charPoly(Matrix)

Synopsis

Function: charPoly
Usage:

charPoly(M)
Inputs:
- M, a matrix
Outputs:
- a ring element, the characteristic polynomial ofM

Description

This computes the characteristic polynomial of M

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : F = {y^2-x^2-1,x-y^2+4*y-2}

         2    2         2
o2 = {- x  + y  - 1, - y  + x + 4y - 2}

o2 : List

i3 : I = ideal F

               2    2         2
o3 = ideal (- x  + y  - 1, - y  + x + 4y - 2)

o3 : Ideal of R

i4 : S = R/I

o4 = S

o4 : QuotientRing

i5 : M = last regularRep(y)

o5 = | 0 0 -3 -2 |
     | 0 0 -1 1  |
     | 0 1 4  0  |
     | 1 0 4  4  |

              4        4
o5 : Matrix QQ  <--- QQ

i6 : charPoly(M)

      4     3      2
o6 = Z  - 8Z  + 19Z  - 16Z + 5

o6 : QQ[Z]