## Is there an error in Maple's BesselI(v,z) function...

I compared the numerical value of an integral expression in Gradshteyn and Rhyzhik (8.431.5) for the BesselI(v,z) function to the BesselI(v,z) function in Maple 2019.2 and got different answers.  The GR expression is the difference of two integrals and it looks like Maple only evaluates the first integral, which is correct only if the order v is an integer.  Please see the attached.

BesselI.mw

## Strange Factorization...

At first, I appology my poor English and I am a non-proessional on mathematics and programing. I am an old retired engineer/researcher.

I found strange phenomena with maple.
Could someone please verify this result?
This is sound like a stupid joke.
This queation is related to factorization of composite number N=p*q
p, q are large prime number respectively.

Degits:=200;
1.    Let p is large prime such as 50 degits
2.    Let R is small integer such as 3
3.    Let q is nearest prime R*p
4.    Let N=p*q
5.    Let f=frac(N/(q+s))

j:=1;
m:=2^b*2^c;
r:=m/2^b;
b:=8; c:=0;
F:=[ ];
for s from -m to m by r do
f:= frac(N/(q+s));
if f=0 OR 1.0 then f:=100000; # zero dev exeption;
elif f <= 0.5 then f:=log10(f);
elif f > 0.5 AND f < 1.0 then f:=-log10(1.0-f);
else print(“error”) break;
end if:
F:=[F[ ], [s, f]];  # maple plot format
j::=j+1;
end do:

6.    Draw a Graph s vs F

You wil find a oscillating graph with step at s=0;

7. b:=8 and c:=75; and try same caluclation.

You will find a graph with dip at s=0;
Caution! Resolution and Scanwidth can not go together.

8.    Let qx=q+10^25;
9.    Nx:=p*qx;
10.    Let ps:=sqrt(N/3.0) and let qs:=3.0*sqrt(N/3.0);
11.    fs:=frac(Nx/(qx+s));
Caution!  Nx not equal Ns:=p*qs
12.     Draw a graph s vs Fs with Nx, p, qs
You will find a similar graph dip point shifted from s=0
13. Verify qx=ps-dip point s

My questions are
1.    Is it a kaind of factorization of Nx?
2.    This phenomena hava posibirity to make a vulneravility for RSA crypto?
3.    Power spectrum of F( c=0) indicates R=q/p; with an peak
4.    Is it an rediscovery of “Wheel”?  Are thea any papers similar to this phenomena

I appreciate to read this questions.

Environment: Windows 10 for workstation and Maple 2019(64bit) CPU: Intel Xeon.

15 Dec 2019  some miss spelling corrected

A graph added   frac(N(q+s)) vs s b=8 c=75

## System of pdes unable to get the solution and plo...

Dear maple user ,while solving the system of pdes i am getting the errors and unable to plot the curves. please help me to  rectify the errors and  plot the curves.

restart;
with(PDETools):
G:=1300:beta:=0.0075:epsilon:=4.9*(10)^(-6):Pa:=100:alpha:=24:Pv:=97:
sys1:= {G*(beta^2*u(r,z)*diff(u(r,z),z)+v(r,z)*diff(u(r,z),r)) = -diff(p(r,z),z) +beta^2*diff(u(r,z), z\$2)+diff(u(r,z),r\$2)+(1/r)*diff(u(r,z),r),G*(beta^2*u(r,z)*diff(v(r,z),z)+v(r,z)*diff(v(r,z),r)) = -diff(p(r,z),r) +beta^2*diff(v(r,z), z\$2)+diff(v(r,z),r\$2)+(1/r)*diff(v(r,z),r)-(v(r,z)/r^2),beta^2*diff(u(r,z),z)+diff(v(r,z),r)+(v(r,z)/r)=0  }:

IBC:=(D[1](u))(0, z) = 0,v(0,z)=0,phi*(D[1](u))(1, z)+u(1,z) = 0,v(1,z)=epsilon*(p(1,z)+(Pa/alpha)-1),p(r,-1)=0,p(1,z)=(Pv-Pa)/alpha:
sol := pdsolve(sys1, IBC, numeric):
r:=0:

p1 := sol:-plot(u(r, z), phi = 0, numpoints = 100, z = -1 .. 1, color = ["Blue"], legend = ["u(r,z)"]):

p2 := sol:-plot(u(r, z), phi = 0.15, numpoints = 100, z = -1. 1, color = ["red"], legend = ["u(r,z)"]):

p3 := sol:-plot(u(r, z), phi = 0.4, numpoints = 100, z = -1 .. 1, color = ["green"], legend = ["u(r,z)"]):

plots:-display({p1, p2,p3});

## i want to subs a function in another function but ...

"a=4 x+1/diff(f(y),y)";
b := 3*(4*x + 1)/(diff(f(y), y)*(3*x + 1));
subs((4*x + 1)/diff(f(y), y) = a, b);

## Is Issimilar function in maple uses a rational met...

I am trying to figure out which computational method is used in function Issimilar, (which determines similarity of matrices) in Maple 2018 and whether or not its a rational one.

## how can i get curve fitting fractions...

how can i use curve fitting tools for get m and n in this equation  for excel data

equation

i want to get m and n?

New_Microsoft_Excel_Worksheet.xlsx

## Code for a clock within maple...

How would one code a real time clock (digital's the easiest - of course, or analog) within maple?

## Why doesn't dsolve[events] return the good result...

Hi,

Why extracting the features of the events doesn't return the good results when executed within a loop (see the pink test) ?

