## How do I solve a set of equations numerically in M...

Hi,

How do I solve numerically this set of equations with the following ICs to plot U1(x), phi(x),diff(phi(x),x) versus x:

diff(U1(x),x)=-diff(phi(x),x)/(U1(x)-T/U1(x));
diff(phi(x),x\$2)=(1+A1*phi(x)+A2*phi(x)**(3/2)+A3*phi(x)**2)-(M1/U1(x));
where

A1:=(2*k-1)/(2*k-3);
A2:=8*sqrt(2/pi)*(beta-1)*k*Gamma(k)/(3*Gamma(k-0.5)*(2*k-3)**(3/2));
A3:=(4*k**2-1)/(2*(2*k-3)**2);
M1=0.1+sqrt(T+(1/A1));
(Gamma is gamma function)

assume, for example, T=0.1, pi=3.14, beta=0.6, k=3.5

ICs:

U1(x=0)=M1, phi(x=0)=0, diff(phi(x=0),x)=0.001.

Thanks.

## Symbolic Linear Programming in maple...

I know we can use Maple LPSolver for linear programming problem (eg. https://www.maplesoft.com/support/help/Maple/view.aspx?path=Optimization/LPSolveMatrixForm), while I am wondering if we can use maple to solve a LP problem symbolically when some of the constants in those examples are unknow parameters.

If no, any suggestions of other solutions？I guess I have to do the simplex method manually? Thanks.

## how to obtain conditions used by coulditbe ?...

From help, it says

coulditbe routine returns true if there is a possible value of x1 that satisfies prop1

my question is, how to find out this condition/possible values that Maple found?  This infomration is very useful, but now I do not see how to obtain it. All what coulditbe retuirn is true or false.

Context of why I am asking:  Sometimes odetest do not verify its own solutions. And coulditbe can help in finding under what conditions the solution can satisfy the ode. Here is an example

```restart;
ode:=diff(y(x),x) = abs(y(x))+1;
solExplicit:=dsolve(ode);
offset := odetest~([solExplicit],ode)
```

gives

`[exp(-x)/_C1 - abs((-exp(-x) + _C1)/_C1) - 1, exp(x)*_C1 - abs(exp(x)*_C1 - 1) - 1]`

Both solution fail odetest.

```coulditbe~(offset,0)
```

gives true

So there are assumptions/conditions which makes the solution satisfy the ODE. In this case, by inspection one can see what these conditions are. They are, for one solution:

`(-exp(-x) + _C1)/_C1  >0`

and for the other, the condition is

`exp(x)*_C1 - 1 >0`

Under these assumptions, odetest would have given 0 for each odetest.

And it is this information I wanted to obtain automatically from coulditbe.

In Mathematica, Reduce is used for this. Reduce gives conditions under which something is satisfied. For example,

`Reduce[ C[1] Exp[x] - Abs[C[1] Exp[x] - 1] - 1 == 0, {x, C[1]}, Reals]`

Gives

`C[1] >= Exp[-x]`

While the above in  Maple

`coulditbe( C[1]*exp(x)- abs( C[1]*exp(x)-1)-1 = 0)`

gives true  only, but without the important information, true under what conditions.

Is there a different command in Maple which could give this information?

## Homotopy Analysis Method, NOPH package and solutio...

Hello, dear forum users!

Does anyone use the method of homotopy analysis (HAM) and the NOPH package in their work. (moderator: link)

It seems to me that only HAM can help.

There are no developments, as I do not own the NOPH package.

## How to start a command-line terminal for Maple in ...

Could anyone help me with: How to start a command-line terminal for Maple in Linux Ubuntu? Thanks a lot

## modpol analogue...

Hi there.

I need to calculate multiplcations of huge polynoms with reducing in GF(2^m) with m>1000.

For example, modpol(a*a,f_t,t,2^N) with N=4007, degree(a)=8008 and degree(f_t)=8009.

Standard modpol calculates this in 4-5 sec on my computer.

Maybe there is an easy way to speed up this calculation?

Thank you.

ex.mw

nn.txt

## Error in Battery operated 4 wheeled driven electri...

Hi all,

I am new to maplesim and trying to learn it.

While simulation of the battery operated 4 wheeled driven electric vehicle

it tells can't find solution.

Same time if i connect a fixed reference all four wheels are running (same place) but not moving since the frame fixed.

HELP ME TO SOLVE THIS.

thank you..

## How can I generate an answer for this question?...

Hi everyone,

I am trying to integrate this function, however, it did not generate any results. Is there any chance to make this run?

