Items tagged with decomposition


Q1: Pascal’s Matrix of order n is given by:
Sij =(i + j)!/ i!*j!
Use Mable to produce Pascal’s Matrix of order 8.

Q2: Study the Matrix decomposition (i.e. QR, LU, and LLT), then use Maple to produce these decompositions for a random Matrix of order 6.

Q3: Write one paragraph of your own to explain Moore-Penrose Inverse of a Matrix. Use Maple to find Moore-Penrose Inverse for a random Matrix of order 8.

Q4: Use Maple to find Jordan Canonical form for a random Matrix of order 10.

Q5: Use the seq command to generate the triple [i,j,k] for all possible values for 1 ≤ i,j,k ≤ 10, then plot this triple. i.e. Use nested seq .

Q6: Let F[n] be the set:
F[n] = {p / q: 1 ≤ q ≤ n,p ≤ p ≤ q}
Use Maple to find F[6].

I have a vector x of this type:

x :=Vector[column]([A__11*u__1+A__12*u__2+...+A__1m*u__m,




If I define u:=Vector[column]([u__1,u__2,...,u__m]), then it is clear that the equation has the form x=A*u.

I want to extract the matrix A, for the given vectors x and u.

IMPORTANT: I know I could create a loop (i=1 to m) and set u__i=1 and all other u__j=0 (for all j not equal i) and then reconstruct each column by this method, but it seems to be a overkill for such an easy problem.

I would be glad, if someone could show me a method how one can achive this in maple.

Has anyone been able to do multivariate partial fraction decomposition in maple (here is a paper introducing the idea

I often find maple generating complicated rational functions that it would be nice to visualise in other ways

Here is an example of such a function if anyone wants to have a play:





Dear all,

I need you help to finish some steps of this idea to approximate the roots of a given equation (polynom). Thanks in advance for your help. 

I have a sturm sequence, I would like to use Bisection method to approximation the roots using Sturm decomposition of my polynom. For example, my polynom is  P=x^6-4*x^3+x-2

s := sturmseq(x^6-4*x^3+x-2,x);

sturm(s,x,-2,2); # The number of roots in the interval (-2,2)

Here, i would like to find the roots in (-M,M) :

Bounding all roots in [-M,M] where M = max{1, sum^(n-1) |ai|/an}.

f0 = f, f1 = f', then use -remainder,

I know that  sturm(s,x,-M,M); gives the number of roots in (-M,M)  but is it possible to use the variation of sign like :

      gives a Sturm sequence for f.

      variation of sign, varsign(a0,a1,...,ar).

      Thm: (Sturm) varsign(f0(alpha),...,fr(alpha)) - varsign(f0(beta),..., fr(beta))

      is the number of distinct roots of f in [alpha,beta].

then i would like Isolating roots of rational polynomials


Method: reduce, remove rational roots, divide and conquer in [-M,M],

      then use bisection  in disjoint closed intervals ctg one root each

 Bisection method :

      Setup: f(a) < 0, f(b) > 0 (or conversely).
      Repeated subdivision of [a,b] guaranteed to get close to a root.

      Error analysis: for error eps, solve (b-a)/ 2^(n+1)  < tol for n. where tol is the tolerance


I have a 30-dimensional, semisimple Lie algebra which I would like to know the decomposition of (and decomposable it must certainly be, as no simple Lie algebra has dimension 30). The function DifferentialGeometry:-LieAlgebras:-Decompose is, I guess, the proper command to use. Unfortunately, on my computer, an Intel Core i3 with 4 GB RAM, it seems to drag on forever. Therefore, I have the following two questions:

1.) Is it possible to gain some useful insight into any progress, while the calculation goes on? To have some status bar, so to speak? The amount of information should not be overwhelming, however.

2.) Does there exist some smarter way of doing a decomposition? Perhaps just a partial one?

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