## 130 Reputation

6 years, 112 days

## How to common a factor appears in many t...

Maple 18

> den := -(-(conjugate(chi)-conjugate(phi))*(chi+phi)*conjugate(lambda)+lambda*(conjugate(chi)+conjugate(phi))*(chi-phi))*(-(conjugate(chi)+conjugate(phi))*(chi-phi)*conjugate(lambda)+lambda*(conjugate(chi)-conjugate(phi))*(chi+phi));

> phi:=exp(I*lambda*(x-t/(4*lambda^2)-w^2)):chi:=exp(-I*lambda*(x-t/(4*lambda^2)-w^2)):

> den1:=simplify(dsubs({phi,chi},den));

> dsubs({exp((1/4*I)*(4*lambda^2*w^2-4*lambda^2*x+t)/lambda), exp(-(1/4*I)*(4*lambda^2*w^2-4*lambda^2*x+t)/lambda)}, 4*conjugate(lambda)^2*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2-4*conjugate(lambda)^2*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2+8*abs(lambda)^2*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2+8*abs(lambda)^2*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2+4*cos((1/4)*(4*w^2*lambda^2-4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda+t)/lambda)^2*lambda^2-4*cos((1/4)*(-4*w^2*lambda^2+4*x*lambda^2+conjugate((4*lambda^2*w^2-4*lambda^2*x+t)/lambda)*lambda-t)/lambda)^2*lambda^2-16*abs(lambda)^2)

Since "cos(...)" appears in every term in last equation (except a last one), how to common it?

## How to verify the solution of PDEs?...

Maple 18

 > restart:
 > with(PDEtools):
 > with(LinearAlgebra):
 >
 > alias(f=f(x,t),g=g(x,t));
 (1)
 >
 >
 > eq1:=diff(f,x)=-I*eta*f +I*exp(-I*t)*g;
 (2)
 > eq2:=diff(g,x)=-I*eta*g +I*exp(I*t)*f;
 (3)
 > eq3:=diff(f,t)=(I*eta^2-I/2)*f +I*eta*exp(-I*t)*g;
 (4)
 > eq4:=diff(g,t)=(-I*eta^2+I/2)*g +I*eta*exp(I*t)*f;
 (5)
 > #### The solution of (2)-(5) is
 > eq5:=f=I*(c1*exp(A)-c2*exp(-A))*exp(-i*t/2);
 (6)
 > eq6:=g=(c2*exp(A)-c1*exp(-A))*exp(i*t/2);
 (7)
 > #### where
 > c1=sqrt(h-sqrt(h^2-1))/sqrt(h^2-1);c2=sqrt(h+sqrt(h^2-1))/sqrt(h^2-1);A=sqrt(h^2-1)*(x+I*h*t);
 (8)
 > #### How to verify (6) and (7) is the solution of (2)-(5)?

## How can we remove c1 from the expression...

Maple

(-(2*I)*c1*eta+c1*sqrt(-e0^2-4*eta^2))/e0 = c2, ((2*I)*c2*eta+c2*sqrt(-e0^2-4*eta^2))/e0 = -c1

How can we remove c1 from the expression of c2 and similarly c2 from c1?

## How to plot Bloch sphere on maple?...

Maple 18

If we have an equation for the generalized Bloch sphere i.e.,

\partial_{t}(u^{2} + v^{2} + w^{2}) = 0,

where u, v and w are functions of x and t and the initial conditions u=v=0, w=-1. Then how to plot this equation on maple?

## Is there any way to write the expression...

Maple

Is there any way to write the expression into the ratio of simple determinants? i..e,

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