## How to solve these two problems?...

Hello dear Maple,

My name is Bulat, I'm student of Kazan National Research Technical University ( Russia). In our High Program we used your product ( Maple V, Release 4). Now I have two problems and I haven't no idea how I resolve their. I am forced to ask for your help. I upload PrintScreen of my two problems. Please help me to solve them. I' ll be grateful for your help. Sorry for my English :(.

Yours very truly, Bulat

## Error, too many levels of recursion...

In Maple V, Release 4 (1996):

 T:=table():i:=1:N:=5000;for i from i to N  do   T[i]:=T[i+1]:   T[i+1]:=1;   eval(T[1]);od:print(i);for i from i to N  do   T[i]:=T[i+1]:   T[i+1]:=1;   eval(T[1]);od:print(i);

N := 5000
Error, too many levels of recursion
3607
5001

Can You explain this occurence, as well as the following one:

In Maple V, Release 4 (1996):

 T:=table():i:=1:N:=5000;for i from i to N  do  T[i]:=T[i+1]:  eval(T[1]);od:print(i); for i from i to N  do  T[i]:=T[i+1]:  eval(T[1]);od:print(i);;

gives:

N := 5000
Error, too many levels of recursion
3607
Error, too many levels of recursion
3607

How does one control allowance for recursion depth?

## What is the expected correct outcome of the follow...

In Maple V, Release 4 (1996):

 _EnvX:=0; b:=0; proc() global b; print(_EnvX, b); assign('_EnvX=1, b=1'); print(_EnvX, b); end();_EnvX:=0: b:=0: proc() global b; print(_EnvX, b); _EnvX:=1; b:=1; print(_EnvX, b); end();;

gives:
0, 0
0, 1

 _EnvX:=0; b:=0; proc() global b; print(_EnvX, b); assign('_EnvX=1, b=1'); print(_EnvX, b); end proc();_EnvX:=0: b:=0: proc() global b; print(_EnvX, b); _EnvX:=1; b:=1; print(_EnvX, b); end proc();

?

## Is this a map execute error?...

Code & result:

> map((a::uneval,b)->'args',[a,b,c,d],1..4,x);
['a, 1 .. 4, x', 'b, 1 .. 4, x', 'c, 1 .. 4, x', 'd, 1 .. 4, x']

> map((a,b::uneval)->'args',[a,b,c,d],1..4,x);
[a, 1 .. 4, x, b, 1 .. 4, x, c, 1 .. 4, x, d, 1 .. 4, x]

Why is the output not:
['a', 1 .. 4, x, 'b', 1 .. 4, x, 'c', 1 .. 4, x, 'd', 1 .. 4, x]
and
[a, '1 .. 4', x, b, '1 .. 4', x, c, '1 .. 4', x, d, '1 .. 4', x]
?

## Procedure for Aitkin's Method...

How do I write a procedure to find a root of f(x)=0 in the vicinity of a given value x0. The procedure should initially use the rearrangement method to produce a linearly convergent sequence of values, and should, when appropriate, switch to Aitkin's Method. The input for the procedure should be the re-arranged function and the velue for x0. The output should be the root and the number of iteration taken. The procedure should check that re-arrangement will converge. This program should do in Maple V Release5.

## Obtaining the splitting field...

I am trying to obtain the splitting field of New_polyq. evala@AFactor did not complete. Applying splitting sequentially produced independent extensions from the first 2 (3?) factors. evala@Indep did not complete for the union of all 4 extensions.

What libraries would handle this better?

restart; _EnvExplicit:=false;interface(labelwidth=200);
Rho_polys:=rho[3,1]^3-2, rho[3,2]^2+rho[3,2]*rho[3,1]+rho[3,1]^2, 2*rho[6,1]^3+rho[6,1]^6-2, rho[12,1]^2+rho[6,1]^2-1, 2*rho[12,2]^2-rho[6,1]^2*rho[3,2]*rho[3,1]^2-2*rho[6,1]^2-2;
New_poly:=1/16*(-rho[6,1]^4*rho[3,2]*rho[3,1]-2-rho[3,1]^2*rho[6,1]^4-2*rho[6,1]*rho[3,2]*rho[3,1]-2*rho[3,1]^2*rho[6,1]+2*lambda^2)*(rho[6,1]^4*rho[3,2]*rho[3,1]+2*rho[6,1]*rho[3,2]*rho[3,1]-2+2*lambda^2)*(-2+2*rho[3,1]^2*rho[6,1]+rho[3,1]^2*rho[6,1]^4+2*lambda^2)*(-2+rho[6,1]^2*rho[3,2]*rho[3,1]^2+2*lambda^2);
sol:=solve({Rho_polys});
alias(op(sol));
New_polyq:=subs(sol,New_poly);

