zeckendorf – Knuth Fibonacci multiplication, Zeckendorf and Bergman representations of big integers

This package extends the \xinteval syntax to do algebra in Q(phi) (where phi is the golden ratio), and compute Fibonacci numbers, Zeckendorf representations of positive integers and Bergman phi-representations of the positive elements of Z[phi]. The $ character is used to compute the Knuth Fibonacci multiplication.

The package can be used either in a LaTeX document, or with Plain ε-TeX, or on the command line in an interactive session using ε-TeX.

Being based upon xintexpr, it allows to compute with “arbitrarily” big integers, the reasonable use being with integers of at most a few hundreds of digits.

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