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Charpoly

compute characteristic polynomial function over a ring of characteristic p

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Charpoly(A,x) mod p

Parameters

A

-

square Matrix

x

-

name; specifies the variable in the characteristic polynomial

p

-

non-zero integer; specifies the characteristic of the ring

Description

• 

Given an n by n matrix A over a ring F of 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 GF(p), p a prime, Maple uses an On3 algorithm. Otherwise, Maple uses an On4 division free algorithm.

Examples

AMatrix2,1,0,1,2,1,0,1,2

A210121012

(1)

CharpolyA,xmod3

x3+x+2

(2)

p3:aliasa=RootOfx2+1modp:

AMatrix1,a,0,a,1,0,0,a

A1a0a1000a

(3)

CCharpolyA,xmodp

Cx3+22+ax2+21+ax+a

(4)

FactorCmodp

x+a+2x+2ax+2+2a

(5)

AMatrix1,t,1t,1t,1,t,t,1t,1

A1t1t1t1tt1t1

(6)

CharpolyA,xmod2

x3+x2+t6+1t3

(7)

See Also

Factor

LinearAlgebra[CharacteristicPolynomial]

LinearAlgebra[Modular]

mod

Modular[CharacteristicPolynomial]

RootOf

 


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