# Hend Dawood

## Senior Assistant Lecturer of Computational Mathematics

Department of Mathematics, Faculty of Science, Cairo University, Giza, PO Box: 12613, Egypt. (email)

Department of Mathematics, Faculty of Science, Cairo University, Giza, PO Box: 12613, Egypt. (email)

in

- Algebraic Computation
- Arbitrary Precision
- Automatic Differentiation
- Bounding Error
- Computational Mathematics
- Computational Physics
- Computer Algebra
- Dawood's InCLosure
- Differentiation Arithmetic
- Guaranteed Enclosures
- Hend Dawood
- InCL
- InCLosure
- InCLosure (Interval enCLosure)
- Interval Analysis
- Interval arithmetic
- Interval automatic differentiation
- Interval computations
- Interval Differentiability
- Interval Enclosures
- Interval Enclosures of Integrals
- Interval Functions
- Interval Mathematics
- Interval Subdivision
- Lisp
- Mathematical Software
- Mathematics
- Multivariate Interval Subdivisions
- Numeric Differentiation
- Numerical Analysis
- Numerical Computation
- Real Automatic Differentiation
- Reliability
- Reliable computing
- Scientific Software
- Set-valued functions
- Symbolic Computation
- Symbolic Differentiation
- Taylor Model Arithmetic
- Taylor Model Computations
- Taylor Model Enclosures
- Uncertainty
- Uncertainty Analysis
- Uncertainty Modeling
- Uncertainty Quantification
- Universal intervals

Copyright (c) 2018-2020 by Hend Dawood. All rights reserved.

Support Link: http://scholar.cu.edu.eg/henddawood/software/InCLosure

Community Link: https://zenodo.org/communities/inclosure/

- Fast and arbitrarily-high precision Taylor model computations.
- Taylor model enclosures of images of real functions.
- Symbolic and numeric differentiation to an arbitrary order.
- Guaranteed interval enclosures of integrals with arbitrary precision.
- Multivariate interval evaluations with arbitrary precision, arbitrary number of subdivisions, and arbitrary number of variables.
- Simplified syntax for direct evaluations of real and interval expressions.
- Enhancements in functionality, speed, language and interface.
- Minor bug fixes.

InCLosure (Interval enCLosure) is a Language and Environment for Reliable Scientific Computing. Interval computations are radically different from traditional numerical approximation methods and reliable computing under uncertainty is a key focus for modern research in mathematics, computer science, physics, and engineering. InCLosure is a system for carrying out reliable and self-validated computations in arbitrary precision. From its name, InCLosure (abbreviated as "InCL") focuses on "computing guaranteed interval enclosures", that is, "enclosing the exact real result in an interval".

InCLosure is powerful enough to carry out computations ranging from simple real and interval arithmetic, through symbolic and numeric differentiation to an arbitrary order, real automatic differentiation, and interval automatic differentiation, up to and including interval enclosures of integrals and Taylor model computations. No matter how complicated the problem under consideration is, InCLosure provides arbitrary precisions and reliable interval results that can be as narrow as possible by the computational power of the hosting machine.

InCLosure supports arbitrary precision in both real and interval computations. In real arithmetic, the precision is arbitrary in the sense that it is governed only by the computational power of the machine (default is 20 significant digits). The user can change the default precision according to the requirements of the application under consideration. Since interval arithmetic is defined in terms of real arithmetic, interval computations inherit the arbitrary precision of real arithmetic with an added property that the interval subdivision method is provided with an arbitrary number of subdivisions which is also governed only by the computational power of the machine. The user can get tighter and tighter guaranteed interval enclosures by setting the desired number of subdivisions to cope with the problem at hand.

All the computations defined in terms of real and interval arithmetic (e.g., real and interval automatic differentiation, Taylor model computations, and so forth) inherit the same arbitrary precision.

InCLosure is designed to support both interactive and batch modes. In the InCLosure interactive interface, the user can input an InCL command and see its result before moving on to the next command. InCLosure can also be used in batch mode in which case sequences of InCL commands can be given to InCLosure via InCL input files with the results saved in simple and intuitively formatted output files.

InCLosure is coded entirely in Lisp, arguably the fastest and most powerful language for scientific computations. InCLosure provides a friendly and easy-to-use user interface, a simple and intuitive language, a detailed documentation, and clear and fast results. Anyone can compute with InCLosure.

InCLosure provides:

- Simplified syntax for direct evaluations of real and interval expressions.
- Evaluation of multivariate real functions with arbitrary precision and arbitrary number of variables.
- Real automatic differentiation (real differentiation arithmetic) with arbitrary precision.
- Evaluation of multivariate interval functions with interval constants.
- Multivariate interval evaluations with arbitrary precision, arbitrary number of subdivisions, and arbitrary number of variables.
- Interval automatic differentiation (interval differentiation arithmetic) with arbitrary precision and arbitrary number of interval subdivisions.
- Guaranteed interval enclosures of images of families of real functions and their derivatives.
- Automatic differentiation of families of real functions.
- Symbolic and numeric differentiation to an arbitrary order.
- Guaranteed interval enclosures of definite integrals with arbitrary precision.
- Fast and arbitrarily-high precision Taylor model computations.
- Taylor model enclosures of images of real functions.
- Simple and intuitive language and user interface.
- Batch evaluation of InCLosure commands via InCL input files with the results saved in simple and intuitively formatted output files.
- Each InCLosure session with all the commands and their results can be saved in a session file. Session files, named by date and time, are saved at the user's disposal to allow future inspection of the computations and their results.

InCLosure is more than just a mathematical software. InCLosure has been developed with a concern for correctness, for computing guaranteed enclosures under uncertainty. InCLosure goal is to provide rigorous, fast, and reliable real and interval computations. It supports arbitrary precision in both real and interval computations. Being subtle and reliable, InCLosure provides guaranteed and viable results for real world uncertainty computations (the exact real result is never missed during computations). If you want to get the right answer, then InCLosure is for you.

InCLosure is designed and coded with passion and joy, with an attempt to make the interaction between users and InCLosure not just easy, but also enjoyable. InCLosure is powerful but easy-to-use and all the functionalities are readily accessible via its friendly interface and intuitive language. From the simplest real and interval evaluations and up to the sophisticated uncertainty problems, InCLosure computations are easy to perform and no learning curve is needed.

Putting these all together, InCLosure is intended for a wide range of audience, including undergraduate students, graduate students, practitioners, and academic researchers in mathematics, computer science, engineering, and physics.

*InCLosure is different. Everyone can compute with InCLosure.*

An appropriate version of Windows. InCLosure runs on *Windows 7 32/64 bit*, *Windows 8 32/64 bit*, and *Windows 10 32/64 bit*.