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Hi All, I have the following procedure to compute the gcd between two integers:

Egcd := proc(a, b)
while b != 0 do
temp := b;
b := a mod b;
a := temp;
od;
return a;  
end proc;

Why does it simply return the value of a when the function was called? (i.e my statements inside the procedure do nothing

I created a triangle whose length of the medians are integral numbers. Please comment to me about my code.

> resrart:

ListTools[Categorize]:

N:=5:

L:=[]:

for x1 from -N to N do

for y1 from x1 to N do

for z1 from y1 to N do

for x2 from -N to N do

for y2 from -N to N do

In geom3d, how can i make a triangle which coordinates of the center circle circumscribed triangle are integer numbers? Please help me. Thank you.

What is the next two terms for this pattern...

1, -2, 2, -4, 0, ...

Suppose I have a matrix M, with rational entries. I need to go row by row and scale each individually by the smallest possible integer such that the entries in each row are integer-valued - anyone have an easy way to do this? It's a large matrix.

We have 1^2 + 2^2 +2^2 = 3^2; 2^2 + 3^2 + 6^2 = 7^2; 2^2 + 10^2 +11^2 = 15^2. Please write for me a command solve the equation a^2 + b^2 + c^2 = d^2, where, a, b, c, d are integer numbers, and d <=100. Thank you very much.

Dear friends, I encounter the following problem. Let k and i be two given positive integers such that k>=2i>=4. How to find all nonnegative integers tuples (x_1, x_2, ..., x_i) such that k-2i<=x_1+2x_2+...+ix_i<=k-i? The buildin command "isolve" seems not work. Thanks.

 

with(numtheory):

f := proc (x) options operator, arrow; sum((-1)^n*(n^(1/n)-1), n = x .. infinity) end proc

proc (x) options operator, arrow; sum((-1)^n*(n^(1/n)-1), n = x .. infinity) end proc

(1)

What are the quotients  ot the  continued fration of the sum of f(1)+f(2)+f(3)+f(4)+...

Here are the  quotients  of some partial sums.

``

cfrac(evalf(sum(f(x), x = 1 .. 2)), 'quotients')

[0, 2, 1, 1, 1, 21, 10, 4, 1, 4, 8, `...`]

(2)

cfrac(evalf(sum(f(x), x = 1 .. 3)), 'quotients')

[0, 6, 1, 2, 3, 1, 1, 2, 3, 3, 24, `...`]

(3)

cfrac(evalf(sum(f(x), x = 1 .. 4)), 'quotients')

[0, 2, 1, 2, 1, 4, 2, 1, 3, 1, 1, `...`]

(4)

cfrac(evalf(sum(f(x), x = 1 .. 5)), 'quotients')

[0, 5, 1, 99, 1, 1, 1, 6, 1, 3, 1, `...`]

(5)

cfrac(evalf(sum(f(x), x = 1 .. 6)), 'quotients')

[0, 2, 1, 6, 1, 2, 1, 2, 2, 1, 1, `...`]

(6)

cfrac(evalf(sum(f(x), x = 1 .. 7)), 'quotients')

[0, 5, 1, 1, 142, 1, 1, 1, 1, 19, 1, `...`]

(7)

cfrac(evalf(sum(f(x), x = 1 .. 8)), 'quotients')

[0, 2, 1, 47, 1, 1, 1, 1, 27, 4, 1, `...`]

(8)

cfrac(evalf(sum(f(x), x = 1 .. 9)), 'quotients')

[0, 5, 5, 3, 1, 7, 1, 1, 1, 2, 1, `...`]

(9)

cfrac(evalf(sum(f(x), x = 1 .. 100)), 'quotients')

[0, 3, 1, 1, 1, 11, 2, 2, 1, 1, 4, `...`]

(10)

cfrac(evalf(sum(f(x), x = 1 .. 200)), 'quotients')

[0, 3, 1, 2, 1, 1, 1, 11, 3, 4, 6, `...`]

(11)

cfrac(evalf(sum(f(x), x = 1 .. 400)), 'quotients')

[0, 3, 1, 3, 3, 3, 1, 18, 1, 2, 1, `...`]

(12)

cfrac(evalf(sum(f(x), x = 1 .. 800)), 'quotients')

[0, 3, 1, 3, 1, 4, 16, 14, 3, 23, 2, `...`]

(13)

cfrac(evalf(sum(f(x), x = 1 .. 1600)), 'quotients')

[0, 3, 1, 4, 7, 4, 436, 1, 1, 1, 2, `...`]

(14)

``

Here are the quotients of the  continued fration  of the sum. 

cfrac(evalf(sum(f(x), x = 1 .. infinity)), 'quotients')

[0, 3, 1, 4, 1, 1, 1, 1, 1, 9, 1, `...`]

(15)

With the exception of the leading 0, that is close to the integer squence of pi.

