JORDANSYMBOLIC _ _ _ _ _ _ _ _ _ _ _ _ operator

The operator jordansymbolic computes the Jordan normal form J of a matrix (A say). It returns {J,L,P,P^-1} where P*J*P^-1 = A. L = {ll,mm} where mm is a name and ll is a list of irreducible factors of p(mm).

syntax:

<matrix> :- a square matrix.

Field Extensions:

By default, calculations are performed in the rational numbers. To extend this field the arnum package can be used. The package must first be loaded by load_package arnum;. The field can now be extended by using the defpoly command. For example, defpoly sqrt2**2-2; will extend the field to include the square root of 2 (now defined by sqrt2). See frobenius for an example.

Modular Arithmetic:

jordansymboliccan also be calculated in a modular base. To do this first type on modular;. Then setmod p; (where p is a prime) will set the modular base of calculation to p. By further typing on balanced_mod the answer will appear using a symmetric modular representation. See ratjordan for an example.

examples:

 a := mat((1,y),(2,5*y)); 

       [1   y ]
  a := [      ]
       [2  5*y]



 jordansymbolic(a); 

  {
   [lambda11     0    ]
   [                  ]
   [   0      lambda12]
   ,
           2
   lambda  - 5*lambda*y - lambda + 3*y,lambda,
   [lambda11 - 5*y  lambda12 - 5*y]
   [                              ]
   [      2               2       ]
   ,
   [ 2*lambda11 - 5*y - 1    5*lambda11*y - lambda11 - y + 1 ]
   [----------------------  ---------------------------------]
   [       2                              2                  ]
   [   25*y  - 2*y + 1             2*(25*y  - 2*y + 1)       ]
   [                                                         ]
   [ 2*lambda12 - 5*y - 1    5*lambda12*y - lambda12 - y + 1 ]
   [----------------------  ---------------------------------]
   [       2                              2                  ]
   [   25*y  - 2*y + 1             2*(25*y  - 2*y + 1)       ]
   }