Equidistributed sequences related to pure morphic words

This page and the embedded Sage code are written by Mélodie Andrieu for the project "Morphic words and equidistributed sequences" by M. Andrieu and A. Frid. For detailed explanations and proofs, see the arXiv preprint.

First, click the “Evaluate” button below to load the functions.

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As you noticed, the inputs are:

- l --> the length of the numerical sequences

- phia (respectively phib) --> the image of a (respectively b) by the morphism.

2) You may want to try the Fibonacci word:

The question mark at the end of the numbers means that they live in the SageMath's real algebraic field - only a finite number of digits can be displayed. If you want more (or less) digits, say 4, you can add: digits=4 in the inputs.

3) Now, feel free to choose any morphism.

Computation may take a while for some specific morphisms, e.g.: a->ababba, b->aabbaa. Most of time, this is due to our resort to the square morphism, and the time needed to then compute the circularity length (for which we have no upper boundary.) SageMath free servers may interrupt the computation after 2 minutes. When this happens, don't forget to reload the functions (first box.)

This software has been made with SageMath, which is an open-source mathematics software system, based on Python language. It is embedded into this webpage using SageMathCell.

Please note that the computations are provided by free servers. To keep on your experiments, you can download the functions here and run them on your own SageMath distribution.