## Setup Differential Equation into a Matrixform...

I'm practicing with matrices in Maple, but I have a question. My question is, how do I set up the differential equation system on matrix form x '(t) = Ax (t) + B?

Here are the equations:

x'1(t) = x1(t) - x2(t) - 3

x'2(t) = 12x1(t) - 8x2(t) + 4

I've been looking around for some help sources, but the only one I could find is this. I tried to set it up like that, but didn't work, it gave me an error.

How should I set it up (using Maple commands)?

## Unexpected behavior of define(orderless)...

I have found an unpleaseant feature of the define command.
@Carl Love
See below for the example. Basically, after declaring a function orderless via the define command,
a simple use of Categorize stops working.  Details in the file.

How can one define a function f(x,y) to be symmetric under interchange x<-> y

primes2.mw

## How do some plot commands evaluate complex express...

In this worksheet, how do the several successful plot commands evaluate the complex expression being plotted, and why do the unsuccessful plot commands fail to do so?

Plot_complex_expression.mw

## How to develop a system for calculating in quatern...

What is the best (easiest) way to build up a small sytem (procedures) for calculating with base4-numbers ?

...  like multiplication, ln, square, root and so on.

I was thinking about padic or convert-procedures in maple, but before I will begin with that it would be very friendly to have a hint or the opinion of a professional maple programmer.

Thanks for helping ðŸ˜ƒ

Arno

## Integration of spline...

I am trying to do the integration on the picture (int1). V,omega,theta,rhotræ,ix,iy,ixy,E,R are constants. a(r),å(r),FL(r),FD(r) are splines. It seems to run forever without any error. I have tried a simpler version to figure out if the problem has to do with the splines or the arctan. They can run independently but not when combined. (int2). I use an i7 6700k. I am fine with an aproximated answer within a couple %.

## what solver PDEtools:-Solve uses by default...

I noticed PDEtools:-Solve hangs sometimes on some input where solve does not. When I change the solver for PDEtools:-Solve to use solve, it did not hang.

This means PDEtools:-Solve default solver is something else. I did not see what it is by looking at help.

Here is an example

```restart;
eq:=[1/3*(-334*I*(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(1/3)-2*(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(2/3)+56978)/(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(1/3)*v[1]-20*I*2^(1/2)*v[2] = 0, (-18000*I*2^(1/2)+33400*I-40*(1746675+72116445*2^(1/2))^(1/2)-40*(-167*I*(1746675+72116445*2^(1/2))^(1/2)+75150*2^(1/2)+10*(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(2/3)+145445)/(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(1/3))/(167*I*(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(1/3)+(-4807763*I+27000*I*2^(1/2)+60*(1746675+72116445*2^(1/2))^(1/2))^(2/3)-28489)*v[2]-20*I*2^(1/2)*t = 0];

solve(eq,[v[1],v[2]]); #OK
PDEtools:-Solve(eq,[v[1],v[2]],solver=solve); #OK
PDEtools:-Solve(eq,[v[1],v[2]]); #hangs
```

Maple 2021

## solving a system of trigonometric equations...

Hey guys I need help solving the following system of trigonometric equations

`invEqs := [a[3]*cos(theta[1] + theta[2] + theta[3]) + a[2]*cos(theta[1] + theta[2]) + a[1]*cos(theta[1]) = px, a[3]*sin(theta[1] + theta[2] + theta[3]) + a[2]*sin(theta[1] + theta[2]) + a[1]*sin(theta[1]) = py, theta[1] + theta[2] + theta[3] = phi]`

which everything except theta[1], theta[2], theta[3] are known.

here what I came up with but no success

`res := solve(invEqs, {theta[2], theta[3], sin(theta[1])})`

or better be like this but no output printed

`res := solve(invEqs, {theta[1], theta[3], cos(theta[2])})`

## Power series solution of nonlinear ODE...

How to find the power series solution of a nonlinear 4th order ordinary differential equation.

