"Error, (in CheapestPaths) too many levels of recursion"

I received this message after trying to execute Zeilberg's GetMicrosoftJob program found here: http://www.math.rutgers.edu/~zeilberg/tokhniot/GetMicrosoftJob but don't know the cause. Any ideas?

I have following expression:

y1:=t->1/(4*cosh(t)^2)

I:=int(y1(t)^2,t=-T/2..T/2)

Now I tried:

MultiSeries:-asympt(I,T,5)

for which I only get the highest order.

Can I increase the order in any way?

What is wrong???

restart;
with(DEtools); with(plots);
epsilon := 'epsilon';

epsilon := 0.3e-1;
h := .75;
p := 2;
q := 0.6e-2;

sol := dsolve([[epsilon*(diff(x(t), t)) = x(t)+y(t)-q*x(t)^2-x(t)*y(t), diff(y(t), t) = h*z(t)-y(t)-x(t)*y(t), p*(diff(z(t), t)) = x(t)-z(t)], [x(0) = 100, y(0) = 1, z(0) = 10]], type = numeric);
%;
Error, (in dsolve/numeric/process_input) system must be entered as a set/list of expressions/equations

Hello, I have quite a complex thing to solve, but would simplify it here. I would like to solve the unknown in a matrix, how can I use the 'solve' function? For example

A:=Matrix(3,1,4)
B:=Matrix(3,1,[2,7,9])
The relation between them is A=B*y

How can I use the below function?
solve(A=B*y,y）

Dear people in this board.

I couldn't solve the following equation.

restart;

solve(gamma*(sigma/(sigma-1))=1,gamma);

On the other hand, I could solve

solve(alpha*(sigma/(sigma-1))=1,alpha);

Error message was 

Error, (in solve) a constant is invalid as a variable, gamma

Why does this sort of things happen?

I hope that you will tell me about this.

Tahnk you in advance.

taro 

I have a programme which examine how well a particular set of data fits a theoretical function.

In fact, I faced a problem : the programme returns only one solution and I guess in an arbitrary way.

I would like to find a way to define an interval in which the programme seeks solutions .

How can I do so?

with (Optimization)
[ImportMPS, Interactive, LPSolve, LSSolve, Maximize, Minimize, NLPSolve,QPSolve];

data := [[2.954488^2, 1.644900e-5], [3.132092^2,1.614900e-5], [3.307416^2, 1.594200e-5], [3.471311^2, 1.550700e-5], [3.559775^2, 1.450200e-5], [3.669332^2, 1.499400e-5], [3.825572^2, 1.476900e-5], [3.962449^2, 4.133000e-8], [4.200714^2, 1.320900e-5],
[4.434636^2, 1.433400e-5], [4.638319^2, 1.259100e-5], [4.832908^2, 1.258500e-5], [5.078484^2,
1.216200e-5], [5.315167^2, 1.164300e-5], [5.662155^2, 1.131000e-5], [5.916080^2, 1.082400e-5],
[6.208865^2, 1.054800e-5], [6.526868^2, 1.002600e-5], [6.880407^2, 1.006200e-5], [7.243618^2, 9.594000e-6], [7.607233^2,
9.288000e-6], [7.916439^2, 8.958000e-6], [8.320457^2, 8.664000e-6], [8.721812^2, 8.439000e-6], [9.007774^2, 8.325000e-6], [8.721812^2, 8.439000e-6], [9.007774^2,8.325000e-6], [9.393083^2, 7.878000e-6], [9.668506^2, 7.755000e-6], [9.988994^2,7.623000e-6], [10.40192^2, 7.367000e-6], [10.94532^2, 6.928000e-6], [11.38244^2,6.812000e-6], [11.85200^2, 6.720000e-6], [12.18811^2, 6.422000e-6], [12.67281^2, 6.403000e-6], [12.96341^2,6.514000e-6], [13.49185^2, 6.032000e-6], [13.76590^2, 6.103000e-6], [14.4072^2,6.143000e-6], [14.45476^2, 6.095000e-6], [14.76313^2, 5.758000e-6], [15.09868^2,6.965000e-6]]:

