Advanced Search

Question: Why Doesn’t simplify Fully Simplify My Expression in Maple?

Question:Why Doesn’t simplify Fully Simplify My Expression in Maple?

FZ 30 Maple 2022
complex simplify simplification
February 10 2025
1

I am working with an expression in Maple that involves complex terms and an integral. After applying the simplify command, some terms remain unsimplified, even though they seem reducible (see (7)). Additionally, an integral in my expression remains unevaluated (see (9)).
 

> 

restart;
> 

kernelopts(version);

`Maple 2022.0, X86 64 WINDOWS, Mar 8 2022, Build ID 1599809`

 (1)
> 

with(plots)
> 

interface(showassumed=0):
> 

assume(x::real);assume(t::real);assume(lambda1::complex);assume(b::real);
> 

alias(psi1 = psi1(x,t), psi2 = psi2(x,t), phi1 = phi1(x,t), phi2 = phi2(x,t), beta = beta(t), alpha =alpha(t));

psi1, psi2, phi1, phi2, beta, alpha

 (2)
> 

rel := {psi1 = exp((-I*lambda1)*x - (1/(4*I*lambda1))*int((alpha + b*beta),t)), psi2 = exp((I*lambda1)*x + (1/(4*I*lambda1))*int((alpha + b*beta),t)), phi1= exp((-I*conjugate(lambda1))*x - (1/(4*I*conjugate(lambda1)))*int((alpha + b*beta),t)), phi2 = exp((I*conjugate(lambda1))*x + (1/(4*I*conjugate(lambda1)))*int((alpha + b*beta),t))}

{phi1 = exp(-I*conjugate(lambda1)*x+((1/4)*I)*(int(b*beta+alpha, t))/conjugate(lambda1)), phi2 = exp(I*conjugate(lambda1)*x-((1/4)*I)*(int(b*beta+alpha, t))/conjugate(lambda1)), psi1 = exp(-I*lambda1*x+((1/4)*I)*(int(b*beta+alpha, t))/lambda1), psi2 = exp(I*lambda1*x-((1/4)*I)*(int(b*beta+alpha, t))/lambda1)}

 (3)
> 

Bnum := psi2*phi1*conjugate(lambda1) + psi1*lambda1*phi2;

psi2*phi1*conjugate(lambda1)+psi1*lambda1*phi2

 (4)
> 

Bnumexp := subs(rel,Bnum):
> 

Den := -phi1*psi2 - phi2*psi1;

-phi1*psi2-phi2*psi1

 (5)
> 

expDen := subs(rel, Den)

-exp(-I*conjugate(lambda1)*x+((1/4)*I)*(int(b*beta+alpha, t))/conjugate(lambda1))*exp(I*lambda1*x-((1/4)*I)*(int(b*beta+alpha, t))/lambda1)-exp(I*conjugate(lambda1)*x-((1/4)*I)*(int(b*beta+alpha, t))/conjugate(lambda1))*exp(-I*lambda1*x+((1/4)*I)*(int(b*beta+alpha, t))/lambda1)

 (6)
> 

sr := Bnumexp/expDen: ratiosr := simplify(diff(sr,t), complex):
> 

B := b - (4*I/beta(t))*ratiosr

b+2*(b*beta+alpha)*exp(((1/4)*I)*(4*conjugate(lambda1)^2*x-(int(b*beta+alpha, t)))/conjugate(lambda1))*exp(-((1/4)*I)*(4*conjugate(lambda1)^2*x-(int(b*beta+alpha, t)))/conjugate(lambda1))*exp(-((1/4)*I)*(4*lambda1^2*x-(int(b*beta+alpha, t)))/lambda1)*(-conjugate(lambda1)+lambda1)^2*exp(((1/4)*I)*(4*lambda1^2*x-(int(b*beta+alpha, t)))/lambda1)/(beta(t)*(exp(((1/4)*I)*(4*conjugate(lambda1)^2*x-(int(b*beta+alpha, t)))/conjugate(lambda1))*exp(-((1/4)*I)*(4*lambda1^2*x-(int(b*beta+alpha, t)))/lambda1)+exp(-((1/4)*I)*(4*conjugate(lambda1)^2*x-(int(b*beta+alpha, t)))/conjugate(lambda1))*exp(((1/4)*I)*(4*lambda1^2*x-(int(b*beta+alpha, t)))/lambda1))^2*lambda1*conjugate(lambda1))

 (7)
> 

p := {alpha(t) = t^2, beta = exp(-t)}

{beta = exp(-t), alpha(t) = t^2}

 (8)
> 

B1 := eval(subs(p, B))

b+2*(b*exp(-t)+alpha)*exp(((1/4)*I)*(4*conjugate(lambda1)^2*x-(int(b*exp(-t)+alpha, t)))/conjugate(lambda1))*exp(-((1/4)*I)*(4*conjugate(lambda1)^2*x-(int(b*exp(-t)+alpha, t)))/conjugate(lambda1))*exp(-((1/4)*I)*(4*lambda1^2*x-(int(b*exp(-t)+alpha, t)))/lambda1)*(-conjugate(lambda1)+lambda1)^2*exp(((1/4)*I)*(4*lambda1^2*x-(int(b*exp(-t)+alpha, t)))/lambda1)/((exp(-t))(t)*(exp(((1/4)*I)*(4*conjugate(lambda1)^2*x-(int(b*exp(-t)+alpha, t)))/conjugate(lambda1))*exp(-((1/4)*I)*(4*lambda1^2*x-(int(b*exp(-t)+alpha, t)))/lambda1)+exp(-((1/4)*I)*(4*conjugate(lambda1)^2*x-(int(b*exp(-t)+alpha, t)))/conjugate(lambda1))*exp(((1/4)*I)*(4*lambda1^2*x-(int(b*exp(-t)+alpha, t)))/lambda1))^2*lambda1*conjugate(lambda1))

 (9)

NULL


 

Download simplify.mw
Please Wait...