## Maple Code for Raifu...

I need help on maple code for solving both linear and non linear boudary condition for fractional order partial differential equation

## Number of solutions of trigonometric equation with...

Hi,

I don't understand the number of solutions of my trigonometric equation if i work with solve command ( see maple file)

Ideas ?

TrigoSolve.mw

## Cannot solve the equation...

I cannot solve the equation. The problem is:

we have the integrals (1) and variable (2)
(1) F := (a1, b1) -> int(1/sqrt(1 + (-1)*b1^2*sin(teta)*sin(teta)), teta = 0 .. a1)

(2) Phi(Pi/2, teta) = 2*(F((Pi/2 - teta_l)/2, sqrt(2/(1 - sin(teta_l)))) - F1(Pi/4, sqrt(2/(1 - sin(teta_L)))))/sqrt(sin(teta_l) - 1)

After the solution for variable (2) I received:

(-InverseJacobiAM(-Pi/4 + teta_l/2, 1/abs(cos(Pi/4 + teta_l/2))) - InverseJacobiAM(Pi/4, 1/abs(cos(Pi/4 + teta_l/2))))^2/(2*(sin(teta_l) - 1))

Next, I have the equation and (by the followed paper) should solve the equation respect to teta_l

M*B*(L/C)^2/G = 1/8*Phi(Pi/2, teta_l)^2

But I received just empty solution. The reference paper 10.1016/j.jmps.2020.104045

Can somebody recommend the way to solve the problem?

## Maple keeps crashing on low-end linux device, what...

Hey!

Student here, and I'm currently using a few year old laptop (amd a4-9125  2-core, 8gb ram) running latest stable ubuntu, and maple keeps crashing on me seemingly out of nowhere, even on very simple tasks, like copy-pasting equations and calculating integrals. This doesn't happend all the time, but when it does, it just shuts the program. I checked the logs and found Maple got this error message:
: free(): invalid next size (normal)
: Aborted (core dumped)

I checked a bit online, and it might be a memory issue.
Is my computer just too old for this program, or is it something fixable?

## Substituting for expressions that contain operator...

What's the simplest way to partially substitute for expressions that contain operators from the Physics package?
(hopefully my worksheet below shows what I mean)
Thanks

 > restart:
 > with(Physics):
 > Physics:-Version();
 (1)
 > Setup(quantumoperators = {sigma__x, sigma__y, sigma__z, rho, H, comm}, mathematicalnotation = true);
 (2)

we could just use Physics:-Psigma, etc... but here let's define these manually:

 > Setup(algebrarules={ %Commutator(sigma__x, sigma__y) = 2*I*sigma__z, %Commutator(sigma__y, sigma__z) = 2*I*sigma__x, %Commutator(sigma__z, sigma__x) = 2*I*sigma__y } );
 (3)

some expression (normally long and complicated that contains many operators):

 > expr:=(sigma__y*sigma__x*rho - sigma__y*rho*sigma__x);
 (4)

say want to make this type of substitution:

 > subs_vars:=sigma__y*sigma__x=H;
 (5)

this doesn't work

 > algsubs(subs_vars, expr);
 (6)

this also doesn't work:

 > subs(subs_vars, expr);
 (7)

this works (here we explicitly specify the whole thing, that includes rho)

 > subs(sigma__y*sigma__x*rho=H*rho, expr);
 (8)

but I would like for the substitution to also work for *parts* of the expression, as in the normal case, when not using operators.

 >
 >
 >

## How to declare variables local with assign?...

I need to declare a whole set of variables as local. The variable names are generates algorithmically using assign. Like so:

`seq(seq(assign(cat(S,i,j)=Vector(datatype=float)),i=1..9),j=1..9);`

Stand-alone, this works and creates all these Vectors for later use. But this:

`local seq(seq(assign(cat(S,i,j)=Vector(datatype=float)),i=1..9),j=1..9);`

does not work; I get an "error; '(' unexpected".

I really do not want to type all these by hand... on the other hand, if I do not declare these as local I get 99 warnings about implicit local declaration; not nice.

Is there a way to do this?

Thanks,

M.D.

PS: I do not upload as the one line really is all that is needed. At the lowest level one does not get the implicit-declaration warning, but with "local" it still fails.

## How do I graph this forced spring mass system?...

My forced spring mass system is 4x"+4x'+3x=sin(wt). I calculated my w=w* value that maximizes the amplitude (0.5) and my initial conditions are x(0)=x'(0)=0. I need to graph x(t) when w= w* and when w=w*/2. How am I supposed to input this information into maple to create a graph?

