## How to solve a multivariate non-linear system of e...

I have a guess about the set of the zeros of the following polynomial

y(1-x^{m+1}z)+(1-x^{n+1}z), (here m,n are positive integers and z is a primitive d-root of unity)

which are located on the complex 2-dimensional torus. The set of solutions is finite (I think the system is zero-dimensional). My goal is to verify my guess numerically using Maple for some small values of m and n and a fixed value of z. I think if (x,y) is a solution, then x is either a (n-m) root of unity or a (n-m) root of 1/z^2 (where n>m).

You can find my code for n=3 and m = 1 attached (I was not able to load the mw format so I put the zip version). I consider z to be a third root of unity but actually, I am interested in putting z= exp(2pi/3*i) and even the real third root z=1 is not interesting for me, but since the exponential representation led to an error, I changed it to z and mentioned that z^3=1. Still, it has an error and  I would be grateful if you could let me know how I can correct this code.

Question.maple.zip

## remove frames arround legend in graph ...

Is there a way to delete frames arround the legend in a plot?

## How to display a solution of the function...

Dear all
Warm Greetings.

I want to display a solution (only numerical value) of the first derivative of the function for the values of x varies from 0 to 7 with step size 0.01.

I have attached the work file.
ODE.mw

## This seems so simple ......

Why does this not return a quick solution?

sol := solve(.2894606222 = .4090662520/((1+0.1481289280e-2*x)^5.034901366*(1/(1+0.1481289280e-2*x)^5.034901366)^.1986136226), x)

mw.mw

## An unexpected & strange error....

Are Maple settings responsible for this error:

## How do i correct "error, illegal use of an object ...

HHow do i correct "error, illegal use of an object as a name"

## Singular Matrix in system of 4 ODEs...

Hello everyone,

I am trying to solve a system of 4 ODEs that describe a physical system, however, I get the message:

Error, (in dsolve/numeric/bvp) matrix is singular

Any help is much appreciated. The initial conditions are such that to find solution in steady state, that means, v(0)=v(period) and so on with all variables.

## ERROR in dsolve numeric: unable to store '...' whe...

Hello everyone,

I want to solve a simple ODE numerically having a piecewise periodic function in the ODE.

The periodic piecewise function definition is taken from this  post.

When solving using "dsolve" numerical, I get this error:

Error, (in f) unable to store '100000*square_wave_periodic' when datatype=float[8]

```restart;
d := .5;
fs := 100*10^3;
Vin := 10;
C := 10*10^(-6);
R := 10;
L := 10*10^(-6);

DEFINE PERIODIC FUNCTION
square_wave := proc (t) options operator, arrow; piecewise(0 <= t and t <= d/fs, Vin, d/fs < t and t < 1/fs, 0) end proc

square_wave_periodic := proc (t) options operator, arrow; square_wave(t-floor(t*fs)/fs) end proc

ode1 := L*(diff(i(t), t))+v(t) = square_wave_periodic
ode2 := C*(diff(v(t), t))+v(t)/R = i(t)
IC := v(0) = 0, i(0) = 0
sol := dsolve({IC, ode1, ode2}, {i(t), v(t)}, numeric)```

LCRcircuit_transient_numerical.mw

Any help is much appreciated ! Thank you !

## contour plot at ...

I tryning to to plot 3d and then contour plot of the function N vs alpha

N_vs_alpha.mw

## NLPsolve non numeric result...

Hello everyone,

I am trying to solve a simple nonlinear 4 variable function with NLPsolve giving real values ranges for the variables but the NLPsolve gives "non numerical" result. Find attached the worksheet.CoreOptimization.mw

Am I doing something wrong?

Regards,

Cata

## how can solve the problem when it says root of?...

Hhow can i solve R it says here root of

Calculate.mws

## Kernel stop. ...

How do you stop Maple during this code execution:

proc()
x:
print(1);
goto(x);
end():

## Solve equation given a list of coefficients...

Hello everyone,

I am trying to solve an equation using the "solve(...)" function but the coefficients of the equation are changing.

I am using the coefficients as list but the "solve(...)" function gives error: "Error, (in assuming) when calling 'Engine:-Dispatch'. Received: 'badly formed input to solve: not fully algebraic'"

I am attaching the Maple document.

However, what I want to achieve, is the solution for each value in the list.

Here is an easy example of what I am saying:

a=3*x+k where k=[list of values], a=[another list of values].

I want to find "x" for each pair of values (a,k) in the list.

Thank you !

LCC Resonant Converter - Frequency Finder

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## how to compute symbolic Expressions ...

H all expert

first this Expression

ni := diff(Q(x, t), t)+a*Q*(x, t)*(diff(Q(x, t), x))+b*(diff(Q(x, t), t\$3))+d*(diff(Q(x, t), t\$5)) = 0

then I want to solve  diff(Q(x, t), t\$5)

diff(Q(x, t), t\$5) = solve(ni, diff(Q(x, t), t\$5))#eq2

p (x, t) :=H1(t)*Q(x*H2(t), H3(t)) #assumption

k := diff(p(x, t), t)+a*p(x, t)*(diff(p(x, t), x))+diff(p(x, t), t\$3)+d*(diff(p(x, t), t\$5))+c*p(x, t) #eq3

r := subs(diff(Q(x, t), t\$5), k) #subs eq2 in eq3

i recived error

SUBS1.mw

## How to produce a graph of a numbers sequence...

Hi,

I have a code (see below) for the following number sequence and want to produce a graph as well as the numerical data, please advise how to do it.

Sequence definition: Lexicographicaly least sequence of nonnegative integers commencing 1,3,5,7 such that any four  consecutive terms are mutually coprime.

The code I have so far is:

ina := proc (n) false end :

a := proc (n) option remember; local k;

if n < 5 then k := 2*n-1

else for k from 2 while ina(k) or igcd(k, a(n-1)) <> 1 or igcd(k, a(n-2)) <> 1 or igcd(k, a(n-3)) <> 1

do  od

fi; ina(k) := true; k

end proc;

seq(a(n), n = 1 .. 100);
1, 3, 5, 7, 2, 9, 11, 13, 4, 15, 17, 19, 8, 21, 23, 25, 16, 27,

29, 31, 10, 33, 37, 41, 14, 39, 43, 47, 20, 49, 51, 53, 22, 35,

57, 59, 26, 55, 61, 63, 32, 65, 67, 69, 28, 71, 73, 45, 34, 77,

79, 75, 38, 83, 89, 81, 40, 91, 97, 87, 44, 85, 101, 93, 46,

95, 103, 99, 52, 107, 109, 105, 58, 113, 121, 111, 50, 119,

127, 117, 62, 115, 131, 123, 56, 125, 137, 129, 64, 133, 139,

135, 68, 143, 149, 141, 70, 151, 157, 153

I have tried listplot but for some reason cant get the correct format

Hope you can help

Best regards

David.

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