sounds good ill definitely do that next time.

I managed to do it out with paper and get the same set of equations twice, so I think im solid.  Thanks!

Oh i did't know about the *.  good to know!

Id assume as this point that im actually quite close, as i would like all of them to be zero, or at least all of them excpet adfm(that is L should be zero in the above). 

unless anyone has tips about rewwrting my big set of tensor equations in single variable form, i guess im all set.

thanks i've learnt quite a lot!

maybe?

I decided to bite the bullet and just do it out by hand.  I managed to get a set of equations which when translated into single variables looks like:a=b
h=j
c=j
k=g
kc-je=al-he-bl+gc
ka-jd=ak-hd-bk+ga
-kb+jb=-aj+ab+bj+gf
kg-jg=am-hg-bm+gf
ge=0
gd=0
gb=0
gg=0
bl-gc=-kc+je+al+me
bk-ga=-ka+jd+ak-md
-bj-gf=-kf-jb-aj+mb
bm-gh=-kh+jg+am-mg
al-he=kc-je+bl-gc
ak-hd=ka-jd+bk-ga
-aj+hb=kf+jb-bj-gf
am-hg=kh-jg+bm-gh

so maple gives me no solutions when i try to use the solve function.  However when i try to do this out by hand i can get all variables equal to m except g=k=0.  as well, f and L appear to be unconstrained.  Is there someway to make maple check this? thanks so much

Thanks for the tips!
 

Apparently I was using the wrong brackets for with, so I didn't see all those errors. Wow.   Apparently It does not like me mixing space and spacetime indices(Roman and greek) in my constraints.  I am puzzled as to how to implement one of my constraints:

 number 1
constraintp := Define(P[epsilon, delta, eta, theta], antisymmetric = {{eta, delta, epsilon}}) = LeviCivita[epsilon, Zeta, eta]

when theta=0 id like this to become the 3d levi civita tensor, but maple isnt a fan of me changing dimensions like that.  I seem to have the rest figured out, as I can get an answer of no solutions back implementing just the other constraint, and the "fundamentalidentity".

New Code!

> with(Physics);

[*, ., Annihilation, AntiCommutator, Bra, Bracket, Check, Commutator,

  Coordinates, Creation, Dagger, Define, Dgamma, FeynmanDiagrams, Fundiff,

  Intc, Inverse, Ket, KroneckerDelta, LeviCivita, Parameters, Projector,

  Psigma, Setup, Simplify, SpaceTimeVector, Trace, Vectors, ^, dAlembertian,

  d_, diff, g_]

>

> Define(A[mu, tau, phi, rho], antisymmetric = {{mu, phi, tau}});

                   Defined objects with tensor properties

      {A[mu, tau, phi, rho], d_[mu], g_[mu, nu], gamma[mu], sigma[mu],

        epsilon[mu, alpha, beta, nu], delta[mu, nu]}

> Define(B[sigma, alpha, rho, beta], antisymmetric = {{rho, alpha, sigma}});

                   Defined objects with tensor properties

   {A[mu, tau, phi, rho], B[sigma, alpha, rho, beta], d_[mu], g_[mu, nu],

     gamma[mu], sigma[mu], epsilon[mu, alpha, beta, nu], delta[mu, nu]}

> Define(C[sigma, alpha, mu, rho], antisymmetric = {{mu, alpha, sigma}});

                   Defined objects with tensor properties

{A[mu, tau, phi, rho], B[sigma, alpha, rho, beta], C[sigma, alpha, mu, rho],

  d_[mu], g_[mu, nu], gamma[mu], sigma[mu], epsilon[mu, alpha, beta, nu],

  delta[mu, nu]}

> Define(D[rho, tau, phi, beta], antisymmetric = {{phi, rho, tau}});

