_2*x_5+x_3*x_5-x_4*x_5-x_5^2-2*x_5*x_6,
 x_2*x_6+x_4*x_6-x_5*x_6-x_6^2,
 -x_0^2-x_0*x_1-x_0*x_3-x_1*x_5-x_2*x_5-x_3*x_5-x_2*x_6-x_4*x_6,
 -x_0*x_1-x_1^2-x_1*x_2}


--------------------------------------------------------------------------------
--------------------------------------------------------------------------------

Graph1245

Edges = {{0,1},{1,2},{2,3},{3,4},{4,5},{5,0},{6,7},{7,8},{8,9},{9,10},{10,11},{11,6},{11,8},{0,6},{2,7},{3,9},{5,10},{1,4}};
EdgePairing = {{5,17},{2,17},{1,3},{2,17},{3,16},{13,16},{7,11},{6,12},{7,15},{8,10},{9,12},{6,12},{7,11},{5,11},{2,7},{3,9},{4,9},{0,4}};


Generators of graph curve ideal:
{x_3*x_4+x_3*x_5,
 x_2*x_4-x_3*x_5,
 x_1*x_4-x_4^2+x_1*x_5+x_5^2-x_4*x_6-x_5*x_6,
 x_0*x_4+x_4^2+x_0*x_5+x_4*x_5,
 x_0*x_3+2*x_1*x_3-2*x_0*x_5-3*x_1*x_5+2*x_3*x_5+x_4*x_5-3*x_5^2+x_0*x_6+2*x_1*x_6-2*x_3*x_6-x_4*x_6+5*x_5*x_6-2*x_6^2,
 x_1*x_2+x_1*x_3+x_2*x_5+x_3*x_5-x_2*x_6-x_3*x_6,
 x_0*x_2-2*x_1*x_3+2*x_0*x_5+3*x_1*x_5-2*x_3*x_5-x_4*x_5+3*x_5^2-x_0*x_6-2*x_1*x_6+2*x_3*x_6+x_4*x_6-5*x_5*x_6+2*x_6^2,
 x_1^2+x_1*x_3-x_4^2+2*x_1*x_5+2*x_3*x_5+x_5^2-x_1*x_6-x_3*x_6-x_4*x_6-x_5*x_6,
 x_0*x_1-2*x_1*x_3+2*x_0*x_5+3*x_1*x_5-2*x_3*x_5-x_4*x_5+3*x_5^2-x_0*x_6-3*x_1*x_6+x_2*x_6+2*x_3*x_6+x_4*x_6-5*x_5*x_6+2*x_6^2,
 x_0^2+4*x_1*x_3+2*x_4^2-x_0*x_5-6*x_1*x_5+2*x_3*x_5+2*x_4*x_5-6*x_5^2-x_0*x_6+5*x_1*x_6-3*x_2*x_6-4*x_3*x_6+8*x_5*x_6-2*x_6^2}


Tangent vectors:
matrix {{0, -x_4^2+x_2*x_5+x_3*x_5+x_5^2-x_4*x_6-x_5*x_6, 0, 0, 0, -x_4^2+x_2*x_5+x_3*x_5+x_5^2-x_4*x_6-x_5*x_6, x_4^2-x_2*x_5-x_3*x_5-x_5^2+x_4*x_6+x_5*x_6, 0, x_4^2-x_2*x_5-x_3*x_5-x_5^2+x_4*x_6+x_5*x_6, -3*x_4^2+3*x_2*x_5+3*x_3*x_5+3*x_5^2-3*x_4*x_6-3*x_5*x_6},
