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

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. ]
 

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).

Could you please help me to fix this?
TIA

Download 2020_issue.mw

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

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: 

Dear all

I tried to redo the same steps as presented in 
https://www.youtube.com/watch?v=l4Y3iQrPBa8
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 

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_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?

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.

Dear all

I just write a code, everything is well written, but using 

M := Multiply(y11, Transpose(s)) 

I get a table and not a matrix,  PLEASE see equation 19 and 20

probem_multiply.mw

Thank you for your help 

When trying to print a Maple Document as a PDF on Mac, I am now getting an "Error while printing" message. A 1-page pdf is created that's empty.   This is a new error, one that I've never seen when printing as PDF for any other Maple Document I've created.

I'm running Mac OS 12.3.1, the latest version of Mac OS and using Maple 2020.

I am trying to develop a recursive code to the above equations.  Note, U,X&Y are multivariate functions (in this case bivariate functions of (x,y)) i.e. U=U(x,y), X=X(x,y) etc.

Irrespective of what help says, both series and taylor return series(...) rather that big-O expression

From help:

> series(x/(1-x-x^2), x=0);
series(1*x+1*x^2+2*x^3+3*x^4+5*x^5+O(x^6),x,6)
> taylor(sin(x),x=Pi);
series(-1*(x-Pi)+1/6*(x-Pi)^3-1/120*(x-Pi)^5+O((x-Pi)^7),x=-(-Pi),7)
 

I am having problems setting up plots on a new computer.

plotsetup(x11);
interface(plotdevice);
x11
plot(sin(x));
Error, plot driver not found
plotsetup()
preplot = [], postplot = [], plotdevice = x11, plotoutput = terminal, plotoptions = ``

Find, using Maple, a triple [m,e,d] where m is the product of two 200 decimal digit primes, e is a random prime number of 100 decimal digits and d is the inverse of e modulo 
                            "phi(m)"

. Use this to encipher some message of your choice of at least 6 lines length using the RSA system. You may copy and paste text from some website. Then, decipher the enciphered text to obtain the original message.