Ruffini-Horner Algorithm for Complex Arguments

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

Suppose we need to calculate a value of the polynomial with real coefficients for the complex argument . We divide the polynomial by , where and . The remainder is then a linear function and the value of the polynomial is the value of the remainder. In the table, that is the value at the bottom right.


The table is defined as follows, where the last row is the sum of the higher rows:


Contributed by: Izidor Hafner (June 2017)
Open content licensed under CC BY-NC-SA



According to [1, p. 1034] this is called the Collatz contribution.


[1] D. Kurepa, Higher Algebra, Book 2 (in Croatian), Zagreb: Skolska knjiga, 1965.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.