polfact

Arguments

p

polynomial with real coefficients.

f

row vector [f0 f1 ... fn] of polynomials with real coefficients, such that p=prod(f). f0=f(1) is a constant polynomial. f(2:$) are polynomials of degree 1 or 2.

The coefficients of f polynomials are computed with a relative uncertainty of %eps1/degree(p).

Examples

x = poly(0,"x");
%eps^[1/3 1/7]

p = (1-x)^3
f = polfact(p)'
prod(f)

p = (1+x)^7
f = polfact(p)'
prod(f)

--> %eps^[1/3 1/7]
 ans  =
   0.0000061   0.0058047

--> p = (1-x)^3
 p  =
  1 -3x +3x² -x³

--> f = polfact(p)'
 f  =
  -1
  1.0000086 -2.0000086x +x²
  -0.9999914 +x

--> prod(f)
 ans  =
  1 -3x +3x² -x³


--> p = (1+x)^7
 p  =
  1 +7x +21x² +35x³ +35x⁴ +21x⁵ +7x⁶ +x⁷

--> f = polfact(p)'
 f  =
  1
  1.0092002 +x
  1.0114552 +2.011371x +x²
  0.9959088 +1.9958255x +x²
  0.9836859 +1.9836034x +x²

--> prod(f)
 ans  =
  1 +7x +21x² +35x³ +35x⁴ +21x⁵ +7x⁶ +x⁷

See also

• factors — factorization in ℝ of a polynomial or a rational fraction
• roots — roots of a polynomial
• lcm — least common (positive) multiple of integers or of polynomials
• cmndred — common denominator form