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i1 : run "date";
Tue May  5 06:53:31 EDT 2026

i2 : needsPackage("LieAlgebraRepresentations");

i3 : so10 = simpleLieAlgebra("D",5);

i4 : rhoV00010 = deGraafRepresentation({0,0,0,1,0},so10);
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
max-lev=17
Finished level 1. {#G,#B}={4, 2}
Finished level 2. {#G,#B}={8, 3}
Finished level 3. {#G,#B}={11, 5}
Finished level 4. {#G,#B}={15, 7}
Finished level 5. {#G,#B}={19, 9}
Finished level 6. {#G,#B}={25, 11}
Finished level 7. {#G,#B}={31, 13}
Finished level 8. {#G,#B}={39, 14}
Finished level 9. {#G,#B}={45, 15}
Finished level 10. {#G,#B}={51, 16}
Finished level 11. {#G,#B}={55, 16}
Finished level 12. {#G,#B}={58, 16}
Finished level 13. {#G,#B}={59, 16}
Finished level 14. {#G,#B}={60, 16}
Finished level 15. {#G,#B}={60, 16}
Finished level 16. {#G,#B}={60, 16}
Finished level 17. {#G,#B}={60, 16}
Compute rho(B_0)
Compute rho(B_1)
Compute rho(B_2)
Compute rho(B_3)
Compute rho(B_4)
Compute rho(B_5)
Compute rho(B_6)
Compute rho(B_7)
Compute rho(B_8)
Compute rho(B_9)
Compute rho(B_10)
Compute rho(B_11)
Compute rho(B_12)
Compute rho(B_13)
Compute rho(B_14)
Compute rho(B_15)
Compute rho(B_16)
Compute rho(B_17)
Compute rho(B_18)
Compute rho(B_19)
Compute rho(B_20)
Compute rho(B_21)
Compute rho(B_22)
Compute rho(B_23)
Compute rho(B_24)
Compute rho(B_25)
Compute rho(B_26)
Compute rho(B_27)
Compute rho(B_28)
Compute rho(B_29)
Compute rho(B_30)
Compute rho(B_31)
Compute rho(B_32)
Compute rho(B_33)
Compute rho(B_34)
Compute rho(B_35)
Compute rho(B_36)
Compute rho(B_37)
Compute rho(B_38)
Compute rho(B_39)
Compute rho(B_40)
Compute rho(B_41)
Compute rho(B_42)
Compute rho(B_43)
Compute rho(B_44)

i5 : rhoV00010star = dual rhoV00010;

i6 : LAB = rhoV00010#"Basis";

