MaplePrimes - Questions and Posts tagged with integer

How do I force simplification of products of square roots of positive integers

charlestmungerjr — Fri, 10 May 2013 23:25:49 Z

In an atomic physics calculation involving the quantum theory of angular momentum, there appear polynomials whose coefficients involve square roots of positive integers, for example

sqrt(6)-sqrt(2)*sqrt(3)

Maple does not cancel such an expression to zero because the code allows for the possibility that a square root can be positive or negative. In the physics context all these square roots are positive. Is there some simple way to induce Maple...

"Is this matrix primitive?": just an idea

Axel Vogt — Fri, 05 Apr 2013 20:34:37 Z

Since it is not possible for me to reply directly in that new Maple Primes:
I branched. Feel free to re-join for a reasonable structure. What a mess.

http://www.mapleprimes.com/questions/145527-Is-This-Matrix-Primitive

I am rusty on such (may be it is 'obvious' via Lie theory). Your group is just the
group of invertible matrices over the integers (this follows from algebra). And as

Is this matrix primitive?

Markiyan Hirnyk — Fri, 05 Apr 2013 09:02:47 Z

   Let GL(2,Z) be the group of all the matrices of dimension 2 over the integers with the determinant equal to +/-1.
   A matrix M in GL(2,Z) is called primitive if M is not equal to K^n for any K in GL(2,Z) and any positive integer n >= 2.
   Is the matrix M:= Matrix([[27,5],[11,2]]) primitive? How to determine it in Maple?

Edit. GL(2,Z) instead of UL(2,Z).

beta function vs. sine

mriedel — Thu, 21 Mar 2013 02:56:37 Z

Dear friends,

I am reporting with a brief comment concerning the integral int(1/(1+x^a), x=0..infinity) with a>=2 a real number. This was evaluated here.

Now Maple 15 (X86 64 LINUX) will quite happily compute this in its most simple form involving the sine when a is not a positive integer or a rational number. If it is, however, a beta function term results,...

The enumeration of non-isomorphic graphs.

mriedel — Sun, 03 Mar 2013 19:32:02 Z

Dear friends,

this is to share with you what a joy it was to work with Maple on the problem of enumerating non-isomorphic graphs. This problem goes back to Polya and Harary and it is a beautiful example of Polya counting, while also being of notable simplicity, so that a high school student or an undergraduate can follow it easily.

I have worked on this problem over the years, adapting my solutions in Cocoa and Lisp as I gained insights. My first attempt used...

How to find vertices of an equilateral triangle knowing coordinates of centroid?

toandhsp — Thu, 24 Jan 2013 15:57:10 Z

I want to find a triangle with the vertices A(x1, y1, z1), B(x2, y2, z2), C(x3, y3, z3) knowing that the point G(1,1,1) is centroid of the triagle ABC and x1, y1, z1, x2, y2, z2, x3, y3, z3 are integer numbers, but I can not find. How do I tell Maple to do that?

Fine $a_{n}$ of sequence (Could you do more clearly?)

yangtheary — Fri, 30 Nov 2012 17:07:57 Z

Fine of sequence

Solving equation system over the integers (mod m)

ozkan — Wed, 14 Nov 2012 17:04:22 Z

Hello, I have a set of equations, and I want to solve it over the integers (mod 13). But msolve command fails. Here is my code:

eq:={a4*a1-11, a4*a2-12, a4*a3-6, a5*a1-3, a5*a2-8, a5*a3-4, a6*a1-2, a6*a2-1, a6*a3-7};
msolve(eq,13);

It fails, but I can solve it manually. Here is a solution:

a4*a1 = 11 => a4:=1 and a1:=11

a4*a2 = 12 => a2:=12

a4*a3 = 6 => a3:=6

a5*a1 = 3 => a5:=3/11 mod 13 = 5

a5*a2 = 8 => a2:=8/5 mod 13 = 12

Sequence (Could you explain to me? )

yangtheary — Sat, 22 Sep 2012 14:54:50 Z

Fine $a_{n}$ of sequence 2 , 3 , 6 , 7 , 10 , 11 , 14 , 15,...

Return Values in Procedures

CodeKingPlusPlus — Wed, 19 Sep 2012 22:07:26 Z

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

Length of the medians are integral numbers

toandhsp — Sat, 15 Sep 2012 04:48:56 Z

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

Coordinates of the center circle circumscribed triangle are integer numbers

toandhsp — Thu, 30 Aug 2012 08:47:30 Z

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 in this pattern?

maddiepaige97 — Wed, 15 Aug 2012 21:21:39 Z

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

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

Scaling the rows of a Matrix in a particular way

gauglertodd — Wed, 01 Aug 2012 14:23:38 Z

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.

integer solution

toandhsp — Tue, 24 Jul 2012 16:08:10 Z

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.