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I am working on an iterative code where I need to save a matrix in an intermediate step. My code is long and it uses a separate data file. So, I am trying to state my problem taking a simple example.

At first, I define a column matrix A0. Using A0, I do some calculations and test some conditions. 
In the next step, I want  to do similar calculations and test some conditions but this time by changing the first element of A0. For the purpose of later use, I need to save the matrix A0 in its original form. I am trying to use the following method but both A0 and A1 (modified A0) turn out to be same.

> restart;
> n := 3;
> A0 := Matrix(n, 1, 1);
> #Do some calculation with A0
> A1 := A0;
> A1[1, 1] := A1[1, 1]+.1*A1[1, 1];
> A1;
> print(A0, A1);

This might be because I set A1:=A0 in the third line. But how do I save A0 in its original form?

 

 

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Hi everyone. I'm going to solve a problem of an article with hpm. well I wrote some initial codes(I uploaded both codes and article). but now I face with a problem. I cant reach to the correct plot that is in the article. could you please help me???

(dont think I am lazy ;))) I found f and g (by make a system with A1 and B1 and solve it i found f[0] and g[0], with p^3 coefficient in A-->f[1] and then with B2 I foud g[1]) and their plot was correct. but the problem is theta and phi and their plots :(( )

Project.mw

2.pdf   this is article



 

restart;

lambda:=0.5;K[r]:=0.5;Sc:=0.5;Nb:=0.1;Nt:=0.1;Pr:=10;

.5

 

.5

 

.5

 

.1

 

.1

 

10

(1)

EQUATIONS

equ1:=diff(f(eta),eta$4)-R*(diff(f(eta),eta)*diff(f(eta),eta$2)-f(eta)*diff(f(eta),eta$2))-2*K[r]*diff(g(eta),eta)=0;

equ2:=diff(g(eta),eta$2)-R*(diff(f(eta),eta)*g(eta)-f(eta)*diff(g(eta),eta))+2*K[r]*diff(f(eta),eta)=0;

equ3:=diff(theta(eta),eta$2)+Pr*R*f(eta)*diff(theta(eta),eta)+Nb*diff(phi(eta),eta)*diff(theta(eta),eta)+Nt*diff(theta(eta),eta)^2=0;

equ4:=diff(phi(eta),eta$2)+R*Sc*f(eta)*diff(phi(eta),eta)+diff(theta(eta),eta$2)*(Nt/Nb)=0;

diff(diff(diff(diff(f(eta), eta), eta), eta), eta)-R*((diff(f(eta), eta))*(diff(diff(f(eta), eta), eta))-f(eta)*(diff(diff(f(eta), eta), eta)))-1.0*(diff(g(eta), eta)) = 0

 

diff(diff(g(eta), eta), eta)-R*((diff(f(eta), eta))*g(eta)-f(eta)*(diff(g(eta), eta)))+1.0*(diff(f(eta), eta)) = 0

 

diff(diff(theta(eta), eta), eta)+10*R*f(eta)*(diff(theta(eta), eta))+.1*(diff(phi(eta), eta))*(diff(theta(eta), eta))+.1*(diff(theta(eta), eta))^2 = 0

 

diff(diff(phi(eta), eta), eta)+.5*R*f(eta)*(diff(phi(eta), eta))+1.000000000*(diff(diff(theta(eta), eta), eta)) = 0

(2)

BOUNDARY*CONDITIONS

ics:=
f(0)=0,D(f)(0)=1,g(0)=0,theta(0)=1,phi(0)=1;
f(1)=lambda,D(f)(1)=0,g(1)=0,theta(1)=0,phi(1)=0;

f(0) = 0, (D(f))(0) = 1, g(0) = 0, theta(0) = 1, phi(0) = 1

 

f(1) = .5, (D(f))(1) = 0, g(1) = 0, theta(1) = 0, phi(1) = 0

(3)

HPMs

hpm1:=(1-p)*(diff(f(eta),eta$4)-2*K[r]*diff(g(eta),eta))+p*(diff(f(eta),eta$4)-R*(diff(f(eta),eta)*diff(f(eta),eta$2)-f(eta)*diff(f(eta),eta$2))-2*K[r]*diff(g(eta),eta))=0;

hpm2:=(1-p)*(diff(g(eta),eta$2)+2*K[r]*diff(f(eta),eta))+p*(diff(g(eta),eta$2)-R*(diff(f(eta),eta)*g(eta)-f(eta)*diff(g(eta),eta))+2*K[r]*diff(f(eta),eta))=0;

hpm3:=(1-p)*(diff(theta(eta),eta$2))+p*(diff(theta(eta),eta$2)+Pr*R*f(eta)*diff(theta(eta),eta)+Nb*diff(phi(eta),eta)*diff(theta(eta),eta)+Nt*diff(theta(eta),eta)^2)=0;

hpm4:=(1-p)*(diff(phi(eta),eta$2)+diff(theta(eta),eta$2)*(Nt/Nb))+p*(diff(phi(eta),eta$2)+R*Sc*f(eta)*diff(phi(eta),eta)+diff(theta(eta),eta$2)*(Nt/Nb))=0;

