Hi,

I have a problem with maple solving diffusion equation. I solved the equation as follows

Es := 0.117108e12;
Ef := 0.78125e11;
l := 0.150e-6;
s := 0.500000e-3;
f := 0.5898334197e-6;
o := 0.9e-5;
d := 0.10e-17;
cb := 0.1e7/(19.9);
c := l*f/(d*cb);
PDE := diff(u(x, t), t)-(diff(u(x, t), x, x)) = 0;
IBC1 := {u(x, 0) = 0, (D[1](u))(0, t) = 0, (D[1](u))(1, t) = c};
S1 := pdsolve(PDE, IBC1, numeric, time = t);
S1:-plot(t = 0.6e-2);

i am plotting cincentration along the thickness of the material. i want to know why the concentration is negative. It should not be negative because constant flux 'c' is present at x=1. and flux at x=0 is 0, and also the initial concentration is 0.

Thanks

 

How can I plot the volume of revolution of the region between the curves y=ln(x) and y=-ln(x)on the interval [1,e]

around the y-axis.please specify the command. I used the command: VolumeOfRevolution(ln(x),-ln(x), x=1..e, scaling=constrained,axis=vertical,output=plot). But this command only plots the revolution of the curves not the region between them.

Best Regards

Yegan 

My exposure to the topic of Fourier Transforms is very cursory--maybe a few weeks work as part of an undergraduate math course (in an engineering program.) However, I am now returning to the subject for a while and, reading material, noticed that some routines scale the Fourier coefficients differently. So now I am wondering: Why do different routines scale the coefficients differently? If the purpose of the Fourier Transform is to extract the components of circular motion from data, shouldn't it all work out the same?

Hi,

I would like to plot E2(t) , but It gives errors. How can I avoid the singularity and solve this problem?

restart: with(plots):
with(Student[NumericalAnalysis]):
g1:=(x,t)->(-sqrt(t)/(2*sqrt(Pi*r^3)))*(sin((r*(x-1)^(2)/(4*t))+(Pi/4))-sin((r*(x+1)^(2)/(4*t))+(Pi/4))):

g2:=(x,t)->int(g1(x,t),r=1..infinity);

g3:=(x,t) -> (diff(g2(x,t),t)):

g4:=(x,t) -> (diff(g2(x,t),x,x)):

g5:=(x,t) -> ((1/2)*(g3(x,t)^2+g4(x,t)^2)):

E2:=t->(int(g5(x,t),x=0..100)):

evalf(E2(0));
Error, (in g1) numeric exception: division by zero
evalf(E2(1));
Error, (in g3) invalid input: diff received 1, which is not valid for its 2nd argument
plot(E2(t),t=0..20);

Best regards,

Hej guys,

in some of my Maple worksheets I'm using Maples fit-function to obtain a rational function fit to some data, as I'm interested in the zeros of enumerator and denominator, I chose my fit function accordingly. Afterwards I need to extract the results (mainly the zeros) and do some more calculation steps with them. When evaluating rational functions of high degree, I noticed that my way of extracting the results (I'm using patmatch) becomes increasingly slow up to the point where it takes a couple of minutes to extract 10 numbers.
E.g. the following minimal example (download link at the bottom) takes more than 20 minutes on my machine (Maple 18.01 Build ID 935137; Red Hat Version 6.6 running on system with an i5-3570, 8 GB of RAM). Additionally, the calculation requires an unreasonable amount of RAM.
I can work around the problem to some degree by extracting the leading coefficient beforehand, resulting in a substantial speed up, still I think that there might be some error in the code or my usage of patmatch.

Is there another way to extract these numbers in a similarly simple fashion?

Cheers,

Sören

Download patmatch-breakdown.mw

I want to test linearly dependence of a polynomial f on a list of polynomials F by additional condition on parametric coefficients of linear parametric polynomial (linear for variables not parameters). Please note that:

1. The polynomial f and the members of F are always homogenous in the variables.
2. The coefficients of f, the coefficients of the members of F are all always polynomials in the parameters or contant and the members of N and W are all always polynomials in the parameters.
   

