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Directory macros/generic/zeckendorf

README.md

Source: zeckendorf.dtx Version: 0.9c, 2025/10/17 Author: Jean-François Burnol Keywords: Zeckendorf representation; Knuth Fibonacci multiplication License: LPPL 1.3c

Aim

This package extends \xinteval's syntax:

  • The four operations are overloaded to do algebra in Q(phi), where phi is a variable standing for the golden ratio.
  • Functions are available in this syntax to compute:
    • Fibonacci numbers,
    • Zeckendorf representations of positive integers (as lists of indices),
    • Bergman phi-representations of positive elements of Z[phi] (as lists of exponents).
  • The $ character serves as infix operator computing the Knuth Fibonacci multiplication of positive integers.

The macro interface also provides conversion of integers to Zeckendorf words and Bergman phi-ary representations.

The functionalities can be used in three ways:

  • as a package: \usepackage{zeckendorf},
  • as a Plain macro file: \input zeckendorfcore.tex,
  • or interactively on the command line: etex zeckendorf. If available use rather rlwrap etex zeckendorf for a smoother experience.

The package is in alpha stage and its user interface may change in backwards incompatible ways. Of course, suggestions are most welcome.

Installation

Exert etex zeckendorf.dtx to extract macro files. To build the documentation run xelatex on the extracted zeckendorf-doc.tex, or directly on zeckendorf.dtx.

The recommended TDS structure is:

/tex/generic/zeckendorf/zeckendorfcore.tex
/tex/generic/zeckendorf/zeckendorf.tex
/tex/generic/zeckendorf/zeckendorf.sty
/source/generic/zeckendorf/zeckendorf.dtx
/doc/generic/zeckendorf/zeckendorf-doc.pdf
/doc/generic/zeckendorf/README.md

License

Copyright © 2025 Jean-François Burnol

This Work may be distributed and/or modified under the conditions of the Project Public License 1.3c. This version of this license is in

http://www.latex-project.org/lppl/lppl-1-3c.txt

and version 1.3 or later is part of all distributions of version 2005/12/01 or later.

This Work has the LPPL maintenance status "author-maintained".

The Author and Maintainer of this Work is Jean-François Burnol.

This Work consists of the main source file and its derived files

zeckendorf.dtx,
zeckendorfcore.tex, zeckendorf.tex, zeckendorf.sty,
README.md, zeckendorf-doc.tex, zeckendorf-doc.pdf

Download the contents of this package in one zip archive (213.8k).

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 document, or with Plain , or on the command line in an interactive session using .

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.

Packagezeckendorf
Version0.9c 2025-10-17
LicensesThe Project Public License 1.3c
Copyright2025 Jean-François Burnol
MaintainerJean-François Burnol
Contained inTeX Live as zeckendorf
MiKTeX as zeckendorf
TopicsArithmetic
Calculation
...
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