A family of curves has polar equation r=cos^n (theta/n), 0<=theta,n*pi, where n is a positive even integer.

Previously Using t = theta as the parameter and finding  a parametric form of the equation of the family of curves it was shown that 

dy/dx = (sin(t)sin(t/n)-cos(t)cos(t/n)) /( sin(t)cos(t/n)+cos(t)sin(t/n)).

Is it possible to show on Maple with a program that there are n+1 points where the tangent to the curve is paralell to the y axis?

Suppose that a finite set of polynomials in C[x,y,z] has a finite number of solutions (i.e. the generated ideal is 0-dimensional).

Suppose also that the Groebner basis wrt plex(x,y,z) is

[f(z), g(y,z), h(y,z), k(x,y,z)]

As well known, the system can be now easily solved: choose a root z0 of f, plug it into g and h and look for a common root (y0) etc.

The question is the following:
Is it true that for EVERY root z0 of f there exist y0, z0 such that (x0,y0,z0) satisfy the system?

In all the examples I have seen this is true, but I don't know whether this is true in general or there is a counterexample.

[This is not a pure Maple question but I know that some members here work in this area].

Thank you.

when i use the command evalf(Int(f(y),y=-b..b)), i expect that the output of this command to be an integer. but the output is to form of below:

i think that the problem is because of the form of the function f(y) that is the form of below:

f(y) = a*10^354*(b*10^-356*g(sin(y) , cos(y) and exp(y)))

but i dont know how i solve this problem:(

please help me. thank you

I followed the steps given in the example of Maple help "Example 5: Adding a MathMLViewer Region" but I get the next error window.

Do you know what is my mistake?

thank you.

Connecting to a linux x2go server with an x2go client (tried Mac and Linux) and try to start maple2016 in a terminal, I get this error:

$ /opt/maple2016/bin/xmaple 
Picked up JAVA_TOOL_OPTIONS: 
Exception in thread "Request id 1" java.lang.UnsupportedOperationException: PERPIXEL_TRANSLUCENT translucency is not supported
    at java.awt.Window.setBackground(Window.java:3842)
    at java.awt.Frame.setBackground(Frame.java:988)
    at com.maplesoft.worksheet.application.WmiSplashScreen.<init>(Unknown Source)
    at com.maplesoft.worksheet.application.WmiGenericStartupStrategy.showSplash(Unknown Source)
    at com.maplesoft.worksheet.application.WmiGenericStartupStrategy.doStartup(Unknown Source)
    at com.maplesoft.worksheet.application.WmiWorksheetStartupStrategy.doStartup(Unknown Source)
    at com.maplesoft.application.Maple.doStartup(Unknown Source)
    at com.maplesoft.application.Application.startup(Unknown Source)
    at com.maplesoft.application.ServerProtocol$StartApplicationHandler.processCommand(Unknown Source)
    at com.maplesoft.application.ServerProtocol.executeCommand(Unknown Source)
    at com.maplesoft.application.ServerProtocol.processNextStep(Unknown Source)
    at com.maplesoft.application.ExchangeProtocol.executeProtocol(Unknown Source)
    at com.maplesoft.application.ApplicationManager$Listener.run(Unknown Source)
    at java.lang.Thread.run(Thread.java:745)

The same xmaple will start graphically if I connect with a normal remote X connection. However a normal remote X connection is unusable on a slow network connection.

This is simplified from a larger example.  I never saw Maple exit from a numercal calculation.

> 123456789 ^ 987654321:
Execution stopped: Stack limit reached.

Process Maple R2016 exited abnormally with code 158

> kernelopts(maxdigits);
                                  38654705646

> lprint(123456789. ^ 987654321.);
.4339566080e7991619731

kernelopts(memusage) shows about 2~3 meg bytes used.

The system has 16G Ram.  16G swap.

Seems like something maple should have caught.

I don't know where to ask this.  Sorry if this is the wrong forum.

I use maplev-mode

;; Version:    2.155
;; X-RCS:      $Id: maplev.el,v 1.14 2006-06-02 14:02:38 joe Exp $
 

I am attempting to modify it so
  f1 invokes maplev-cmaple-send-line
  f2 invokes maplev-cmaple-send-region
  f3 invokes maplev-cmaple-send-buffer
 

tried adding
(define-key map [(control c) (control c) ?l] 'maplev-cmaple-send-line)
(define-key map [(f1)]  'maplev-cmaple-send-line)

but, emacs seems to not recognize this.  I can change the global keymap to get this behavior.
Is there a way to do this in maplev.el?
 

Tom Dean

What can i do in this case? I,m traying solve a system of non linear equation like this, i want to know Rs and Rsh:

I have the following fuction in Laplace domain,

restart:with(plots):with(inttrans):

u:=Pi^4*s3^(alpha-1)/((s1^2+Pi^2)*(s2^2+Pi^2)*(-s1^2+Pi^2*s3^alpha-s2^2))-Pi*s1*s2^(alpha-1)/(s3*(1+s2^alpha)*(-s1^2+Pi^2*s3^alpha-s2^2))-Pi*s1*s2^(alpha-1)/(-s1^2+Pi^2*s3^alpha-s2^2);

Where, s1, s2, s3 are the Laplace variables.

x1:=invlaplace(u, s1, x);

This worked. But the next two doesn't work.

y1:=invlaplace(x1, s2, y);

uu:=invlaplace(y1, s3,t);

Even, I tried to plot the unevaluated invlaplace but no luck.

alpha:=1:t:=1:
plot3d(uu,x =1..2, y=1..2);
 

Am I missing something?

