## Error, (in fsolve) number of equations, 4, does no...

dear all

I have a system of 4 equations with 4 unkowns, but maple says that there 7 unknowns, and fsolve does return any solution

problem_solve_system.mw

Thanks

## Vector spaces from sets...

Hi! I'm new to Maplesoft. I would like to use it for my research. However, in order to do so, i have to construct an n-dimensional vector space, with vectors of the form A_1*B, A_2*B, ..., A_k*B, where A_i is a set of  n components from a Field (or ring) and B is the basis for the vector space.

It would REALLY help if you could give some ideas for me to bring this up, or else i will be forced to typset every one of the vectors i'll use in a matrix-multiplication form and will make considerably harder my work.

## loop over table...

Just wondering how I do a loop over the contents of the table. I need both the index variable and the stored value associated with it.

This one apparently doesn't work.

 (1)

 (2)

 (3)

 (4)

## simplifying complex expressions...

How do I simplify :

```Zin := Rin + omega*L*I + (omega*L)^2/(RL + omega*L*I);

```

so that there are no imaginary terms in the denominator?

I've tried,

```assum := Rin::real, omega::real, L::real, RL::real, 0 < Rin, 0 < omega, 0 < RL, 0 < L
Zin := Rin + omega*L*I + (omega*L)^2/(RL + omega*L*I);

(simplify(Zin) assuming assum);
```

but this doesn't work.

## dsolve ode with Bcs...

Dear all

I tried to solve a second order ODE, using dsolve but maple doest not return an explicit solution and no solution plotted.

solve_ode.mw

Hey everyone,

I am trying to solve this differential equation for h(u):

h(u)^2 + 2*a*h(u)/sqrt(1 + diff(h(u), u)^2) = b^2

for given values of a and b. For a=3 and b=1 maple gives :
u - Intat((_a + 1)*(_a - 1)/sqrt(-(_a^2 + 6*_a - 1)*(_a^2 - 6*_a - 1)), _a = h(u)) - _C1 = 0, u - Intat(-(_a + 1)*(_a - 1)/sqrt(-(_a^2 + 6*_a - 1)*(_a^2 - 6*_a - 1)), _a = h(u)) - _C1 = 0

and I dont know what to do from there. Any help would be very much appreciated

## Fermat Factorization in RSA...

Suppose you know that a person's public key modulus m is the following 200 digit number :

"166571820085905498772938593207359906487315774156514145089564134\

67009247675308229223573508773729914408724747749233779284765414\

62530835296763930087228227919982503096221081674037688617693027\

1167988018683"

Factor m and check your factorization after the factors are found.  Use the following Fermat factorization method:  Note that if
"m = x^2 - y^2"

then
"m = (x - y)*(x + y)"

. So if
"1 < x - y"

we have a non-trivial factorization of m. If m is a product of just two primes then one will be
"x - y"

and the other will be x + y.  This is the basis of the Fermat factorization method. Note that
"m = x^2 - y^2"

is equivalent to
"x^2 - m = y^2"

.  So if for some number x we have type(sqrt(x^2 - m),integer) = true then we can set y = sqrt(x^2 - m) and using the above idea we may factor m.  Fermat's method is to take x =
"ceil(sqrt(m))"

and keep incrementing x by 1 till an x is found such that
"x^2 - m"

is a square.   [Note that you may need to use ceil(evalf(sqrt(m),200)).]

If the number m is a product of two primes that are relatively close together then this method will factor m quickly. If you do not find the factors in just a few seconds, you probably have a bug in your program. For some reason Maple does not have this method builtin.

[N.B. This exercise shows that if care is not taken in choosing the primes p and q used in the RSA system, than the system can be easily broken

## Decipher RSA Message...

Alice sent a message to Bob using the RSA system. The public key used to encode the message was
[m,e] = [187454749788911503119994043213682616233000961, 23073697474256143563].

The enciphered message was
[99763088506717050716379498520357841718875740, 120165413768425112311337085191282286020515442, 130554852152844850464253187688342192964186591, 30831038803473309186944039044693095063005267, 43791870977158745785820581340119798552660187, 69969965042359538654291028155927734707714502, 33869965925699990903801791477929460546990002, 33844215332363231914638130818590411552396086, 61034870951899306892357141802983347226683758, 152680702248950827958295294572717135277913525, 109591116592896191360922558098912453060002989, 155489947789995346755966254731407091292570943, 30508537854841352888337386800131678916944679, 45657204694505066046067342403378233363404150, 122580283375455701674982424288406984864898071, 63190645718352016104824679398188140019415424, 17253386795565064409576412640690151622064852, 76432681365602448262013510061731737725777808, 4419855123469897669096067167819380964828479, 87913005918401414546998775379426321338719933, 155434516526735215629181544556450169276890711, 74695381359901114443168866905755723039288800, 246854149837977729662442017899408430336317, 121766227774612543867361050340041336298158533, 166784352080096633524033563364825999607054575, 72405993088552642775735865911360107823805504]

Decipher this message.

[Hint: Use of ifactor with the option 'pollard' may help. When you are finished with the decryption, you should use colons where possible to suppress unnecessary output. ]

## evalf/Int issue with Maple 2020...

Hi,

This chunk of code gives me almost instantly the desired result with Maple 2015 but fails returning a result after 5 minutes when ran from  Maple 2020.
Changing the method or trying to tune their options doesn't fix the issue (for a larger value of the absolute tolerance the result, close to 1, is even obviously false).

