compute characteristic polynomial function over a ring of characteristic p - Maple Help

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Charpoly - compute characteristic polynomial function over a ring of characteristic p

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

A:=Matrix2,1,0,1,2,1,0,1,2

A:=210121012

(1)

CharpolyA,xmod3

x3+x+2

(2)

p:=3:aliasa=RootOfx2+1modp:

A:=Matrix1,a,0,a,1,0,0,a

A:=1a0a1000a

(3)

C:=CharpolyA,xmodp

C:=x3+22+ax2+21+ax+a

(4)

FactorCmodp

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

(5)

A:=Matrix1,t,1t,1t,1,t,t,1t,1

A:=1t1t1t1tt1t1

(6)

CharpolyA,xmod2

x3+x2+t6+1t3

(7)

See Also

Factor, LinearAlgebra[CharacteristicPolynomial], LinearAlgebra[Modular], mod, Modular[CharacteristicPolynomial], RootOf


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