coreli 0.0.6

The Collatz Research Library provides tools for experimenting and testing hypothesises related to the Collatz Process.

Coreli

Coreli stand for "Collatz Research Library". Archangelo Corelli.

The Collatz process is a very simple to describre: take any number x, if even do x/2 if odd do (3x+1)/2. Repeat.

Starting from 5: [5, 8, 4, 2, 1, 2, 1, 2, 1, ...].

Starting from 43: [43, 65, 98, 49, 74, 37, 56, 28, 14, 7, 11, 17, 26, 13, 20, 10, 5, 8, 4, 2, 1, 2, 1, 2, 1, ...].

The Collatz Conjecture, unresolved since the 60s, states that, any stritcly positive natural numbers reaches 1.

The appararent simplicity of this problem hides a very difficult mathematical problem. Actually, we believe that this problem has a lot to do with Computer Science. That's why we created Coreli, a library for experimenting and testing hypothesises regarding the Collatz process.

Doc

Coreli's doc is hosted here.

Dev: deploy to pypi

python setup.py sdist
twine upload dist/*

References

• David Applegate and Jeffrey Lagarias. Density bounds for the 3x + 1 problem. ii. krasikov inequalities. Mathematics of Computation - Math. Comput., 64:427–438, 01 1995. doi: 10.2307/2153346.

• Jean Berstel, Jr. and Christophe Reutenauer. Rational Series and Their Languages. Springer- Verlag, Berlin, Heidelberg, 1988.

• Jose Capco. Odd Collatz Sequence and Binary Representations. Preprint, March 2019. URL: https://hal.archives-ouvertes.fr/hal-02062503.

• Livio Colussi. The convergence classes of Collatz function. Theor. Comput. Sci., 2011. URL: https://doi.org/10.1016/j.tcs.2011.05.056, doi:10.1016/j.tcs.2011.05.056.

• J.H Conway. Unpredictable iterations. Number Theory Conference, 1972. Zachary Franco and Carl Pomerance. On a Conjecture of Crandall Concerning the qx + 1 Problem. Mathematics of Computation, 64(211):1333–1336, 1995. URL: http://www.jstor. org/stable/2153499.

• Patrick Chisan Hew. Working in binary protects the repetends of 1/3h : Comment on Colussi’s ’The convergence classes of Collatz function’. Theor. Comput. Sci., 618:135–141, 2016. URL: https://doi.org/10.1016/j.tcs.2015.12.033, doi:10.1016/j.tcs.2015.12.033.

• Pascal Koiran and Cristopher Moore. Closed-form analytic maps in one and two dimen- sions can simulate universal Turing machines. Theoretical Computer Science, 210(1):217– 223, January 1999. URL: https://doi.org/10.1016/s0304-3975(98)00117-0, doi:10.1016/ s0304-3975(98)00117-0.

• Stuart A. Kurtz and Janos Simon. The Undecidability of the Generalized Collatz Problem. In TAMC 2007, pages 542–553, 2007. URL: https://doi.org/10.1007/978-3-540-72504-6_49, doi:10.1007/978-3-540-72504-6_49.

• Jeffrey C. Lagarias. The 3x + 1 problem and its generalizations. The American Mathematical Monthly, 92(1):3–23, 1985. URL: http://www.jstor.org/stable/2322189.

• Jeffrey C. Lagarias. The 3x+1 problem: An annotated bibliography (1963–1999) (sorted by author), 2003. arXiv:arXiv:math/0309224.

• Jeffrey C. Lagarias. The 3x+1 problem: An annotated bibliography, ii (2000-2009), 2006. arXiv:arXiv:math/0608208.

• Kenneth Monks. The sufficiency of arithmetic progressions for the 3x + 1 conjecture. Proceed- ings of the American Mathematical Society, 134, 10 2006. doi:10.2307/4098142.

• Terence Tao. Almost all orbits of the collatz map attain almost bounded values, 2019. arXiv:arXiv:1909.03562.

• Riho Terras. A stopping time problem on the positive integers. Acta Arithmetica, 30(3):241–252, 1976. URL: http://eudml.org/doc/205476.

• Günther Wirsching. On the combinatorial structure of 3n + 1 predecessor sets. Discrete Math- ematics, 148(1-3):265–286, January 1996. URL: https://doi.org/10.1016/0012-365x(94)00243-c, doi:10.1016/0012-365x(94)00243-c.

• Günther J. Wirsching. The dynamical system generated by the 3n + 1 function. Springer, Berlin New York, 1998.