## Phase portrait of fractional differential equation...

How to plot the phase portrait of the system of fractional DEs?

0< nu<1

## Expanding infinite product...

Consider the infinite product

(1-qi)(1-qiz-1)(1-qi-1z)

For i > 0

How would I expand this into a power series in qz in Maple? Say I would like the coefficient of q6z2

Or how would I get the first n terms up to some order of qz?

## Collocating a vector to make a square matrix...

Dear Users!

Hope everyone fine here. I want to collocate Vector IntXYZ1 and IntXYZ2 present in file Q1 in such a way that the first M1M2 + 2(M3-1)M2 + 2(M3-1)(M1-2) rows are zero and other rows are collocated at x=(i-1)/(M1-1), y=(j-1)/(M2-1), t=(k-1)/(M3-1) for i = 2,3,…,M1-1, j = 2,3,…,M2-1, k = 2,3,…,M3 as given as XX (of order 27 by 27 with first 25 rows are zero) for M1=M2=M3=3

I am waiting for positive response to fix this issue. Thanks in advance

Q1.mw

## How to find number a, b, c, d, m so that this equa...

I  am trying to find the integer numbers `a, b, c, d, m` so that the equation

(x−a)(x−b)(x−c)(x−d)=m

where a+d=b+c  and m≠0 has four integer solutions.

I found this equation randomly
solve((x-5) (x-3) (x+6) (x+8)=504, x);
How to find number a, b, c, d, m so that the equation
(x−a)(x−b)(x−c)(x−d)=m
has four integer solutions?

## Rules to force [X,X] = 0 ?...

I am still a novice of Maple, but I want to carry out recurvive applications of some formula that involves non-commutative operators X and Y ([X,Y] = XY-YX). I used the following code, but I do not know how to tell Maple a rule that [X,X] = [Y,Y] = 0:

```with(Physics);
Setup(mathematicalnotation = true);
Setup(noncommutativeprefix = {X, Y});

Z := X + Y + (1/2)*Commutator(X,Y);
subs(X=Y,Z);```

The output is like this:

```> Z := X + Y + (1/2)*Commutator(X,Y);
Z := X + Y + 1/2 [X, Y][-]

> subs(X=Y,Z);
2 Y + 1/2 [Y, Y][-]```

The above [Y,Y] must be interpreted as zero, of course.

Thank you very much.

## How to remove the first column from my Tabulate co...

Hi,

How to remove the first column from my Tabulate command ?

SYRACUSEFina.mw

Thanks

## Measuring execution time...

The simple test procedure P constructs a large matrix.
Measuring the real time twice  (t1 and t2), t2 was by about 25% larger!
Now, if we remove the comment  before "Start",  t1 increases by 25% and t2 ~ t1.
So, the timing depends on whether some output is already on screen (standard interface).
Can you explain this?

```restart;
P := proc(n,A)
local i, j;
for i from 1 to n do  for j from 1 to n do
A[i,j]:=sin(arcsin(1/i-1/j+1/n))-1/i+1/j-1/n+i+j
od od;
NULL  #A;
end proc:

# "Start";
n := 300:
s := time[real]():
A:=Matrix(n,datatype=float[8]):
P(n,A):
t1:=time[real]()-s;

s := time[real]():
A:=Matrix(n,datatype=float[8]):
P(n,A):
t2:=time[real]()-s;
t2/t1;  # 1.24   WHY?
```

(For one of my programs, I found t2/t1 = 1.7)

## Why is "global" only allowed in procedures?...

Hi,

Why does the use of  global  at the top level of a worksheet is no longer accepted in the most recent versions of Maple (it still was in Maple 2015), but only within procedures?

