polytrans, polygcf | R Documentation |
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.
polyval
# (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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