Hi, I have a homework to do that I am strugling with:

write a procedure which uses euler's method to solve a given initial value problem.
the imput should be the differential equation and the initial value.
using this programme find y(1) if dy/dx= x^2*y^3 and y(0)=1, and use maple dsolve command to check the solution.

That is what I have managed to do, but somehow it is not working correctelly, can somebody help please?

eul:=proc(f,h,x0,y0,xn)
local no_points,x_old,x_new,y_old,y_new,i:
no_points:=round(evalf((xn-x0)/h)):
x_old:=x0:
y_old:=y0:

for i from 1 to no_points do
x_new:=x_old+h:
y_new:=y_old+evalf(h*f(x_old,y_old)):
x_old:=x_new:
y_old:=y_new:
od:
y_new:
end:

Thanks

## taking limit with assume on indexed variable on li...

```I am also having trouble with limits when I have indexed
variables.   That is, how do I tell Maple to assume every element of
an indexed variable is positive?

uxb3% maple < te7a

|\^/|     Maple V Release 3 (Governors State University)

Here, I show that normal limits work.
> int (exp(-x^2),x=3..infinity);

1/2         1/2

1/2 Pi    - 1/2 Pi    erf(3)

> assume(a>0);

> int(exp(-a*x^2...```

## How would I write the procedure?...

A curve has the equation y=f(x).

Find the eqn of the normal to the curve at the point x=xin the form y=g(x, x0) and write a procedure to plot curve y=f(x) with its normal at any point on the curve.

Animate the plot so that the normal is seen sliding along the curve.

## eqn output split long lines...

`I use the eqn feature from Maple to generate troff output.Each equation is longer than one line.  How does one get the eqn/troffcombination to automatically break the equation into multiple lines.(I tried finding the division point myself and could not do it.  I am generating the output and I have a perl script that puts together the indivdualequations into the document to be printed.  Thus, I need something automatic)I tried Google and...`

## Old maple software on a new computer error...

Division by zero, overflow error

A recent question brought to me some old applications in the application center, loading those applications in newer Maple versions shows critical information missing.

This prompted me to install MapleV on my computer to properly view these applications however after installing, sadly we get a division by zero, overflow error message.

Since probably no has done this in this day and age, this is a real stab in the...

## Problem with integration involving Dirac delta fun...

We need to compute some integral, containing product of some "regular" function (e.g. gaussian)
and Dirac delta-function. The problem is that argument of delta-function is itself a function.

A simplified example is

d1:=s->int( g(x,5,0.025)*Dirac( s-f1(x) ) , x=0..infinity);

By trials and errors, we figured out that Maple runs such calculation successfully
when this function is very simple and fails in more complex cases, i.e., integration  returns zero.

## Historical Video: Maple V - The Future of Mathemat...

by: Maple V

Back when I was working at the University of Waterloo, I found several copies of a VHS tape sitting on a dusty bookshelf full of old Maple boxes and manuals. The tape's cover had a line drawing of Issac Newton on it and the title "Maple V: The Future of Mathematics".

There was...

## pointplot3D spherical cartesian...

Hello everybody,

I have a numerical list of points' coordonées defined as :

{P1,P2,P3, ...}

where P1 is defined by [r,theta,phi] radius, azimut, elevation.

Can I plot this in a cartesian coords whitout calculing X=r*cos()*sin() .... ?

Thank's

## Function modulo Pi...

Hello,

I have a parametric function which represent an angle and parameters are angles too.

theta=f(nu,phi)

I plot theta whith plot3d but when theta become inferior to -90°, maple draw a gap of 180°

How can I plot theta without gap ?

Thank's

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