## Invoking algebraic axioms that programmatically wo...

So, basically i plan to define procedures based on if conditions that will assume arbitarily large float approximations as being infinity, as with the example i have uploaded, but i feel that i need some people from here that are smarter than me to tell me why this is going to be terrible or what i need to consider.

I am willing to consider my current view naive and or inept, however i feel as if computer algebra systems will eventually develop means of reducing the need for floating point results by making concise implicit steps of manipulation on floating point computations, naturally i feel as if these routines are evidence that maybe some of the maple programmers have such an objective, but i do tend to misinterpret everything all the time.

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## Students discount...

Please may I know if you can offer ma student's discount ob the seleted version.

Thank you.

Fred.

## How to apply differential transformation method di...

How can I apply differential transformation method in differential equations with maple commands .DE is y'''(x)+xy''(x)-y(x)=0;

## How to calculate flux in the heat equation?...

I solve a boundary value problem for a linear system of first order PDEs
in the unknowns  and   Ultimately, I am interested in the graph
of the function  but numerical artifacts distort that graph badly by
imposing spurious oscillation.

Is there a way to maneuver the calculations to obtain the graph of
without the oscillation?

 > restart;
 > pde1 := diff(u(x,t),t)=diff(v(x,t),x);

 > pde2 := diff(u(x,t),x)=v(x,t);

 > ibc := u(x,0)=1, u(0,t)=0, u(1,t)=0;

 > dsol := pdsolve({pde1,pde2}, {ibc}, numeric, spacestep=0.01, timestep=0.01);

 > dsol:-value(output=listprocedure): my_u := eval(u(x,t), %): my_v := eval(v(x,t), %%):
 > plot3d(my_u(x,t), x=0..1, t=0..0.5);

 > plot3d(my_v(x,t), x=0..1, t=0..0.5);

The oscillations are numerical artifacts.  Can they be avoided?

 > plot(my_v(0,t), t=0..0.5);

A side comment: By eliminating between the two PDEs we see that
satisfies the standard heat equation, thus is the flux.  The expression
expresses the heat flux at the boundary, and that's what I am after.

## I can't do even basic stuff on maple, what is goin...

I open a completely new document, type in a few simple expressions and get this weird complex number out. Can someone pleas help me fix this?

## How to find coordinates of the points A and B of t...

In this question at here https://tex.stackexchange.com/questions/503745/how-can-i-get-correct-the-point-a-and-b-automatically-in-this-picture/503838?noredirect=1#comment1272706_503838
The points A and B lie on the circle is intersection of the sphere x^2 + y^2 + (z-3)^2 = 25 and the plane z = 0.
How can I find coordinates of the points A and B by Maple?

## searchtext with non-ASCII characters...

searchtext and SearchText do not work well with non-ASCII characters.
Strangely, StringTools:-Search is OK.

restart;
m:=convert([77,97,116,104,195,169,109,97,116,105,113,117,101], bytes);
m := "Mathématique"
seq(searchtext(m[i..7], m), i=1..7);
1, 0, 0, 4, 0, 0, 1
seq(SearchText(m[i..7], m), i=1..7);
1, 0, 0, 4, 0, 0, 7
seq(StringTools:-Search(m[i..7], m), i=1..7);
1, 2, 3, 4, 5, 6, 7

## How can I get Maple to find the Fourier transform ...

I'm a Maple novice.  I have two questions.  (1) I'm trying to use Maple to confirm some Fourier transforms of selected probability density functions.  In general I've succeeded, but Maple fails to find the Fourier transform of the pdf of a logistic random variable with mean 0.  Please explain how I can get Maple to carry out this request.  I've attached a Maple file with my work to this question.  (2) At several points in my computations, I wish to substitute 2*Pi*xi for omega.  I have an expression containing two omegas.  If I use algsubs(), only one of the two omegas is replaced.  I have to use subs() to replace both omegas.  Why is this?

Use Maple to confirm selected Fourier transform of logistic random variable

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Wikipedia's article on "Logistic distribution" gives a characteristic function that implies that the Fourier transform of this pdf should equal Pi*a*omega/sinh(Pi*a*omega).

