-- Note: this file contains functions for evaluating invariant polynomials associated to Mukai's models.
-- The polynomials themselves could be obtained by composing the formulas in the files loaded below,
-- but we do not recommend this as the resulting expressions would be very complicated

-- 7-1
load "V30001inW7V00010star.m2";
load "V30000inS2V30001.m2";
load "V00000InS2V30000.m2";

-- 7-2
load "V40000inW8V00010star.m2";
load "V00000InS2V40000.m2";

-- 8-1
load "V02002inW8W2Stdstar.m2";
load "V02000inS2V02002.m2";
load "V00000inS3V02000.m2";

-- 8-2
load "V30100inW9W2Stdstar.m2";
load "V00030inW9W2Stdstar.m2";
load "V03000inS2V30100.m2";
load "V00000inS3V00030.m2";
load "V00000inS3V03000.m2";
load "V00000inV00030otimesV03000.m2";
load "V00000inV11011otimesV11011.m2";
load "V11011inW9W2Stdstar.m2";

-- 9-1
load "V500InW9V001star.m2";
load "V200inS2V500.m2";
load "V000InS2V200.m2";

-- 9-2
load "V000InW10V001star.m2";

-- 10-1
load "V01inW10V01star.m2";
load "V00inS2V01.m2";

-- 10-2
load "V00inW11V01star.m2";



-- When finding linear spaces, we worked in a basis of V(\omega_4) that was selected by hand
-- The invariant polynomials F_{7,1} and F_{7,2} computed in Macaulay2 are written in the de Graaf basis of V(\omega_3)
-- Need to change coordinates. The matrix P below is the change of basis matrix [P]_{dG <- DS}

F71 = (M) -> (
    s7 := subsets(apply(16, i -> i),7);
    P := matrix {{0/1, 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, 0, 1, 0, 0, 0}, {0, 0, 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, 0, 0, 0, 0, 0}, {0, 0, 0, 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, 0, 0, 0, 0}, {0, 0, 0, 0, 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, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 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, 0, 0, -1, 0, 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, 0, 1, 0, 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, 0, -1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
    MdG:=transpose(P*(transpose M));
    p := apply(s7, i -> det((MdG)_i));
    V30001:=V30001inW7V00010star(p);
    V30000:=V30000inS2V30001(V30001);
    first V00000InS2V30000(V30000)
)



F72 = (M) -> (
    s8 := subsets(apply(16, i -> i),8);
    P := matrix {{0/1, 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, 0, 1, 0, 0, 0}, {0, 0, 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, 0, 0, 0, 0, 0}, {0, 0, 0, 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, 0, 0, 0, 0}, {0, 0, 0, 0, 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, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 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, 0, 0, -1, 0, 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, 0, 1, 0, 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, 0, -1, 0, 0, 0, 0, 0}, {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}};
    MdG:=transpose(P*(transpose M));
    p := apply(s8, i -> det((MdG)_i));
    V40000:=V40000inW8V00010star(p);
    first V00000InS2V40000(V40000)
)



F81 = (M) -> (
    s8 := subsets(apply(15, i -> i),8);
    p := apply(s8, s -> det(M_s));
    V02002 := V02002inW8W2Stdstar(p);
    V02000 := V02000inS2V02002(V02002);
    first V00000inS3V02000(V02000)
);



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)
);


F82 = F82d


-- When finding linear spaces, we worked in a basis of V(\omega_3) that was selected by hand
-- The invariant polynomials F_{9,1} and F_{9,2} computed in Macaulay2 are written in the de Graaf basis of V(\omega_3)
-- Need to change coordinates. The matrix P below is the change of basis matrix [P]_{dG <- DS}
-- Updated my basis and P on May 29, 2026


F91 = (M) -> (
    s9 := subsets(apply(14, i -> i),9);
    P:=matrix {{1, 0, 0, 0, 0, 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, 1, 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, 1, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 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, -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, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/1}};
    MdG:=transpose(P*(transpose M));
    p := apply(s9, i -> det((MdG)_i));
    V500:=V500InW9V001star(p);
    V200:=V200inS2V500(V500);
    first V000InS2V200(V200)
)



F92 = (M) -> (
    s10 := subsets(apply(14, i -> i),10);
    P:=matrix {{1, 0, 0, 0, 0, 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, 1, 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, 1, 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, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 1, 0, 0, 0, 0, 0, 0, 0, 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, -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, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1/1}};
    MdG:=transpose(P*(transpose M));
    p := apply(s10, i -> det((MdG)_i));
    first V000InW10V001star(p)
)



F101 = (M) -> (
    s10 := subsets(apply(14, i -> i),10);
    p := apply(s10, i -> det(M_i));
    V01:=V01inW10V01star(p);
    first V00inS2V01(V01)
)



F102 = (M) -> (
    s11 := subsets(apply(14, i -> i),11);
    p := apply(s11, i -> det(M_i));
    first V00inW11V01star(p)
)