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Question: Difference between 'simplify(expression)' and 'simplify(expression,size)'

Question:Difference between 'simplify(expression)' and 'simplify(expression,size)'

WA573 80 Maple 2022
simplify size
February 14 2024
1

Are the results consistent either we use simplify(expression) or simplify(expression,size)? It seems (2) and (3) are not consistent.

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restart
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with(PDEtools); with(LinearAlgebra)
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b := -(2*I)*exp(2*t*Im(lambda1))*(exp(I*a*x/conjugate(lambda1))*exp((2*I)*a*x/lambda1)*exp((-I*a*x)*(1/conjugate(lambda1)))*exp(I*conjugate(lambda1)*t)+exp(I*lambda1*t)*exp(I*a*x/lambda1)*exp((-I*a*x)*(1/lambda1))*exp((2*I)*a*x/conjugate(lambda1))*(abs(`ε1`)^2+abs(`ε2`)^2))*conjugate(`ε1`)*Im(lambda1)/(exp((2*I)*a*x/lambda1)*abs(`ε1`)^2*exp(-(2*I)*a*x/conjugate(lambda1))*exp(2*t*Im(lambda1))+exp(-(2*I)*a*x/lambda1)*abs(`ε1`)^2*exp((2*I)*a*x/conjugate(lambda1))*exp(2*t*Im(lambda1))+exp(I*a*x/lambda1)*exp((-I*a*x)*(1/lambda1))*exp(I*a*x/conjugate(lambda1))*exp((-I*a*x)*(1/conjugate(lambda1)))*(abs(`ε2`)^4+2*abs(`ε1`)^2*abs(`ε2`)^2+abs(`ε1`)^4+2*abs(`ε2`)^2*exp(2*t*Im(lambda1))+exp(4*t*Im(lambda1))))

-(2*I)*exp(2*t*Im(lambda1))*(exp(I*a*x/conjugate(lambda1))*exp((2*I)*a*x/lambda1)*exp(-I*a*x/conjugate(lambda1))*exp(I*conjugate(lambda1)*t)+exp(I*lambda1*t)*exp(I*a*x/lambda1)*exp(-I*a*x/lambda1)*exp((2*I)*a*x/conjugate(lambda1))*(abs(epsilon1)^2+abs(epsilon2)^2))*conjugate(epsilon1)*Im(lambda1)/(exp((2*I)*a*x/lambda1)*abs(epsilon1)^2*exp(-(2*I)*a*x/conjugate(lambda1))*exp(2*t*Im(lambda1))+exp(-(2*I)*a*x/lambda1)*abs(epsilon1)^2*exp((2*I)*a*x/conjugate(lambda1))*exp(2*t*Im(lambda1))+exp(I*a*x/lambda1)*exp(-I*a*x/lambda1)*exp(I*a*x/conjugate(lambda1))*exp(-I*a*x/conjugate(lambda1))*(abs(epsilon2)^4+2*abs(epsilon1)^2*abs(epsilon2)^2+abs(epsilon1)^4+2*abs(epsilon2)^2*exp(2*t*Im(lambda1))+exp(4*t*Im(lambda1))))

 (1)
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bdif := simplify(diff(b, x)); bdifxzero := simplify(subs({x = 0}, bdif))