        {x_2^2+x_2*x_3+x_2*x_5+x_3*x_5-x_2*x_6-x_3*x_6, -x_2^2-x_2*x_3-x_2*x_5-x_3*x_5+x_2*x_6+x_3*x_6, 0, 0, 0, 0, 0, x_2^2+x_2*x_3+x_2*x_5+x_3*x_5-x_2*x_6-x_3*x_6, 0, -2*x_2^2-2*x_2*x_3-2*x_2*x_5-2*x_3*x_5+2*x_2*x_6+2*x_3*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_2*x_3-x_3^2, 3*x_2*x_3+3*x_3^2},
        {x_2*x_6+x_3*x_6, -x_2*x_6-x_3*x_6, 0, 0, 0, 0, 0, x_2*x_6+x_3*x_6, 0, -2*x_2*x_6-2*x_3*x_6},
        {0, x_4^2+x_4*x_5+x_4*x_6+x_5*x_6, 0, 0, 0, x_4^2+x_4*x_5+x_4*x_6+x_5*x_6, -x_4^2-x_4*x_5-x_4*x_6-x_5*x_6, 0, -x_4^2-x_4*x_5-x_4*x_6-x_5*x_6, 3*x_4^2+3*x_4*x_5+3*x_4*x_6+3*x_5*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, -x_4^2-x_4*x_5, 3*x_4^2+3*x_4*x_5},
        {0, 0, 0, 0, 2*x_4^2-2*x_1*x_5-2*x_3*x_5-2*x_5^2+2*x_1*x_6-2*x_2*x_6+2*x_4*x_6+2*x_5*x_6, 0, -2*x_4^2+2*x_1*x_5+2*x_3*x_5+2*x_5^2-2*x_1*x_6+2*x_2*x_6-2*x_4*x_6-2*x_5*x_6, 0, -2*x_4^2+2*x_1*x_5+2*x_3*x_5+2*x_5^2-2*x_1*x_6+2*x_2*x_6-2*x_4*x_6-2*x_5*x_6, 6*x_4^2-6*x_1*x_5-6*x_3*x_5-6*x_5^2+6*x_1*x_6-6*x_2*x_6+6*x_4*x_6+6*x_5*x_6},
        {0, 0, 0, 0, 0, 0, 0, 2*x_0*x_5+2*x_1*x_5+2*x_3*x_5+2*x_5^2-2*x_5*x_6, -2*x_0*x_5-2*x_1*x_5-2*x_3*x_5-2*x_5^2+2*x_5*x_6, 2*x_0*x_5+2*x_1*x_5+2*x_3*x_5+2*x_5^2-2*x_5*x_6},
        {0, 0, 0, 0, -4*x_1*x_3-2*x_4^2+4*x_1*x_5-4*x_3*x_5-2*x_4*x_5+4*x_5^2-4*x_1*x_6+2*x_2*x_6+4*x_3*x_6-6*x_5*x_6+2*x_6^2, 0, 4*x_1*x_3+2*x_4^2-4*x_1*x_5+4*x_3*x_5+2*x_4*x_5-4*x_5^2+4*x_1*x_6-2*x_2*x_6-4*x_3*x_6+6*x_5*x_6-2*x_6^2, 0, 4*x_1*x_3+2*x_4^2-4*x_1*x_5+4*x_3*x_5+2*x_4*x_5-4*x_5^2+4*x_1*x_6-2*x_2*x_6-4*x_3*x_6+6*x_5*x_6-2*x_6^2, -8*x_1*x_3-4*x_4^2+8*x_1*x_5-8*x_3*x_5-4*x_4*x_5+8*x_5^2-8*x_1*x_6+4*x_2*x_6+8*x_3*x_6-12*x_5*x_6+4*x_6^2},
