BUILT-IN MATHEMATICA SYMBOL

HornerForm

HornerForm[poly]
puts the polynomial poly in Horner form.

HornerForm

puts poly in Horner form with respect to the variable or variable list vars.

HornerForm

puts the rational function

in Horner form by nesting

and

.

HornerForm

puts

in Horner form using the variables or variable lists

and

for

and

, respectively.

MORE INFORMATION

When variables are not specified, HornerForm puts the polynomial or rational function into Horner form with respect to the variables identified using Variables.

EXAMPLES

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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:

Horner form of a polynomial in x:

In[1]:=

Out[1]=

Put a polynomial into Horner form with respect to a given variable:

In[1]:=

Out[1]=

Horner form of a rational function:

In[1]:=

Out[1]=

Scope (2)

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:

Applications (1)

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:

Neat Examples (1)