/usr/share/axiom-20170501/src/algebra/CPIMA.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 | )abbrev package CPIMA CharacteristicPolynomialInMonogenicalAlgebra
++ Author: Claude Quitte
++ Date Created: 10/12/93
++ Description:
++ This package implements characteristicPolynomials for monogenic algebras
++ using resultants
CharacteristicPolynomialInMonogenicalAlgebra(R,PolR,E) : SIG == CODE where
R : CommutativeRing
PolR : UnivariatePolynomialCategory(R)
E : MonogenicAlgebra(R, PolR)
SIG ==> with
characteristicPolynomial : E -> PolR
++ characteristicPolynomial(e) returns the characteristic polynomial
++ of e using resultants
CODE ==> add
Pol ==> SparseUnivariatePolynomial
import UnivariatePolynomialCategoryFunctions2(R, PolR, PolR, Pol(PolR))
XtoY(Q : PolR) : Pol(PolR) == map(x+->monomial(x, 0), Q)
P : Pol(PolR) := XtoY(definingPolynomial()$E)
X : Pol(PolR) := monomial(monomial(1, 1)$PolR, 0)
characteristicPolynomial(x : E) : PolR ==
Qx : PolR := lift(x)
-- on utilise le fait que resultant_Y (P(Y), X - Qx(Y))
return resultant(P, X - XtoY(Qx))
|