``evalf((65241/65251)*Pi)

3.141111191

(16)

The exponents of 2 that sum the numerator and denominator, in the following way, of that multiple of pi give rise to the integer sequences {0,1,2,3,8,16},numbers such that floor[a(n)^2 / 7] is a square, and {0,2,3,4,8,16},{0,3} union powers of 2.

evalf((2^16-2^8-2^5-2^2-2-2^0)*Pi/(2^16-2^8-2^4-2^3-2^2-2^0))

3.141111191

(17)

We can do the same thing for the first 20 quotients giving rise to the integer sequences {0,1,2,5,6,8,10,13,17,19,22,23,24,28,31} and {0,4,6,9,12, 14,15,16,18,22, 23,24,28,31}. What can be said of these sequences?

cfrac(evalf(sum(f(x), x = 1 .. infinity), 20), 20, 'quotients')``

[0, 3, 1, 4, 1, 1, 1, 1, 1, 9, 1, 3, 1, 2, 1, 1, 1, 5, 1, 3, 11, `...`]

(18)

evalf((1849023129/1849306543)*Pi, 20)

3.1411111913121115131

(19)

````

evalf((2^31-2^28-2^24-2^23-2^22-2^19-2^17-2^13-2^10-2^8-2^6-2^5-2^2-2-2^0)*Pi/(2^31-2^28-2^24-2^23-2^22-2^18-2^16-2^15-2^14-2^12-2^9-2^6-2^4-2^0), 20)

3.1411111913121115131

(20)

``


 

Let a sequence( an  ) defined by an=1,3,6,12,33,51,...and n=1,2,3,.... Find formula an?

HI,

 

I want to create a Textbox which will be opened in the beginning of a Maple code. In this Textbox I want to write an integer, which will be used for a following calculation.

I already found this code:

 

> restart; with(Maplets[Elements]);
print(`output redirected...`); # input placeholder
> maplet := Maplet([["Insert Text", BoxCell(TextBox['IB1'](1 .. 10))], [Button("OK", Shutdown(['IB1'])), Button("Cancel", Shutdown())]]);

Hello everyone

I want to check whether a recurrence relation produces integers. What I have written is rather messy, I ideally would like some kind of Proc where I can just put in the recurrence relation, the initial conditions and the number of terms I would like to check. Then get a result out which tells me whether the terms in the sequence are all integer. 

 

I have written the following (which tells me what I want to know but in a crude way)

I have a 3rd order nonlinear recurrence relation and I would like to produce the associated sequence.

Here is the relation x[n+2]:=(((x[n+1]*x[n])^2+x[n]^2+x[n+1]^3))/x[n-1]. At the moment the method I am using (a standard do command) is very computationally heavy when I want lots of iterates. I was wondering if there were faster loops, or procs.

Also I would like some kind of way to check if all the terms are integers, maybe some kind of summation where an...

HI,

 

at first I have to admit, that I'm totaly new to maple and have only few experience with the programm.

 

That's the problem. I've got an old maple-code which I want to rewrite in the 2d-Math-syntax. In the code there are a lot of variables of the type "numerical integer" with a form like

"rho_a"

"N_A"

....

--> with index in the name

It's a code for a physical-/chemical- process so the...

How can i trunc (find closest integer) each element in a matrix ? 

This is my matrix equation:

for n to 20 do 'CD'^n, 'F' = evalf(C[1].D[1]^n.F[1]) end do

And i want to show  "trunced" results

Hi,

I am new to Maple, so sorry for asking this TRIVIAL question but I got quite frustrated after so much time unsuccessfully trying to figure out how to perform integer computations.

Lets take the simple example below:

3k - 5 = 0

I wanna get k=1 not 5/3

Isolve doesn’t work  for this as I would like. Introduced assumptions re ignored:

Solve(3*k -5=0, k, useassumptions) assuming k :: nonnegint

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