(1-p)*(diff(diff(diff(diff(f(eta), eta), eta), eta), eta)-1.0*(diff(g(eta), eta)))+p*(diff(diff(diff(diff(f(eta), eta), eta), eta), eta)-R*((diff(f(eta), eta))*(diff(diff(f(eta), eta), eta))-f(eta)*(diff(diff(f(eta), eta), eta)))-1.0*(diff(g(eta), eta))) = 0

 

(1-p)*(diff(diff(g(eta), eta), eta)+1.0*(diff(f(eta), eta)))+p*(diff(diff(g(eta), eta), eta)-R*((diff(f(eta), eta))*g(eta)-f(eta)*(diff(g(eta), eta)))+1.0*(diff(f(eta), eta))) = 0

 

(1-p)*(diff(diff(theta(eta), eta), eta))+p*(diff(diff(theta(eta), eta), eta)+10*R*f(eta)*(diff(theta(eta), eta))+.1*(diff(phi(eta), eta))*(diff(theta(eta), eta))+.1*(diff(theta(eta), eta))^2) = 0

 

(1-p)*(diff(diff(phi(eta), eta), eta)+1.000000000*(diff(diff(theta(eta), eta), eta)))+p*(diff(diff(phi(eta), eta), eta)+.5*R*f(eta)*(diff(phi(eta), eta))+1.000000000*(diff(diff(theta(eta), eta), eta))) = 0

(4)

f(eta)=sum(f[i](eta)*p^i,i=0..1);

f(eta) = f[0](eta)+f[1](eta)*p

(5)

g(eta)=sum(g[i](eta)*p^i,i=0..1);

g(eta) = g[0](eta)+g[1](eta)*p

(6)

theta(eta)=sum(theta[i](eta)*p^i,i=0..1);

theta(eta) = theta[0](eta)+theta[1](eta)*p

(7)

phi(eta)=sum(phi[i](eta)*p^i,i=0..1);

phi(eta) = phi[0](eta)+phi[1](eta)*p

(8)

FORequ1

A:=collect(expand(subs(f(eta)=f[0](eta)+f[1](eta)*p,g(eta)=g[0](eta)+g[1](eta)*p,hpm1)),p);

(-1.*R*(diff(f[1](eta), eta))*(diff(diff(f[1](eta), eta), eta))+R*f[1](eta)*(diff(diff(f[1](eta), eta), eta)))*p^3+(-1.*R*(diff(f[0](eta), eta))*(diff(diff(f[1](eta), eta), eta))-1.*R*(diff(f[1](eta), eta))*(diff(diff(f[0](eta), eta), eta))+R*f[0](eta)*(diff(diff(f[1](eta), eta), eta))+R*f[1](eta)*(diff(diff(f[0](eta), eta), eta)))*p^2+(diff(diff(diff(diff(f[1](eta), eta), eta), eta), eta)-1.0*(diff(g[1](eta), eta))-1.*R*(diff(f[0](eta), eta))*(diff(diff(f[0](eta), eta), eta))+R*f[0](eta)*(diff(diff(f[0](eta), eta), eta)))*p+diff(diff(diff(diff(f[0](eta), eta), eta), eta), eta)-1.0*(diff(g[0](eta), eta)) = 0

(9)

A1:=diff(f[0](eta),eta$4)-2*K[r]*(diff(g[0](eta),eta))=0;
A2:=diff(f[1](eta),eta$4)-2*K[r]*(diff(g[1](eta),eta))-R*(diff(f[0](eta),eta))*(diff(f[0](eta),eta$2))+R*f[0](eta)*(diff(f[0](eta),eta$2))=0;

diff(diff(diff(diff(f[0](eta), eta), eta), eta), eta)-1.0*(diff(g[0](eta), eta)) = 0

 

diff(diff(diff(diff(f[1](eta), eta), eta), eta), eta)-1.0*(diff(g[1](eta), eta))-R*(diff(f[0](eta), eta))*(diff(diff(f[0](eta), eta), eta))+R*f[0](eta)*(diff(diff(f[0](eta), eta), eta)) = 0