                   Defined objects with tensor properties

{A[mu, tau, phi, rho], B[sigma, alpha, rho, beta], C[sigma, alpha, mu, rho],

  D[rho, tau, phi, beta], d_[mu], g_[mu, nu], gamma[mu], sigma[mu],

  epsilon[mu, alpha, beta, nu], delta[mu, nu]}

> Define(E[sigma, alpha, tau, rho], antisymmetric = {{rho, alpha, sigma}});

                   Defined objects with tensor properties

{A[mu, tau, phi, rho], B[sigma, alpha, rho, beta], C[sigma, alpha, mu, rho],

  D[rho, tau, phi, beta], E[sigma, alpha, tau, rho], d_[mu], g_[mu, nu],

  gamma[mu], sigma[mu], epsilon[mu, alpha, beta, nu], delta[mu, nu]}

> Define(G[mu, rho, phi, beta], antisymmetric = {{mu, phi, rho}});

                   Defined objects with tensor properties

{A[mu, tau, phi, rho], B[sigma, alpha, rho, beta], C[sigma, alpha, mu, rho],

  D[rho, tau, phi, beta], E[sigma, alpha, tau, rho], G[mu, rho, phi, beta],

  d_[mu], g_[mu, nu], gamma[mu], sigma[mu], epsilon[mu, alpha, beta, nu],

  delta[mu, nu]}

> Define(H[sigma, alpha, phi, rho], antisymmetric = {{phi, alpha, sigma}});

                   Defined objects with tensor properties

{A[mu, tau, phi, rho], B[sigma, alpha, rho, beta], C[sigma, alpha, mu, rho],

  D[rho, tau, phi, beta], E[sigma, alpha, tau, rho], G[mu, rho, phi, beta],

  H[sigma, alpha, phi, rho], d_[mu], g_[mu, nu], gamma[mu], sigma[mu],

  epsilon[mu, alpha, beta, nu], delta[mu, nu]}

> Define(F[mu, tau, rho, beta], antisymmetric = {{mu, rho, tau}});

                   Defined objects with tensor properties

{A[mu, tau, phi, rho], B[sigma, alpha, rho, beta], C[sigma, alpha, mu, rho],

  D[rho, tau, phi, beta], E[sigma, alpha, tau, rho], F[mu, tau, rho, beta],

  G[mu, rho, phi, beta], H[sigma, alpha, phi, rho], d_[mu], g_[mu, nu],

  gamma[mu], sigma[mu], epsilon[mu, alpha, beta, nu], delta[mu, nu]}

> fundamentalidentity := AB = CD+EG+HF;

                              AB = CD + EG + HF

> constraintp := Define(P[tau, phi, chi, psi], antisymmetric = {{chi, phi, tau}}) = Physics[`*`](Physics[`*`](LeviCivita[chi, phi, tau], when), psi) and Physics[`*`](Physics[`*`](LeviCivita[chi, phi, tau], when), psi) = 0;

                   Defined objects with tensor properties

Error, (in index/Physics/LeviCivita) expected 4 indices for the Levi-Civita symbol in a 4-dimensional spacetime; received 3

> constraintq := P = 0;

                                    P = 0

> mu = 0;

                                   mu = 0

>

>

> for rho from 0 to 3 do for tau to 3 do for phi to 3 while phi < tau do for sigma from 0 to 3 do for alpha from 0 to 3 while `or`(alpha < sigma, alpha < rho) do for beta from 0 to 3 do for chi to 3 while `or`(chi < phi, chi < tau) do for psi from 0 to 3 do if `and`(`and`(`and`(tau > 0, phi > 0), chi > 0), psi > 0) then print(solve(Physics[`*`]({constraintq, fundamentalidentity}, [A]))) else print(solve({fundamentalidentity}, [A])) end if end do end do end do end do end do end do end do end do;

View 11002_structureconstantcalculation.mw on MapleNet or Download 11002_structureconstantcalculation.mw
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there's a first attempt, which returns a runaway list of empty sets.  Any thoughts?

I should add that, I counted 13 combinations of indices in my F's, for my 24 unique equations.  Does this system just have no solutions subject to my constraints?{it would still be cool to check this somehow without a pen though}