coreli-tcosmo 0.0.2
The Collatz Research Library provides tools for experimenting and testing hypothesises related to the Collatz Process.
Requires Python: >=3.6

# Coreli

Coreli stand for "Collatz Research Library". [Archangelo Corelli](https://www.youtube.com/watch?v=5BPhkY6xIP8).      

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](https://dna.hamilton.ie/tsterin/coreli/docs/).

# References

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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.