Dear all,

I have the following question, this code:

restart:
with(DifferentialGeometry):
DGsetup([w1,w2],N):
eq1 := ExteriorDerivative(w1);  
eq2 := ExteriorDerivative(w1) &wedge ExteriorDerivative(w2);
eq1 &wedge eq2;

Gives the error:
Error, (in DifferentialGeometry:-Tools:-DGzero)  given degree, 3, exceeds that of frame dimension, 2

Unfortunately, I am not so familiar with differential geometry but as far as I know dw1  (dw1  dw2) = 0 should be correct.

Thank you for your help
best
baustamm1

I am looking for persons with experience in setting up maple for the blind. The setting is a 21-year old blind
 student who wants to do math. He uses Mac OS/X and the built-in VoiceOver screen reader, plus refreshable Braille display (one-line), a Braille printer, and Nemeth, the Braille extension for math symbols.

Initially, we are working from no experience whatsoever, trying ideas, mostly failure. Getting some advice from persons who are blind and using maple would be wonderful. If anyone knows of an instance, a person who is blind and regularly uses maple, then we would both would be delighted to receive advice on what to install, how to set it up, and how to use maple on a daily basis.

One trouble for the VoiceOver screen reader is verbosity of maple output. Any methods to reduce the amount of output would be welcome. To uderstand the issue, look at the output of these two commands when interface(prettyprint=0) has been set to help out the VoiceOver screen reader:

matrix([[1,2],6,7]]); Matrix([[1,2],[6,7]]);

The first outputs the same text, which VoiceOver will read accurately. The second dumps out two lines of extraneous and confusing information, only 20% of which is useful. The verbosity is not restricted to matrix packages linalg or LinearAlgebra. It is a problem wtih nearly all packages.

-Grant Gustafson, Salt Lake City, Univ of Utah Math Dept

Dear friends:

I am facing two problems

1. one is to get solution of the below system of ODE for L=100 (highlited as red) and

2. the other is I want the graph in the form of solid line not poit, asterisk etc.

restart; epsilon := .1; Pr := 1; beta := .1; Sc := 1; S := 1; L := 20;
for i from -L while i <= L do;
a[i] := 1.0*i/L;
end do;
for i2 from -L while i2 <= L do;

fw := a[i2]; 

Eq1[i2] := eval(diff(F(eta), eta, eta, eta)+F(eta)*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2+S*(epsilon-(diff(F(eta), eta)))+epsilon^2);
Eq2[i2] := eval((diff(G(eta), eta, eta))/Pr-G(eta)*(diff(F(eta), eta))+F(eta)*(diff(G(eta), eta))); 
Eq3[i2] := eval(diff(H(eta), eta, eta)+Sc*(F(eta)*(diff(H(eta), eta))-beta*H(eta)));
IC[i2] := F(0) = a[i2], (D(F))(0) = 1, (D(F))(L) = epsilon, G(0) = 1, G(L) = 0, H(0) = 1, H(L) = 0;
dsys1[i2] := {Eq1[i2], Eq2[i2], Eq3[i2], IC[i2]};
dsol1[i2] := dsolve(dsys1[i2], numeric, output = listprocedure, range = 0 .. L);
dsol1x[i2] := subs(dsol1[i2], diff(F(eta), eta, eta));
dsol1y[i2] := subs(dsol1[i2], G(eta));
dsol1z[i2] := subs(dsol1[i2], H(eta)) end do;

for j from -L while j <= L do; 
g[j] := eval(-dsol1x[j](0)) end do;
with(plots); 

g6 := pointplot({seq([n/L, g[n]], n = -L .. L)}, symbol = asterisk, symbolsize = 15, color = red);
display(g6);

Please see the problem and correct as soon as possible. I am waiting your positive respone.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

It is well known that fsolve usually increases (internally) Digits in order to obtain the desired accuracy.

But in the following example, it seems that fsolve highly exaggerates :-)   

restart;
N:=40:
Digits:=100:
F:=expand(mul(x-k,k=1..N)):
f:=evalf(F):
S:=[fsolve(f,complex)];

Error, (in fsolve) Digits cannot exceed 38654705646

Note that the bug does not appear if e.g. F:=expand(mul(x-k-I, k=1..N)):

How to pdeplot Curl(A(x,y,z))=0 in maple

it has A1(x,y,z) , A2(x,y,z) and A3(x,y,z)

Hi all,

I have a partial differential equation similar to the following:

The solution is that f is identically equal to 0.

However, I am having trouble solving this equation in Maple. I type the following:

pde := diff(f(x, y), x)+diff(f(x, y), y) = f(x, y)+f(x, 0);

bv1 := f(x, 10) = 0;

bv2 := f(10, y) = 0;

solution := pdsolve(pde, {bv1, bv2}, numeric, time = x, range = 0 .. 10);

When Maple tries to evaluate the last expression, I get the error

Error, (in pdsolve/numeric/process_PDEs) PDEs can only contain dependent variables with direct dependence on the independent variables of the problem, got {f(x, 0)}

It seems to have difficulties with the expression "f(x,0)". Is there some trick to typing this in a way that makes Maple interpret it correctly?

Edit: I encounter the same problem, when I try to solve the ODE f'(x) = f(x) + f(0), where f(10) = 0.

Best regards.