f:= x -> abs(((2*(c*exp(-b*1.5e-6)/(2*150*(c^2-((1+I)*(sqrt(3.14*x/8.5e-5)))^2)))*(2*(((1-I)*c/(2*(sqrt(3.14*x/8.5e-5))))-((0.026/150)*sqrt(8.5e-5/2e-5)))*exp(-c*0.5e-3)+((1+((0.026/150)*sqrt(8.5e-5/2e-5)))*(1-((1-I)*c/(2*(sqrt(3.14*x/8.5e-5)))))*exp(((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3))-((1-((0.026/150)*sqrt(8.5e-5/2e-5)))*(1+((1-I)*c/(2*(sqrt(3.14*x/8.5e-5)))))*exp(-((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3)))+(b/(2*a*(b^2-((1+I)*(sqrt(3.14*x/9e-6)))^2)*((2*(1-((0.026/150)*sqrt(8.5e-5/2e-5)))*(1+((1-I)*b*a/(2*(sqrt(3.14*x/8.5e-5))*150)))*exp(-((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3-b*1.5e-6))-(2*(1+((0.026/150)*sqrt(8.5e-5/2e-5)))*(1-((1-I)*b*a/(2*(sqrt(3.14*x/8.5e-5))*150)))*exp(((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3-b*1.5e-6))-((1-((0.026/150)*sqrt(8.5e-5/2e-5)))*(1-((a/150)*sqrt(8.5e-5/9e-6)))*(1-((1-I)*b*a/(2*(sqrt(3.14*x/8.5e-5))*150))/((a/150)*sqrt(8.5e-5/9e-6)))*exp(-((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3+((1+I)*(sqrt(3.14*x/9e-6)))*1.5e-6))-((1-((0.026/150)*sqrt(8.5e-5/2e-5)))*(1+((a/150)*sqrt(8.5e-5/9e-6)))*(1+((1-I)*b*a/(2*(sqrt(3.14*x/8.5e-5))*150))/((a/150)*sqrt(8.5e-5/9e-6)))*exp(-((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3-((1+I)*(sqrt(3.14*x/9e-6)))*1.5e-6))+((1+((0.026/150)*sqrt(8.5e-5/2e-5)))*(1+((a/150)*sqrt(8.5e-5/9e-6)))*(1-((1-I)*b*a/(2*(sqrt(3.14*x/8.5e-5))*150))/((a/150)*sqrt(8.5e-5/9e-6)))*exp(((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3+((1+I)*(sqrt(3.14*x/9e-6)))*1.5e-6))+((1+((0.026/150)*sqrt(8.5e-5/2e-5)))*(1-((a/150)*sqrt(8.5e-5/9e-6)))*(1+((1-I)*b*a/(2*(sqrt(3.14*x/8.5e-5))*150))/((a/150)*sqrt(8.5e-5/9e-6)))*exp(((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3-((1+I)*(sqrt(3.14*x/9e-6)))*1.5e-6))))/(((1-((0.026/150)*sqrt(8.5e-5/2e-5)))*exp(-((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3))*(((1-((a/150)*sqrt(8.5e-5/9e-6)))*(1+((0.026/150)*sqrt(8.5e-5/2e-5))/((a/150)*sqrt(8.5e-5/9e-6)))*exp(((1+I)*(sqrt(3.14*x/9e-6)))*1.5e-6))+((1+((a/150)*sqrt(8.5e-5/9e-6)))*(1-((0.026/150)*sqrt(8.5e-5/2e-5))/((a/150)*sqrt(8.5e-5/9e-6)))*exp(-((1+I)*(sqrt(3.14*x/9e-6)))*1.5e-6)))-((1+((0.026/150)*sqrt(8.5e-5/2e-5)))*exp(((1+I)*(sqrt(3.14*x/8.5e-5)))*0.5e-3))*(((1+((a/150)*sqrt(8.5e-5/9e-6)))*(1+((0.026/150)*sqrt(8.5e-5/2e-5))/((a/150)*sqrt(8.5e-5/9e-6)))*exp(((1+I)*(sqrt(3.14*x/9e-6)))*1.5e-6))+((1-((a/150)*sqrt(8.5e-5/9e-6)))*(1-((0.026/150)*sqrt(8.5e-5/2e-5))/((a/150)*sqrt(8.5e-5/9e-6)))*exp(-((1+I)*(sqrt(3.14*x/9e-6)))*1.5e-6)))))))*((1+I)*(sqrt(3.14*x/2e-5)))*exp(-190e-6*((1+I)*(sqrt(3.14*x/2e-5))))):

residuals := map(p -> (f(p[1])-p[2]), data):
R:= LSSolve(residuals);

