Maple Questions and Posts

These are Posts and Questions associated with the product, Maple


Hi

I have to create a function "I(epsilonc)" by integrating a function "sigma(y)"  from 0 to the variable "epsilonc"

but maple doesn t give me the actual formula of the integrated function, it only gives me equation 4 which is utterly useless to me.

 

How do I get Maple to actually calculate and give me the integrated function ??

Any help will be greatly appreciated

restart


#data

`ϵc1` := 2.1*10^(-3);

0.2100000000e-2

(1)

`ϵcu1` := 3.5*10^(-3):

Ecm := 31000:

fcm := 25:

Fy := 500:

Es := 200000:

#geometry

As := 1885:

b = 250:

d := 450:


#coefficients

eta := epsilon/`ϵc1`:

k := 1.05*Ecm*`ϵc1`/fcm:

``


#formula

 

``

`σc` := proc (epsilon) options operator, arrow; fcm*(k*epsilon/`ϵc1`-epsilon^2/`ϵc1`^2)/(1+(k-2)*epsilon/`ϵc1`) end proc;

proc (epsilon) options operator, arrow; fcm*(k*epsilon/`ϵc1`-epsilon^2/`ϵc1`^2)/(1+(k-2)*epsilon/`ϵc1`) end proc

(2)

plot(`σc`, 0 .. `ϵcu1`);

 

``

#Pressure as a function of y (y=`ϵc`*y/x) :

`σc` := proc (y) options operator, arrow; fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)) end proc;

proc (y) options operator, arrow; fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)) end proc

(3)

Iy := proc (y) options operator, arrow; int(fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)), y = 0 .. `ϵc`/(`ϵc`+Fy/Es)) end proc;

proc (y) options operator, arrow; int(fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)), y = 0 .. `ϵc`/(`ϵc`+Fy/Es)) end proc

(4)

Iy(`ϵc`/(`ϵc`+Fy/Es))

Error, (in int) integration range or variable must be specified in the second argument, got `ϵc`/(`ϵc`+1/400) = 0 .. `ϵc`/(`ϵc`+1/400)

 

solve(Iyy*b = Fy*As, `ϵc`);

``

``


 

Download HW1_-_EC2_strain-pressure_graph.mw
 

restart


#data

`ϵc1` := 2.1*10^(-3);

0.2100000000e-2

(1)

`ϵcu1` := 3.5*10^(-3):

Ecm := 31000:

fcm := 25:

Fy := 500:

Es := 200000:

#geometry

As := 1885:

b = 250:

d := 450:


#coefficients

eta := epsilon/`ϵc1`:

k := 1.05*Ecm*`ϵc1`/fcm:

``


#formula

 

``

`σc` := proc (epsilon) options operator, arrow; fcm*(k*epsilon/`ϵc1`-epsilon^2/`ϵc1`^2)/(1+(k-2)*epsilon/`ϵc1`) end proc;

proc (epsilon) options operator, arrow; fcm*(k*epsilon/`ϵc1`-epsilon^2/`ϵc1`^2)/(1+(k-2)*epsilon/`ϵc1`) end proc

(2)

plot(`σc`, 0 .. `ϵcu1`);

 

``

#Pressure as a function of y (y=`ϵc`*y/x) :

`σc` := proc (y) options operator, arrow; fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)) end proc;

proc (y) options operator, arrow; fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)) end proc

(3)

Iy := proc (y) options operator, arrow; int(fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)), y = 0 .. `ϵc`/(`ϵc`+Fy/Es)) end proc;

proc (y) options operator, arrow; int(fcm*(k*`ϵc`*y/(x*`ϵc1`)-`ϵc`^2*y^2/(x^2*`ϵc1`^2))/(1+(k-2)*`ϵc`*y/(x*`ϵc1`)), y = 0 .. `ϵc`/(`ϵc`+Fy/Es)) end proc

(4)

Iy(`ϵc`/(`ϵc`+Fy/Es))

Error, (in int) integration range or variable must be specified in the second argument, got `ϵc`/(`ϵc`+1/400) = 0 .. `ϵc`/(`ϵc`+1/400)

 

solve(Iyy*b = Fy*As, `ϵc`);

``

``


 

Download HW1_-_EC2_strain-pressure_graph.mw

 

Possibly related to this. One has to remember that the result of convert/MeijerG for sin(z) is actually csgn(z)*sin(z):

convert(sin(z), MeijerG, include = all);
         sqrt(Pi)*MeijerG([[], []], [[1/2], [0]], (1/4)*z^2)

simplify(%);
         csgn(z)*sin(z)

That is the case for some other functions as well. Wouldn't it be better to return csgn(z)*MeijerG? For the sine, the form z*MeijerG is also a possibility. Might help to avoid issues similar to this one:

int(sin(a*x)*MeijerG([[], []], [[0], []], x)/x, x = 0 .. infinity); # incorrect for Re(a)<0
             -arctan(1/a)+(1/2)*Pi

 

I know that the Fourier transform of the triangle function is the sinc function squared, but I cannot seem to reproduce this in MAPLE.  How do I get from R2 to the square of the sinc function or do I have a screw up in defining the integral?  I need another set of eyes.  I have been at this for awhile & cannot seem to breakthrough.