## How do I label endpoints automatically in pointplo...

I drew a polygon using some point coordinates combined with the pointplot.

c1 := <0, -2>:
c2 := <1, 2>:
c3 := <2, 2>:
c4 := <0.5, 6>:
c5:=<1, 4>:
with(plots):
p1:=pointplot([c1, c2, c3, c4,c5, c1], color = red, connect = true);

I ‘d like to add  label  of endpoints to polygons, although I did this via textplot, but it didn't feel very neat. I hope when the polygon is drawn, labels of  every endpoints appear . These labels are the names of the assignment variable for the coordinates of the endpoints.

c1 := <0, -2>:
c2 := <1, 2>:
c3 := <2, 2>:
c4 := <0.5, 6>:
c5:=<1, 4>:
with(plots):

t1 :=textplot([0, -2, 'typeset'("c1")], 'align' = 'above'):
t2 :=textplot([1, 2, 'typeset'("c2")], 'align' = 'above'):
t3 :=textplot([2, 2, 'typeset'("c3")], 'align' = 'above'):
t4 :=textplot([0.5, 6, 'typeset'("c4")], 'align' = 'above'):
t5 :=textplot([1, 4, 'typeset'("c5")], 'align' = 'above'):
p1:=pointplot([c1, c2, c3, c4,c5, c1], color = red, connect = true):
display({p1, t1,t2,t3,t4,t5});

I think  DrawGraph command  in graph theory package  is very good to achieve this in a sense.

Hello everyone.

## Choice of Branch cuts in HeunC...

Hi all,
i'm working with the confluent Heun function (Maple 2019).
Since for the case of an integer coefficient delta or gamma there are two integer Frobenius roots at the regular singularities 0 or 1, there is a logarithmic term in the Frobenius solution at these singularities. So, my question is the following:
When moving around this singularity in the complex plane, the value of the logarithmic term might depend on the choice of the complex logarithm's branch cuts. So, does anybody know just about how HeunC is implemented? Is there sth like a power series solution, which value would in my oppinion depend on this choice of a branch cut?
Or is there another implementation that preserves us from this ambiguity in the case of logarithmic singularities (i.e. integer coefficients in the confluent Heun equation)?

Many thanks,

## have an issue when summation, derivatives and inte...

integration_doubt.mw
Hello all,

I am trying to solve for the first-order derivative of a function f2 w.r.t variable a when it is equated to 0. the function f2 is a summation of two integrals as shown in the file. Kindly help me if there is any way to obtain solutions without numerical settings. Can functionalities like the Leibnitz rule be done in MAPLE? Thanks for your advice/help.

## Adding outputs from a loop to an array...

Could you please give an example of a code where I can add outputs from a loop to a list. I am using the break command to end the loop so I don't have the number of elements in advance.

Edit: I have also changed the title accordingly. There was more to this question, somehow which was omitted. I am writing it again. My code looks like below:
if ...
do H[i]:=int(K);
...
... end do;
end if;

I want an array of H[i]'s. The loop breaks when a condition is met, so I can't create an array with a given dimension beforehand. Thank you.

## Implementing a quadratic equation with a parameter...

How do I find with maple's help  for which parameter m does the equation:

x^2+2*m*x-6*x=m^3 have one of its roots equal to the square of the other root?

Thanks!

## Multipliers and Conservation Laws Using GeM Maple ...

I wrote the following orders

With(GeM):
gem_decl_vars(indeps=[t,x], deps=[u(t,x)]);
gem_decl_eqs([diff(u(t,x),t,t)+a∗diff(u(t,x),x,x)+b∗
u(t,x)+c∗(u(t,x))^3=0],solve_for=[diff(u(t,x),t,t)])

det_eqs:=gem_conslaw_det_eqs([t,x,u(t,x),diff(u(t,x),
t),diff(u(t,x),x)]):
CL_multipliers:=gem_conslaw_multipliers();
simplified_eqs:=DEtools[rifsimp](det_eqs,
CL_multipliers, mindim=1)

in maple 17, but the program cannot calculate and gives me an error. Does anyone help me to solve this problem.

```
```

.

## I want sin( phi*n ) not sin(n*phi) in an axis labe...

BTW "recusant" is an old word, religious in origin, for someone who refuses to do what they're told, or believe what they're told to believe.

Here's my problem:

phi := (1+sqrt(5))/2;

plots[pointplot]([seq([n, sin(n*phi)], n = 1000 .. 2000)], symbol = point, axes = boxed, labels = [n, typeset('sin(n*phi)')], labeldirections = [horizontal, vertical])

produces a label sin( n phi ).  I want it to say sin( phi n ).

I've tried the noncommuting times &*  (which prints &*) and the matrix product . (which prints as a function call).

Is there a way to typeset this product in the order that I want?  Here "n" is the variable and "phi" is the constant (yes that looks weird, but so does the graph).  I suspect that there is; I think "typeset" is probably much more powerful than I have been kludging it as.  Help?

screenshot:

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