Maple Questions and Posts

These are Posts and Questions associated with the product, Maple

How could one simplify the following expression, preferably over z in large parts of the complex plane, and with few calls under different assumptions, and preferably gracefully.

expr := 2*Pi*(-z)^(1/2)-z^(1/2)*(2*ln(-z^(1/2))-ln(z));

 Dear all

Is there a nice idea to determine the Lyapunov function of the following system

Lyapunov_function.mw

Some parameters used in the code:

b fixed parameter

a any parameter in R

Many thanks for your help

 

 

I was trying to learn more about the commands in this package and found it to be someone non satisfying:


 

Download sockets_strangeness.mw

 

In the attached maple worksheet integral.mw, I am trying to compute an integral involving hyperbolic cosines. While not straightforward to compute, it should be completely well behaved at zero and both infinities as long as rho is real:

Much to my surprise, maple gives "undefined" as the answer, even if I attach an "assuming rho > 0" to make completely sure that the denominator never vanishes.

If I fix rho to 1 (or any other value) and compute the integral numerically, maple happily gives a numeric value. Moreover, I can scale the R, use the fact that the integrand is an even function of R, factor the denominator, and use partial fraction decomposition to transform it into the equivalent form

which maple integrates happily and gives a completely well-defined function in terms of polylogarithms, which agrees with the numeric answer.

Now, I am not expecting maple to just solve every integral I throw at it, but why does it give "undefined" as the answer to a completely well-defined integral?

Hello

I have maple code saved as a text file f.txt.

It resides here

mydd:=“C:/Users/User/Downloads/f.txt”

what is the most expedient way to convert to f.mpl ?

Is there any easy way to use logical "operatives"(not sure what they are called)?

 

e.g., x^2[x=3] = if x = 3 then 3^2 or 0

f(x)[g(x)=x^2] = f(x) when g(x)=x^2

or whatever. I don't care about the syntax but would like it to be short and distinct. There are obviously ways to get the same behavior but they are too verbose. I like the bracket syntax but I doubt maple works with it. It could be done with a binary operator that does the comparison and returns if true...

 

But curious if maple has such a thing built in?

Maple gave Lie algebras of a system of PDE in which some of them do not leave the system invariant. Dont know whether the mistake is maple's or mine. File attached.



Maple_2016_bug_or...mw

 

I have an arc length parametrization problem. I got the right answer for the speed. The lines of code before the long dividing line I successfully got to work. The main problem I am having is with the code underneath that. It is producing weird answers and just returning the same words without computing any mathematical calculation.

 

with(VectorCalculus):

with(plots):

T:= 4:

r := t -> <t^2 + t, sin(t^2)*(t + 1), cos(t^2)*(t + 1)>;

speed := Norm(diff(r(t), t));

evalf(Int(speed, t = 0 .. T)); (I got 62.98633182 for this part)

----------------------------This is where I started running into problems with the arc length parametrization.

L := b -> int(speed, t = 0 .. b);

speed := t -> subs(c = t, Norm(diff(r(c), c)));

speed2 := t -> sqrt(factor(simplify(speed(t)^2)));

solve(s = L(t), s);

assume(b > 0 'real');

g := s -> solve(s = L(b), b, useassumptions = true);

newr := s -> r(g(s));

newr(s);

 

I like to see this solution step by step. I used DiffTutor before, is there something similar for implicit differentials?

I want to find dz:

z*t = cos(z + t)

 

I am trying to enter an ODE into Maple and I remember that Dr. Lopez showed how to use a prime to denote differentiation. When I try I get conflicting results: if I type

>  y''+y'+3*y=0;;

Error, unexpected single forward quote
But if I copy that command from the Help page Maple understands what I want. What is going on?

BTW, there is no entry for Differential Equations on the Help page.
 

 

 

In Maple outputs, long fraction bars occur quite frequently. A common example is of the type A(x)/x, where A(x) may be a complicated expression made up by standard functions, derivatives, integrals etc. in terms of x and some constants, denoted by names. Maple displays such an expression in terms of a long solidus and x as the denominator. This looks rather weird. A preferable display would be of the form x^-1 A(x) or A(x) multiplied by 1/x. I have unsuccessfully tried to achieve this but failed. Can this be done?

 

restart

with(numapprox):

with*plots:

I

 

Warning, The imaginary unit, I, has been renamed _I

 

M__h := .50; 1; beta[o] := 0.34e-1; 1; beta[1] := 0.25e-1; 1; mu[r] := 0.4e-3; 1; sigma := .7902; 1; alpha := .11; 1; psi := 0.136e-3; 1; xi := 0.5e-1; 1; gamma := .7; 1; M__c := .636; 1; mu[b] := 0.5e-2; 1; `&varpi;` := .134

.50

 

0.34e-1

 

0.25e-1

 

0.4e-3

 

.7902

 

.11

 

0.136e-3

 

0.5e-1

 

.7

 

.636

 

0.5e-2

 

.134

(1)

B(0) := .50;

.50

 

.30

 

.21

 

.14

 

.70

 

.45

 

.14

(2)

ODEs := {diff(J[1](T), T) = M__h-beta[1]*psi*(J[1](T)+J[2](T))*J[7](T)-sigma*psi*beta[1]*J[4](T)*J[7](T)-mu[r]*J[1](T), diff(J[2](T), T) = beta[1]*psi*(J[1](T)+J[2](T))*J[7](T)-(alpha+xi+mu[r])*J[2](T), diff(J[3](T), T) = alpha*J[2](T)-(`&varpi;`+mu[r])*J[3](T), diff(J[4](T), T) = `&varpi;`*J[3](T)-(gamma+mu[r])*J[4](T), diff(J[5](T), T) = gamma*J[4](T)+sigma*psi*beta[1]*J[5](T)*J[7](T)-mu[r]*J[5](T), diff(J[6](T), T) = M__c-psi*beta[o]*J[6](T)*J[3](T)-mu[b]*J[6](T), diff(J[7](T), T) = psi*beta[o]*J[6](T)*J[3](T)-mu[b]*J[7](T)}

{diff(J[1](T), T) = .50-0.3400e-5*(J[1](T)+J[2](T))*J[7](T)-0.26866800e-5*J[4](T)*J[7](T)-0.4e-3*J[1](T), diff(J[2](T), T) = 0.3400e-5*(J[1](T)+J[2](T))*J[7](T)-.1604*J[2](T), diff(J[3](T), T) = .11*J[2](T)-.1344*J[3](T), diff(J[4](T), T) = .134*J[3](T)-.7004*J[4](T), diff(J[5](T), T) = .7*J[4](T)+0.26866800e-5*J[5](T)*J[7](T)-0.4e-3*J[5](T), diff(J[6](T), T) = .636-0.4624e-5*J[6](T)*J[3](T)-0.5e-2*J[6](T), diff(J[7](T), T) = 0.4624e-5*J[6](T)*J[3](T)-0.5e-2*J[7](T)}

(3)

ic1 := {J[1](0) = B(0), J[2](0) = C(0), J[3](0) = DD(0), J[4](0) = E(0), J[5](0) = F(0), J[6](0) = G(0), J[7](0) = H(0)};

{J[1](0) = .50, J[2](0) = .30, J[3](0) = .21, J[4](0) = .14, J[5](0) = .70, J[6](0) = .45, J[7](0) = .14}

(4)

sol1 := dsolve(`union`(ODEs, ic1), {J[1](T), J[2](T), J[3](T), J[4](T), J[5](T), J[6](T), J[7](T)}, type = numeric, output = listprocedure)