        {0, 0, 0, 0, -4*x_1*x_3-4*x_4^2+4*x_1*x_5+4*x_5^2-4*x_1*x_6+4*x_2*x_6+4*x_3*x_6-4*x_4*x_6-4*x_5*x_6, 0, 4*x_1*x_3+4*x_4^2-4*x_1*x_5-4*x_5^2+4*x_1*x_6-4*x_2*x_6-4*x_3*x_6+4*x_4*x_6+4*x_5*x_6, 0, 4*x_1*x_3+4*x_4^2-4*x_1*x_5-4*x_5^2+4*x_1*x_6-4*x_2*x_6-4*x_3*x_6+4*x_4*x_6+4*x_5*x_6, -12*x_1*x_3-12*x_4^2+12*x_1*x_5+12*x_5^2-12*x_1*x_6+12*x_2*x_6+12*x_3*x_6-12*x_4*x_6-12*x_5*x_6},
        {0, 0, 0, 0, -x_4^2+x_1*x_5+2*x_3*x_5+x_5^2-x_1*x_6+x_2*x_6-x_4*x_6-x_5*x_6, 0, x_4^2-x_1*x_5-2*x_3*x_5-x_5^2+x_1*x_6-x_2*x_6+x_4*x_6+x_5*x_6, 0, x_4^2-x_1*x_5-2*x_3*x_5-x_5^2+x_1*x_6-x_2*x_6+x_4*x_6+x_5*x_6, -2*x_4^2+2*x_1*x_5+4*x_3*x_5+2*x_5^2-2*x_1*x_6+2*x_2*x_6-2*x_4*x_6-2*x_5*x_6},
        {0, 0, 0, 0, 0, 0, 0, x_4^2-2*x_0*x_5-4*x_1*x_5-2*x_3*x_5+x_4*x_5-4*x_5^2+x_0*x_6+3*x_1*x_6-x_2*x_6+6*x_5*x_6-2*x_6^2, -x_4^2+2*x_0*x_5+4*x_1*x_5+2*x_3*x_5-x_4*x_5+4*x_5^2-x_0*x_6-3*x_1*x_6+x_2*x_6-6*x_5*x_6+2*x_6^2, x_4^2-2*x_0*x_5-4*x_1*x_5-2*x_3*x_5+x_4*x_5-4*x_5^2+x_0*x_6+3*x_1*x_6-x_2*x_6+6*x_5*x_6-2*x_6^2},
        {0, 0, 0, 0, -x_4^2+2*x_3*x_5+x_4*x_5-x_1*x_6+x_2*x_6-x_4*x_6, 0, x_4^2-2*x_3*x_5-x_4*x_5+x_1*x_6-x_2*x_6+x_4*x_6, 0, x_4^2-2*x_3*x_5-x_4*x_5+x_1*x_6-x_2*x_6+x_4*x_6, -3*x_4^2+6*x_3*x_5+3*x_4*x_5-3*x_1*x_6+3*x_2*x_6-3*x_4*x_6},
        {2*x_4^2-2*x_1*x_5-2*x_3*x_5-2*x_5^2+x_1*x_6-x_2*x_6+2*x_4*x_6+2*x_5*x_6, -2*x_4^2+2*x_1*x_5+2*x_3*x_5+2*x_5^2-x_1*x_6+x_2*x_6-2*x_4*x_6-2*x_5*x_6, 0, -2*x_4^2+2*x_1*x_5+2*x_3*x_5+2*x_5^2-x_1*x_6+x_2*x_6-2*x_4*x_6-2*x_5*x_6, 4*x_4^2-4*x_1*x_5-4*x_3*x_5-4*x_5^2+2*x_1*x_6-2*x_2*x_6+4*x_4*x_6+4*x_5*x_6, 0, -4*x_4^2+4*x_1*x_5+4*x_3*x_5+4*x_5^2-2*x_1*x_6+2*x_2*x_6-4*x_4*x_6-4*x_5*x_6, 2*x_4^2-2*x_1*x_5-2*x_3*x_5-2*x_5^2+x_1*x_6-x_2*x_6+2*x_4*x_6+2*x_5*x_6, -4*x_4^2+4*x_1*x_5+4*x_3*x_5+4*x_5^2-2*x_1*x_6+2*x_2*x_6-4*x_4*x_6-4*x_5*x_6, 4*x_4^2-4*x_1*x_5-4*x_3*x_5-4*x_5^2+2*x_1*x_6-2*x_2*x_6+4*x_4*x_6+4*x_5*x_6},
