# Items tagged with algebraalgebra Tagged Items Feed

### How to put linear algebra command in a function...

Yesterday at 11:36 AM
1 1

Hello,
my question may be simple but I don't find the answer in any help guide.
when I define a function I cannot use a linearalgebra expression such as Trace.
Here is an example of what I would like to do:

If anyone can help me...
Thank you

### How to write a PDE system in a Weyl Algebra?...

December 03 2013
3 7

I have been struggling (reading Ore/Weyl Algebra documentation) to understand how to input a PDE system with polynomial coeff. in Weyl algebra notation so I can compute a Groebner basis for it. I would be very grateful if someone could  show, using the simple example below, which differential operators in Ore_algebra[diff_algebra] should one declare to express the system in Weyl algebra notation. The systems I'm working are more complicated but all have many dependent variables, f and g functions in this example:

pdesys:= [ x*diff( f(x,y,z),x)- z*diff( g(x,y,z),y) = 0, (x^2-y)*diff( f(x,y,z),z)- y*diff( g(x,y,z),z) = 0 ]

### How to deal with formal parameters in linear syste...

November 14 2013
2 0

Hi,

I have a Matrix whose entries are polynomials in several formal parameters (the matrix is sparse and the polynomials are rather simple, though inverses of the parameters may also arise).
Then, when I compute the kernel with LinearAlgebra-NullSpace, maple naturally gives a basis of solutions over the same ring of polynomials.

Now for some reason there are some parameters that I don't want to see in the solutions (all but two of them, actually).

How can I compute the part of the kernel that lives in $\mathbb{Z}[a,a^{-1}, b,b^{-1}]$, i.e. that involves only the first two parameters?

Thank you,

NoThik

Edit : the coefficients of the polynomials are integers, and I expect the kernel elements to have integer coefficients as well.

### assist with algebra problems...

November 10 2013
0 3

4(x-7) =6

(2x+3)(2x2-5x-3)=0

### Cryptography inverse matrix (Matriz inverza a la c...

November 09 2013 Maple 17
0 2

La aplicacion de las matrices en su más claro ejemplo, dirigido explicitamente a la criptografia; solo hay que tener conocimiento de algebra de matrices y calculo de matriz inversa. (versión español).

The application of the matrices in its most obvious example, explicitly directed to cryptography; just have to have knowledge of matrix algebra and inverse matrix calculation. (version english).

Criptografia.mw

Lenin Araujo Castillo

Physics Pure

Computer Science

### Creating Sliders...

November 03 2013
1 6

I am coming back to maple after being years out of it (Maple 9). I am writing a paper in class of how to use Maple with Algebra. I would like to create a document so that students can manipulate the graph of  and se how parameters a, h and k effect the function.  However, I can't seem to figure out how to create a slider linked with each parameter so students can manipulate it.

Is this possible? Any help wold be great!

Nicholas

### Transposing this formula in terms of...

October 31 2013
0 1
1.   The formula to calculate a length of rafter may be given as

Length of rafter = √ (rise)squared + (run)squared

(The whole of the RHS has been square rooted but cant type that symbol)

Transpose this equation and express in terms of the rise. Describe each stage so as to clearly identify what you have done.  Using this new equation calculate the rise if the length of the rafter is 7m and the run is 6. Write your answer to 3 s.f.

If anyone has any ideas or could help it would be really appreciated. Thanks.

### computer algebra develop an algorithm for computin...

October 13 2013
0 1

(i)develop an algorithm for computing f¡ÊF[x,y],F a field,where the degree of f in y is less than n and and f(x,ui)=vi; for i=0,1......,n-1, for distinct ui∈F,and arbitrary Vi∈F[x].showthat f is unique.

(ii) assuming that the degree of each Vi is less than m, what is the computing time of your algorithm (in term of m and n)?

(iii) computer f∈ F[11][x,y]such thatf(x,0)=x^2+7,f(x,1)=x^3+2*x+3,f(x,2)=x^3+5.

### Let F[7]=Z[7 ]be the finite field with 7 elements ...

October 13 2013
0 1

> 1) letJ subset F[7][x] be the set of all polynomials h in F[7][x] sloving the interpolation problem h(0);
=1,h(1)=5,h(6)=2. computer the unique polynomial f∈J of least degree.

2) find a surjective ring homomorphism ×:F[7][x]->F[7]^(3) such that Ker×=={rm:r∈F[7][x]};and computer ×(f)and×(x^2+3*x+2).

3) show thatJ=f+Ker×={f+rm:r∈ F[7][x]}.

October 12 2013
1 1

### Cubic Equation...

September 17 2013
0 1

If $x_{1},x_{2},x_{3}>0$ are the roots of the equations $ax^3+bx^2+cx+d=0$.
Prove that min

### How to write standard decomposition of a polynomia...

August 31 2013
2 1

Let $F, f_1, \ldots f_5$ be polynomials in $\mathbb{Z}_p[r,s,t,u,v]$, the ring of polynomials in 5 variables over the integers modulo an odd prime $p$. By forming the ideal $J:=<>$ I can test whether $F$ is a member of $J$. Indeed $F$ is a member of $J$ and so I know there exists polynomials $a_1,\dots,a_r \in \mathbb{Z}_p[r,s,t,u,v]$ such that $$F = a_1f_1+\dots+ a_rf_r$$ My question is how to explicitly compute $a_1,\dots,a_r$ in Maple, or Sage if you prefer. Thank...

### Why isn't -b+sqrt(b^2)=0?...

August 19 2013
1 3

I tried the following, but did not get 0. Why not?

>restart;

>b:=3*beta*Pi*(3-4*cos(z)+cos(2*z))/(16*z);

>-b+sqrt(b^2)

I know I can do this by hand, but this is part of a larger equation which I narrowed down to this issue.

### the nine digit pi approximation challenge...

July 19 2013 Maple
6 0

Greetings to all.

A recent post at math.stackexchange.com asked for good approximations to pi using the nine nonzero digits, the four arithmetic operations and exponentiation. The problem definition definitely suggests a computational solution, which is actually non-trivial because the search space of all legal mathematical expressions over the nine digits and with the aforementioned operations is so huge that it cannot possibly be searched exhaustively.

### convert to vector mode...

July 01 2013
0 2

i had 3 nonlinear equations and i want to convert them to the form of multiplications of a MATRIX in a VECTOR, but none of these two methods give me the right answer,what should i do?

#method one#

restart:
with(LinearAlgebra):
eq1:=a[1]+a[2]*a[3]^2*a[1]+a[2]*a[3]-a[1]^2:
eq2:=a[3]+a[1]^3+a[2]*a[3]+a[2]^2-a[1]^2:
eq3:=a[1]^3+a[2]^3+a[1]*a[2]*a[3]+a[1]*a[2]-a[3]:
for i to 3 do
B || i := eq || i ; K || i := Vector[row](3):
for j to 3 do

 1 2 3 4 5 6 7 Last Page 1 of 15
﻿