 

plot(piecewise(-1 < x and x < 0, 1+x, 0 < x and x < 1, 1-x), x = -2 .. 2, linestyle = solid, thickness = 5, scaling = constrained, title = "Symmetric Triangle Wave")

 

(int((1+t)*exp(-I*(2*Pi*n*t/T)), t = -(1/2)*T .. 0)+int((1-t)*exp(-I*(2*Pi*n*t/T)), t = 0 .. (1/2)*T))/T = ((-(2*I)*n*Pi-T+I*T*n*Pi)*exp(I*n*Pi)+(2*I)*n*Pi+T-(2*I)*n*Pi+T+((2*I)*n*Pi-T-I*T*n*Pi)*exp(-I*n*Pi))/(2^2*n^2*Pi^2)
"(->)"true"(->)"true

(int((1+t)*exp(-I*(2*Pi*n*t/T)), t = -(1/2)*T .. 0)+int((1-t)*exp(-I*(2*Pi*n*t/T)), t = 0 .. (1/2)*T))/T = ((-T+I*T*n*Pi)*exp(I*n*Pi)+2*T-(T+I*T*n*Pi)*exp(-I*n*Pi))/(2^2*n^2*Pi^2)
"(->)"true"(->)"true

R1 := ((-T+I*T*n*Pi)*exp(I*n*Pi)+2*T-(T+I*T*n*Pi)*exp(-I*n*Pi))/(2^2*n^2*Pi^2)

(1/4)*((-T+I*T*n*Pi)*exp(I*n*Pi)+2*T-(T+I*T*n*Pi)*exp(-I*n*Pi))/(n^2*Pi^2)

(1)

R1 = (1/4)*(2*T-T*(exp(-I*n*Pi)+exp(I*n*Pi))-I*(exp(-I*n*Pi)-exp(I*n*Pi))*Pi*T*n)/(n^2*Pi^2)"(->)"true

NULL

exp(-I*n*Pi)+exp(I*n*Pi)"(=)"2*cos(Pi*n)

exp(-I*n*Pi)+exp(I*n*Pi) = 2*cos(Pi*n)"(->)"false

exp(-I*n*Pi)-exp(I*n*Pi)"(=)"-(2*I)*sin(Pi*n)

exp(-I*n*Pi)-exp(I*n*Pi) = -(2*I)*sin(Pi*n)"(->)"false

R2 := (1/4)*(-2*cos(Pi*n)*T-2*sin(Pi*n)*T*n*Pi+2*T)/(n^2*Pi^2)

(1/4)*(-2*cos(Pi*n)*T-2*sin(Pi*n)*T*n*Pi+2*T)/(n^2*Pi^2)

(2)

R2 = 2*T*(1-cos(Pi*n)-Pi*n*sin(Pi*n))/(2^2*n^2*Pi^2)"(->)"true"(->)"true"(->)"true"(->)"true"(->)"true

-2*cos(Pi*n)*T-2*sin(Pi*n)*T*n*Pi+2*T"(=)"-2*T*(cos(Pi*n)+Pi*n*sin(Pi*n)-1)``

1-cos(a) = 2*sin((1/2)*a)^2"(->)"true

(1/2)*(-exp(I*n*Pi)+1+I*n*Pi)/(Pi^2*n^2)-(1/2)*(I*exp(I*n*Pi)*Pi*n-exp(I*n*Pi)+1)*exp(-I*n*Pi)/(Pi^2*n^2) = (1/2)*(2-exp(I*n*Pi)-exp(-I*n*Pi))/(Pi^2*n^2)"(->)"true

2-exp(I*n*Pi)-exp(-I*n*Pi) = -exp(-I*n*Pi)*(exp(I*n*Pi)-1)^2"(->)"true

2-exp(I*n*Pi)-exp(-I*n*Pi) = -exp(-I*n*Pi)*(exp(I*n*Pi)-exp(I*n*Pi)*exp(-I*n*Pi))^2"(->)"true

2-exp(I*n*Pi)-exp(-I*n*Pi) = -exp(-I*n*Pi)*(exp(I*n*Pi)*(exp(I*n*Pi)-exp(-I*n*Pi)))^2"(->)"true"(->)"true

2-exp(I*Pi*n)-exp(-I*Pi*n) = -exp(-I*Pi*n)*exp((2*I)*Pi*n)*(exp(I*Pi*n)-exp(-I*Pi*n))^2"(->)"true"(->)"true

exp(I*Pi*n)-exp(-I*Pi*n)"(=)"(2*I)*sin(Pi*n)

``


 

Download symmetric_triangle_fourier_coeffs.mw

This question caught my eye on Mathematics Stack Exchange forum and doesnt seem to be resolved even with Mapel 2017.3:

Please follow the question and the discussion here

The question simply is to find the Fourier Transform of arctan(x)/x and use its inverse to verify if the solution provided by Maple was consistent.

