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# Hoon Hong: Research Overview

## Goal

My current research goal is to develop
- mathematical theories
- algorithms
- software libraries/packages

for efficiently
solving algebraic constraints
arising in mathematics, science and engineering.

A constraint is an expression (well formed formula)
involving rational numbers, variables (ranging over real numbers),
arithemetic functions such as ` +, -, * , /, `
relations such as =, >, >=,
logical connectives such as ` and `, ` or `, ` not `,
quantifers such as ` forall ` and ` exists ` (formally
a formula in the first order theory of real closef field).

A constraint defines a subset of the free variable space,
we naturally calls it the solution set.
Solving means to extract some useful information
about the solution set such as
- Emptiness
- Finiteness
- Dimension
- Number of components
- Topological type
- Volume
- A defining quantifier-free formula
- An approximate simple defining formula.
- Plotting
- ....

## Motivation

The main motivation for tackling this problem comes from
the observation that numerous problems
in mathematics, science and engineering can be reduced
to that of solving constraints.
Thus, making progress in solving constraints
will have a broad impact.
## Approach

I try to achieve efficiency
by
- Developing new/better mathematical theories and more efficient algorithms.
- Utilizing the structure (in particular composition).
- Allowing approximate answers (but to a given precision).

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