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Question: How do you simplify the equations and show that they are equal?

Question:How do you simplify the equations and show that they are equal?

Gabriel Barcellos 75 Maple 2024
simplify simplification
4 hours ago
0

I have two equations developed in different ways and I want to compare them.
The first is a development done using maple, while the second is an algebraic analysis.

I need to find out if both are identical and, therefore, if the subtraction would be equal to zero.

How should I proceed?

I had thought about simplifying the first and comparing it with the second; is that a good approach?

 
> 

restart
> 

with(plots)
> 

H0 := -S1^2*eta1-S2^2*eta2-S1*gamma1-S2*gamma2

-S1^2*eta1-S2^2*eta2-S1*gamma1-S2*gamma2

 (1)
> 

NULL
> 

Z0 := exp(-beta*H0)

exp(-beta*(-S1^2*eta1-S2^2*eta2-S1*gamma1-S2*gamma2))

 (2)
> 

Z0 := add(Z0, S1 = [-2, -1, 0, 1, 2])
> 

Z0 := add(Z0, S2 = [-2, -1, 0, 1, 2])
> 

G0 := -ln(Z0^((1/2)*N))/beta
> 

G01 := -ln((2*exp(4*beta*eta1)*cosh(2*beta*gamma1)+2*exp(beta*eta1)*cosh(beta*gamma1)+1)^((1/2)*N)*(2*exp(4*beta*eta2)*cosh(2*beta*gamma2)+2*exp(beta*eta2)*cosh(beta*gamma2)+1)^((1/2)*N))/beta

-ln((2*exp(4*beta*eta1)*cosh(2*beta*gamma1)+2*exp(beta*eta1)*cosh(beta*gamma1)+1)^((1/2)*N)*(2*exp(4*beta*eta2)*cosh(2*beta*gamma2)+2*exp(beta*eta2)*cosh(beta*gamma2)+1)^((1/2)*N))/beta

 (3)
> 

Teste := G0-G01

NULL

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