Type "help" to see useful commands

i1 : run "date";
Mon May  4 05:15:59 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 : rhoV30001 = deGraafRepresentation({3,0,0,0,1},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=41
Finished level 1. {#G,#B}={3, 3}
Finished level 2. {#G,#B}={6, 7}
Finished level 3. {#G,#B}={8, 15}
Finished level 4. {#G,#B}={12, 28}
Finished level 5. {#G,#B}={16, 48}
Finished level 6. {#G,#B}={22, 78}
Finished level 7. {#G,#B}={28, 120}
Finished level 8. {#G,#B}={36, 176}
Finished level 9. {#G,#B}={44, 249}
Finished level 10. {#G,#B}={57, 340}
Finished level 11. {#G,#B}={76, 449}
Finished level 12. {#G,#B}={106, 577}
Finished level 13. {#G,#B}={150, 722}
Finished level 14. {#G,#B}={212, 881}
Finished level 15. {#G,#B}={293, 1052}
Finished level 16. {#G,#B}={394, 1230}
Finished level 17. {#G,#B}={513, 1410}
Finished level 18. {#G,#B}={645, 1588}
Finished level 19. {#G,#B}={785, 1759}
Finished level 20. {#G,#B}={928, 1918}
Finished level 21. {#G,#B}={1066, 2063}
Finished level 22. {#G,#B}={1194, 2191}
Finished level 23. {#G,#B}={1309, 2300}
Finished level 24. {#G,#B}={1407, 2391}
Finished level 25. {#G,#B}={1488, 2464}
Finished level 26. {#G,#B}={1552, 2520}
Finished level 27. {#G,#B}={1601, 2562}
Finished level 28. {#G,#B}={1636, 2592}
Finished level 29. {#G,#B}={1661, 2612}
Finished level 30. {#G,#B}={1677, 2625}
Finished level 31. {#G,#B}={1687, 2633}
Finished level 32. {#G,#B}={1693, 2637}
Finished level 33. {#G,#B}={1696, 2639}
Finished level 34. {#G,#B}={1697, 2640}
Finished level 35. {#G,#B}={1698, 2640}
Finished level 36. {#G,#B}={1698, 2640}
Finished level 37. {#G,#B}={1698, 2640}
Finished level 38. {#G,#B}={1698, 2640}
Finished level 39. {#G,#B}={1698, 2640}
Finished level 40. {#G,#B}={1698, 2640}
Finished level 41. {#G,#B}={1698, 2640}
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 : rhoV30001 = lieAlgebraRepresentation(rhoV30001#"Module",LAB,rhoV30001#"RepresentationMatrices");

i9 : wts = representationWeights(rhoV00010star);

i10 : s7 = subsets(apply(#wts, i -> i),7);

i11 : t=first select(s7, s -> sum apply(s, j -> wts_j)=={3,0,0,0,1})

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

o11 : List

i12 : hwv1 = transpose matrix {apply(s7, s -> if s==t then 1/1 else 0/1)};

               11440       1
o12 : Matrix QQ      <-- QQ

i13 : V30001inW7V00010star = VInWedgekW(rhoV30001,7,rhoV00010star,hwv1,"SaveAsFunction"=>"V30001inW7V00010star");
Length 1 complete. 14 new words found
Length 2 complete. 85 new words found
Length 3 complete. 344 new words found
Length 4 complete. 1051 new words found
Length 5 complete. 849 new words found
Length 6 complete. 242 new words found
Length 7 complete. 49 new words found
Length 8 complete. 5 new words found

i14 : run "date";
Mon May  4 07:05:24 EDT 2026

i15 : quit


Type "help" to see useful commands

i1 : run "date";
Mon May  4 07:05:25 EDT 2026

i2 : needsPackage("LieAlgebraRepresentations");