 (1)

## RE: Rewriting an expression ...

Hello all,

Would you please tell me how to rewrite the expression 'Is_square' like 'Is_square2'?

The way how the first expression is re-written is that both numerator and denominator were divided by 'sigma^2*omega[rK]^2':

One attempt I made was to use 'algsub' command using the subexpression ''sigma^2*omega[rK]'', but somehow it missed the term in the denominator.

 > restart;
 > Is_square := M[dmax]*(sigma^2*omega[rK]^2 + omega[r]^2)*L[sigma]/(3*p*omega[r]*omega[rK]*L[mu]^2*sigma^2);
 (1)
 > Is_square2 := M[dmax]*(1 + omega[r]^2/(sigma^2*omega[rK]^2))*L[sigma]/(3*p*omega[r]*L[mu]^2/omega[rK]);
 (2)
 > algsubs(omega[rK]*sigma^2=tt, Is_square);
 (3)
 >

## GraphTheory EigenvectorCentrality...

Suppose I have

with(GraphTheory):
vertices:=["M","P","C"]:
edge_weights:={[{"M","P"},3],[{"M","C"},1]}:

G1:=Graph(vertices,edge_weights)

EigenvectorCentrality(G1)

Is it right to say the EigenvalueCentrality values correspond to the names in the vertices correspondingly?  ie M corresponds to 0.4415.. P corresponds to  0.4188.. and C corresponds to 0.1396... ?

## why algsubs does not replace all instances of vari...

```restart;
sub:=x/C;
expr:=1/2*x*(p^2+a)/p;```

And now

`subs(p = sub, expr)`

But

`algsubs(p = sub,expr)`

Notice one "p" is still not replaced.

This is very annoying. I looked at help and did not see anything about this. I could have missed it. It looks like it does not replace "p" when it is in denominator:

```algsubs(p = x,1/p)
```

Remains 1/p but

```subs(p = x,1/p)
```

gives 1/x as expected.

May be this is documented somewhere? But why it does this?

## Error, (in discont/zero) too many levels of recurs...

This was generated when running some code on Maple 2020.1.

Just wondering if this might indicate some problem internally, or is this something that can happen.

```restart;
ZZ:=Int(-(a*_a^2+(_a^4*a^2-4*_a*b*y(x))^(1/2))/(a*_a^3+_a*(_a^4*a^2-4*_a*b*y(x))^(1/2)+6*y(x)),_a = _b .. x)+Intat(-2/(a*x^3+x*(a^2*x^4-4*_f*b*x)^(1/2)+6*_f)-Int(2/(_a^4*a^2-4*_a*_f*b)^(1/2)*b*_a/(a*_a^3+_a*(_a^4*a^2-4*_a*_f*b)^(1/2)+6*_f)+(a*_a^2+(_a^4*a^2-4*_a*_f*b)^(1/2))/(a*_a^3+_a*(_a^4*a^2-4*_a*_f*b)^(1/2)+6*_f)^2*(-2*_a^2/(_a^4*a^2-4*_a*_f*b)^(1/2)*b+6),_a = _b .. x),_f = y(x))+_C1 = 0;

timelimit(30,value(ZZ))```

Error, (in discont/zero) too many levels of recursion

The problem is that I am not able to trap the error. This does not work

```try
ZZ:=Int(-(a*_a^2+(_a^4*a^2-4*_a*b*y(x))^(1/2))/(a*_a^3+_a*(_a^4*a^2-4*_a*b*y(x))^(1/2)+6*y(x)),_a = _b .. x)+Intat(-2/(a*x^3+x*(a^2*x^4-4*_f*b*x)^(1/2)+6*_f)-Int(2/(_a^4*a^2-4*_a*_f*b)^(1/2)*b*_a/(a*_a^3+_a*(_a^4*a^2-4*_a*_f*b)^(1/2)+6*_f)+(a*_a^2+(_a^4*a^2-4*_a*_f*b)^(1/2))/(a*_a^3+_a*(_a^4*a^2-4*_a*_f*b)^(1/2)+6*_f)^2*(-2*_a^2/(_a^4*a^2-4*_a*_f*b)^(1/2)*b+6),_a = _b .. x),_f = y(x))+_C1 = 0;
timelimit(30,value(ZZ));
catch:
print("ignore");
end try;

```

Error, (in discont/zero) too many levels of recursion

Why can't one catch this error inside try/catch? It means the whole program can not  continue.

Maple 2020.1

## I have Math problem...

by using its expansion Write the Maple  program.

## Type the Maple command string that calculates this...

Type the Maple command string that calculates this expression for the number of n arbitrarily entered from the keyboard.Can you help me please ?