ufs_rootsystem, ufs_rootlength - calculate a rootsystem of a quadratic form

Calling sequence:

ufs_rootsystem(M)

ufs_rootlength(M)

Parameters:

M - a symmetric matrix definig a unit form

Synopsis:

ufs_rootsystem calculates a root system of the quadratic form associated to the matrix M. A rootsystem is a set of vectors { ,.., } such that any vector with may be written as or for some and some radical vector .

ufs_rootlength gives just the length of such a root system

The argument must be a symmetric matrix definig a unit form, otherwise an error occurs.

Example:

> A:=matrix([[2,1,1,0,0],[1,2,1,1,0],[1,1,2,1,1],[0,1,1,2,1],[0,0,1,1,2]]);

> ufs_rootsystem(A);

> ufs_rootlength(A);