Unit rectangular function

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## how to get good 3d figure...

restart;

K := -3;
-3
m := 1;
1
w := -4*K;
12
alpha[0] := -2;
-2
alpha[1] := 0;
0
a := 2;
2
b := 3;
3
1
beta[1] := (12*(m^2+K))/(a+b);
-24
---
5
xi := -t*w+x+y;
-12 t + x + y

F := -sqrt(-K)*tanh(sqrt(-K)*xi);
(1/2)     / (1/2)                \
-3      tanh\3      (-12 t + x + y)/
U := alpha[0]+alpha[1]*(m+F)+beta[1]/(m+F);
24
-2 - -------------------------------------------
/     (1/2)     / (1/2)                \\
5 \1 - 3      tanh\3      (-12 t + x + y)//
1
y := 0;
0

plot3d(U, x = -10 .. -10, t = -10 .. 10);

t := 0;
0
plot(U, x = -10 .. 10);

## Order of convergence for multiple roots...

How can find order of convergence  for multiple roots for example x-2*f(x)/Df(x)

WHICH have quadratic  order of convergence how find out in maple software????

## Intersection of 3D-plane with a 3D-drop...

How do I calculate the intersection curve between a plane and a drop?
The "drop" is defined in the following way:

R1 := 3.;R2 := 1.0;DR := 4;g := R2 + DR;

f1 := h -> sqrt(R1^2 - h^2);
f2 := h -> sqrt(g^2 - h^2);
f3 := h -> (1 - h/g)*f1(h*R1/g) + h*f2(h)/g;
f4 := h -> sqrt(1/2*g - 1/2*h);
f5 := h -> (1 - h/g)*f3(h) + h*f4(h)/g;
gg := h -> piecewise(h < 0, f1(h), 0 <= h, f5(h));#Radius depending on the z-position h
cir := (h, phi, R) -> <sin(phi)*R, cos(phi)*R, h>; # a circle at the hight h with radius R
#The plane is placed inside the drop.
n := (x, y, z) -> <x, y, z>/sqrt(x^2 + y^2 + z^2);

# the following lines show, how it looks like:
with(plots);
with(plottools);
dro1 := plot3d(cir(h, phi, gg(h)), h = -R1 .. g, phi = 0 .. 2*Pi, scaling = constrained, orientation = [-60, 72, 0]);
plotDropWithPlane := (x, y, z) -> display(dro1, arrow(Vector([0, 0, 0]), 2*R1*n(x, y, z), 0.2, 0.4, 0.1, cylindrical_arrow, fringe = blue, color = "Green"), implicitplot3d(x*x1 + y*y1 + z*z1 = 0, x1 = -R1 .. R1, y1 = -R1 .. R1, z1 = -R1 .. g, color = blue));
plotDropWithPlane(3, 1, 2);

#I'm searching a function like
fintersect:=theta-><"?,?,?>"

Any idea how to solve?

Best regards,

Andreas

## why order of coeffs not respected...

unprotect(D); f := proc (x, y) options operator, arrow; (295849/5841396)*x^2-(29441/324522)*y*x+(33995/216348)*y^2-(5989/14751)*x+(3635/4917)*y+1 end proc; 295849 2 29441 33995 2 5989 f := (x, y) -> ------- x - ------ y x + ------ y - ----- x 5841396 324522 216348 14751 3635 + ---- y + 1 4917 coeffs(f(x, y)); -5989 3635 295849 33995 -29441 1, -----, ----, -------, ------, ------ 14751 4917 5841396 216348 324522 A, B, C, D, E, F := %; -5989 295849 33995 -29441 3635 A, B, C, D, E, F := 1, -----, -------, ------, ------, ---- 14751 5841396 216348 324522 4917

## Recursive Assignment Errors...

Is there any way we can get maple to tell us which variable we are recursively assigning?

## How to simplify sin(4*pi*w)/sin(2*pi*w) (Answer:...

I would like to simplify

sin(4*pi*w)/sin(2*pi*w)

The answer I am looking for is 2*cos(2*pi*w).

Does anyone have an idea how to do this is Maple? Some earlier version of Maple I used could do this,

simplify( sin(4*pi*w)/sin(2*pi*w) ) =  2*cos(2*pi*w)

There a plenty of different trigonometric representations for the answer, so my hypothesis is that I should somehow tell to Maple which I am looking for.

For example

Gives

Which is better, but still not the answer I am looking for

Best Regards,

P

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