TIA

 > restart;
 > interface(version)
 (1)
 > with(Statistics):
 > Model_1 := (X, Y, Z) -> 1.3479120558270161+(-1)*.3390713110446567*X+1.0332964944900824*Y+(-1)*.8046331250569234*Z+0.9028899142595827e-1*X^2+(-1)*.28022910356641223*Y^2+1.3698461513469624*Z^2+0.6023630210658247e-1*Y*X+(-1)*.1988111077193626*Z*X+.6782902277463169*Z*Y+(-1)*0.7589729001497135e-1*X*Y*Z: Model_2 := (X, Y, Z) -> .7215754021067852-.961682838202105*X+.4890842364596477*Y-.8214961524335734*Z+.15745942215497866*X^2-1.8023544416693338*Y^2+.36598799463016246*Z^2+1.3957614823018496*Y*X+.725398415577742*Z*X+1.9474707393604542*Z*Y-1.1780201448596594*X*Y*Z: ExpMod_2 := unapply(expand(Model_2(Model_1(X1, Y1, Z1), Y2, Z2)), (X1, Y1, Z1, Y2, Z2)):
 > fy1 := PDF(Normal(0.1055, 0.0297), Y1): fz1 := PDF(Normal(1, 0.2/3), Z1): fy2 := PDF(Normal(0.17, 0.0476), Y2): fz2 := PDF(Normal(1, 0.2/3), Z2): C   := evalf(          (1-eval(CDF(Normal(0.1055, 0.0297), Y), Y=0))          *          (1-eval(CDF(Normal(0.17, 0.0476), Y), Y=0))          *          (eval(CDF(Normal(1, 0.2/3), Z), Z=1.2)-eval(CDF(Normal(1, 0.2/3), Z), Z=0.8))^2        ): J  := Int(         fy1*fz1*fy2*fz2*(1+tanh(10^4*(ExpMod_2(2.14, Y1, Z1, Y2, Z2)-1.25)))/2,         Y1=0..0.4,         Z1=0.8..1.2,         Y2=0..0.4817,         Z2=0.8..1.2,         method = _CubaDivonne, methodoptions=[absepsilon=1e-8]       ): Prob(X__2 > 1.25) = nprintf("%1.3e", evalf(J)/C);
 (2)
 >

## Lie Symmetries of ODE-Systems for a given form of ...

Hi everyone,

I'm new to using Maple and I've got a question concerning the calculation of the Lie Symmetries of an ODE. Basically, I want to us the method described in this paper: https://doi.org/10.1063/1.3097304 in order to find a perturbative solution to a system of first oder ODE's.

I thus need a special form of the generator. However I can't quite figure out the notation from the examples provided in the maple helt. I also can't figure out why I can't calculate the general form of the Symmetries using the following code:

```restart;
with(PDEtools);
with(DEtools);
Imp := 2*diff(y(x), x)*y(x)/A(x) - diff(y(x), x) - diff(A(x), x)*(y(x)/A(x))^2 - C_p*diff(A(x), x) - eta(x)*lambda(x)*sqrt(A(x)*pi)/4*(y(x)/A(x) - 1)^2 = 0;
Conti := diff(y(x), x) - 2*sqrt(A(x)*pi)*beta(x)*(1 - H + C/A(x)) = 0
Cons := diff(eta(x), x) = 0

sys := {Cons, Conti, Imp};
DepVars = {A(x), eta(x), y(x)};
deteqs := DeterminingPDE(sys);
```

Help or a link to some more examples would be much appreciated.

Regards,

Johannes

## loops in parallel...

hello,

I have 3 loops that I want to run, each loop runs a different procedure and have no interaction with the other, each loop takes about 5 hours to run so if I run the program in Series it takes about 15 hours, I can't separate the sheet into a few sheets and run it manually because there is initial data and calculations before the loops, so what I'm looking for is a way to parallel run these 3 loops.

The script I wrote so it would be clearer –

for i from 1 to n do

for j from 1 to n do

x__Up[i,j]:= `Xmax__UP,m`(`P__m`(i,j),`I__m`(i,j),`data__upNc`);

od:

if (i mod 10 =0 ) then  print(evalf((i)/(n))*100); fi:

od:

for k from 1 to n do

for m from 1 to n do

x__U[k,m]:= `Xmin__UP`(`P__m`(k,m),`I__m`(k,m),`data__upNc`);

od:

if (k mod 10 =0 ) then  print(evalf((k)/(n))*100); fi:

od:

## Error, bad index into Vector...

Dear all

I tried to redo the same steps as presented in
using Maple

BUT, I  have an error,

Error, (in assembly) bad index into Vector
I hope find the error in maple code

code1.mw

thank you

## How do i solve State Space system in Maple??...

Hii!!

I need your help in state space system.... kindly guide me how to solve State Space system in maplesoft.....i excecute the command but i didn't find the answer....can you plz help me?I have been trying for two weeks now but it is not working.Thank you!!

## piezoelectric circuit with rectifier...

piezoelectric_equivalent_with_ac-dc_(1).msim

I try to build a piezoelectric equivalent circuit (a sine current source, a capacitor and a resistor), but it doesn't act as a voltage source. I also try to change the forward voltage of the ideal diode in full-bridge rectifier and find that the output voltage of piezoelectric equivalent circuit cannot exceed forward voltage.

By the way, the parameters of piezoelectric equivalent circuit are well set according to a paper.

Could you give me some advice?

## Approximating Riemann Sums Numerically...

Hello, we need to do an integral based on two numerically approximated functions given by a second degree coupled differential equation.

The integral:
Where xs and xu are functions of the variable t.

We wish to do a half-sums to approximate the integral, that is:

Define an N = number of points, such that we get a delta_x = L/N.

We then wish to get two vectors x_s = [x_s(0),x_s(1),...,x_s(N)] and x_u = [x_u(0),x_u(1),...,x_u(N)] by running some kind of for loop over our approximation procedure.

Is there any function for this already inside of Maple? We need to approximate the integral using Riemann sums and no other method.

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