[Top][All Lists]
[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
Re: [Axiom-developer] evaluate a polynom for a matrix.
From: |
Martin Rubey |
Subject: |
Re: [Axiom-developer] evaluate a polynom for a matrix. |
Date: |
01 Apr 2007 20:39:19 +0200 |
User-agent: |
Gnus/5.09 (Gnus v5.9.0) Emacs/21.4 |
Please direct questions of this kind to address@hidden
Francois Maltey <address@hidden> writes:
> Hello,
>
> Let P in Ring[X] and M in SquareMatrix(Ring)
>
> The mathematics evaluate P(M)
> by sum (ak*M^k, k=0..deg P) in SquareMatrix(Ring)
> where P = sum (ak*X^k, k=0..deg P)
>
> How can I do this in axiom.
-- work in SquareMatrix(n, FRAC POLY INT)
n := 4;
SM ==> SquareMatrix(n, FRAC POLY INT)
--
-- Create a generic matrix
--
M: SM := matrix [[a[i,j] for j in 1..n] for i in 1..n]
-- Create an identity matrix
I: SM := 1;
-- Computes determinant (M - x*Id) where M is the previous generic matrix.
-- note that characteristicPolynomial would do this for youm however, for some
-- strange reason, it accepts an element of Matrix R instead of SquareMatrix R.
P := determinant (M - x * I)
-- Now evaluate P(M). We find the (0)_4 matrix. Note that you can coerce only
-- to a univariate polynomial, since matrix multiplication is not
-- commutative...
(P::UP(x, SM))(M)