For example let

and

(a,b,c,d,e,h are parameters and A1,A2,A3 are variables).

If I use PolyLinearCombo(F,f,{A1,A2,A3}) (see http://www.mapleprimes.com/questions/204469-How-Can-I-Find-The-Coefficients-Of-Linear#comment217621)then its output is false,[].

Now we let to condition sets for parameters as the following:

N:=[ebc+ahd]

W:=[a,c]

The elements of N must be zero means that ebc+ahd=0

and the elements of W are non-zero that is a<>0 and c <>0.

Let a=b=c=d=h=1 and e=-1. This specialization satisfy in the above condition sets N and W. By this specialization we have:

and

Now if I use PolyLinearCombo(F,f,{A1,A2,A3}) then its output is true,[-1,1].

By this additional two condition sets I have to check that whether f is linearly independent of F or not. How can I do this without specialization? In fact I want an algorithm that its input is (null condition N, not-null condition W, list of polynomials F, a polynomial f, the set of variables) and its output is true and coefficients if f is linearly dependent of F w.r.t. null and not-null conditions N and W, else its output is false.

If the name of new procedure is ExtPolyLinearCombo and 

N:=[ebc+ahd]

W:=[a,c]

I want the output of

ExtPolyLinearCombo(N,W,F,f,{A1,A2,A3}) be true,[coefficients]

Thank you very much in advance.

not a full combinations yet

restart;
G := (L::list(name),n::posint)->op((`*`@op)~(combinat[choose](L,n))):
G( [q,r,s], 3 );
with(LinearAlgebra):
aa := Matrix([[1,3,1],[3,1,3],[3,3,3]]);
num1 := 1;
for i from 1 to 3 do
for j from 1 to 3 do
num1 := num1* nops([G( [a,b,c], aa[i,j] )]);
od:
od:
numcol := nops(aa);
for ii from 1 to numcol do
for jj from 1 to numcol do
alist := [G( [a,b,c], aa[ii,jj] )];
num1 := num1 - nops(alist);
for zz from 1 to nops(alist) do
m := Matrix([[0,0,0],[0,0,0],[0,0,0]]);
m[ii,jj]:=alist[zz];
for ii2 from 1 to numcol do
for jj2 from 1 to numcol do
if ii <> ii2 && jj <> jj2 then
m[ii2,jj2] := aa[ii2, jj2];
end if:
od:
od:
print(m);
od:
od:
od:

then i change simpler

m := Matrix([[0,0,0],[0,0,0],[0,0,0]]);
delta := proc(m,bb,ii2,jj2,poin)
finish := 0;
for ii from 1 to numcol do
for jj from 1 to numcol do
num1 := num1 - nops(alist);
if poin <= 3 and finish = 0 and ii = ii2 and jj = jj2 then
m[ii,jj]:=bb[poin];
finish := 1;
end if:
od:
od:
return m;
end proc:
ii := 1;
jj := 1;
alist := [G([a,b,c], aa[ii,jj] )];
delta(m,alist,ii,jj,2);

not completed yet

if input n = 3 which means total 3 alphabet

if value = 2, expect output

a*b, a*c, b*c

if value = 1 expect output

a, b, c

if total n = 4, four alphabets

value = 3, expect output

a*b*c, a*b*d, a*c*d, b*c*d

value = 2 expect output

a*b, *a*c, a*d, b*c, b*d, c*d

https://en.wikipedia.org/wiki/Surgery_theory

glue two geometric object

i use maple 17, 

will future version of maple do this?

or which software can do this?

I want to paste a list of points generated by another program into a maple worksheet. 

However, when I paste the list of points into the Maple worksheet, I get a command prompt after each defined point in the list.  Whereby, the executable code will not run.

