load "V30100inW9W2Stdstar.m2";
load "V00030inW9W2Stdstar.m2";
load "V03000inS2V30100.m2";
load "V00000inS3V00030.m2";
load "V00000inS3V03000.m2";
load "V00000inV00030otimesV03000.m2";
load "V00000inV11011otimesV11011.m2";
load "V11011inW9W2Stdstar.m2";


F82a = (M) -> (
    s9 := subsets(apply(15, i -> i),9);
    p := apply(s9, s -> det(M_s));
    V00030 := V00030inW9W2Stdstar(p);
    first V00000inS3V00030(V00030)
);



F82b = (M) -> (
    s9 := subsets(apply(15, i -> i),9);
    p := apply(s9, s -> det(M_s));
    V30100 := V30100inW9W2Stdstar(p);
    V03000 := V03000inS2V30100(V30100);
    first V00000inS3V03000(V03000)
);



F82c = (M) -> (
    s9 := subsets(apply(15, i -> i),9);
    p := apply(s9, s -> det(M_s));
    V30100 := V30100inW9W2Stdstar(p);
    V00030 := V00030inW9W2Stdstar(p);
    V03000 := V03000inS2V30100(V30100);
    first V00000inV00030otimesV03000(V00030,V03000)
);



F82d = (M) -> (
    s9 := subsets(apply(15, i -> i),9);
    p := apply(s9, s -> det(M_s));
    V11011 := V11011inW9W2Stdstar(p);
    V00000inV11011otimesV11011(V11011,V11011)
);

matrixFromHyperplaneEquations = (L) -> (
    R:=ring(L_0);
    eqnMatrix:=matrix apply(L, f -> apply(numgens R, i -> coefficient(R_i,f)));
    transpose gens ker eqnMatrix
);


R = QQ[x_12,x_13,x_23,x_14,x_24,x_34,x_15,x_25,x_35,x_45,x_16,x_26,x_36,x_46,x_56];

M82 = matrix {{10, 5, -6, -9, -3, -1, -8, 3, 5, 10, 5, -6, -5, 4, -1}, {-10, 1, 5, -10, 4, 2, -10, -1, 1, 3, -8, 8, 1, -3, -6}, {3, -3, 8, -5, 9, 3, -3, 2, 7, 0, -4, 3, -7, 0, 4}, {4, 4, -4, 2, -8, -5, 9, 8, -3, 0, -9, 5, -5, -10, -3}, {-7, -3, -6, -4, 5, -9, 9, -5, -8, 5, 0, 3, -10, -6, -1}, {-9, -6, 1, 4, 0, 7, 9, -2, 6, 2, -10, 9, 3, 2, -10}, {9, 7, 6, -3, -10, 7, 9, -5, 4, 1, 10, 0, -2, -9, 1}, {7, 9, 10, -4, -3, 7, -8, 7, 3, 4, -5, -8, 1, 0, 2},{8, 6, 6, -7, 7, -6, 1, -8, 3, 1, 6, -3, 4, 9, 7}}
g1 = matrix {{4, -5, -2, -8, -1, 7}, {-2, -10, 7, -4, -9, 7}, {-10, -6, 5, 5, 6, 4}, {-3, -4, 9, -2, -3, -6}, {10, -1, -3, -8, -9, 0}, {-1, -3, -3, 5, 3, -1}};
g2 = matrix {1/3*{-8, 4, -6, 6, 5, -1}, {-4, -8, -1, -4, -6, -2}, {1, -7, -7, -5, -2, -3}, {9, -2, 8, -9, -8, 4}, {-10, -8, -10, -1, 5, -5}, {8, -3, 6, 9, 2, -6}};


LTD8 = {x_23-(5/3)*x_14, x_24-5*x_15, x_25-15*x_16, x_34-20*x_16, x_35-5*x_26, x_45-(5/3)*x_36};
MTD8 = matrixFromHyperplaneEquations LTD8;
-- matrix {{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 5/3, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 5, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 20, 0, 15, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 5/3, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}

-- Example 8c: a genus 8 reducible surface with four components, each generically nonreduced
LNonRedSurf8 = {x_12-x_34, x_12-x_13, x_14-x_45, x_16-x_23, x_24-x_35, x_26-x_36};
MNonRedSurf8 = matrixFromHyperplaneEquations LNonRedSurf8;
-- matrix matrix {{1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}}

F82a(M82)
F82a(transpose(exteriorPower(2,g1)*transpose(M82)))
F82a(transpose(exteriorPower(2,g2)*transpose(M82)))
F82a(MTD8)
F82a(MNonRedSurf8)



F82b(M82)
F82b(transpose(exteriorPower(2,g1)*transpose(M82)))
F82b(transpose(exteriorPower(2,g2)*transpose(M82)))
F82b(MTD8)
F82b(MNonRedSurf8)




F82c(M82)
F82c(transpose(exteriorPower(2,g1)*transpose(M82)))
F82c(transpose(exteriorPower(2,g2)*transpose(M82)))
F82c(MTD8)
F82c(MNonRedSurf8)





F82d(M82)
F82d(transpose(exteriorPower(2,g1)*transpose(M82)))
F82d(transpose(exteriorPower(2,g2)*transpose(M82)))
F82d(MTD8)
F82d(MNonRedSurf8)