PS: please, spare me  replies of the type "you can solve this equation formally"

 > restart;
 > interface(version);
 (1)
 > sys := { diff(x(t), t) = 1, x(0) = 0 }: evs := [ [x(t)-0.1, none],  [x(t)-0.3, none], [x(t)-0.5, none] ]: sol := dsolve(sys, numeric, events=evs): plots:-odeplot(sol, [t, x(t)], t=0..0.5, gridlines=true);
 > # times that fired the events sol(1): # initialization sol(eventfired=[1]); sol(eventfired=[2]); sol(eventfired=[3]);
 (2)
 > # Same times computed  within a loop for i from 1 to 3 do   te := op(sol(eventfired=[i])); end do;
 (3)
 > # Values of x(t) computed  within a loop # # Why are calues for events 2 and 3 wrong ? for i from 1 to 3 do   te := op(sol(eventfired=[i])); # xe := sol(te);             # this doesn't return the correct result, # xe := subs(sol(te), x(t)); # this doesn't work neither   xe := eval(x(t), sol(te)); # this doesn't work neither end do;
 (4)
 >

## Solve a set a of equation or a on complex equation...

Dear experts

I am using Maple to solve a complex equation. My idea is to separate real and imaginary parts and then solve a set of the equation when both real and imaginary parts are zero. the following are the equation and the way I made real and imaginary parts;

eq:= (K*( Q*sinh(K)*cosh(Q)-K*cosh(K)*sinh(Q))*(1+s*K^2)+p*(-4*K^2*Q*(K^2+Q^2)+Q*(Q^4+2*K^2*Q^2+5*K^4)*cosh(K)*cosh(Q)-K*(Q^4+6*K^2*Q^2+K^4)*sinh(K)*sinh(Q)))/(K^2*Q*cosh(Q)):

so the K and the Q are both complex variables and p and s are constant.

K:=Kr+I*Kim;

Q:= sqrt(K^2-I*h^2*2*Pi/1e-6);

therefore the real and imaginary parts of the equation are

finally, I tried to solve it as following

sys:={eval(A,[p=nu^2/g/h^3,s=sigma/rho/g/h^2])=0,eval(B,[p=nu^2/g/h^3,s=sigma/rho/g/h^2])=0}:

sol2:=fsolve(sys,{Kr=0..5,Kim=0..5},maxsols=5);

the problem is that Maple can not solve it and returns the command. I  know that there is solutions. How can I solve this equation?

the maple file is attached.mapleprime.mw

==============================================================

I guess Maple use Newton method to solve equation or system of equations. Is there an alternative? I mean what are the possible methods?

## Error, invalid input: expand expects 1 argument, b...

Hello users. I have a question on my work.

I'm trying to construct the equation and plot it. And I got 2 errors(warning).

Please help me how to solve this problem check the image below and attached file.

Question_plot_the_curvature.mw

## Error, (in fprintf) number expected for floating p...

Hello,

I am trying to pass the graphics to .txt format so that I can plot them in Origin (OriginLab).

npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
t[i] := i*dt;
PA[i] := x[i](t);
printf("%e %e\n", t[i], PA[i]);
fprintf(fd, "%e %e\n", t[i], PA[i]);
end do;
0.000000e+00

Error, (in fprintf) number expected for floating point format
fclose(fd);
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
t[i] := i*dt;
PB[i] := x[i + n](t);
printf("%e %e\n", t[i], PB[i]);
fprintf(fd, "%e %e\n", t[i], PB[i]);
end do;
fclose(fd);
0.000000e+00

Error, (in fprintf) number expected for floating point format
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
t[i] := i*dt;
qA[i] := x[i + 2*n](t);
printf("%e %e\n", t[i], qA[i]);
fprintf(fd, "%e %e\n", t[i], qA[i]);
end do;
fclose(fd);
0.000000e+00

Error, (in fprintf) number expected for floating point format
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
t[i] := i*dt;
qB[i] := x[i + 3*n](t);
printf("%e %e\n", t[i], qB[i]);
fprintf(fd, "%e %e\n", t[i], qB[i]);
end do;
fclose(fd);
0.000000e+00

Error, (in fprintf) number expected for floating point format
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
t[i] := i*dt;
Tg[i] := x[i + 4*n](t);
printf("%e %e\n", t[i], Tg[i]);
fprintf(fd, "%e %e\n", t[i], Tg[i]);
end do;
fclose(fd);
0.000000e+00

Error, (in fprintf) number expected for floating point format
npontos := 10;
dt := 0.02;
fd := fopen("out.txt", WRITE);
for i from 0 to npontos do
t[i] := i*dt;
Ts[i] := x[i + 5*n](t);
printf("%e %e\n", t[i], Ts[i]);
fprintf(fd, "%e %e\n", t[i], Ts[i]);
end do;
fclose(fd);
0.000000e+00

Error, (in fprintf) number expected for floating point format

trabalho_final_2019.mw

## problem with solving N coupled differential equati...

Hello,

I want to write a code about numerical solving N(for example N=150) coupled differential equations (ODE ) with M boundary conditions in Maple but I do not know how to do it and I cannot find anything useful. in particular, I have trouble inserting boundary conditions which are a lot for N coupled difrential equations.

Does somebody have a code script on this matter? please let me know.

## How to create a group with known elements and a mo...

I would like to know how to create a group with some elements (numbers) {1,2,4,...} with a defined operation on it like X_42 (modular  multiplication by 42).

## write the matrix...

Hi everyone:

I'm going to write code to give me the following matrix A?

## Plot two functions as one curve (3Dplot)...

Hello everyone, thank you in advance

I am trying to plot two functions in the same graph. I didn't realize how to copy the real functions here but:

At the same 3D plot

I need to use the function F1(x,xi,k,B) for values of x*xi <6  and other function F2(x,xi,k,B) for values of x*xi  >= 6

Thank you again and sorry for my rusty English.

I attached a file with these 2 functions Functions_MAPLE_PLOT_TOGETHER.mw

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