4*Im(lambda1)*exp(2*t*Im(lambda1))*a*conjugate(epsilon1)*(conjugate(lambda1)*abs(epsilon1)^2*(abs(epsilon1)^2+abs(epsilon2)^2)*exp((t*(I*lambda1+2*Im(lambda1))*abs(lambda1)^2+(4*I)*a*(lambda1-(1/2)*conjugate(lambda1))*x)/abs(lambda1)^2)+exp(((I*conjugate(lambda1)+2*Im(lambda1))*t*abs(lambda1)^2-(2*I)*(lambda1-2*conjugate(lambda1))*a*x)/abs(lambda1)^2)*abs(epsilon1)^2*lambda1+2*abs(epsilon1)^2*(conjugate(lambda1)-(1/2)*lambda1)*exp((I*conjugate(lambda1)^2*t+(2*I)*a*x+2*t*Im(lambda1)*conjugate(lambda1))/conjugate(lambda1))+2*abs(epsilon2)^2*lambda1*(abs(epsilon1)^2+abs(epsilon2)^2)*exp((I*t*abs(lambda1)^2+(2*I)*a*x+2*t*Im(lambda1)*conjugate(lambda1))/conjugate(lambda1))+lambda1*(abs(epsilon1)^2+abs(epsilon2)^2)*exp((I*t*abs(lambda1)^2+(2*I)*a*x+4*t*Im(lambda1)*conjugate(lambda1))/conjugate(lambda1))+2*conjugate(lambda1)*exp((I*t*abs(lambda1)^2+(2*I)*a*x+2*t*Im(lambda1)*lambda1)/lambda1)*abs(epsilon2)^2+conjugate(lambda1)*exp((I*t*abs(lambda1)^2+(2*I)*a*x+4*t*Im(lambda1)*lambda1)/lambda1)+(-abs(epsilon1)^2*(conjugate(lambda1)-2*lambda1)*exp((I*lambda1^2*t+(2*I)*a*x+2*t*Im(lambda1)*lambda1)/lambda1)+(abs(epsilon1)^2+abs(epsilon2)^2)*(lambda1*(abs(epsilon1)^2+abs(epsilon2)^2)*exp(I*(t*abs(lambda1)^2+2*a*x)/conjugate(lambda1))+conjugate(lambda1)*exp(I*(t*abs(lambda1)^2+2*a*x)/lambda1)))*(abs(epsilon1)^2+abs(epsilon2)^2))/((abs(epsilon1)^4+2*abs(epsilon1)^2*abs(epsilon2)^2+abs(epsilon2)^4+2*abs(epsilon2)^2*exp(2*t*Im(lambda1))+exp((2*t*Im(lambda1)*abs(lambda1)^2-(2*I)*(lambda1-conjugate(lambda1))*a*x)/abs(lambda1)^2)*abs(epsilon1)^2+exp((2*t*Im(lambda1)*abs(lambda1)^2+(2*I)*(lambda1-conjugate(lambda1))*a*x)/abs(lambda1)^2)*abs(epsilon1)^2+exp(4*t*Im(lambda1)))^2*abs(lambda1)^2)

  

12*Im(lambda1)*exp(2*t*Im(lambda1))*((2/3)*abs(epsilon2)^2*lambda1*(abs(epsilon1)^2+abs(epsilon2)^2)*exp(t*(I*abs(lambda1)^2+2*Im(lambda1)*conjugate(lambda1))/conjugate(lambda1))+(1/3)*lambda1*(abs(epsilon1)^2+abs(epsilon2)^2)*exp(t*(I*abs(lambda1)^2+4*Im(lambda1)*conjugate(lambda1))/conjugate(lambda1))+(2/3)*conjugate(lambda1)*exp(t*(I*abs(lambda1)^2+2*lambda1*Im(lambda1))/lambda1)*abs(epsilon2)^2+(1/3)*conjugate(lambda1)*exp(t*(I*abs(lambda1)^2+4*lambda1*Im(lambda1))/lambda1)+(1/3)*lambda1*(abs(epsilon1)^2+abs(epsilon2)^2)^3*exp(I*abs(lambda1)^2*t/conjugate(lambda1))+(1/3)*conjugate(lambda1)*(abs(epsilon1)^2+abs(epsilon2)^2)^2*exp(I*abs(lambda1)^2*t/lambda1)+((-I*Im(lambda1)+(1/3)*lambda1+(1/3)*Re(lambda1))*exp((I*conjugate(lambda1)+2*Im(lambda1))*t)+(I*Im(lambda1)+(1/3)*conjugate(lambda1)+(1/3)*Re(lambda1))*(abs(epsilon1)^2+abs(epsilon2)^2)*exp(t*(I*lambda1+2*Im(lambda1))))*abs(epsilon1)^2)*a*conjugate(epsilon1)/(abs(lambda1)^2*((2*abs(epsilon2)^2+2*abs(epsilon1)^2)*exp(2*t*Im(lambda1))+abs(epsilon2)^4+2*abs(epsilon1)^2*abs(epsilon2)^2+abs(epsilon1)^4+exp(4*t*Im(lambda1)))^2)

