PisotArith v.1.3.9/CGI


On this page, you can find CGI front-end to my library PisotArith. It performs arithmetic operations (addition, subtraction and multiplication) with beta-expansions in the numeration system with base beta - Pisot number.

How to use the programme

Because the base of the system can be greater than 9, the coefficients in the expansions can have also two or more digits. Therefore the coeficients have to be entered separated by gaps for the program be able to differentiate them.

Example of correctly entered expansion: 21 0 0 21 . 1 0 3

If some of the input numbers are eventually periodic, use '[' and ']' to identificate the period. None that these brackets have to be separated by gaps on both sides too.

Example of correcty entered eventually periodic Renyi development: 3 [ 1 2 ]

The numeration system can be also specified using the minimal polynomial of beta instead of the Renyi development. In that case, only the coefficients have to be entered, seperated by gaps, but with no gap between coefficient and possible '-' sign in front of it.

Example of correcty entered minimal polynomial: 1 -1 -1
This string will be interpreted as x2 - x - 1, i.e. as a minimal polynomial of Golden mean.


If you want to use the batch version of the library (for performing large amounts of computation in one batch), please contact me via email.

The numeration system

Renyi development Minimal polynomial

The expansions

Number x:
Number y:

Type of operation

Addition Multiplication Subtraction