i7 : rhoV40000 = deGraafRepresentation({4,0,0,0,0},so10);
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
Warning:  F4 Algorithm not available over current coefficient ring or inhomogeneous ideal.
Converting to Naive algorithm.
max-lev=39
Finished level 1. {#G,#B}={4, 2}
Finished level 2. {#G,#B}={7, 4}
Finished level 3. {#G,#B}={10, 7}
Finished level 4. {#G,#B}={11, 13}
Finished level 5. {#G,#B}={13, 20}
Finished level 6. {#G,#B}={14, 31}
Finished level 7. {#G,#B}={16, 45}
Finished level 8. {#G,#B}={20, 64}
Finished level 9. {#G,#B}={26, 86}
Finished level 10. {#G,#B}={35, 114}
Finished level 11. {#G,#B}={48, 145}
Finished level 12. {#G,#B}={65, 182}
Finished level 13. {#G,#B}={87, 221}
Finished level 14. {#G,#B}={115, 264}
Finished level 15. {#G,#B}={148, 307}
Finished level 16. {#G,#B}={186, 353}
Finished level 17. {#G,#B}={229, 396}
Finished level 18. {#G,#B}={275, 439}
Finished level 19. {#G,#B}={323, 478}
Finished level 20. {#G,#B}={373, 515}
Finished level 21. {#G,#B}={421, 546}
Finished level 22. {#G,#B}={467, 574}
Finished level 23. {#G,#B}={510, 596}
Finished level 24. {#G,#B}={548, 615}
Finished level 25. {#G,#B}={581, 629}
Finished level 26. {#G,#B}={609, 640}
Finished level 27. {#G,#B}={631, 647}
Finished level 28. {#G,#B}={648, 653}
Finished level 29. {#G,#B}={661, 656}
Finished level 30. {#G,#B}={670, 658}
Finished level 31. {#G,#B}={676, 659}
Finished level 32. {#G,#B}={680, 660}
Finished level 33. {#G,#B}={682, 660}
Finished level 34. {#G,#B}={683, 660}
Finished level 35. {#G,#B}={684, 660}
Finished level 36. {#G,#B}={684, 660}
Finished level 37. {#G,#B}={684, 660}
Finished level 38. {#G,#B}={684, 660}
Finished level 39. {#G,#B}={684, 660}
Compute rho(B_0)
Compute rho(B_1)
Compute rho(B_2)
Compute rho(B_3)
Compute rho(B_4)
Compute rho(B_5)
Compute rho(B_6)
Compute rho(B_7)
Compute rho(B_8)
Compute rho(B_9)
Compute rho(B_10)
Compute rho(B_11)
Compute rho(B_12)
Compute rho(B_13)
Compute rho(B_14)
Compute rho(B_15)
Compute rho(B_16)
Compute rho(B_17)
Compute rho(B_18)
Compute rho(B_19)
Compute rho(B_20)
Compute rho(B_21)
Compute rho(B_22)
Compute rho(B_23)
Compute rho(B_24)
Compute rho(B_25)
Compute rho(B_26)
Compute rho(B_27)
Compute rho(B_28)
Compute rho(B_29)
Compute rho(B_30)
Compute rho(B_31)
Compute rho(B_32)
Compute rho(B_33)
Compute rho(B_34)
Compute rho(B_35)
Compute rho(B_36)
Compute rho(B_37)
Compute rho(B_38)
Compute rho(B_39)
Compute rho(B_40)
Compute rho(B_41)
Compute rho(B_42)
Compute rho(B_43)
Compute rho(B_44)

i8 : rhoV40000 = lieAlgebraRepresentation(rhoV40000#"Module",LAB,rhoV40000#"RepresentationMatrices");

i9 : wts = representationWeights(rhoV00010star);

i10 : s8 = subsets(apply(#wts, i -> i),8);

i11 : t=first select(s8, s -> sum apply(s, j -> wts_j)=={4,0,0,0,0})

o11 = {6, 8, 10, 11, 12, 13, 14, 15}

o11 : List

i12 : hwv1 = transpose matrix {apply(s8, s -> if s==t then 1/1 else 0/1)};

               12870       1
o12 : Matrix QQ      <-- QQ

i13 : V40000inW8V00010star = VInWedgekW(rhoV40000,8,rhoV00010star,hwv1,"SaveAsFunction"=>"V40000inW8V00010star");
Length 1 complete. 8 new words found
Length 2 complete. 36 new words found
Length 3 complete. 120 new words found
Length 4 complete. 330 new words found
Length 5 complete. 120 new words found
Length 6 complete. 36 new words found
Length 7 complete. 8 new words found
Length 8 complete. 1 new words found

i14 : hwv2 = weightMuHighestWeightVectorsInSymdW({0,0,0,0,0},2,rhoV40000);
Constructing the Casimir operator...
Other EVs: {128, 100, 88, 84, 64, 48, 36, 20}
Beginning projections...
    j=0:
        EV 128 complete
        EV 100 complete
        EV 88 complete
        EV 84 complete
        EV 64 complete
        EV 48 complete
        EV 36 complete
        EV 20 complete
    #hwvs=0

i15 : rhoV00000=trivialRepresentation(so10);

i16 : rhoV00000 = lieAlgebraRepresentation(rhoV00000#"Module",LAB,rhoV00000#"RepresentationMatrices");

i17 : V00000InS2V40000=VInSymdW(rhoV00000,2,rhoV40000,hwv2_0,"SaveAsFunction"=>"V00000InS2V40000");
Length 1 complete. 0 new words found
0

i18 : run "date";
Tue May  5 07:43:43 EDT 2026

i19 : 
      
      quit