I need a way to paste the list of points into the worksheet without any command prompts.  Is there a special entry mode?  

Here's the list of points I want to paste into the worksheet:

[

[20,0,0],

[20,4,0],

[19,8,0],

[17,11,0],

[14,14,0],

[11,17,0]

],

Below is the worksheet code that I want to paste the list of points.

However, when I paste the list of points within the "pointPlot3D" function -- I get a command prompt after each defined point in the list of points.  (So 30 points gives 30 command prompts.)  Whereby, when this code is executed, there is an error.    What I need is a means to paste this list of points into the worksheet WITHOUT the command prompts showing up. 

> with(geom3d):

> with(plots):

> sphere1:=(x,y,z,R)->[x+R*cos(phi)*cos(theta),y+R*cos(phi)*sin(theta),z+R*sin(phi)]:

> Explore(display(        

       plot3d(sphere1(0,0,0,Rp),phi=-Pi/2..Pi/2,theta=0..2*Pi),  

               scaling = constrained, axes = boxed, style=wireframe, labels=[x,y,z],                

       pointplot3d(

> [
> [20,0,0],
> [20,4,0],
> [19,8,0],
> [17,11,0],
> [14,14,0],
> [11,17,0]

> ],

               symbol=circle,symbolsize=10)  ),        

       parameters=[Rp=3..20],         initialvalues=[Rp=20] );

I'm trying to plot the region bounded by the coordinate planes, the plane z=2-y and the cylinder x=4-y^2

This is what I have so far.  I want to know how to get rid of the portions of the planes and cylinder that are not enclosing the region.

restart;

with(plots);

xmin := 0;
xmax := 4;
ymin := 0;
ymax := 2;
zmin := 0;
zmax := 2;

a := plot3d([2-y], x = xmin .. xmax, y = ymin .. ymax, orientation = [40, 70], transparency = 0, color = green, filled = false, title = "");
%;

b := implicitplot3d([z = 0, y = 0, x = 0], x = xmin .. xmax, y = ymin .. ymax, z = zmin .. zmax, transparency = .5, axes = normal);
%;
c := implicitplot3d([x = -y^2+4], x = xmin .. xmax, y = ymin .. ymax, z = zmin .. zmax, transparency = .5, filled = true, axes = normal, color = blue, orientation = [45, 35]);

display(a, b, c);

A duck, pursued by a fox, escapes to the center of a perfectly circular pond. The fox cannot swim, and the duck cannot take flight from the water. The fox is four times faster than the duck. Assuming the fox and duck pursue optimum strategies, is it possible for the duck to reach the edge of the pond and fly away without being eaten? If so, how?

http://www.crazyforcode.com/fox-duck-puzzle/

there is an animation here

https://www.youtube.com/watch?v=Zw9cHEnhzWo

wonder if the equations of motion can be derived usingg maple and an animaton...?

Hallo. I'd like to make a loop for two variables. Let say:

for i from 1..10, j from 1..10

How to do it?

Thanks.

Hi everyone:

I have two functions in terms of theta variable, how can I expressed function Y(X)?

X :=(theta)->cos(theta)+0.8e-1*cos(3.*theta)

Y :=(theta)->-sin(theta)+0.8e-1*sin(3.*theta)

I will earn Y(X) infact.

Thanks alot...

Mehran.

At the first note that in this question all polynomials have parametric coefficients. Let F be a list of polynomials and f be a polynomial. I want to convert F and f into a linear homogeneous FF and ff resp. At the first I want to sortvthe monomials appears in F and f  w.r.t. a monomial order T and then replace by the new variables A_i.

For example if

and

(a,b,c are parameters and x,y,z are variables) then I want to convert F and f into FF and ff resp:

please note that the variables appears in F and f are:

where sorted by T=plex(x,y,z). Please note that we consider all constants and alone parameters (4, b-4, c-1) as A9. I want to convert v into

and then F into FF and f into ff.