Computer calculations for "Some singular curves in Mukai's model of \(\overline{M}_7\)", Section 6

Code 6.11: An \( \operatorname{SO}(10)\) invariant polynomial in 20 variables

i120 : -- Now simplify F5w1 in Sym5 Std otimes Sym5 Std
       R = QQ[join(gens R1,gens R2)];

i121 : inc1 = map(R,R1,apply(10, i -> R_i));

o121 : RingMap R <--- R1

i122 : inc2 = map(R,R2,apply(10, i -> R_(10+i)));

o122 : RingMap R <--- R2

i123 : F5w1 = sum apply(4722, i -> (F5w1_i)*(inc1(MyBasis1#(Wt0TensorBasis_i_0)))*(inc2(MyBasis2#(Wt0TensorBasis_i_1))));

i124 : fn = openOut "F5w1 as polynomial in xy.m2";

i125 : fn << toString(F5w1) << endl;

i126 : close fn;

Here is the file loaded in this session. WeylSO10.m2.txt

i127 : -- Check W invariance of F5w1 and express it as a sum of Weyl group orbits
       s = WeylGensStd(5);

i128 : load "WeylSO10.m2";

i129 : W = WeylSO10(s_1,s_2,s_3,s_4,s_5);

i130 : diagonalJoin = (M) -> (
           R:=ring(M);
           Z:=matrix apply(numRows M, i -> apply(numColumns M, j -> 0_R));
           (M|Z)||(Z|M)
       );

i131 : W = apply(W, M -> map(R,R,diagonalJoin(M)));

i132 : orbitSum = (f,W) -> (
           sum apply(W, F -> F(f))  
       );

i133 : sortIntoOrbits = (inputF,W) -> (
           F:=inputF;
           OrbitList:={};
           L:={};
           LM:={};
           c:=0;
           j:=0;
           while F!=0 do (
       	print concatenate("j=",toString(j)," loops, #terms(F) = ",toString(#(terms F)),", #Orbits=",toString(#OrbitList)) << endl;
               L = orbitSum(leadMonomial(F),W);
       	c = leadCoefficient(F)/leadCoefficient(L);
       	OrbitList = append(OrbitList,{leadMonomial(F),c,L});
       	F = F - c*L;
       	j=j+1;	
           );
           return OrbitList
       );

i134 : time A = sortIntoOrbits(F5w1,W);
j=0 loops, #terms(F) = 7502, #Orbits=0
j=1 loops, #terms(F) = 7492, #Orbits=1
j=2 loops, #terms(F) = 7412, #Orbits=2
j=3 loops, #terms(F) = 7332, #Orbits=3
j=4 loops, #terms(F) = 7092, #Orbits=4
j=5 loops, #terms(F) = 6852, #Orbits=5
j=6 loops, #terms(F) = 6532, #Orbits=6
j=7 loops, #terms(F) = 6516, #Orbits=7
j=8 loops, #terms(F) = 6506, #Orbits=8
j=9 loops, #terms(F) = 6466, #Orbits=9
j=10 loops, #terms(F) = 6386, #Orbits=10
j=11 loops, #terms(F) = 6306, #Orbits=11
j=12 loops, #terms(F) = 6066, #Orbits=12
j=13 loops, #terms(F) = 5986, #Orbits=13
j=14 loops, #terms(F) = 5906, #Orbits=14
j=15 loops, #terms(F) = 5666, #Orbits=15
j=16 loops, #terms(F) = 5626, #Orbits=16
j=17 loops, #terms(F) = 5586, #Orbits=17
j=18 loops, #terms(F) = 5466, #Orbits=18
j=19 loops, #terms(F) = 5226, #Orbits=19
j=20 loops, #terms(F) = 4746, #Orbits=20
j=21 loops, #terms(F) = 4266, #Orbits=21
j=22 loops, #terms(F) = 4026, #Orbits=22
j=23 loops, #terms(F) = 3786, #Orbits=23
j=24 loops, #terms(F) = 3546, #Orbits=24
j=25 loops, #terms(F) = 3066, #Orbits=25
j=26 loops, #terms(F) = 2906, #Orbits=26
j=27 loops, #terms(F) = 2426, #Orbits=27
j=28 loops, #terms(F) = 2266, #Orbits=28
j=29 loops, #terms(F) = 2250, #Orbits=29
j=30 loops, #terms(F) = 2240, #Orbits=30
j=31 loops, #terms(F) = 2200, #Orbits=31
j=32 loops, #terms(F) = 2160, #Orbits=32
j=33 loops, #terms(F) = 2100, #Orbits=33
j=34 loops, #terms(F) = 2060, #Orbits=34
j=35 loops, #terms(F) = 2020, #Orbits=35
j=36 loops, #terms(F) = 1980, #Orbits=36
j=37 loops, #terms(F) = 1860, #Orbits=37
j=38 loops, #terms(F) = 1740, #Orbits=38
j=39 loops, #terms(F) = 1620, #Orbits=39
j=40 loops, #terms(F) = 1500, #Orbits=40
j=41 loops, #terms(F) = 1460, #Orbits=41
j=42 loops, #terms(F) = 1420, #Orbits=42
j=43 loops, #terms(F) = 1380, #Orbits=43
j=44 loops, #terms(F) = 1260, #Orbits=44
j=45 loops, #terms(F) = 1140, #Orbits=45
j=46 loops, #terms(F) = 1020, #Orbits=46
j=47 loops, #terms(F) = 900, #Orbits=47
j=48 loops, #terms(F) = 780, #Orbits=48
j=49 loops, #terms(F) = 720, #Orbits=49
j=50 loops, #terms(F) = 600, #Orbits=50
j=51 loops, #terms(F) = 540, #Orbits=51
j=52 loops, #terms(F) = 300, #Orbits=52
j=53 loops, #terms(F) = 180, #Orbits=53
j=54 loops, #terms(F) = 60, #Orbits=54
     -- used 0.218105 seconds

i135 : fn = openOut "F5w1 as orbital sum.m2";

i136 : for i from 0 to #A-1 do (
         fn <<  toString({A_i_0,A_i_1}) << endl;
       );

i137 : close fn

o137 = F5w1 as orbital sum.m2

o137 : File