Hi

I  have a system of second order differential equation to be solved numerically. I would like to set up events to halt integration  to find the values of phi when r(phi)=2/3 . Here is my code

DE:=diff(1/r(phi),phi,phi)+(1/r(phi))=(G*M/h^2)+(3*G*M/c^2*r(phi)^2));

ics:=r(0)=2/3,D(r)(0)=0;G:=1;M:=1;h:=1;c:=1;

p:=dsolve({DE,ics},numeric,events=[[r(phi),r(phi),halt]],[diff(r(phi),phi)=0,halt]]);

The code only works for the second event so it halts for r(phi)=1.63... etc

How do i stop this?

Thanks for any help.

I have a list of the structure like

['true', ['true','false'], ['true',['false','true'],'false'],...]

Is it possible to complete 'and' operation with all elements of list without knowing exact structure of list?

¿Que tipos de programas ayudan en  el desarrollo de problemas geometricos?

¿como puedo resolver problemas en maple17?  

I have to make a plot for experimental data where x corresponds to time and y is the concentration. So I loaded the values in two lists, ran fit to least squares and got the best fitting curve (it's linear). However, the line has to start at (0,0). How can I Maple to do that for me?

Due to the seemingly persistent tabbing-problem, I would like to learn how to work with Maple using an external editor: If I could recreate my packages using an external editor, thereby avoiding both the tabbing-issue and the blowup associated with what I call the 'XML-contamination of documents', and from them create the associated libraries, then I would be satisfied. For then I would use only a single document in Maple worksheet mode as a front end. Therefore:

Can anyone point me to some information concerning 1.) choice of an editor, and 2.) how to use an external editor to create packages and libraries in Maple?

hi, I have tried to run this program unfortunately the program give some errors.

anneal < -function(fun, N, rho, t, theta)

{y=NULL  

theta.old=theta repea {  

s=0  for k from 1 to N  

{

f.old=fun(theta.old)

 theta.new=runif(1,-1,1)+theta.old

 f.new=fun(theta.new)  

if(f.new<f.old){

 theta.star=theta.new  

s=s+1

}

 else  

{

u=runif(1)

 b=(u<=exp(-(f.new-f.old)/(t)))

 theta.star=theta.new*b+theta.old*(1-b)

 s=s+b  

}  

theta.old=theta.star

 y=c(y,theta.star)  

}  

write(y,file="anneal.result",ncol=1,append=T)

y=NULL

 if(s==0)break

 t=rho*t  

if(t<0.1)break  }

 return(y)  

}

cauchy.1=function(alpha){x=c(-4.20,-2.85,-2.30,-1.02,0.70,0.98,2.72,3.50)  return(sum(log(0.01+(x-alpha)^(2))))}

x=seq(-6,6,,300)

y=sapply(as.list(x),cauchy.1)

plot(x, y, type = "1", ylab = "cauchy.1(beta=.1,alpha)", xlab = "alpha")

anneal.result=anneal(cauchy.1,300,.95,10,4)

plot(x, y, type = "1", ylab = "cauchy.1(beta=.1,alpha)", xlab = "alpha")

anneal.result=anneal(cauchy.1,300,.95,10,4)

x = scan("anneal.result")

plot(1:length(x),x,type="1"

can anyone help me on this? can i do something about it

Many thanks.

Hi everyone,

I have been  trying to solve a coupled system of 2 differencial equations, 1 PDEs with 1 ODE.

The code is below.

