# Hend Dawood

## Senior Lecturer of Computational Mathematics

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

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

in

- Algebraic Computation
- Arbitrary Precision
- Automatic Differentiation
- Bounding Error
- CLisp
- Common Lisp
- Computational Mathematics
- Computational Physics
- Computer Algebra
- Computer Science
- Dawood's InCLosure
- Differentiation Arithmetic
- Guaranteed Enclosures
- Hend Dawood
- InCL
- InCLosure
- InCLosure (Interval enCLosure)
- InCLosure v2.0
- Interval Analysis
- Interval arithmetic
- Interval automatic differentiation
- Interval computations
- Interval Differentiability
- Interval Differentiation Arithmetic
- Interval Enclosures
- Interval Functions
- Interval Mathematics
- Interval Subdivision
- Lisp
- Mathematical Software
- Mathematics
- Numerical Analysis
- Numerical Computation
- Optimizational intervals
- Quantitative Knowledge
- Real Automatic Differentiation
- Real Differentiation Arithmetic
- Real Functions
- Reliability
- Reliable computing
- Scientific Software
- Set-valued functions
- Software
- Symbolic Computation
- Uncertainty
- Uncertainty Analysis
- Uncertainty Modeling
- Uncertainty Quantification
- Universal intervals

InCLosure (Interval enCLosure) is a Language and Environment for Reliable Scientific Computing. InCLosure provides rigorous and reliable results in arbitrary precision. From its name, InCLosure (abbreviated as "InCL") focuses on "enclosing the exact real result in an interval". The interval result is reliable and can be as narrow as possible.

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 guranteed interval enclosures by setting the desired number of subdivisions to cope with the problem at hand.

All the computaions defined in terms of real and interval arithmetic (e.g., real and interval automatic differentiation) inherit the same arbitrary precision.

InCLosure is written in Lisp, the most powerful and fast language in scientific computations. InCLosure provides easy user interface, detailed documentation, clear and fast results. Anyone can compute with InCLosure.

InCLosure provides:

- Evaluation of multivariate real functions.

- Real automatic differentiation (real differentiation arithmetic) with arbitrary precision.

- Evaluation of multivariate interval functions with interval constants.

- Interval evaluations with arbitrary precision and arbitrary number of subdivisions.

- 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.

- 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 thier results.

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 guranteed and viable results for real world uncertainty computations (the exact real result is never missed during computations).

InCLosure is different, anyone can compute with InCLosure.

InCLosure runs on:

-Windows 7 32/64 bit

-Windows 8 32/64 bit

-Windows 10 32/64 bit