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HomotopyContinuation.jl is a Julia package for solving systems of polynomial equations by numerical homotopy continuation. Many models in the sciences and engineering are expressed as sets of real solutions to systems of polynomial equations. We can optimize any objective whose gradient is an algebraic function using homotopy methods by computing all critical points of the objective function. An important special case is when the objective function is the euclidean distance to a given point. An example of an non-algebraic objective function whose derivative is algebraic is the Kullback–Leibler divergence. Homotopy continuation methods allow us to study the conformation space of molecules as for example cyclooctane (CH₂)₈. This molecule consists of eight carbon atoms aligned in a ring, and eight hydrogen atoms, each of which is attached to one of the carbon atoms.
Features
- Julia package
- HomotopyContinuation.jl aims at having easy-to-understand top-level commands
- Documentation available
- Examples available
- For solving systems of polynomial equations
- Kinematic synthesis
- Computational Chemistry
- Topological Data Analysis
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