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875 lines
25 KiB
875 lines
25 KiB
subroutine Dfill_recur4(p1,p2,p3,p4,p1p2,p2p3,m1,m2,m3,m4,N0)
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implicit none
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C Implements the calculation of the formfactors
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C for small momenta AND small f(k), as in DD Eq.5.71 and 5.72
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C N0 is the offset in the common block
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C--- Currently: calculates up to rank 3 with at least one recursion
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c--- calculates ranks 4 and 5 with no recursion
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c--- calculates D00iiii, D00iiiii components of ranks 6 and 7
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include 'lib/TensorReduction/Include/types.f'
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include 'lib/TensorReduction/Include/TRconstants.f'
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include 'lib/TensorReduction/Include/pvCnames.f'
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include 'lib/TensorReduction/Include/pvCv.f'
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include 'lib/TensorReduction/Include/pvDnames.f'
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include 'lib/TensorReduction/Include/pvDv.f'
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include 'lib/TensorReduction/recur/Include/Darraydef.f'
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integer C234,C134,C124,C123,np,ep,N0,j,k,pvCcache,
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. i1,i2,i3,i4,i5,step,kmin
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parameter(np=3)
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real(dp):: p1,p2,p3,p4,p1p2,p2p3,m1,m2,m3,m4,f(np),
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. Gr(np,np),DetGr
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complex(dp):: S0000(-2:0),S0000i(np,-2:0),
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. Shat3zz(np,-2:0),Shat4zz(np,z1max,-2:0),
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. Shat5zz(np,z2max,-2:0),Shat6zz(np,z3max,-2:0),
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. Shat5zzzz(np,-2:0),Shat6zzzz(np,z1max,-2:0),
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. Shat7zz(np,z4max,-2:0),Shat7zzzzzz(np,-2:0),
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. Shat1(np,-2:0),Shat2(np,z1max,-2:0),
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. Shat3(np,z2max,-2:0),Shat4(np,z3max,-2:0),Shat5(np,z4max,-2:0),
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. Shat6(np,z5max,-2:0),Shat7(np,z6max,-2:0)
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complex(dp):: csum0(-2:0),csum1(-2:0),csum2(-2:0),
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. csum11(-2:0),csum00(-2:0),csum12(-2:0),csum22(-2:0),
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. csum111(-2:0),csum112(-2:0),csum122(-2:0),csum222(-2:0),
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. csum1111(-2:0),csum1112(-2:0),csum1122(-2:0),
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. csum1222(-2:0),csum2222(-2:0),
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. csum11111(-2:0),csum11112(-2:0),csum11122(-2:0),
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. csum11222(-2:0),csum12222(-2:0),csum22222(-2:0),
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. csum001(-2:0),csum002(-2:0),csum0011(-2:0),
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. csum0012(-2:0),csum0022(-2:0),csum0000(-2:0),
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. csum00111(-2:0),csum00112(-2:0),csum00122(-2:0),csum00222(-2:0),
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. Czero5(z5max,-2:0),Czero4(z4max,-2:0),
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. Czero3(z3max,-2:0),Czero2(z2max,-2:0),Czero1(z1max,-2:0),
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. Czero0(-2:0)
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logical,save:: first=.true.
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!$omp threadprivate(first)
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if (first) then
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first=.false.
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c--- These lines must be uncommented
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c call Array3dim
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c call DArraysetup
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write(6,*) 'Need to uncomment lines in Dfill_recur3'
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stop
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endif
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c--- Not necessary, routine upgraded now
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c if ((m1 .ne. 0d0).or.(m2 .ne. 0d0).or.(m3 .ne. 0d0)) then
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c write(6,*) 'Dfill: nonzero internal masses not foreseen'
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c stop
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c endif
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C234=pvCcache(p2,p3,p2p3,m2,m3,m4)
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C134=pvCcache(p1p2,p3,p4,m1,m3,m4)
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C124=pvCcache(p1,p2p3,p4,m1,m2,m4)
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C123=pvCcache(p1,p2,p1p2,m1,m2,m3)
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C----We have changed the sign of fi (different from Dfill) to agree
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C----with notation of Denner-Dittmaier
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f(1) = -m2 + m1 + p1
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f(2) = -m3 + m1 + p1p2
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f(3) = -m4 + m1 + p4
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Gr(1,1) = 2*(p1)
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Gr(2,2) = 2*(p1p2)
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Gr(3,3) = 2*(p4)
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Gr(1,2) = (p1+p1p2 - p2)
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Gr(2,1) = Gr(1,2)
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Gr(1,3) = (p1+p4 - p2p3)
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Gr(3,1) = Gr(1,3)
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Gr(2,3) = (p1p2 - p3+p4)
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Gr(3,2) = Gr(2,3)
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call determinant(3,np,Gr,DetGr)
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write(6,*) 'small F: 3x3 DetGr = ',DetGr
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do ep=-2,0
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csum0(ep)=Cv(cc0+C234,ep)+Cv(cc1+C234,ep)+Cv(cc2+C234,ep)
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csum1(ep)=Cv(cc1+C234,ep)+Cv(cc11+C234,ep)+Cv(cc12+C234,ep)
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csum2(ep)=Cv(cc2+C234,ep)+Cv(cc12+C234,ep)+Cv(cc22+C234,ep)
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enddo
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do ep=-2,0
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csum00(ep)=Cv(cc00+C234,ep)+Cv(cc001+C234,ep)+Cv(cc002+C234,ep)
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csum11(ep)=Cv(cc11+C234,ep)+Cv(cc111+C234,ep)+Cv(cc112+C234,ep)
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csum12(ep)=Cv(cc12+C234,ep)+Cv(cc112+C234,ep)+Cv(cc122+C234,ep)
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csum22(ep)=Cv(cc22+C234,ep)+Cv(cc122+C234,ep)+Cv(cc222+C234,ep)
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csum111(ep)=
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& Cv(cc111+C234,ep)+Cv(cc1111+C234,ep)+Cv(cc1112+C234,ep)
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csum112(ep)=
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& Cv(cc112+C234,ep)+Cv(cc1112+C234,ep)+Cv(cc1122+C234,ep)
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csum122(ep)=
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& Cv(cc122+C234,ep)+Cv(cc1122+C234,ep)+Cv(cc1222+C234,ep)
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csum222(ep)=
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& Cv(cc222+C234,ep)+Cv(cc1222+C234,ep)+Cv(cc2222+C234,ep)
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csum001(ep)=
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& Cv(cc001+C234,ep)+Cv(cc0011+C234,ep)+Cv(cc0012+C234,ep)
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csum002(ep)=
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& Cv(cc002+C234,ep)+Cv(cc0012+C234,ep)+Cv(cc0022+C234,ep)
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csum0000(ep)=Cv(cc0000+C234,ep)+Cv(cc00001+C234,ep)
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& +Cv(cc00002+C234,ep)
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csum0011(ep)=
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& Cv(cc0011+C234,ep)+Cv(cc00111+C234,ep)+Cv(cc00112+C234,ep)
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csum0012(ep)=
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& Cv(cc0012+C234,ep)+Cv(cc00112+C234,ep)+Cv(cc00122+C234,ep)
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csum0022(ep)=
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& Cv(cc0022+C234,ep)+Cv(cc00122+C234,ep)+Cv(cc00222+C234,ep)
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csum1111(ep)=
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& Cv(cc1111+C234,ep)+Cv(cc11111+C234,ep)+Cv(cc11112+C234,ep)
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csum1112(ep)=
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& Cv(cc1112+C234,ep)+Cv(cc11112+C234,ep)+Cv(cc11122+C234,ep)
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csum1122(ep)=
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& Cv(cc1122+C234,ep)+Cv(cc11122+C234,ep)+Cv(cc11222+C234,ep)
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csum1222(ep)=
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& Cv(cc1222+C234,ep)+Cv(cc11222+C234,ep)+Cv(cc12222+C234,ep)
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csum2222(ep)=
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& Cv(cc2222+C234,ep)+Cv(cc12222+C234,ep)+Cv(cc22222+C234,ep)
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csum11111(ep)=
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& Cv(cc11111+C234,ep)+Cv(cc111111+C234,ep)+Cv(cc111112+C234,ep)
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csum11112(ep)=
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& Cv(cc11112+C234,ep)+Cv(cc111112+C234,ep)+Cv(cc111122+C234,ep)
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csum11122(ep)=
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& Cv(cc11122+C234,ep)+Cv(cc111122+C234,ep)+Cv(cc111222+C234,ep)
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csum11222(ep)=
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& Cv(cc11222+C234,ep)+Cv(cc111222+C234,ep)+Cv(cc112222+C234,ep)
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csum12222(ep)=
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& Cv(cc12222+C234,ep)+Cv(cc112222+C234,ep)+Cv(cc122222+C234,ep)
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csum22222(ep)=
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& Cv(cc22222+C234,ep)+Cv(cc122222+C234,ep)+Cv(cc222222+C234,ep)
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csum00111(ep)=
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& Cv(cc00111+C234,ep)+Cv(cc001111+C234,ep)+Cv(cc001112+C234,ep)
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csum00112(ep)=
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& Cv(cc00112+C234,ep)+Cv(cc001112+C234,ep)+Cv(cc001122+C234,ep)
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csum00122(ep)=
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& Cv(cc00122+C234,ep)+Cv(cc001122+C234,ep)+Cv(cc001222+C234,ep)
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csum00222(ep)=
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& Cv(cc00222+C234,ep)+Cv(cc001222+C234,ep)+Cv(cc002222+C234,ep)
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enddo
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do ep=-2,0
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include 'lib/TensorReduction/recur/Include/Shat.f'
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enddo
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c--- Note: these functions are not used in this recursion
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c--- definitions of the S00 functions from Dfill_recur
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c include 'lib/TensorReduction/recur/Include/S00_def.f'
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c include 'lib/TensorReduction/recur/Include/S00i_def.f'
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c include 'lib/TensorReduction/recur/Include/S0000_def.f'
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c include 'lib/TensorReduction/recur/Include/S00ii_def.f'
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c include 'lib/TensorReduction/recur/Include/S0000i_def.f'
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c include 'lib/TensorReduction/recur/Include/S00iii_def.f'
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c include 'lib/TensorReduction/recur/Include/S000000_def.f'
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c include 'lib/TensorReduction/recur/Include/S0000ii_def.f'
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c include 'lib/TensorReduction/recur/Include/S00iiii_def.f'
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do ep=-2,0
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Shat3zz(1,ep)=Cv(cc00+C134,ep)-Cv(cc00+C234,ep)
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Shat3zz(2,ep)=Cv(cc00+C124,ep)-Cv(cc00+C234,ep)
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Shat3zz(3,ep)=Cv(cc00+C123,ep)-Cv(cc00+C234,ep)
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Shat4zz(1,1,ep)=Csum00(ep)
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Shat4zz(2,1,ep)=Csum00(ep)+Cv(cc001+C124,ep)
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Shat4zz(3,1,ep)=Csum00(ep)+Cv(cc001+C123,ep)
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Shat4zz(1,2,ep)=+Cv(cc001+C134,ep)-Cv(cc001+C234,ep)
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Shat4zz(2,2,ep)=-Cv(cc001+C234,ep)
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Shat4zz(3,2,ep)=-Cv(cc001+C234,ep)+Cv(cc002+C123,ep)
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Shat4zz(1,3,ep)=+Cv(cc002+C134,ep)-Cv(cc002+C234,ep)
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Shat4zz(2,3,ep)=+Cv(cc002+C124,ep)-Cv(cc002+C234,ep)
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Shat4zz(3,3,ep)=-Cv(cc002+C234,ep)
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Shat5zz(1,z2(1,1),ep)=-Csum00(ep)-Csum001(ep)-Csum002(ep)
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Shat5zz(2,z2(1,1),ep)=-Csum00(ep)-Csum001(ep)-Csum002(ep)
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& +Cv(cc0011+C124,ep)
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Shat5zz(3,z2(1,1),ep)=-Csum00(ep)-Csum001(ep)-Csum002(ep)
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& +Cv(cc0011+C123,ep)
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Shat5zz(1,z2(1,2),ep)=Csum001(ep)
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Shat5zz(2,z2(1,2),ep)=Csum001(ep)
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Shat5zz(3,z2(1,2),ep)=Csum001(ep)+ Cv(cc0012+C123,ep)
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Shat5zz(1,z2(2,2),ep)=Cv(cc0011+C134,ep)- Cv(cc0011+C234,ep)
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Shat5zz(2,z2(2,2),ep)=- Cv(cc0011+C234,ep)
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Shat5zz(3,z2(2,2),ep)=Cv(cc0022+C123,ep)- Cv(cc0011+C234,ep)
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Shat5zz(1,z2(2,3),ep)=Cv(cc0012+C134,ep)- Cv(cc0012+C234,ep)
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Shat5zz(2,z2(2,3),ep)=-Cv(cc0012+C234,ep)
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Shat5zz(3,z2(2,3),ep)=-Cv(cc0012+C234,ep)
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Shat5zz(1,z2(1,3),ep)=Csum002(ep)
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Shat5zz(2,z2(1,3),ep)=Csum002(ep)+ Cv(cc0012+C124,ep)
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Shat5zz(3,z2(1,3),ep)=+Csum002(ep)
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Shat5zz(1,z2(3,3),ep)=Cv(cc0022+C134,ep)- Cv(cc0022+C234,ep)
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Shat5zz(2,z2(3,3),ep)=Cv(cc0022+C124,ep)- Cv(cc0022+C234,ep)
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Shat5zz(3,z2(3,3),ep)=-Cv(cc0022+C234,ep)
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Shat6zz(1,z3(1,1,1),ep)=Csum0011(ep)+Csum0022(ep)+2D0*Csum0012(ep)
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& +Csum00(ep) + 2D0*Csum001(ep)+ 2D0*Csum002(ep)
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Shat6zz(2,z3(1,1,1),ep)=Csum0011(ep)+Csum0022(ep)+2D0*Csum0012(ep)
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& +2.D0*Csum002(ep)+2.D0*Csum001(ep)+Csum00(ep)
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& +Cv(cc00111+C124,ep)
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Shat6zz(3,z3(1,1,1),ep)=Csum0011(ep)+Csum0022(ep)+2D0*Csum0012(ep)
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& +2.D0*Csum002(ep)+2.D0*Csum001(ep)+Csum00(ep)
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& +Cv(cc00111+C123,ep)
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Shat6zz(1,z3(1,1,2),ep)=-Csum0011(ep)-Csum0012(ep)-Csum001(ep)
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Shat6zz(2,z3(1,1,2),ep)=-Csum0011(ep)-Csum0012(ep)-Csum001(ep)
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Shat6zz(3,z3(1,1,2),ep)=-Csum0011(ep)-Csum0012(ep)-Csum001(ep)
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& +Cv(cc00112+C123,ep)
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Shat6zz(1,z3(1,1,3),ep)=-Csum0022(ep)-Csum0012(ep)-Csum002(ep)
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Shat6zz(2,z3(1,1,3),ep)=-Csum0022(ep)-Csum0012(ep)
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& -Csum002(ep)+Cv(cc00112+C124,ep)
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Shat6zz(3,z3(1,1,3),ep)=-Csum0022(ep)-Csum0012(ep)-Csum002(ep)
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Shat6zz(1,z3(1,2,2),ep)=+Csum0011(ep)
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Shat6zz(2,z3(1,2,2),ep)=+Csum0011(ep)
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Shat6zz(3,z3(1,2,2),ep)=+Csum0011(ep)+Cv(cc00122+C123,ep)
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Shat6zz(1,z3(1,2,3),ep)=+Csum0012(ep)
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Shat6zz(2,z3(1,2,3),ep)=+Csum0012(ep)
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Shat6zz(3,z3(1,2,3),ep)=+Csum0012(ep)
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Shat6zz(1,z3(1,3,3),ep)=+Csum0022(ep)
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Shat6zz(2,z3(1,3,3),ep)=+Csum0022(ep)+Cv(cc00122+C124,ep)
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Shat6zz(3,z3(1,3,3),ep)=+Csum0022(ep)
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Shat6zz(1,z3(2,2,2),ep)=+Cv(cc00111+C134,ep)-Cv(cc00111+C234,ep)
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Shat6zz(2,z3(2,2,2),ep)=-Cv(cc00111+C234,ep)
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Shat6zz(3,z3(2,2,2),ep)=-Cv(cc00111+C234,ep)+Cv(cc00222+C123,ep)
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Shat6zz(1,z3(2,2,3),ep)=+Cv(cc00112+C134,ep)-Cv(cc00112+C234,ep)
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Shat6zz(2,z3(2,2,3),ep)=-Cv(cc00112+C234,ep)
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Shat6zz(3,z3(2,2,3),ep)=-Cv(cc00112+C234,ep)
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Shat6zz(1,z3(3,3,2),ep)=+Cv(cc00122+C134,ep)-Cv(cc00122+C234,ep)
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Shat6zz(2,z3(3,3,2),ep)=-Cv(cc00122+C234,ep)
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Shat6zz(3,z3(3,3,2),ep)=-Cv(cc00122+C234,ep)
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Shat6zz(1,z3(3,3,3),ep)=+Cv(cc00222+C134,ep)-Cv(cc00222+C234,ep)
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Shat6zz(2,z3(3,3,3),ep)=+Cv(cc00222+C124,ep)-Cv(cc00222+C234,ep)
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Shat6zz(3,z3(3,3,3),ep)=-Cv(cc00222+C234,ep)
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Shat5zzzz(1,ep)=Cv(cc0000+C134,ep)-Cv(cc0000+C234,ep)
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Shat5zzzz(2,ep)=Cv(cc0000+C124,ep)-Cv(cc0000+C234,ep)
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Shat5zzzz(3,ep)=Cv(cc0000+C123,ep)-Cv(cc0000+C234,ep)
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Shat6zzzz(1,1,ep)=Csum0000(ep)
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Shat6zzzz(2,1,ep)=Csum0000(ep)+Cv(cc00001+C124,ep)
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Shat6zzzz(3,1,ep)=Csum0000(ep)+Cv(cc00001+C123,ep)
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Shat6zzzz(1,2,ep)=+Cv(cc00001+C134,ep)-Cv(cc00001+C234,ep)
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Shat6zzzz(2,2,ep)=-Cv(cc00001+C234,ep)
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Shat6zzzz(3,2,ep)=-Cv(cc00001+C234,ep)+Cv(cc00002+C123,ep)
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Shat6zzzz(1,3,ep)=+Cv(cc00002+C134,ep)-Cv(cc00002+C234,ep)
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Shat6zzzz(2,3,ep)=+Cv(cc00002+C124,ep)-Cv(cc00002+C234,ep)
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Shat6zzzz(3,3,ep)=-Cv(cc00002+C234,ep)
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Shat7zz(1,z4(1,1,1,1),ep) =
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& - Csum00(ep)
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& - 3.D0*Csum001(ep)
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& - 3.D0*Csum002(ep)
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& - 3.D0*Csum0011(ep)
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& - 3.D0*Csum0022(ep)
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& - 6.D0*Csum0012(ep)
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& - Csum00111(ep)
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& - Csum00222(ep)
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& - 3.D0*Csum00122(ep)
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& - 3.D0*Csum00112(ep)
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Shat7zz(2,z4(1,1,1,1),ep) =
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& - Csum00(ep)
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& - 3.D0*Csum001(ep)
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& - 3.D0*Csum002(ep)
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& - 3.D0*Csum0011(ep)
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& - 3.D0*Csum0022(ep)
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& - 6.D0*Csum0012(ep)
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& - Csum00111(ep)
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& - Csum00222(ep)
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& - 3.D0*Csum00122(ep)
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& - 3.D0*Csum00112(ep)
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& + Cv(cc001111 + C124,ep)
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Shat7zz(3,z4(1,1,1,1),ep) =
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& - Csum00(ep)
|
|
& - 3.D0*Csum001(ep)
|
|
& - 3.D0*Csum002(ep)
|
|
& - 3.D0*Csum0011(ep)
|
|
& - 3.D0*Csum0022(ep)
|
|
& - 6.D0*Csum0012(ep)
|
|
& - Csum00111(ep)
|
|
& - Csum00222(ep)
|
|
& - 3.D0*Csum00122(ep)
|
|
& - 3.D0*Csum00112(ep)
|
|
& + Cv(cc001111 + C123,ep)
|
|
|
|
Shat7zz(1,z4(1,1,1,2),ep) =
|
|
& + Csum001(ep)
|
|
& + 2.D0*Csum0011(ep)
|
|
& + 2.D0*Csum0012(ep)
|
|
& + Csum00111(ep)
|
|
& + Csum00122(ep)
|
|
& + 2.D0*Csum00112(ep)
|
|
|
|
Shat7zz(2,z4(1,1,1,2),ep) =
|
|
& + Csum001(ep)
|
|
& + 2.D0*Csum0011(ep)
|
|
& + 2.D0*Csum0012(ep)
|
|
& + Csum00111(ep)
|
|
& + Csum00122(ep)
|
|
& + 2.D0*Csum00112(ep)
|
|
|
|
Shat7zz(3,z4(1,1,1,2),ep) =
|
|
& + Csum001(ep)
|
|
& + 2.D0*Csum0011(ep)
|
|
& + 2.D0*Csum0012(ep)
|
|
& + Csum00111(ep)
|
|
& + Csum00122(ep)
|
|
& + 2.D0*Csum00112(ep)
|
|
& + Cv(cc001112 + C123,ep)
|
|
|
|
Shat7zz(1,z4(1,1,1,3),ep) =
|
|
& + Csum002(ep)
|
|
& + 2.D0*Csum0022(ep)
|
|
& + 2.D0*Csum0012(ep)
|
|
& + Csum00222(ep)
|
|
& + 2.D0*Csum00122(ep)
|
|
& + Csum00112(ep)
|
|
|
|
Shat7zz(2,z4(1,1,1,3),ep) =
|
|
& + Csum002(ep)
|
|
& + 2.D0*Csum0022(ep)
|
|
& + 2.D0*Csum0012(ep)
|
|
& + Csum00222(ep)
|
|
& + 2.D0*Csum00122(ep)
|
|
& + Csum00112(ep)
|
|
& + Cv(cc001112 + C124,ep)
|
|
|
|
Shat7zz(3,z4(1,1,1,3),ep) =
|
|
& + Csum002(ep)
|
|
& + 2.D0*Csum0022(ep)
|
|
& + 2.D0*Csum0012(ep)
|
|
& + Csum00222(ep)
|
|
& + 2.D0*Csum00122(ep)
|
|
& + Csum00112(ep)
|
|
|
|
Shat7zz(1,z4(1,1,2,2),ep) =
|
|
& - Csum0011(ep)
|
|
& - Csum00111(ep)
|
|
& - Csum00112(ep)
|
|
|
|
Shat7zz(2,z4(1,1,2,2),ep) =
|
|
& - Csum0011(ep)
|
|
& - Csum00111(ep)
|
|
& - Csum00112(ep)
|
|
|
|
Shat7zz(3,z4(1,1,2,2),ep) =
|
|
& - Csum0011(ep)
|
|
& - Csum00111(ep)
|
|
& - Csum00112(ep)
|
|
& + Cv(cc001122 + C123,ep)
|
|
|
|
Shat7zz(1,z4(1,1,2,3),ep) =
|
|
& - Csum0012(ep)
|
|
& - Csum00122(ep)
|
|
& - Csum00112(ep)
|
|
|
|
Shat7zz(2,z4(1,1,2,3),ep) =
|
|
& - Csum0012(ep)
|
|
& - Csum00122(ep)
|
|
& - Csum00112(ep)
|
|
|
|
Shat7zz(3,z4(1,1,2,3),ep) =
|
|
& - Csum0012(ep)
|
|
& - Csum00122(ep)
|
|
& - Csum00112(ep)
|
|
|
|
Shat7zz(1,z4(1,1,3,3),ep) =
|
|
& - Csum0022(ep)
|
|
& - Csum00222(ep)
|
|
& - Csum00122(ep)
|
|
|
|
Shat7zz(2,z4(1,1,3,3),ep) =
|
|
& - Csum0022(ep)
|
|
& - Csum00222(ep)
|
|
& - Csum00122(ep)
|
|
& + Cv(cc001122 + C124,ep)
|
|
|
|
Shat7zz(3,z4(1,1,3,3),ep) =
|
|
& - Csum0022(ep)
|
|
& - Csum00222(ep)
|
|
& - Csum00122(ep)
|
|
|
|
Shat7zz(1,z4(1,2,2,2),ep) =
|
|
& + Csum00111(ep)
|
|
|
|
Shat7zz(2,z4(1,2,2,2),ep) =
|
|
& + Csum00111(ep)
|
|
|
|
Shat7zz(3,z4(1,2,2,2),ep) =
|
|
& + Csum00111(ep)
|
|
& + Cv(cc001222 + C123,ep)
|
|
|
|
Shat7zz(1,z4(1,2,2,3),ep) =
|
|
& + Csum00112(ep)
|
|
|
|
Shat7zz(2,z4(1,2,2,3),ep) =
|
|
& + Csum00112(ep)
|
|
|
|
Shat7zz(3,z4(1,2,2,3),ep) =
|
|
& + Csum00112(ep)
|
|
|
|
Shat7zz(1,z4(1,2,3,3),ep) =
|
|
& + Csum00122(ep)
|
|
|
|
Shat7zz(2,z4(1,2,3,3),ep) =
|
|
& + Csum00122(ep)
|
|
|
|
Shat7zz(3,z4(1,2,3,3),ep) =
|
|
& + Csum00122(ep)
|
|
|
|
Shat7zz(1,z4(1,3,3,3),ep) =
|
|
& + Csum00222(ep)
|
|
|
|
Shat7zz(2,z4(1,3,3,3),ep) =
|
|
& + Csum00222(ep)
|
|
& + Cv(cc001222 + C124,ep)
|
|
|
|
Shat7zz(3,z4(1,3,3,3),ep) =
|
|
& + Csum00222(ep)
|
|
|
|
Shat7zz(1,z4(2,2,2,2),ep) =
|
|
& + Cv(cc001111 + C134,ep)
|
|
& - Cv(cc001111 + C234,ep)
|
|
|
|
Shat7zz(2,z4(2,2,2,2),ep) =
|
|
& - Cv(cc001111 + C234,ep)
|
|
|
|
Shat7zz(3,z4(2,2,2,2),ep) =
|
|
& - Cv(cc001111 + C234,ep)
|
|
& + Cv(cc002222 + C123,ep)
|
|
|
|
Shat7zz(1,z4(2,2,2,3),ep) =
|
|
& + Cv(cc001112 + C134,ep)
|
|
& - Cv(cc001112 + C234,ep)
|
|
|
|
Shat7zz(2,z4(2,2,2,3),ep) =
|
|
& - Cv(cc001112 + C234,ep)
|
|
|
|
Shat7zz(3,z4(2,2,2,3),ep) =
|
|
& - Cv(cc001112 + C234,ep)
|
|
|
|
Shat7zz(1,z4(2,2,3,3),ep) =
|
|
& + Cv(cc001122 + C134,ep)
|
|
& - Cv(cc001122 + C234,ep)
|
|
|
|
Shat7zz(2,z4(2,2,3,3),ep) =
|
|
& - Cv(cc001122 + C234,ep)
|
|
|
|
Shat7zz(3,z4(2,2,3,3),ep) =
|
|
& - Cv(cc001122 + C234,ep)
|
|
|
|
Shat7zz(1,z4(2,3,3,3),ep) =
|
|
& + Cv(cc001222 + C134,ep)
|
|
& - Cv(cc001222 + C234,ep)
|
|
|
|
Shat7zz(2,z4(2,3,3,3),ep) =
|
|
& - Cv(cc001222 + C234,ep)
|
|
|
|
Shat7zz(3,z4(2,3,3,3),ep) =
|
|
& - Cv(cc001222 + C234,ep)
|
|
|
|
Shat7zz(1,z4(3,3,3,3),ep) =
|
|
& + Cv(cc002222 + C134,ep)
|
|
& - Cv(cc002222 + C234,ep)
|
|
|
|
Shat7zz(2,z4(3,3,3,3),ep) =
|
|
& + Cv(cc002222 + C124,ep)
|
|
& - Cv(cc002222 + C234,ep)
|
|
|
|
Shat7zz(3,z4(3,3,3,3),ep) =
|
|
& - Cv(cc002222 + C234,ep)
|
|
|
|
c--- definitions of Shat7zzzz have not been completed yet, so current
|
|
c--- implementation of D000000i will not be correct
|
|
|
|
c Shat7zzzz(1,z2(1,1),ep) =
|
|
c & - Csum00001(ep)
|
|
c & - Csum00002(ep)
|
|
c & - Csum0000(ep)
|
|
c & - 4.D0*D0000001(P,K,L,m0,m1,m2,m3)
|
|
|
|
c Shat7zzzz(2,z2(1,1),ep) =
|
|
c & - Csum00001(ep)
|
|
c & - Csum00002(ep)
|
|
c & - Csum0000(ep)
|
|
c & + Cv(cc000011 + C124,ep)
|
|
|
|
c Shat7zzzz(3,z2(1,1),ep) =
|
|
c & - Csum00001(ep)
|
|
c & - Csum00002(ep)
|
|
c & - Csum0000(ep)
|
|
c & + Cv(cc000011 + C123,ep)
|
|
|
|
c Shat7zzzz(1,z2(1,2),ep) =
|
|
c & + Csum00001(ep)
|
|
c & - 2.D0*D0000002(P,K,L,m0,m1,m2,m3)
|
|
|
|
c Shat7zzzz(2,z2(1,2),ep) =
|
|
c & + Csum00001(ep)
|
|
c & - 2.D0*D0000001(P,K,L,m0,m1,m2,m3)
|
|
|
|
c Shat7zzzz(3,z2(1,2),ep) =
|
|
c & + Csum00001(ep)
|
|
c & + Cv(cc000012 + C123,ep)
|
|
|
|
c Shat7zzzz(1,z2(1,3),ep) =
|
|
c & + Csum00002(ep)
|
|
c & - 2.D0*D0000003(P,K,L,m0,m1,m2,m3)
|
|
|
|
c Shat7zzzz(2,z2(1,3),ep) =
|
|
c & + Csum00002(ep)
|
|
c & + Cv(cc000012 + C124,ep)
|
|
|
|
c Shat7zzzz(3,z2(1,3),ep) =
|
|
c & + Csum00002(ep)
|
|
c & - 2.D0*D0000001(P,K,L,m0,m1,m2,m3)
|
|
|
|
c Shat7zzzz(1,z2(2,2),ep) =
|
|
c & + Cv(cc000011 + C134,ep)
|
|
c & - Cv(cc000011 + C234,ep)
|
|
|
|
c Shat7zzzz(2,z2(2,2),ep) =
|
|
c & - 4.D0*D0000002(P,K,L,m0,m1,m2,m3)
|
|
c & - Cv(cc000011 + C234,ep)
|
|
|
|
c Shat7zzzz(3,z2(2,2),ep) =
|
|
c & - Cv(cc000011 + C234,ep)
|
|
c & + Cv(cc000022 + C123,ep)
|
|
|
|
c Shat7zzzz(1,z2(2,3),ep) =
|
|
c & + Cv(cc000012 + C134,ep)
|
|
c & - Cv(cc000012 + C234,ep)
|
|
|
|
c Shat7zzzz(2,z2(2,3),ep) =
|
|
c & - 2.D0*D0000003(P,K,L,m0,m1,m2,m3)
|
|
c & - Cv(cc000012 + C234,ep)
|
|
|
|
c Shat7zzzz(3,z2(2,3),ep) =
|
|
c & - 2.D0*D0000002(P,K,L,m0,m1,m2,m3)
|
|
c & - Cv(cc000012 + C234,ep)
|
|
|
|
c Shat7zzzz(1,z2(3,3),ep) =
|
|
c & + Cv(cc000022 + C134,ep)
|
|
c & - Cv(cc000022 + C234,ep)
|
|
|
|
c Shat7zzzz(2,z2(3,3),ep) =
|
|
c & + Cv(cc000022 + C124,ep)
|
|
c & - Cv(cc000022 + C234,ep)
|
|
|
|
c Shat7zzzz(3,z2(3,3),ep) =
|
|
c & - 4.D0*D0000003(P,K,L,m0,m1,m2,m3)
|
|
c & - Cv(cc000022 + C234,ep)
|
|
|
|
Shat7zzzzzz(1,ep) =
|
|
& + Cv(cc000000 + C134,ep)
|
|
& - Cv(cc000000 + C234,ep)
|
|
|
|
Shat7zzzzzz(2,ep) =
|
|
& + Cv(cc000000 + C124,ep)
|
|
& - Cv(cc000000 + C234,ep)
|
|
|
|
Shat7zzzzzz(3,ep) =
|
|
& + Cv(cc000000 + C123,ep)
|
|
& - Cv(cc000000 + C234,ep)
|
|
|
|
enddo
|
|
|
|
do ep=-2,0
|
|
|
|
c--- note: these are the triangle parts of the S00 functions that
|
|
c--- are defined above (and commented out), except that these
|
|
c--- are a factor of two smaller
|
|
|
|
c--- definitions of Czero5 in include file for now
|
|
include 'lib/TensorReduction/recur/Include/Czero5.f'
|
|
|
|
Czero4(z4(1,1,1,1),ep)=+Csum0(ep)+3d0*Csum1(ep)
|
|
. +3d0*Csum2(ep)+3d0*Csum11(ep)+6d0*Csum12(ep)+3d0*Csum22(ep)
|
|
. +Csum111(ep)+Csum222(ep)+3d0*Csum112(ep)+3d0*Csum122(ep)
|
|
Czero4(z4(1,1,1,2),ep)=-(Csum1(ep)+2d0*Csum11(ep)
|
|
. +2d0*Csum12(ep)+Csum111(ep)+2d0*Csum112(ep)+Csum122(ep))
|
|
Czero4(z4(1,1,1,3),ep)=-(Csum2(ep)+2d0*Csum12(ep)
|
|
. +2d0*Csum22(ep)+Csum112(ep)+2d0*Csum122(ep)+Csum222(ep))
|
|
Czero4(z4(1,1,2,2),ep)=+Csum11(ep)+Csum111(ep)+Csum112(ep)
|
|
Czero4(z4(1,1,2,3),ep)=+Csum12(ep)+Csum112(ep)+Csum122(ep)
|
|
Czero4(z4(1,1,3,3),ep)=+Csum22(ep)+Csum122(ep)+Csum222(ep)
|
|
Czero4(z4(1,2,2,2),ep)=-Csum111(ep)
|
|
Czero4(z4(1,2,2,3),ep)=-Csum112(ep)
|
|
Czero4(z4(1,2,3,3),ep)=-Csum122(ep)
|
|
Czero4(z4(1,3,3,3),ep)=-Csum222(ep)
|
|
Czero4(z4(2,2,2,2),ep)=+Cv(cc1111+C234,ep)
|
|
Czero4(z4(2,2,2,3),ep)=+Cv(cc1112+C234,ep)
|
|
Czero4(z4(2,2,3,3),ep)=+Cv(cc1122+C234,ep)
|
|
Czero4(z4(2,3,3,3),ep)=+Cv(cc1222+C234,ep)
|
|
Czero4(z4(3,3,3,3),ep)=+Cv(cc2222+C234,ep)
|
|
|
|
Czero3(z3(1,1,1),ep)=
|
|
& - Csum0(ep)
|
|
& - 2.D0*Csum1(ep)
|
|
& - 2.D0*Csum2(ep)
|
|
& - Csum11(ep)
|
|
& - Csum22(ep)
|
|
& - 2.D0*Csum12(ep)
|
|
|
|
Czero3(z3(2,2,2),ep)=
|
|
& + Cv(cc111 + C234,ep)
|
|
Czero3(z3(3,3,3),ep)=
|
|
& + Cv(cc222 + C234,ep)
|
|
|
|
Czero3(z3(1,1,2),ep)=
|
|
& + Csum1(ep)
|
|
& + Csum11(ep)
|
|
& + Csum12(ep)
|
|
|
|
Czero3(z3(1,1,3),ep)=
|
|
& + Csum2(ep)
|
|
& + Csum22(ep)
|
|
& + Csum12(ep)
|
|
|
|
Czero3(z3(1,2,2),ep)=
|
|
& - Csum11(ep)
|
|
|
|
Czero3(z3(1,3,3),ep)=
|
|
& - Csum22(ep)
|
|
|
|
Czero3(z3(2,2,3),ep)=
|
|
& + Cv(cc112 + C234,ep)
|
|
|
|
Czero3(z3(2,3,3),ep)=
|
|
& + Cv(cc122 + C234,ep)
|
|
|
|
Czero3(z3(1,2,3),ep)=
|
|
& - Csum12(ep)
|
|
|
|
Czero2(z2(1,1),ep)=
|
|
& + Csum0(ep)
|
|
& + Csum1(ep)
|
|
& + Csum2(ep)
|
|
|
|
Czero2(z2(2,2),ep)=
|
|
& + Cv(cc11 + C234,ep)
|
|
|
|
Czero2(z2(3,3),ep)=
|
|
& + Cv(cc22 + C234,ep)
|
|
|
|
Czero2(z2(1,2),ep)=
|
|
& - Csum1(ep)
|
|
|
|
Czero2(z2(1,3),ep)=
|
|
& - Csum2(ep)
|
|
|
|
Czero2(z2(2,3),ep)=
|
|
& + Cv(cc12 + C234,ep)
|
|
|
|
Czero1(1,ep)=
|
|
& - Csum0(ep)
|
|
|
|
Czero1(2,ep)=
|
|
& + Cv(cc1 + C234,ep)
|
|
|
|
Czero1(3,ep)=
|
|
& + Cv(cc2 + C234,ep)
|
|
|
|
Czero0(ep)=
|
|
& + Cv(cc0 + C234,ep)
|
|
|
|
enddo
|
|
|
|
|
|
c--- find the smallest f(k) for C00 recursion relation
|
|
kmin=1
|
|
do k=2,np
|
|
if (abs(f(k)) .le. abs(f(kmin))) kmin=k
|
|
enddo
|
|
|
|
write(6,*) 'f(kmin) =',f(kmin)
|
|
|
|
C----Begin the iteration scheme
|
|
|
|
C set all the Cv to zero
|
|
do ep=-2,0
|
|
do j=1,Ndd
|
|
Dv(j+N0,ep)=czip
|
|
enddo
|
|
enddo
|
|
|
|
do step=0,2
|
|
if (step .eq. 3) goto 103
|
|
if (step .eq. 2) goto 102
|
|
if (step .eq. 1) goto 101
|
|
if (step .eq. 0) goto 100
|
|
|
|
C--- step 3
|
|
103 continue
|
|
|
|
C--- step 2: calculate D00iiii, D00iiiii, Diiii, Diiiii,
|
|
c--- D0000ii, D0000iii, D000000,D000000i [NOT THESE]
|
|
102 continue
|
|
|
|
C--- a) Calculate D00iiii
|
|
C--- Small terms of order f(i)*Dijklm,Gr(i,j)*Dijklmn
|
|
do i1=1,2
|
|
do i2=i1,2
|
|
do i3=i2,2
|
|
do i4=i3,2
|
|
call runF_00iiii(i1,i2,i3,i4,f,Gr,Shat6,N0)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
c--- b) Calculate D00iiiii
|
|
C--- Small terms of order f(i)*Dijklmn,Gr(i,j)*Dijklmno
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do i1=1,2
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do i2=i1,2
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|
do i3=i2,2
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|
do i4=i3,2
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|
do i5=i4,2
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call runF_00iiiii(i1,i2,i3,i4,i5,f,Gr,Shat7,N0)
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enddo
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enddo
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enddo
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|
enddo
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|
enddo
|
|
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C--- c) Calculate Diiiii, requires D00iiiii
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C--- Small terms of order Gr(i,j)*Dijklmno
|
|
do i1=1,2
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|
do i2=i1,2
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|
do i3=i2,2
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|
do i4=i3,2
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|
do i5=i4,2
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|
call runF_iiiii(i1,i2,i3,i4,i5,m1,Gr,Czero5,N0)
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enddo
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|
enddo
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|
enddo
|
|
enddo
|
|
enddo
|
|
|
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C--- d) Calculate Diiii, requires D00iiii
|
|
C--- Small terms of order Gr(i,j)*Dijklmn
|
|
do i1=1,2
|
|
do i2=i1,2
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|
do i3=i2,2
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|
do i4=i3,2
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|
call runF_iiii(i1,i2,i3,i4,m1,Gr,Czero4,N0)
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|
enddo
|
|
enddo
|
|
enddo
|
|
enddo
|
|
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|
C--- step 1: calculate D00ii, D00iii, Dii, Diii, D0000, D0000i
|
|
101 continue
|
|
|
|
C--- a) Calculate D00ii
|
|
C--- Small terms of order f(i)*Dijk,Gr(i,j)*Dijkl
|
|
do i1=1,np
|
|
do i2=i1,np
|
|
call runF_00ii(i1,i2,f,Gr,Shat4,N0)
|
|
enddo
|
|
enddo
|
|
|
|
c--- b) Calculate D00iii
|
|
C--- Small terms of order f(i)*Dijkl,Gr(i,j)*Dijklm
|
|
do i1=1,np
|
|
do i2=i1,np
|
|
do i3=i2,np
|
|
call runF_00iii(i1,i2,i3,f,Gr,Shat5,N0)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
C--- c) Calculate Diii, requires D00iii
|
|
C--- Small terms of order Gr(i,j)*Dijklm
|
|
do i1=1,np
|
|
do i2=i1,np
|
|
do i3=i2,np
|
|
call runF_iii(i1,i2,i3,m1,Gr,Czero3,N0)
|
|
enddo
|
|
enddo
|
|
enddo
|
|
|
|
C--- d) Calculate Dii, requires D00ii
|
|
C--- Small terms of order Gr(i,j)*Dijkl
|
|
do i1=1,np
|
|
do i2=i1,np
|
|
call runF_ii(i1,i2,m1,Gr,Czero2,N0)
|
|
enddo
|
|
enddo
|
|
|
|
c--- e) Calculate S0000i (needs D00i) - required for D0000i
|
|
include 'lib/TensorReduction/recur/Include/S0000i_def.f'
|
|
|
|
C--- Fixes D0000i, with corrections of order Gr(i,j)*D00iii
|
|
do i1=1,np
|
|
call runP_0000i(i1,Gr,S0000i,N0)
|
|
enddo
|
|
|
|
c--- f) Calculate S0000 (needs D00) - required for D0000
|
|
include 'lib/TensorReduction/recur/Include/S0000_def.f'
|
|
|
|
C--- Fixes D0000, with corrections of order Gr(i,j)*D00ii
|
|
call runP_0000(Gr,S0000,N0)
|
|
|
|
|
|
C--- step 0: calculate D00,D00i,D0 and Di
|
|
100 continue
|
|
C--- a) Calculate D00
|
|
C--- Small terms of order f(i)*Di,Gr(i,j)*Dij
|
|
call runF_00(kmin,f,Gr,Shat2,N0)
|
|
|
|
C--- b) Calculate D00i
|
|
C--- Small terms of order f(i)*Dij,Gr(i,j)*Dijk
|
|
do i1=1,np
|
|
call runF_00i(i1,f,Gr,Shat3,N0)
|
|
enddo
|
|
|
|
C--- c) Calculates D0, requires D00
|
|
C--- Small terms of order Gr(i,j)*Dij
|
|
call runF_0(m1,Gr,Czero0,N0)
|
|
|
|
C--- d) Calculate Di, requires D00i
|
|
C--- Small terms of order Gr(i,j)*Dijk
|
|
do i1=1,np
|
|
call runF_i(i1,m1,Gr,Czero1,N0)
|
|
enddo
|
|
|
|
enddo
|
|
|
|
|
|
c--- check the contents of box array
|
|
c write(6,*) 'D array'
|
|
c do ip=1,Ndd
|
|
c if (abs(Dsing(ip,p1,p2,p3,p4,p1p2,p2p3,m1,m2,m3,m4)).ne.0d0) then
|
|
c write(6,'(i3,2f20.15)') ip,Dv(ip+N0,-1)
|
|
c . /Dsing(ip,p1,p2,p3,p4,p1p2,p2p3,m1,m2,m3,m4)
|
|
c endif
|
|
c enddo
|
|
c pause
|
|
|
|
|
|
c 77 format(a3,i2,a5,3('(',e13.6,',',e13.6,') '))
|
|
|
|
return
|
|
end
|
|
|
|
|