        {0, x_1*x_3-x_2*x_3+x_4^2-x_1*x_5-x_3*x_5-x_5^2+x_1*x_6-x_2*x_6+x_4*x_6+x_5*x_6, 0, 0, 0, x_1*x_3-x_2*x_3+x_4^2-x_1*x_5-x_3*x_5-x_5^2+x_1*x_6-x_2*x_6+x_4*x_6+x_5*x_6, -2*x_1*x_3+2*x_2*x_3-2*x_4^2+2*x_1*x_5+2*x_3*x_5+2*x_5^2-2*x_1*x_6+2*x_2*x_6-2*x_4*x_6-2*x_5*x_6, 0, -2*x_1*x_3+2*x_2*x_3-2*x_4^2+2*x_1*x_5+2*x_3*x_5+2*x_5^2-2*x_1*x_6+2*x_2*x_6-2*x_4*x_6-2*x_5*x_6, 6*x_1*x_3-6*x_2*x_3+6*x_4^2-6*x_1*x_5-6*x_3*x_5-6*x_5^2+6*x_1*x_6-6*x_2*x_6+6*x_4*x_6+6*x_5*x_6},
        {0, 0, 0, 0, 0, -8*x_1*x_3-4*x_4^2+8*x_0*x_5+16*x_1*x_5-4*x_4*x_5+16*x_5^2-4*x_0*x_6-12*x_1*x_6+4*x_2*x_6+4*x_3*x_6-24*x_5*x_6+8*x_6^2, 16*x_1*x_3+8*x_4^2-16*x_0*x_5-32*x_1*x_5+8*x_4*x_5-32*x_5^2+8*x_0*x_6+24*x_1*x_6-8*x_2*x_6-8*x_3*x_6+48*x_5*x_6-16*x_6^2, -8*x_1*x_3-4*x_4^2+8*x_0*x_5+16*x_1*x_5-4*x_4*x_5+16*x_5^2-4*x_0*x_6-12*x_1*x_6+4*x_2*x_6+4*x_3*x_6-24*x_5*x_6+8*x_6^2, 16*x_1*x_3+8*x_4^2-16*x_0*x_5-32*x_1*x_5+8*x_4*x_5-32*x_5^2+8*x_0*x_6+24*x_1*x_6-8*x_2*x_6-8*x_3*x_6+48*x_5*x_6-16*x_6^2, -32*x_1*x_3-16*x_4^2+32*x_0*x_5+64*x_1*x_5-16*x_4*x_5+64*x_5^2-16*x_0*x_6-48*x_1*x_6+16*x_2*x_6+16*x_3*x_6-96*x_5*x_6+32*x_6^2},
        {-(1/2)*x_4^2-(1/2)*x_0*x_5-(1/2)*x_1*x_5-(1/2)*x_5^2-(1/2)*x_4*x_6+(1/2)*x_5*x_6, (1/2)*x_4^2+(1/2)*x_0*x_5+(1/2)*x_1*x_5+(1/2)*x_5^2+(1/2)*x_4*x_6-(1/2)*x_5*x_6, -(1/2)*x_4^2-(1/2)*x_0*x_5-(1/2)*x_1*x_5-(1/2)*x_5^2-(1/2)*x_4*x_6+(1/2)*x_5*x_6, x_4^2+x_0*x_5+x_1*x_5+x_5^2+x_4*x_6-x_5*x_6, -(1/2)*x_4^2-(1/2)*x_0*x_5-(1/2)*x_1*x_5-(1/2)*x_5^2-(1/2)*x_4*x_6+(1/2)*x_5*x_6, 0, (1/2)*x_4^2+(1/2)*x_0*x_5+(1/2)*x_1*x_5+(1/2)*x_5^2+(1/2)*x_4*x_6-(1/2)*x_5*x_6, -x_4^2-x_0*x_5-x_1*x_5-x_5^2-x_4*x_6+x_5*x_6, (1/2)*x_4^2+(1/2)*x_0*x_5+(1/2)*x_1*x_5+(1/2)*x_5^2+(1/2)*x_4*x_6-(1/2)*x_5*x_6, x_4^2+x_0*x_5+x_1*x_5+x_5^2+x_4*x_6-x_5*x_6},