The same sequence was tested on Wolfram Mathematica, and correct result was obtained.

Experienced users on this forum please advise what could be the possible explaination for this result.

Maple test:

Hi all, 

I am stuck in the follow sum:

Write a procedure to evaluate the sum of Sn and use this to find the value of n=10^p, p=1,2,3,4,5.

I started with defining Sn, 

restart:
Sn:=sum((1/k^(1/10))*sin(1/k), k=1..n);

Perhaps sum is not the correct one? Perhaps add?

And help appreciated

 

Hello, 

I've created a model of a rose flower that I'd like to export as a high quality picture without the white space.  Is there a way to do this?  

deq := FunctionAdvisor(DE, hypergeom([a, b], [c], z))[2, 1];
          diff(f(z), z, z) = ((-a-b-1)*z+c)*(diff(f(z), z))/(z*(z-1))-f(z)*a*b/(z*(z-1))

dsolve(deq, f(z));
Error, (in dsolve) Not an ODE w.r.t. f(z)

Apparently FunctionAdvisor is doing something special for the variable names in order to avoid collisions with user variables, but if I want to use the output programmatically, without copying and pasting it, is there a better way than something like this:

dsolve(subs(op(0, indets(deq)[-1]) = f, deq), f(z));
          f(z) = _C1*hypergeom([a, b], [c], z)+_C2*z^(1-c)*hypergeom([b-c+1, a-c+1], [2-c], z)

 

Hi there,

I was using maple 2016 and would like to plot the following:
Question.mw

However,when I run the code,only the axis are shown.How should I fix it?

Thanks!

For a numerical integration in Maple, one only adds evalf(...) to the integration commend. Now my question is that is it also the case for the multi-integration? Also consider that the multi-integration of the Maple doen't give any answer for some examples. So I think putting evalf around them, doesn't help. How can someone compute a numerical approximation of a multi-integration by Maple? Is there any prepared commend or package for it?


i have a PDE of heat equation, i can solve this using two boundary and initial condition, but i can not handle it using second boundary condition and maple also can not ! hoc can i solve it ?
 

Download pde.mw

Dear 

Hope everyone is good. I am face to attaine the converges solution of the attached problem. Please have a look and fix my problem. I am waiting your response

diverges.mw

I have 6 equations, eq1,...,eq6, with 6 unknowns a,b,c,d,f,g. I can find all the solutions with "solve".
If "solve" has found only one solution, then the ith solution number is given by sol[i]. For example,
c:=sol[3]. This comes from

sol:=solve({eq1,eq2,eq3,eq4,eq5,eq6},{a,b,c,d,f,g});

However, if solve has found more than one solution,
then the jth element of the ith solution is sol[i][j]. It is thus imperative to know how many solutions
the command "solve" has found. Also, how do we restrict "solve" to look only for real soultions?
Thank you very much!

mapleatha

I have a code in Maple that solves a system of polynomial equations (18 equations, 18 variables) using the command 'RootFinding[Isolate]' (it takes to Maple about 40 minutes to find all the solutions to the equations). Is it possible to see the implementation of the Isolate command? if not, is there any other open source code that implements the equivalent to Isolate command and also able to solve such equations? (I'm talking about the  numeric solutions. not symbolic).

I already tried to use the command 'solve_poly_system' in python (sympy package) which is open source. but the function didn't return a solution after a very long time (and I used a system of 9 equations and 9 variables which were much simpler than the equations Maple was able to solve using Isolate command).

I'm attaching the equations Maple solved using Isolate command. and also the equivalent in python with the simpler equations (that it wasn't able to solve).

solving_18_polynomial_equations.mw

trying_to_solve_polynomial_equations_python.txt

I'd appreciate any idea of how to use open source code that produces the same results as the code in Maple (if it's possible).

Thanks

 

Hey MaplePrimes

I have a problem with opening some of my documents in maple. When i try to open them, a box pops up with the text "How do you want to open this file?" with the options "Maple Text, Plain Text, Maple Inputs". None of these options work (document is blank) and "Plain Text" and "Maple Inputs" causes maple to crash. Is it possible to recover the documents?

ps. when i try to upload one the documents this happens:

 
Maple Worksheet - Error
Failed to load the worksheet /maplenet/convert/Maple_docs_til_mat.mw .

Download Maple_docs_til_mat.mw

Maple_docs_til_mat.mw
 

 

 

 

 

 

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