Polynomial Transformations
Transform a polynomial, find a greatest common factor, or determine the multiplicity of a root.
polytrans(p, q) polygcf(p, q, tol = 1e-12)
p, q |
vectors representing two polynomials. |
tol |
tolerance for coefficients to tolerate. |
Transforms polynomial p replacing occurences of x with
another polynomial q in x.
Finds a greatest common divisor (or factor) of two polynomials. Determines the multiplicity of a possible root; returns 0 if not a root. This is in general only true to a certain tolerance.
polytrans and polygcf return vectors representing polynomials.
rootsmult returns a natural number (or 0).
There are no such functions in Matlab or Octave.
# (x+1)^2 + (x+1) + 1 polytrans(c(1, 1, 1), c(1, 1)) #=> 1 3 3 polytrans(c(1, 1, 1), c(-1, -1)) #=> 1 1 1 p <- c(1,-1,1,-1,1) #=> x^4 - x^3 + x^2 - x + 1 q <- c(1,1,1) #=> x^2 + x + 1 polygcf(polymul(p, q), q) #=> [1] 1 1 1 p = polypow(c(1, -1), 6) #=> [1] 1 -6 15 -20 15 -6 1 rootsmult(p, 1) #=> [1] 6
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