puts the polynomial poly in Horner form.
puts poly in Horner form with respect to the variable or variable list vars.
puts the rational function poly1/poly2 in Horner form by nesting poly1 and poly2.
puts poly1/poly2 in Horner form using the variables or variable lists vars1 and vars2 for poly1 and poly2, respectively.
- When variables are not specified, HornerForm puts the polynomial or rational function into Horner form with respect to the variables identified using Variables.
Examplesopen allclose all
Basic Examples (3)
Horner form of a polynomial in x:
Put a polynomial into Horner form with respect to a given variable:
Horner form of a rational function:
Order a bivariate polynomial with respect to x then y:
With respect to y then x:
Construct a rational function in two variables:
Convert the function to Horner form:
Convert to Horner form using y before x in the numerator:
Generalizations & Extensions (1)
An expression with rational exponents:
Improve speed and stability for numeric evaluation of large polynomials:
Properties & Relations (2)
Horner form of a rational function is the ratio of Horner forms:
Obtained as a ratio of Horner forms:
HornerForm recursively factors out powers of variables:
Collect groups based on powers of variables:
Factor gives the factored form:
Possible Issues (1)
Exponents must be integers or rationals: