I have an expression as below:
−12A[a,v]A[b,h]A[c,v]A[d,h]Cos[θ]2+12A[a,h]A[b,v]A[c,v]A[d,h]Cos[θ]2+12A[a,v]A[b,h]A[c,h]A[d,v]Cos[θ]2−12A[a,h]A[b,v]A[c,h]A[d,v]Cos[θ]2+12A[a,v]2A[b,h]A[d,h]Cos[θ]Sin[θ]−12A[a,h]A[a,v]A[b,v]A[d,h]Cos[θ]Sin[θ]+12A[b,v]A[c,h]A[c,v]A[d,h]Cos[θ]Sin[θ]−12A[b,h]A[c,v]2A[d,h]Cos[θ]Sin[θ]−12A[a,h]A[a,v]A[b,h]A[d,v]Cos[θ]Sin[θ]+12A[a,h]2A[b,v]A[d,v]Cos[θ]Sin[θ]−12A[b,v]A[c,h]2A[d,v]Cos[θ]Sin[θ]+12A[b,h]A[c,h]A[c,v]A[d,v]Cos[θ]Sin[θ]−12A[a,v]A[b,v]A[c,h]A[d,h]Sin[θ]2+12A[a,v]A[b,h]A[c,v]A[d,h]Sin[θ]2+12A[a,h]A[b,v]A[c,h]A[d,v]Sin[θ]2−12A[a,h]A[b,h]A[c,v]A[d,v]Sin[θ]2
There are 16 terms here and every term has for function A.
In some terms the first parameter of four function A are different from each other( a,b,c,d), in the other terms the four first paramenter are partial overlap(a,a,b,d;...).
how can I get the first kind. (the result is as below:)
−12A[a,v]A[b,h]A[c,v]A[d,h]Cos[θ]2+12A[a,h]A[b,v]A[c,v]A[d,h]Cos[θ]2+12A[a,v]A[b,h]A[c,h]A[d,v]Cos[θ]2−12A[a,h]A[b,v]A[c,h]A[d,v]Cos[θ]2−12A[a,v]A[b,v]A[c,h]A[d,h]Sin[θ]2+12A[a,v]A[b,h]A[c,v]A[d,h]Sin[θ]2+12A[a,h]A[b,v]A[c,h]A[d,v]Sin[θ]2−12A[a,h]A[b,h]A[c,v]A[d,v]Sin[θ]2
this is the input form for our mma:
-(1/2) A[a, v] A[b, h] A[c, v] A[d, h] Cos[\[Theta]]^2 +
1/2 A[a, h] A[b, v] A[c, v] A[d, h] Cos[\[Theta]]^2 +
1/2 A[a, v] A[b, h] A[c, h] A[d, v] Cos[\[Theta]]^2 -
1/2 A[a, h] A[b, v] A[c, h] A[d, v] Cos[\[Theta]]^2 +
1/2 A[a, v]^2 A[b, h] A[d, h] Cos[\[Theta]] Sin[\[Theta]] -
1/2 A[a, h] A[a, v] A[b, v] A[d, h] Cos[\[Theta]] Sin[\[Theta]] +
1/2 A[b, v] A[c, h] A[c, v] A[d, h] Cos[\[Theta]] Sin[\[Theta]] -
1/2 A[b, h] A[c, v]^2 A[d, h] Cos[\[Theta]] Sin[\[Theta]] -
1/2 A[a, h] A[a, v] A[b, h] A[d, v] Cos[\[Theta]] Sin[\[Theta]] +
1/2 A[a, h]^2 A[b, v] A[d, v] Cos[\[Theta]] Sin[\[Theta]] -
1/2 A[b, v] A[c, h]^2 A[d, v] Cos[\[Theta]] Sin[\[Theta]] +
1/2 A[b, h] A[c, h] A[c, v] A[d, v] Cos[\[Theta]] Sin[\[Theta]] -
1/2 A[a, v] A[b, v] A[c, h] A[d, h] Sin[\[Theta]]^2 +
1/2 A[a, v] A[b, h] A[c, v] A[d, h] Sin[\[Theta]]^2 +
1/2 A[a, h] A[b, v] A[c, h] A[d, v] Sin[\[Theta]]^2 -
1/2 A[a, h] A[b, h] A[c, v] A[d, v] Sin[\[Theta]]^2
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