TIA

Hello,

How I can Plot this structure using define new coordinate such as cylinderical om\ne or addcoords?

plot.mw

## Bug in plot3d or Display...

eq:= x^2-y^2*z-y*z^2;

plot3d(eq,x=0..1,y=0..1);

memory used=177.9MB, alloc=44.3MB, time=2.29
Picked up JAVA_TOOL_OPTIONS:
Initializing Java runtime environment.
munmap_chunk(): invalid pointer
Error, (in Maplets:-Display) computation interrupted

## Test solutions of a polynomial equation...

Suppose I have the equation C := y^2*z + yz^2 = x^2, then I want to test for which triples (x,y,z) with x,y,z in {0,1} the equation is satisfied? Is there a quick way of doing this in Maple?

## Solving vorticity equation...

Hello,

I'm having some difficulty solving a set of equations. For example

dn/dt = Const*(phi - n)

ds/dt= Const*(phi-n)

s = d2 phi/dx2 + d2 phi/dy2

How do you solve a system like this? It is 2 equations with 2 unknowns, but it is the s variable that is evolved, i.e. ds/dt, instead of phi.

Anyone know of some code that could do this? (periodic boundary conditions)

Better yet, how do you formulate this as a regular ODE for n and phi?

## Solving system of equations including trigonometri...

I stumpled upon an exercise involving calculating double points for the spacecurve for a vector function defined in the plane. It reduces to solving two equations with two variables. The command solve is usually the way to find solutions, but since the equation contain a trigonometric function, Maple gives the solutions parametrized by aritrary constants _Z and _B. It is however cumbersome to 'decipher' the possible solutions as I do in the attached Maple file.

I wonder if Maple have a way to deliver the solutions numerically in the interval from -4 to 4? If it had been a single equation this would have been possible, I know.

NB! I know I can use the symmetri in the current example, but I am interested in a general technique to solve these kind of equations.

Regards,

Erik

## Some queries in matrix evaluation ...

Dear Users!

Hope everyone fine here. I have following three quires that need to be fix.

1. I want to collocate Vector IntXYZ1 and IntXYZ2 present in file Q1 in such a way that the first M1M2 + 2(M3-1)M2 + 2(M3-1)(M1-2) rows are zero and other rows are collocated at x=(i-1)/(M1-1), y=(j-1)/(M2-1), t=(k-1)/(M3-1) for i = 2,3,…,M1-1, j = 2,3,…,M2-1, k = 2,3,…,M3 as given as XX (of order 27 by 27 with first 25 rows are zero) for M1=M2=M3=3

2. Next, in file Q2 we have a Vector b with some entries which are actually the values of chi[1, 1, 1], chi[1, 1, 2],...,chi[2, 2, 2] in such a following way

(Vector(8, {(1) = chi[1, 1, 1], (2) = chi[1, 1, 2], (3) = chi[1, 2, 1], (4) = chi[1, 2, 2], (5) = chi[2, 1, 1], (6) = chi[2, 1, 2], (7) = chi[2, 2, 1], (8) = chi[2, 2, 2]})) = (Matrix(8, 1, {(1, 1) = 0, (2, 1) = 0, (3, 1) = 0, (4, 1) = 0, (5, 1) = 1.000000000, (6, 1) = 1.000000000, (7, 1) = 1.000000000, (8, 1) = .3678794412}))

Matrix B given in file Q2 have entires which are the linear cobiniation of chi[1, 1, 1], chi[1, 1, 2],...,chi[2, 2, 2]. I want to evaluate matrix B at the values of chi[1, 1, 1], chi[1, 1, 2],...,chi[2, 2, 2] which are obtained in vector b.

3. I want to recall a vector B in file Q3 at highlighted portion and B matrix is present in Q4. Which is the command to recall or export a matrix which contain in some other file like in file Q4.

I shall be very grateful for your support.

## Proof of an inequality...

``` Let d an integer ">=5 " and
"lambda  in ]-(1)/(2),-(1)/(d+1)[. "
Put
> gamma[s+1,d]=((s+1)[d]((d+1)lambda+s))/(2^(d+1)(lambda+s)[d+1]).;
We need to show that
> gamma[s+1,d]>=-(1)/(2^(s+1)),;
for
> s=1,...,[(d+1)/(2)].;

a[k] designates the pochhammer symbol.
```

Thanks a lot

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