(10)

icsA1:=f[0](0)=0,D(f[0])(0)=1,g[0](0)=0,f[0](1)=lambda,D(f[0])(1)=0,g[0](1)=0;
icsA2:=f[1](0)=0,D(f[1])(0)=0,g[1](0)=0,f[1](1)=0,D(f[1])(1)=0,g[1](1)=0;

f[0](0) = 0, (D(f[0]))(0) = 1, g[0](0) = 0, f[0](1) = .5, (D(f[0]))(1) = 0, g[0](1) = 0

 

f[1](0) = 0, (D(f[1]))(0) = 0, g[1](0) = 0, f[1](1) = 0, (D(f[1]))(1) = 0, g[1](1) = 0

(11)

NULLFORequ2

B:=collect(expand(subs(f(eta)=f[0](eta)+f[1](eta)*p,g(eta)=g[0](eta)+g[1](eta)*p,hpm2)),p);

(-1.*R*(diff(f[1](eta), eta))*g[1](eta)+R*f[1](eta)*(diff(g[1](eta), eta)))*p^3+(-1.*R*(diff(f[0](eta), eta))*g[1](eta)-1.*R*(diff(f[1](eta), eta))*g[0](eta)+R*f[0](eta)*(diff(g[1](eta), eta))+R*f[1](eta)*(diff(g[0](eta), eta)))*p^2+(diff(diff(g[1](eta), eta), eta)+1.0*(diff(f[1](eta), eta))-1.*R*(diff(f[0](eta), eta))*g[0](eta)+R*f[0](eta)*(diff(g[0](eta), eta)))*p+diff(diff(g[0](eta), eta), eta)+1.0*(diff(f[0](eta), eta)) = 0

(12)

B1:=diff(g[0](eta),eta$2)+2*K[r]*(diff(f[0](eta),eta))=0;
B2:=diff(g[1](eta),eta$2)+2*K[r]*(diff(f[1](eta),eta))-R*(diff(f[0](eta),eta))*g[0](eta)+R*f[0](eta)*(diff(g[0](eta),eta))=0;

diff(diff(g[0](eta), eta), eta)+1.0*(diff(f[0](eta), eta)) = 0

 

diff(diff(g[1](eta), eta), eta)+1.0*(diff(f[1](eta), eta))-R*(diff(f[0](eta), eta))*g[0](eta)+R*f[0](eta)*(diff(g[0](eta), eta)) = 0

(13)

icsB1:=f[0](0)=0,D(f[0])(0)=1,g[0](0)=0,f[0](1)=lambda,D(f[0])(1)=0,g[0](1)=0;
icsB2:=f[1](0)=0,D(f[1])(0)=0,g[1](0)=0,f[1](1)=0,D(f[1])(1)=0,g[1](1)=0;

f[0](0) = 0, (D(f[0]))(0) = 1, g[0](0) = 0, f[0](1) = .5, (D(f[0]))(1) = 0, g[0](1) = 0

 

f[1](0) = 0, (D(f[1]))(0) = 0, g[1](0) = 0, f[1](1) = 0, (D(f[1]))(1) = 0, g[1](1) = 0

(14)

FORequ3

C:=collect(expand(subs(theta(eta)=theta[0](eta)+theta[1](eta)*p,phi(eta)=phi[0](eta)+phi[1](eta)*p,f(eta)=f[0](eta)+f[1](eta)*p,hpm3)),p);

(10.*R*f[1](eta)*(diff(theta[1](eta), eta))+.1*(diff(phi[1](eta), eta))*(diff(theta[1](eta), eta))+.1*(diff(theta[1](eta), eta))^2)*p^3+(10.*R*f[0](eta)*(diff(theta[1](eta), eta))+10.*R*f[1](eta)*(diff(theta[0](eta), eta))+.1*(diff(phi[0](eta), eta))*(diff(theta[1](eta), eta))+.1*(diff(phi[1](eta), eta))*(diff(theta[0](eta), eta))+.2*(diff(theta[0](eta), eta))*(diff(theta[1](eta), eta)))*p^2+(diff(diff(theta[1](eta), eta), eta)+10.*R*f[0](eta)*(diff(theta[0](eta), eta))+.1*(diff(phi[0](eta), eta))*(diff(theta[0](eta), eta))+.1*(diff(theta[0](eta), eta))^2)*p+diff(diff(theta[0](eta), eta), eta) = 0

(15)

