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I have an expression that contains Sinh[x], Cosh[x] and Sin[g], and I want to simplify it into an easier form, based on the physics situation (I am doing some general relativity calculation), I know it should be simplified into a polynomial of u, and none of the coefficients of u should contain any fractional numbers.

What I am doing right now is just using Simplify and some really simple patterns as transformation rules. Could someone give me some suggestion on how to simplify it?

Or could someone please give me some materials or examples on how to simplify really complicated expressions?

Here is my expression that needs to be simplifyed.

((2 m^2-3 m r+r^2+a^2 u^2+m (2 m-r) Cos[2 g]) Cosh[p4]^2-4 I a m u Cos[g] Cosh[p4] Sinh[p4]-(r^2+a^2 u^2) Sinh[p4]^2) ((-m r+r^2+a^2 u^2-m r Cos[2 g]) Cosh[q4]^2+4 m Cosh[q4] (-I a u Cosh[p4] Sin[g]-1/2 r Sin[2 g] Sinh[p4]) Sinh[q4]+1/2 (-4 m^2+5 m r-2 r^2-2 a^2 u^2-m r Cos[2 g]+m (-4 m+3 r+r Cos[2 g]) Cosh[2 p4]+4 I a m u Cos[g] Sinh[2 p4]) Sinh[q4]^2) (-(m^2 Cosh[p4] ((4 m r-3 r^2+3 a^2 u^2+(4 m r-r^2+a^2 u^2) Cos[2 g]) Cosh[p4]-8 I a r u Cos[g] Sinh[p4]) (2 I a u Cosh[q4] Sin[g] Sinh[p4]-2 I a u Cos[g] Cosh[p4]^2 Sinh[q4]+(-2 I a u Cos[g] Sinh[p4]^2+m (1+Cos[g]^2) Sinh[2 p4]) Sinh[q4]-Cosh[p4] ((2 m-r) Cosh[q4] Sin[2 g]+(m+3 r+(-m+r) Cos[2 g]) Sinh[p4] Sinh[q4])))/((r^2+a^2 u^2) ((-2 m^2+3 m r-r^2-a^2 u^2-m (2 m-r) Cos[2 g]) Cosh[p4]^2+4 I a m u Cos[g] Cosh[p4] Sinh[p4]+(r^2+a^2 u^2) Sinh[p4]^2)^2)+(2 m (-2 I a r u Cos[g] Cosh[p4]^2 Sinh[q4]+Cosh[p4] ((-4 m r+r^2-a^2 u^2) Cos[g] Cosh[q4] Sin[g]+(2 (2 m-r) r Cos[g]^2+(-r^2+a^2 u^2) Sin[g]^2) Sinh[p4] Sinh[q4])+a u (2 I r Cosh[q4] Sin[g] Sinh[p4]+Cos[g] (-2 I r Sinh[p4]^2+a u Cos[g] Sinh[2 p4]) Sinh[q4])))/((r^2+a^2 u^2) ((2 m^2-3 m r+r^2+a^2 u^2+m (2 m-r) Cos[2 g]) Cosh[p4]^2-4 I a m u Cos[g] Cosh[p4] Sinh[p4]-(r^2+a^2 u^2) Sinh[p4]^2))-(m^2 (2 Cosh[q4] (7 I a m u Cos[g]+I a m u Cos[g]^3+2 I a u Cos[g] (3 m-4 r+m Cos[2 g]) Cosh[p4]^2-3 I a m u Cos[g] Sin[g]^2-2 Cosh[p4] (r^2 Cos[g]^2+a^2 u^2 Sin[g]^2) Sinh[p4]+2 I a u Cos[g] (3 m-4 r+m Cos[2 g]) Sinh[p4]^2+4 m r Sinh[2 p4]-3 r^2 Sinh[2 p4]+3 a^2 u^2 Sinh[2 p4]+4 m r Cos[g]^2 Sinh[2 p4]+a^2 u^2 Cos[g]^2 Sinh[2 p4]-4 m r Sin[g]^2 Sinh[2 p4]+r^2 Sin[g]^2 Sinh[2 p4])+(4 (3 m^2-4 m r+r^2-a^2 u^2) Cosh[p4] Sin[2 g]+4 m^2 Cosh[p4]^3 Sin[2 g]-12 I a m u Cosh[p4]^2 Sin[g]^3 Sinh[p4]-I Sinh[p4] (a u (m-16 r-m Cos[2 g]) Sin[g]+2 a m u Cosh[2 p4] Sin[g]^3+6 I m^2 Sin[2 g] Sinh[2 p4])) Sinh[q4]) (8 I a u Cosh[p4] Cosh[2 q4] Sin[g]+8 r Cos[g] Cosh[q4]^2 Sin[g] Sinh[p4]+(4 m-3 r+7 r Cos[2 g]-r (3+Cos[2 g]) Cosh[2 p4]) Cosh[q4] Sinh[q4]+8 r Cos[g] Sin[g] Sinh[p4] Sinh[q4]^2+(4 m-3 r-r Cos[2 g]) Cosh[p4]^2 Sinh[2 q4]+2 m Cosh[2 p4] Sinh[2 q4]-4 I a u Cos[g] Sinh[2 p4] Sinh[2 q4]))/(16 ((-2 m^2+3 m r-r^2-a^2 u^2-m (2 m-r) Cos[2 g]) Cosh[p4]^2+4 I a m u Cos[g] Cosh[p4] Sinh[p4]+(r^2+a^2 u^2) Sinh[p4]^2)^2 ((m r-r^2-a^2 u^2+m r Cos[2 g]) Cosh[q4]^2+4 I a m u Cosh[p4] Cosh[q4] Sin[g] Sinh[q4]+(4 m^2-4 m r+r^2+a^2 u^2) Cosh[p4]^2 Sinh[q4]^2-4 I a m u Cos[g] Cosh[p4] Sinh[p4] Sinh[q4]^2-Sinh[p4] ((-m r+r^2+a^2 u^2+m r Cos[2 g]) Sinh[p4] Sinh[q4]^2-m r Sin[2 g] Sinh[2 q4]))))

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What kind of transformation rules have you tried? –  mmal Sep 21 '13 at 9:27
    
Unfortunately you have not supplied any additional information about the occurring variables. What about p4, q4, g and so on, which ones are actual variables and which ones are constants. Also not clear: What is the domain of the variables? –  Wizard Sep 30 '13 at 17:43
    
One more common hint: FullSimplify applies more complicated transformation rules. Maybe worth a try. –  Wizard Sep 30 '13 at 17:44

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