> restart;

> with(linalg):with(plots):
> PDE:=[diff(x(z,t),t)=(a/Pe)*diff(x(z,t),z$2)-a*diff(x(z,t),z)-(1-epsilon)/epsilon*3*Bi*(x(z,t)-1)/(1-Bi*(1-1/ksi(z,t)))]:
> a=2:Pe=3:Bi=5:epsilon=0.85:

> ODE := [diff(ksi(z,t),t) = (b*Bi*x(z,t)-1)/ksi(z,t)^2/(1-Bi*(1-1/ksi(z,t)))]:
> IC1:=c(z,0)=0:
> IC2:=ksi(z,0)=1:
> bc2:=diff(x(z,t),z):
> bc1:=x(z,t)-1/pe*diff(x(z,t),z):
> N:=10:
> L:=1:
> dyduf:=1/2*(-x[2](t)-3*x[0](t)+4*x[1](t))/h:
> dydub:=1/2*(-x[N-1](t)+3*x[N+1](t)+4*x[N](t))/h:
> dydu:=1/2/h*(x[m+1](t)-x[m-1](t)):
> d2ydu2:=1/h^2*(x[m-1](t)-2*x[m](t)+x[m+1](t)):
> bc1:=subs(diff(x(z,t),z)=dyduf,x(z,t)=x[0](t),z=1,bc1):
> bc2:=subs(x(z,t)-1/pe*diff(x(z,t),z)=dydub,x(z,t)=x[N+1](t),t=0,bc2):
> eq[0]:=bc1:
> eq[N+1]:=bc2:
> eq[m]:=subs(diff(x(z,t),z$2)=d2ydu2,diff(x(z,t),z)=dydu,diff(x(z,t),t)=dydu,x(z,t)=x[m](t),z=m*h,PDE):
> for i from 1 to N do eq[i]:=subs (m=i,eq[m]);od:
> x[0](t):=(solve(eq[0],x[0](t)));

> x[N+1](t):=solve(eq[N+1],x[N+1](t));

> for i from 1 to N do eq[i]:=eval(eq[i]);od:
> eqs:=[seq((eq[i]),i=1..N)]:
> Y:=[seq(x[i](t),i=1..N)];

> A:=genmatrix(eqs,Y,'B1'):
Error, (in linalg:-genmatrix) equations are not linear

> evalm(B1);

[B1[1], B1[2], B1[3], B1[4], B1[5], B1[6], B1[7], B1[8], B1[9],

B1[10]]

> B:=matrix(N,1):for i to N do B[i,1]:=B1[i]:od:evalm(B);

> h:=eval(L/(N+1));

> A:=map(eval,A);

> if N > 10 then A:=map(evalf,A);end:
> evalm(A);

> mat:=exponential(A,t);
Error, (in linalg:-matfunc) input must be a matrix

> mat:=map(evalf,mat):
> Y0:=matrix(N,1):for i from 1 to N do
> Y0[i,1]:=evalf(subs(x=i*h,rhs(IC)));od:evalm(Y0);
Error, invalid input: rhs received IC, which is not valid for its 1st argument, expr

> s1:=evalm(Y0+inverse(A)&*b):
Error, (in linalg:-inverse) expecting a matrix

> Y:=evalm(mat&*s1-inverse(A)&*b):
Error, (in linalg:-inverse) expecting a matrix

> Y:=map(simplify,Y):
> Digits:=5;

Digits := 5

> for i from 1 to N do x[i](t):=evalf((Y[i,1]));od:
Error, invalid subscript selector

> for i from 0 to N+1 do x[i](t):=eval(x[i](t));od;

> setcolors(["Red", "Blue", "LimeGreen", "Goldenrod", "maroon",
> "DarkTurquoise", "coral", "aquamarine", "magenta", "khaki", "sienna",
> "orange", "yellow", "gray"]);

["Red", "LimeGreen", "Goldenrod", "Blue", "MediumOrchid",

"DarkTurquoise"]

> pp:=plot([seq(x[i](t),i=0..N+1)],t=0..10,thickness=4);pt:=textplot([[0.28,0.15,typeset("Follow the arrow: ",x[0],"(t), ..., ",
> x[N+1],"(t).")]]):
Warning, unable to evaluate the functions to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct

pp := PLOT(THICKNESS(4), AXESLABELS(t, ""),

VIEW(0. .. 10., DEFAULT))

> display([pp,pt,arw],title="Figure 5.13",axes=boxed,labels=[t,"x"]);
Error, (in plots:-display) expecting plot structures but received: [arw]

In advance, thanks for the time of reading it!

Regards

Ozlem