I want to find AutomorphismGroup  of star S₄ (ie, K_1,3).

the  has six automorphisms: (1, 2, 3), (1, 3, 2), (2, 1, 3), (2, 3, 1), (3, 1, 2,), (3, 2, 1):

For the output of maple ,I cannot understand.

Maybe I don’t understand the group enough. May somebody explain in detail,  Thanks!

ode.mw

I found an assignment question concerning an ODE from 20 years ago. This was before I had discovered Maple.

So I put it through Maple and got a complex solution, But the lecturer's solution was non-imaginary.

For a) gamma <> Beta and b) gamma = beta.

Actually for b) I couldn't follow his solution

Consider

restart;
L := [1,2,3,4];
x[j];
seq(%, x[j] in L);
x[j];

What would you expect the output of the last line to be?

Answer:   Maple says 4.   Why?

This proc is valid, yet Maple mint thinks there is syntax error

foo:= proc(x)
local z := "";
    if not x in ["A","B"] then
        return;
    fi;

    z:=cat("A
            B");    
end proc;

mint t.mpl gives

on line     7:     z:=cat("A
                          ^ Syntax error
A "then" was found without a previous matching "if".
An "end" may be needed to close the "in" construct from line 3.

But these two below procs below it gives no syntax error

foo:= proc(x)
local z := "";
    if not x in ["A","B"] then
        return;
    fi;  
end proc;

And

foo:= proc(x)
local z := "";
    z:=cat("A
            B");    
end proc;

No syntax error on either one. the syntax error only shows up when combining them. 

What does if not x in ["A","B"] then  have to do with the cat  below it? And why when they are combined, the syntax error shows?

I know of workaround, such as changing the cat to  z:=cat("A\nB");     or keep the strings on two lines, but do it like this

    z:=cat("A\n
           B");

Or write it like this

   z:=cat("A "
           "B"); 

But none of these changes were needed before adding the not x in ["A","B"]  before.

Is this a bug in mint? Is there a work around so the first example above still works using 

    z:=cat("A
            B");   

?

The purpose of this document is:

a) to correct the physics that was used in the document "Minimal Road Radius for Highway Superelevation" recently submitted to the Maple Applications Center;

b) to confirm the values found in the manual for the American Association of State Highway and Transportation Officials (AASHTO) that engineers use to design and build these banked curves are physically sound. 

c) to highlight the pedagogical value inherent in the Maple language to distinguish between assignment ( := )  and equivalence (  =  );

d) but most importantly, to demonstrate the pedagogical value Maple has in thinking about solving a problem involving a physical process. Given Maple's symbolic mathematics capabilities, one can implement a top-down approach to the physics and the mathematics, working from the general principle to the specific example. This allows one to avoid the types of errors that occur when translating the problem into a bottom up approach, from specific values of the example to the general principle, an approach that is required by most other computational systems.

I hope that others are willing to continue to engage in discussions related to the pedagogical value of Maple beyond mathematics.

I was asked to post this document to both here and the Maple Applications Center

[Document edited for typos.]

Minimum_Road_Radius.mw

Let say the procedure MyProc returns two variables as

A,B:= MyProc(…);

However, for programming purpose, I do not want to create an unused variable. Assuming one only needs B, not A, is there a way not to create and assign A?

For information, in Matlab, it is a commonly used technique. The syntax is

[~,B]= MyProc(…);

In Maple, the meaning of ~ is different, but I am looking for something similar.

 Today I read the  Problem 5.21 from book Maple and Mathematica, A Problem Solving Approach for Mathematics:

The book uses following codes:

But I think  these codes just verify rather than prove(n is always specific number). This example is not difficult to prove by hand. but I'd like to know Maple how to prove it. It seems not easy.

I want to solve the following IBVP:

However, the answer given by pdsolve doesn't give  with pdetest.

Download IBVP.mw

Please everybody, help me to make phaseportrait 3D

Maple's pdsolve() is quite capable of solving the PDE that describes the motion of a single-span Euler beam.  As far as I have been able to ascertain, there is no obvious way of applying pdsolve() to solve multi-span beams.  The worksheet attached to this post provides tools for solving multi-span Euler beams.  Shown below are a few demos.  The worksheet contains more demos.

Download worksheet: euler-beam-with-method-of-lines.mw

The uploaded worksheet contains a contourplot whose display I can't understand. Can you explain it?

Countourplot.mw

From Wikipedia,

However, when I plug the formula of u(x, t) into Maple, it doesn't seem to satisfy the PDE and is stuck evaluating.
 

Download InhomoHeat.mw

The uploaded worksheet contains two examples of the use of VectorCalculus[VectorSpace]. The first example seems explicable but the second does not.

I have tried and failed to find a full, clear explanation of how a vector describing a simple vector, spacecurve, or surface in the default vector space is transformed to appear in a user defined vector space.

Can anyone direct me to such an explanation, so that I can understand Maple's processing within the uploaded worksheet and enable me to use this Maple feature to future advantage?

VectorSpaceTest.mw

Hello again,

I have two functions f and h, that I want to show by pointplot as a diagramm (with a range from -10 to +10).

I know how to do it with "normal" functions, but what if for example the function f has 2 variables but h only has one?

f:= (sin(sqrt(x^2+y^2)))/(sqrt(x^2+y^2));

h:= f(x, 1.8);

These are the two functions.

So far I've made a list for each function for x  = -10 to x = 10

ListF:= [seq(f, x = -10..10, 1)];

ListH:= [seq(h, x = -10..10, 1)];

But I don't know how to go from there. Can I already use pointplot to connect the two lists? Or do I have to connect these two lists as one (which is what I originally planned) But I don't know how to do that, without always copying the results of one and then the other and putting both in a new list.

e.g Both lists show the values for the function for x = -10..10. If the first value of ListF is 5 and the first value of ListH is 1, then connecting both in a new list ListFH: = [[5,1]...], followed by the 9 other values.)

(5 and 1 aren't the actual results, I just used them for simplification.)

(Even if this isn't the right beginning for the solution of my original problem, I still want to know if it's even possible to take all values of one list of a function 'a' and all values of a second list of function 'b' and put them in a new list 'c' with c: = [a,b] without manually putting them together. So that the first value of list a is paired with the first of list b, the second of list a with the second of list b, etc... I hope you know what I mean)

In regards to my original problem I thought I could do something like this:

pointplot( [ [ListF], [ListH] ]);

I'm grateful for every answer :)

When making a function and using the return type, I found Maple is not catching the case when the function returns wrong type.

Actually there are two issues in this example I like to ask about. First, here is the example

restart;
kernelopts(assertlevel):=2;
TypeTools:-AddType(type_A, record(x::integer)):

foo:=proc( A::type_A ) ::type_A;  #this is what return type should be
     print( type(A,'type_A')); #this prints TRUE
     A:-x :=1.5; #opps, wrong type, changes type of record now!
     print( type(A,'type_A')); #This now prints FALSE
     return A;
end proc:

A:=Record('x' = 1);
B:=foo(A):
eval(B)

The call to foo() goes through as expected since type is correct.

First issue: Inside the function doing A:-x :=1.5;  changed the type of record now, since x is supposed to be integer and now become real. Is there a way to have Maple detect this at run time?

Second issue: The function was defined to return type_A  but due to this overwriting the field of the record by wrong value, it is no longer type_A  (the print now says false). But why Maple did not detect this? Since the function is defined to only return type_A ?

Is it possible to change the code above to catch these type mistakes I made?