 (2)
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bdif1 := simplify(diff(b, x), size); bdif1xzero := simplify(subs({x = 0}, bdif1), size)

4*Im(lambda1)*(2*exp(I*a*x/lambda1)*exp(I*conjugate(lambda1)*t)*(exp(I*a*x/conjugate(lambda1)))^2*exp(-I*a*x/lambda1)*((1/2)*abs(epsilon1)^4+abs(epsilon1)^2*abs(epsilon2)^2+(1/2)*abs(epsilon2)^4+abs(epsilon2)^2*exp(2*t*Im(lambda1))+(1/2)*exp(4*t*Im(lambda1)))*exp((2*I)*a*x/lambda1)*conjugate(lambda1)*(exp(-I*a*x/conjugate(lambda1)))^2+2*exp(I*a*x/conjugate(lambda1))*(((exp(I*a*x/lambda1))^2*lambda1*exp(I*lambda1*t)*((1/2)*abs(epsilon1)^4+abs(epsilon1)^2*abs(epsilon2)^2+(1/2)*abs(epsilon2)^4+abs(epsilon2)^2*exp(2*t*Im(lambda1))+(1/2)*exp(4*t*Im(lambda1)))*(abs(epsilon1)^2+abs(epsilon2)^2)*(exp(-I*a*x/lambda1))^2+exp(-(2*I)*a*x/lambda1)*exp((2*I)*a*x/lambda1)*exp(2*t*Im(lambda1))*exp(I*conjugate(lambda1)*t)*abs(epsilon1)^2*(conjugate(lambda1)-(1/2)*lambda1))*exp((2*I)*a*x/conjugate(lambda1))+(1/2)*(exp((2*I)*a*x/lambda1))^2*exp(2*t*Im(lambda1))*exp(I*conjugate(lambda1)*t)*exp(-(2*I)*a*x/conjugate(lambda1))*lambda1*abs(epsilon1)^2)*exp(-I*a*x/conjugate(lambda1))+exp(I*a*x/lambda1)*abs(epsilon1)^2*exp(I*lambda1*t)*exp(-I*a*x/lambda1)*exp((2*I)*a*x/conjugate(lambda1))*(conjugate(lambda1)*exp(-(2*I)*a*x/lambda1)*exp((2*I)*a*x/conjugate(lambda1))-exp((2*I)*a*x/lambda1)*exp(-(2*I)*a*x/conjugate(lambda1))*(conjugate(lambda1)-2*lambda1))*exp(2*t*Im(lambda1))*(abs(epsilon1)^2+abs(epsilon2)^2))*conjugate(epsilon1)*a*exp(2*t*Im(lambda1))/((2*exp(I*a*x/lambda1)*exp(I*a*x/conjugate(lambda1))*exp(-I*a*x/lambda1)*((1/2)*abs(epsilon1)^4+abs(epsilon1)^2*abs(epsilon2)^2+(1/2)*abs(epsilon2)^4+abs(epsilon2)^2*exp(2*t*Im(lambda1))+(1/2)*exp(4*t*Im(lambda1)))*exp(-I*a*x/conjugate(lambda1))+exp(2*t*Im(lambda1))*abs(epsilon1)^2*(exp(-(2*I)*a*x/lambda1)*exp((2*I)*a*x/conjugate(lambda1))+exp((2*I)*a*x/lambda1)*exp(-(2*I)*a*x/conjugate(lambda1))))^2*lambda1*conjugate(lambda1))

  

2*Im(lambda1)*exp(0)*conjugate(epsilon1)*exp(2*t*Im(lambda1))*a*(conjugate(lambda1)*exp(I*conjugate(lambda1)*t)+exp(I*lambda1*t)*lambda1*(abs(epsilon1)^2+abs(epsilon2)^2))/((((exp(0))^2*abs(epsilon2)^2+abs(epsilon1)^2)*exp(2*t*Im(lambda1))+(1/2)*(exp(0))^2*(exp(4*t*Im(lambda1))+(abs(epsilon1)^2+abs(epsilon2)^2)^2))*lambda1*conjugate(lambda1))

 (3)
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NULL

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