Charpoly
compute characteristic polynomial function over a ring of characteristic p
Calling Sequence
Parameters
Description
Examples
Charpoly(A,x) mod p
A
-
square Matrix
x
name; specifies the variable in the characteristic polynomial
p
non-zero integer; specifies the characteristic of the ring
Given an n by n matrix A over a ring F of prime characteristic p, the Charpoly( A, x ) mod p calling sequence computes the characteristic polynomial of A, a monic polynomial in x of degree n over F.
For matrices over the prime field GFp, for p a prime, Maple uses an On3 algorithm. Otherwise, Maple uses an On4 division free algorithm.
A≔Matrix2,1,0,1,2,1,0,1,2
A≔210121012
CharpolyA,xmod3
x3+x+2
p≔3:aliasa=RootOfx2+1modp:
A≔Matrix1,a,0,a,1,0,0,a
A≔1a0a1000a
C≔CharpolyA,xmodp
C≔x3+22+ax2+21+ax+a
FactorCmodp
x+2+2ax+2ax+a+2
A≔Matrix1,t,1t,1t,1,t,t,1t,1
A≔1t1t1t1tt1t1
CharpolyA,xmod2
x3+x2+t6+1t3
See Also
Factor
LinearAlgebra[CharacteristicPolynomial]
LinearAlgebra[Modular]
mod
Modular[CharacteristicPolynomial]
RootOf
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