>ode:=U""+c^2*U"+k*c*U"-(3U^2+a)*U''=0

## HUE shading for implicit function...

hi! is there any kind of formula for coloring functions by HUE like this

contourplot(abs(sin(x) + y^2 + y + x*I), x = -6 .. 6, y = -5 .. 5, contours = [seq(1/2^n, n = 1 .. 3), seq(2^n, n = 1 .. 5)], numpoints = 200000, thickness = 1.5, color = black);

I wonder about situation when we don't have function for example f(z)=z but f(x,y)=x+I*y and we want to use domain coloring for that. Thanks in advance.

## How do I solve a equation ln in Maple?...

Hi!

How do I solve a equation ln in Maple:ln.mw

## How to compute te expectation of an abstract rando...

Let E be a random variable of expectation mu and A an algebraic expression containing no random variable.
If E has any known Maple distribution, then  Mean(A+E) = A+mu.

But if E is an "abstract" random variable, Mean doesn't seem capable to compute the expectation of A+E.
Notional example:

```restart:
with(Statistics):
E := RandomVariable(Normal(mu, sigma)):
Mean(f(x)+E)
f(x) + mu
E := RandomVariable(Distribution(PDF = (z -> f(z)), Mean=mu)):
Mean(f(x)+E);
int((f(x) + _t) f(_t), _t = -infinity .. infinity)

IntegrationTools:-Expand(%);
f(x) (int(f(_t), _t = -infinity .. infinity)) + (int(f(_t) _t, _t = -infinity .. infinity))
```

Questions:

• Why does Mean not behave as expected for an abstract random variable?
• Is there a simple way to obtain the expected result (Mean (A+E) = A+mu) (maybe by completing the definition of the distribution of E, or by any other means)?

TIA

PS: I know that I can replace Mean(A+E)  by A+Mean(E)  to obtain the desired result: this is not the type of answer I look for.

PS: I know (since Carl Love showed me how long ago) that I can define a "random variable" plus an operator Expectation such that Expectation(A+E)  by A+Expectation(E) ... but it's not a way I would call simple

```Expectation := proc(e::algebraic)
local a,b;
if not hastype(e, RV) then e
elif e::RV then 'procname'(e)
elif e::`+` then map(thisproc, e)
elif e::`*` then
(a,b):= selectremove(hastype, e, RV);
b*thisproc(a)
else 'procname'(e)
end if
end proc:

#------------------------------------------------------------------------

RV,
{RandomVariable,
'RandomVariable^posint',
'`*`'({RandomVariable, 'RandomVariable^posint'})
}
):
eval(Expectation(f(x)+E), Expectation=Mean)
f(x) + mu
```

## How to run this: ` Computes A*B mod b^d by convolu...

13.5.2021

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Hi ðŸ˜Š

I have found this Code here somewhere in MaplePrimes.

I am very interested in that Procedure, but it doesn't run.

I will be very happy, to get help with that.

Thanks a lot,

Arno

## How to output "(mol/L)^2" instead of "L^2/mol^2"?...

Hello

When doing chemistry in Maple, I want to be able to do my calculations with units.

Maple does not support the unit [M] (molar concentration), so I have to manually type the unit as [mol/L].

That is not a problem in itself, but I have encountered som issues with Maple's own formatting of the units.

For example, in the attached document I want the output unit to be (mol/L)^(-2). However, Maple automatically formats it as

It even does the same thing in the "Maple Math" here on MaplePrimes - Here I try to type (mol/L)^(-2):

So does anyone know a way to avoid Maple's auto-formatting of the output, or is there a way to customize it so I get my desired output?

I have attached the document with some screenshots in it: chemistry_units.mw

// Frederik

## typematch behaving differently after/before copy a...

primes.mw

As a result of a calculation I have a long expression. I give it a name, say, X,

X:= long expression.

I try to use typematch to extract different parts of X and its does not work (it returns false).

If, however, I copy and paste the long expression from the output and plug into my typematch query it works!

It seems that copy and paste change the type of the expression. I am very confused with this.

I have uploaded a file with the problem at the beggining.  Thank you!
Max