C1:=diff(theta[0](eta),eta$2)=0;
C2:=diff(theta[1](eta), eta, eta)+Pr*R*f[0](eta)*(diff(theta[0](eta), eta))+Nb*(diff(phi[0](eta), eta))*(diff(theta[0](eta), eta))+Nt*(diff(theta[0](eta), eta))^2=0;

diff(diff(theta[0](eta), eta), eta) = 0

 

diff(diff(theta[1](eta), eta), eta)+10*R*f[0](eta)*(diff(theta[0](eta), eta))+.1*(diff(phi[0](eta), eta))*(diff(theta[0](eta), eta))+.1*(diff(theta[0](eta), eta))^2 = 0

(16)

icsC1:=theta[0](0)=1,theta[0](1)=0;
icsC2:=f[0](0)=0,D(f[0])(0)=1,f[1](1)=0,D(f[1])(1)=0,theta[1](0)=0,theta[1](1)=0,phi[0](0)=0,phi[0](1)=0;

theta[0](0) = 1, theta[0](1) = 0

 

f[0](0) = 0, (D(f[0]))(0) = 1, f[1](1) = 0, (D(f[1]))(1) = 0, theta[1](0) = 0, theta[1](1) = 0, phi[0](0) = 0, phi[0](1) = 0

(17)

FORequ4

E:=collect(expand(subs(theta(eta)=theta[0](eta)+theta[1](eta)*p,phi(eta)=phi[0](eta)+phi[1](eta)*p,f(eta)=f[0](eta)+f[1](eta)*p,hpm4)),p);

.5*R*f[1](eta)*p^3*(diff(phi[1](eta), eta))+(.5*R*f[0](eta)*(diff(phi[1](eta), eta))+.5*R*f[1](eta)*(diff(phi[0](eta), eta)))*p^2+(diff(diff(phi[1](eta), eta), eta)+1.000000000*(diff(diff(theta[1](eta), eta), eta))+.5*R*f[0](eta)*(diff(phi[0](eta), eta)))*p+diff(diff(phi[0](eta), eta), eta)+1.000000000*(diff(diff(theta[0](eta), eta), eta)) = 0

(18)

E1:=diff(phi[0](eta),eta$2)+Nt*(diff(theta[0](eta),eta$2))/Nb=0;
E2:=diff(phi[1](eta),eta$2)+Nt*(diff(theta[1](eta),eta$2))/Nb+R*Sc*f[0](eta)*(diff(phi[0](eta),eta))=0;

diff(diff(phi[0](eta), eta), eta)+1.000000000*(diff(diff(theta[0](eta), eta), eta)) = 0

 

diff(diff(phi[1](eta), eta), eta)+1.000000000*(diff(diff(theta[1](eta), eta), eta))+.5*R*f[0](eta)*(diff(phi[0](eta), eta)) = 0

(19)

icsE1:=phi[0](0)=1,phi[0](1)=0;
icsE2:=f[0](0)=0,D(f[0])(0)=1,f[1](1)=0,D(f[1])(1)=0,theta[1](0)=0,theta[1](1)=0,phi[1](0)=0,phi[1](1)=0;

phi[0](0) = 1, phi[0](1) = 0

 

f[0](0) = 0, (D(f[0]))(0) = 1, f[1](1) = 0, (D(f[1]))(1) = 0, theta[1](0) = 0, theta[1](1) = 0, phi[1](0) = 0, phi[1](1) = 0

(20)

``

NULL



Download Project.mw


Project.mw

Download Project.mw

thanks for your favorits

Please check this:

N:=3;

sum1 := lcm(N, 0)+lcm(N, 1)+lcm(N, 2)+lcm(N, 3);

sum2 := sum(lcm(N, k), k = 0 .. N);

 

Why is sum2 wrong?

 

Regards,

César Lozada

 

Hi everyone.

I'm going to solve a problem with HPM in Maple. I wrote some initial codes but now I'm confused becouse of P^0 coefficients in A1 and B1. I mean I can't reach to f0 and g0.

