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# Edit detail for SandBox Qubic revision 1 of 1

 1 Editor: Time: 2007/11/18 18:32:43 GMT-8 Note:

changed:
-
\begin{axiom}
digits 20
-- n:=x^3+a1*x^2+a2*x+a3 ::Polynomial Fraction Integer

Q:=(3*a2-a1^2)/9
R:=(9*a1*a2-27*a3-2*a1^3)/54
S:=(R+(Q^3+R^2)^(1/2))^(1/3)
T:=(R-(Q^3+R^2)^(1/2))^(1/3)
x1:=S+T-a1/3
x2:=-(S+T)/2-a1/3 + %i*sqrt(3)*(S-T)/2
x3:=-(S+T)/2-a1/3 - %i*sqrt(3)*(S-T)/2

a5:=x^3+a1*x^2+a2*x+a3 ::Polynomial AlgebraicNumber
a6:=(x-x11)  ::Polynomial AlgebraicNumber;

a7:=monicDivide(a5,a6,x) ;

a77:=a7.quotient;
a78:=a7.remainder;

qu1 :=eval(a77,x11,x1)
rem1:=eval(a78,x11,x1)
eval(rem1,[a3=1.0, a2=1.0, a1=1.0])
\end{axiom}

From wyscc Mon Nov 14 02:53:03 -0600 2005
From: wyscc
Date: Mon, 14 Nov 2005 02:53:03 -0600
Subject:
Message-ID: <20051114025303-0600@page.axiom-developer.org>

\begin{axiom}
pkg:= SOLVEFOR(UP('x,Complex Float), Complex Float)
root := aCubic(1,1,1,1)$pkg qfactor := monicDivide(x^3 + x^2 + x + 1,x - root) qfactor.quotient qfactor.remainder \end{axiom} From unknown Mon Jan 30 11:54:36 -0600 2006 From: unknown Date: Mon, 30 Jan 2006 11:54:36 -0600 Subject: Message-ID: <20060130115436-0600@wiki.axiom-developer.org> $$myeq := (x-9)^3-(x/2)^2+13*x$$  fricas digits 20  (1) Type: PositiveInteger? fricas -- n:=x^3+a1*x^2+a2*x+a3 ::Polynomial Fraction Integer Q:=(3*a2-a1^2)/9  (2) Type: Polynomial(Fraction(Integer)) fricas R:=(9*a1*a2-27*a3-2*a1^3)/54  (3) Type: Polynomial(Fraction(Integer)) fricas S:=(R+(Q^3+R^2)^(1/2))^(1/3)  (4) Type: Expression(Integer) fricas T:=(R-(Q^3+R^2)^(1/2))^(1/3)  (5) Type: Expression(Integer) fricas x1:=S+T-a1/3  (6) Type: Expression(Integer) fricas x2:=-(S+T)/2-a1/3 + %i*sqrt(3)*(S-T)/2  (7) Type: Expression(Complex(Integer)) fricas x3:=-(S+T)/2-a1/3 - %i*sqrt(3)*(S-T)/2  (8) Type: Expression(Complex(Integer)) fricas a5:=x^3+a1*x^2+a2*x+a3 ::Polynomial AlgebraicNumber  (9) Type: Polynomial(AlgebraicNumber?) fricas a6:=(x-x11) ::Polynomial AlgebraicNumber; Type: Polynomial(AlgebraicNumber?) fricas a7:=monicDivide(a5,a6,x) ; Type: Record(quotient: Polynomial(AlgebraicNumber?),remainder: Polynomial(AlgebraicNumber?)) fricas a77:=a7.quotient; Type: Polynomial(AlgebraicNumber?) fricas a78:=a7.remainder; Type: Polynomial(AlgebraicNumber?) fricas qu1 :=eval(a77,x11,x1)  (10) Type: Expression(Integer) fricas rem1:=eval(a78,x11,x1)  (11) Type: Expression(Integer) fricas eval(rem1,[a3=1.0, a2=1.0, a1=1.0])  (12) Type: Expression(Float) How about this: fricas pkg:= SOLVEFOR(UP('x,Complex Float), Complex Float)  (13) Type: Type fricas root := aCubic(1,1,1,1)$pkg
 (14)
Type: Complex(Float)
fricas
qfactor := monicDivide(x^3 + x^2 + x + 1,x - root)
 (15)
Type: Record(quotient: UnivariatePolynomial(x,Float),remainder: UnivariatePolynomial(x,Float))
fricas
qfactor.quotient
 (16)
Type: UnivariatePolynomial(x,Float)
fricas
qfactor.remainder
 (17)
Type: UnivariatePolynomial(x,Float)