DnE (version 1.0)

Cubic: Cubic

Description

solve cubic equation.

Usage

Cubic(b)

Arguments

b

a four-dimensional vetor, its components are descending dimension coefficients of the equation.

Value

• all the solution to the equation

Details

the function is used to solve an cubic equation. the parameter of this function is the coefficients of your function. if you want to solve the equation x^3+5x^2-4x+9, then the parameter should be a<-c(1,5,-4,9)

References

the function includes some other functions which have been exsisted in R

See Also

DnE-package

Examples

require(stats)
a <- c(1,5,-4,9)
Cubic(a)
##---- Should be DIRECTLY executable !! ----
##-- ==>  Define data, use random,
##--	or do  help(data=index)  for the standard data sets.

## The function is currently defined as
function (b) 
{
    a = c(0, 0, 0)
    for (i in 2:4) {
        a[i - 1] = b[i]/b[1]
    }
    p = a[2] - a[1]^2/3
    q = a[3] - a[1] * a[2]/3 + 2 * a[1]^3/27
    if (is.complex(sqrt1(q^2/4 + p^3/27))) {
        A = (-q/2 + sqrt1(q^2/4 + p^3/27))^(1/3)
        B = (-q/2 - sqrt1(q^2/4 + p^3/27))^(1/3)
    }
    else {
        if ((-q/2 + sqrt(q^2/4 + p^3/27)) < 0) {
            A = -(-(-q/2 + sqrt(q^2/4 + p^3/27)))^(1/3)
        }
        else {
            A = (-q/2 + sqrt(q^2/4 + p^3/27))^(1/3)
        }
        if ((-q/2 - sqrt(q^2/4 + p^3/27)) < 0) {
            B = -(-(-q/2 - sqrt(q^2/4 + p^3/27)))^(1/3)
        }
        else {
            B = (-q/2 - sqrt(q^2/4 + p^3/27))^(1/3)
        }
    }
    y = A + B
    y[2] = -(A + B)/2 + sqrt(3) * (A - B) * complex(real = 0, 
        imaginary = 1)/2
    y[3] = -(A + B)/2 - sqrt(3) * (A - B) * complex(real = 0, 
        imaginary = 1)/2
    x = c(0, 0, 0)
    for (i in 1:3) {
        x[i] = y[i] - a[1]/3
    }
    print(x)
  }