## Solving a system of nonlinear equations...

Hello!

How can I make MAPLE to put out the numerical solution of the following system?
(a =0.12, c = 47.04)  Neither solve nor fsolve does the job!

>restart:
>S:=t->c*exp(-a*t)+18;

S := t -> c*exp(-a*t)+18

> sys:={S(2)=55,S(8)=36};

sys := {c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55}

> solve(sys);

{a = -1/2*ln(18/37*RootOf(18*_Z^3-37)^2), c = 37*RootOf(18*_Z^3-37)}

> fsolve(sys);

fsolve({c*exp(-8*a)+18 = 36, c*exp(-2*a)+18 = 55},{a, c})

## Bug in my Division by Zero Calculator...

Basically it spits out the subset of values for which a division by zero error will occur for the function you specify on  range you specify for each of it's arguments, but I get an ambigous error when ever exponentiation features in the function I specify, which of course dramatically reduces the application of the calculator. Division,addition,substraction and multiplication are currently the only available arithmetic operators availble for the function window that I know the error will not occur.

If some one can help it is much appriciated

DIVISION_BY_ZERO_CALCULATOR.mw

## Simplify command on Binomial expressions...

Is there something I should be doing whenever I use simplify to avoid things like this, or should I stop using the "is" function all together?

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## Exponentiation by Squaring Issue...

My problem is explained with sufficient detail in the below worksheet:

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So I know I have obviously done something wrong, but it has proven very difficult to establish where given how little i know about the solve function

## Document Tools package "Generate Component" comman...

As useful as the SetProperty and GetProperty commands are in this package, I am seeking a command that is called by the action of a user input prompt, for example, the prompt window question is something like:

"How many parameters of silly do you want to specifiy for this analysis? (maximum is 10)"

And once the user has entered a natural number between 1 and 10, that number of components of a specified type is generated  in the worksheet.

Is this a real thing already and I can't find it or is there a round about way to do it without an actual command existing?

## modp has bugs and it's disgusting...

All of his should work very readily

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## Sieving failures...

I recieved the following error:

But when I review the procedure ifactor, it doesnt tell me anything about A Quadratic Sieve algorithm, and it's really long and looks dodgey and suspicious, like line 24 for example, why is it computing the greatest integer divisor of a local variable and a random enormous square free number? and then another with an additional factor a few lines later?

## DocumentTools Component Actions...

I need the final line of the uploaded worksheet to be the "Select Action", preprogrammed prior to the execution of the insert xml command, how do i do this?

Maple Worksheet - Error

## How can I extract DE coefficients to form a system...

Hi,

How can I extract the coefficients of uij in Eq.(3) to form a system of PDEs in F, P and Q?

coeff_of_DE.mw

## Analytical integration bug...

Hi

I use Maple 2016.

The following command calculates semicircle perimeter, but it returns infinity.

`assuming`([int(sqrt(1+(diff(sqrt(R^2-(x-R)^2), x))^2), x = 0 .. 2*R)], [R > 0])

## Sockets package Command entanglement phenomena ...

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

## Maple 2016 bug or a mistake?...

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.

## Exact solution of a PDE...

```restart:
with(PDEtools);
PDE :=  diff(y(x,t), t)-diff(y(x,t), x,x,t)-diff(y(x,t), x\$2)+ diff(y(x,t), x)+y(x,t)*diff(y(x,t),x)=exp(-t)*(cos(x)-sin(x)+1/2*exp(-t)*sin(2*x));

# Initial/boundary conditions
BCs:=y(0,t) = 0, y(Pi,t)=0;
ICs:=y(x,0) =sin(x) ;

pdsolve(PDE, {BCs,ICs});
exact_solution:=exp(-t)*sin(x);
Test1:=pdetest(exact_solution,[PDE, BCs,ICs]);
```

The solution of the PDE is exp(-t)*sin(x).

I want to check whether it is right or not by Maple.