        {0, 0, 0, 0, 0, 0, 0, 0, x_2*x_5+x_3*x_5, -3*x_2*x_5-3*x_3*x_5}}


Sum of tangent vectors:
{x_2^2+x_2*x_3+(3/2)*x_4^2-(1/2)*x_0*x_5-(5/2)*x_1*x_5+x_2*x_5-x_3*x_5-(5/2)*x_5^2+x_1*x_6-x_2*x_6+(3/2)*x_4*x_6+(5/2)*x_5*x_6,
 -x_2^2+x_1*x_3-2*x_2*x_3-(1/2)*x_4^2+(1/2)*x_0*x_5+(3/2)*x_1*x_5+x_3*x_5+x_4*x_5+(5/2)*x_5^2-(1/2)*x_4*x_6-(3/2)*x_5*x_6,
 -(1/2)*x_4^2-(1/2)*x_0*x_5-(1/2)*x_1*x_5-(1/2)*x_5^2-(1/2)*x_4*x_6+(1/2)*x_5*x_6,
 -x_4^2+x_0*x_5+3*x_1*x_5+2*x_3*x_5+3*x_5^2-x_1*x_6+x_2*x_6-x_4*x_6-3*x_5*x_6,
 -8*x_1*x_3-(5/2)*x_4^2-(1/2)*x_0*x_5+(5/2)*x_1*x_5-6*x_3*x_5-x_4*x_5+(5/2)*x_5^2-6*x_1*x_6+4*x_2*x_6+8*x_3*x_6-(1/2)*x_4*x_6-(9/2)*x_5*x_6+2*x_6^2,
 -7*x_1*x_3-x_2*x_3-3*x_4^2+8*x_0*x_5+15*x_1*x_5+x_2*x_5-3*x_4*x_5+16*x_5^2-4*x_0*x_6-11*x_1*x_6+3*x_2*x_6+4*x_3*x_6+x_4*x_6-23*x_5*x_6+8*x_6^2,
 22*x_1*x_3+2*x_2*x_3+(17/2)*x_4^2-(31/2)*x_0*x_5-(65/2)*x_1*x_5-x_2*x_5+7*x_3*x_5+8*x_4*x_5-(67/2)*x_5^2+8*x_0*x_6+28*x_1*x_6-10*x_2*x_6-16*x_3*x_6-(3/2)*x_4*x_6+(101/2)*x_5*x_6-18*x_6^2,
 x_2^2-8*x_1*x_3+x_2*x_3-2*x_4^2+7*x_0*x_5+11*x_1*x_5+x_2*x_5-x_3*x_5-3*x_4*x_5+11*x_5^2-3*x_0*x_6-8*x_1*x_6+2*x_2*x_6+4*x_3*x_6+x_4*x_6-17*x_5*x_6+6*x_6^2,
 22*x_1*x_3+x_2*x_3-x_3^2+(13/2)*x_4^2-(31/2)*x_0*x_5-(61/2)*x_1*x_5+8*x_3*x_5+6*x_4*x_5-(63/2)*x_5^2+7*x_0*x_6+25*x_1*x_6-9*x_2*x_6-16*x_3*x_6-(3/2)*x_4*x_6+(93/2)*x_5*x_6-16*x_6^2,
 -2*x_2^2-46*x_1*x_3-5*x_2*x_3+3*x_3^2-16*x_4^2+33*x_0*x_5+69*x_1*x_5-2*x_2*x_5-16*x_3*x_5-10*x_4*x_5+72*x_5^2-15*x_0*x_6-56*x_1*x_6+22*x_2*x_6+36*x_3*x_6-103*x_5*x_6+34*x_6^2}