MathAction SandBox Qubic

Topics

axiom
digits 20

axiom
-- n:=x^3+a1*x^2+a2*x+a3 ::Polynomial Fraction Integer

Q:=(3*a2-a1^2)/9

Type: Polynomial Fraction Integer

axiom
R:=(9*a1*a2-27*a3-2*a1^3)/54

Type: Polynomial Fraction Integer

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S:=(R+(Q^3+R^2)^(1/2))^(1/3)

Type: Expression Integer

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T:=(R-(Q^3+R^2)^(1/2))^(1/3)

Type: Expression Integer

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x1:=S+T-a1/3

Type: Expression Integer

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x2:=-(S+T)/2-a1/3 + %i*sqrt(3)*(S-T)/2

Type: Expression Complex Integer

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x3:=-(S+T)/2-a1/3 - %i*sqrt(3)*(S-T)/2

Type: Expression Complex Integer

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a5:=x^3+a1*x^2+a2*x+a3 ::Polynomial AlgebraicNumber

Type: Polynomial AlgebraicNumber

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a6:=(x-x11)  ::Polynomial AlgebraicNumber;

Type: Polynomial AlgebraicNumber

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

Type: Record(quotient: Polynomial AlgebraicNumber,remainder: Polynomial AlgebraicNumber)

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a77:=a7.quotient;

Type: Polynomial AlgebraicNumber

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a78:=a7.remainder;

Type: Polynomial AlgebraicNumber

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qu1 :=eval(a77,x11,x1)

Type: Expression Integer

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rem1:=eval(a78,x11,x1)

Type: Expression Integer

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eval(rem1,[a3=1.0, a2=1.0, a1=1.0])

Type: Expression Float

... --wyscc, Mon, 14 Nov 2005 02:53:03 -0600 reply

How about this:

axiom
pkg:= SOLVEFOR(UP('x,Complex Float), Complex Float)

Type: Domain

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root := aCubic(1,1,1,1)$pkg

Type: Complex Float

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qfactor := monicDivide(x^3 + x^2 + x + 1,x - root)

Type: Record(quotient: UnivariatePolynomial(x,Float),remainder: UnivariatePolynomial(x,Float))

axiom
qfactor.quotient

axiom
qfactor.remainder

... --unknown, Mon, 30 Jan 2006 11:54:36 -0600 reply