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

i4 : rhoV30001 = deGraafRepresentation({3,0,0,0,1},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=41
Finished level 1. {#G,#B}={3, 3}
Finished level 2. {#G,#B}={6, 7}
Finished level 3. {#G,#B}={8, 15}
Finished level 4. {#G,#B}={12, 28}
Finished level 5. {#G,#B}={16, 48}
Finished level 6. {#G,#B}={22, 78}
Finished level 7. {#G,#B}={28, 120}
Finished level 8. {#G,#B}={36, 176}
Finished level 9. {#G,#B}={44, 249}
Finished level 10. {#G,#B}={57, 340}
Finished level 11. {#G,#B}={76, 449}
Finished level 12. {#G,#B}={106, 577}
Finished level 13. {#G,#B}={150, 722}
Finished level 14. {#G,#B}={212, 881}
Finished level 15. {#G,#B}={293, 1052}
Finished level 16. {#G,#B}={394, 1230}
Finished level 17. {#G,#B}={513, 1410}
Finished level 18. {#G,#B}={645, 1588}
Finished level 19. {#G,#B}={785, 1759}
Finished level 20. {#G,#B}={928, 1918}
Finished level 21. {#G,#B}={1066, 2063}
Finished level 22. {#G,#B}={1194, 2191}
Finished level 23. {#G,#B}={1309, 2300}
Finished level 24. {#G,#B}={1407, 2391}
Finished level 25. {#G,#B}={1488, 2464}
Finished level 26. {#G,#B}={1552, 2520}
Finished level 27. {#G,#B}={1601, 2562}
Finished level 28. {#G,#B}={1636, 2592}
Finished level 29. {#G,#B}={1661, 2612}
Finished level 30. {#G,#B}={1677, 2625}
Finished level 31. {#G,#B}={1687, 2633}
Finished level 32. {#G,#B}={1693, 2637}
Finished level 33. {#G,#B}={1696, 2639}
Finished level 34. {#G,#B}={1697, 2640}
Finished level 35. {#G,#B}={1698, 2640}
Finished level 36. {#G,#B}={1698, 2640}
Finished level 37. {#G,#B}={1698, 2640}
Finished level 38. {#G,#B}={1698, 2640}
Finished level 39. {#G,#B}={1698, 2640}
Finished level 40. {#G,#B}={1698, 2640}
Finished level 41. {#G,#B}={1698, 2640}
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 : LAB = rhoV30001#"Basis";

i6 : rhoV30000 = deGraafRepresentation({3,0,0,0,0},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=31
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}={12, 12}
Finished level 5. {#G,#B}={14, 18}
Finished level 6. {#G,#B}={16, 27}
Finished level 7. {#G,#B}={20, 37}
Finished level 8. {#G,#B}={26, 50}
Finished level 9. {#G,#B}={34, 64}
Finished level 10. {#G,#B}={46, 80}
Finished level 11. {#G,#B}={60, 96}
Finished level 12. {#G,#B}={78, 114}
Finished level 13. {#G,#B}={99, 130}
Finished level 14. {#G,#B}={122, 146}
Finished level 15. {#G,#B}={146, 160}
Finished level 16. {#G,#B}={172, 173}
Finished level 17. {#G,#B}={196, 183}
Finished level 18. {#G,#B}={219, 192}
Finished level 19. {#G,#B}={240, 198}
Finished level 20. {#G,#B}={258, 203}
Finished level 21. {#G,#B}={272, 206}
Finished level 22. {#G,#B}={284, 208}
Finished level 23. {#G,#B}={292, 209}
Finished level 24. {#G,#B}={298, 210}
Finished level 25. {#G,#B}={302, 210}
Finished level 26. {#G,#B}={304, 210}
Finished level 27. {#G,#B}={305, 210}
Finished level 28. {#G,#B}={306, 210}
Finished level 29. {#G,#B}={306, 210}
Finished level 30. {#G,#B}={306, 210}
Finished level 31. {#G,#B}={306, 210}
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)

i7 : rhoV30000 = lieAlgebraRepresentation(rhoV30000#"Module",rhoV30001#"Basis",rhoV30000#"RepresentationMatrices");

i8 : hwv2 = weightMuHighestWeightVectorsInSymdW({3,0,0,0,0},2,rhoV30001);
Constructing the Casimir operator...
Other EVs: {121, 105, 101, 99, 93, 91, 89, 83, 81, 75, 69, 65, 63, 57, 55, 49, 41, 35, 27, 25, 9}
Beginning projections...
    j=0:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
    j=1:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=2:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=3:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=4:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=5:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=6:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=7:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=8:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=9:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=10:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=11:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=12:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=13:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=14:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=15:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
    j=16:
        EV 121 complete
        EV 105 complete
        EV 101 complete
        EV 99 complete
        EV 93 complete
        EV 91 complete
        EV 89 complete
        EV 83 complete
        EV 81 complete
        EV 75 complete
        EV 69 complete
        EV 65 complete
        EV 63 complete
        EV 57 complete
        EV 55 complete
        EV 49 complete
        EV 41 complete
        EV 35 complete
        EV 27 complete
        EV 25 complete
        EV 9 complete
    #hwvs=0

i9 : V30000inS2V30001 = VInSymdW(rhoV30000,2,rhoV30001,hwv2_0,"SaveAsFunction"=>"V30000inS2V30001");
Length 1 complete. 8 new words found
Length 2 complete. 36 new words found
Length 3 complete. 120 new words found
Length 4 complete. 36 new words found
Length 5 complete. 8 new words found
Length 6 complete. 1 new words found
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i10 : run "date";
Tue May  5 05:18:23 EDT 2026

i11 : quit