I upload that file. these are codes that i typed. could you please help me how can I reach to them(f0 & g0)?

http://www.filehosting.org/file/details/573095/Maple%20Project+.mw

The following code is part of my attempt to answer the recent Question about the bifurcation of the map f:= x-> exp(x^2*(a-x)). Two very weird things are happening. They can be seen by applying trace to f. The first is that the input argument to f seems to be changed to a very large integer. The second is that for some real values of a and x, I get imaginary results from this obviously real-valued function. Why are these things happening?

restart:

f:= x-> exp(x^2*(a-x)):

trace(f):

Iterate:= proc(a, x0:= 1., n:= 2000)
local A:= hfarray(1..n, [x0]), f:= subs(:-a= a, eval(:-f));          
     #evalhf(
          proc(f, A, n)
          local k;
               for k from 2 to n do A[k]:= f(A[k-1]) end do
          end proc
          (f, A, n);
     #);
     evalf[4]~(convert(A[1000..], set))
end proc:

Iterate(1.05);

{--> enter f, args = 4607182418800017408

 

HFloat(1.0512710963760241)

 

<-- exit f (now in unknown) = 4607413323290551347}
{--> enter f, args = 4607413323290551347

 

HFloat(0.9985962074909431)

 

<-- exit f (now in unknown) = 4607169774561176020}
{--> enter f, args = 4607169774561176020

 

HFloat(1.0525960836530153)

 

Warning,  computation interrupted

 

Iterate(.75);

{--> enter f, args = 4607182418800017408

 

.754589752755861+.192678397202388*I

 

<-- exit f (now in unknown) = HFloat(0.7545897527558614)+HFloat(0.19267839720238844)*I}

Error, (in unknown) unable to store 'HFloat(0.7545897527558614)+HFloat(0.19267839720238844)*I' when datatype=float[8]

 

 

 

Download bifurcation.mw

Hi!

In a paper due to Borwein

http://www.cecm.sfu.ca/personal/pborwein/PAPERS/P172.pdf

it is shown a (very beautiful) graph of the zeros of a partial sum of the Zeta-Riemann, where he indicates that the plot is "the normalized zeros of the 5th partial sum of the Zeta function". Somebody know how one can plot this with Maple?

Thank you!

✐♦❝❄t✉⑥♠❧❄❞❢❤❡⑦⑧❛❋⑨⑤⑦⑧❛✯ts❝⑩❦✑❝❄❜❚qs❴❇❛ ✈❇❜❶q✉❴❷♥♦❧❄t✇q✉❤❡❧❄❞★❦sr❇⑥✤❝❄❜✫qs❴❇❛❹❸✫❤❡❛⑧⑥✜❧❺✐❇✐❻⑦⑧❛⑧q✉❧❈❼❽❜❀r❇✐♦♣✒qs❤❡❝❄✐

Here is my Maple 16 code:

 I expected to get outuput

a [a,b,c]

a [a,c,b]

But I get no output.

Why?

 

 

 

Every time I try to type in a procedure I get the error:  

Error, unterminated procedure

immediately after typing in the first line.  How can I type in the remaining lines of my procedure?

Note:  in maple 7 (years ago) I never had this problem.

Hi everyone. This problem is driving me nuts. I'm pretty sure it's a glitch but I'm not sure how to solve it. I'm trying to do some data analysis with Maple:

(as a side note, even if I remove the for loop but don't execute the restart command the error remains, however if I get rid of the for loop and execute the restart command it is fine.)

Any help would be greatly appreciated. As it stands this is really driving me insane.

We are running Maple16 in a virtual lab setup using Citrix, when exporting to PDF and saving the file to the local machine the PDF comes out as a 0kb file and the PDF is corrupt.  Has anyone else had an issue like this before?

hi all

 

i have tow equations and i want plot q vs.A , that A change beetwin 0..phi. vn and a are definite and positive.

f is a function of y.

becouse i have a physical problem so infinity can be 20 , and a can be 10 ,

so whit terms , f[infinity]=f[-infinity]=1 and f'[infinity]=f'[-infinity]=0 .

also phiB[y]=q*int(f,y=-infinity..y) , but i want plot q vs phiB[infinity] when phiB[infinity] change between 0..phi

plz plz help me

 

(diff(f,y))^2-(f[y]^4)/4+q^2/(f[y]^2)+(1+2*q^2)*(f[y]^2)/2=piecewise(y<-a,1/4+2*q^2,-a<y<a,vn*(f[y]^2)-vn+1/4+2*q^2,y>a,1/4+2*q^2);

phiB[infinity]=q*int(f,y=-infinity..infinity):
A:=phiB[infinity]:

Hello,

I've tried to find the solution to my problem, but none of my attempts was succesful.

I have a function which is one-to-one in a particular domain which I am interested in. I would like to get the inverse function of it only in this domain. Here is my function and plot for xp=0..10000:

x := xp-> (-1)*720.5668720*sinh(0.2043018094e-3*xp-0.8532729286)+84952.59423+4.014460003*10^5*arcsinh(0.1219272144e-1*sinh(0.2043018094e-3*xp-0.8532729286)-0.2032498888)

I would appreciate any help,

Iza

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