About
=====

The OTI numbers, and its corresponding computational implementation, were initially developed by Dr. Mauricio Aristizabal during his Ph.D. studies as he was researching the use of hypercomplex algebras and other automatic differentiation approaches to compute high-order shape derivatives in Finite Element analyses for optimization appliations. Although hypercomplex algebras like Hyperdual numbers and Multicomplex numbers were options for obtaining high-order derivatives, its exponential growth in size prevents its deployment high performance multivariate analysis. 

The focus has always been to provide support for linear-algebra applications, like the Finite Element analses, with a robust an efficient implementation of an algebra that allows arbitrary order multivariable derivatives.

The development of the library (otilib and pyoti), began in 2016 and has been actively developed by Dr. Aristizabal since then. In 2024, Samuel Roberts (PhD Student, UTSA) started contributing to the development of the library, specially integrating Fotran and C versions of the static-dense implementation of the library.


Contributors
============
The following is a list of contributors for the development of the ``otilib/pyoti`` library.

Mauricio Aristizabal,
Manuel J. Garcia,
Harry Millwater,
Samuel Roberts,
Jose-Leonel Hernandez-Estrada


Acknowledgements
================

The development of the OTIlib and pyoti libraries has been developed with support from:


- National Aeronautics and Space Administration (NASA), grant 80NSSC23K1342.
- Army Research Office (U.S. Department of Defense), grant W911NF2010315.
- U.S. Department of Defense, grant W911NF1510456.
- COLCIENCIAS (now Minciencias) scholarship program 647-2014.
- University of Texas at San Antonio.
- Universidad EAFIT.