## SYNAPS

### Summary

SYNAPS (Symbolic and Numeric APplicationS)

is a library developed in C++. The aim of this open source project

is to provide a coherent and efficient library for symbolic and

numeric computation. It implements data-structures and classes for the

manipulation of basic objects, such as (dense, sparse, structured) vectors,

matrices, univariate and multivariate polynomials. It also provides

fundamental methods such as algebraic number manipulation tools, different

types of univariate and multivariate polynomial root solvers, resultant

computations, ...

### Authors

B. Mourrain, J.P. Pavone, Ph. Trebuchet, E. Tsigaridas

### Links

### Status

officially approved by the authors### Aims and scope

### Mathematical Classification

### Keywords

- 2d curve sweeping
- algebraic field extensions
- Bezout matrices
- curves
- dense matrices
- dense vectors
- determinants
- duals of polynomials
- equation solvers
- finite fields
- floating point arithmetic
- geometry
- Hankel matrices
- implicit curves
- linear algebra
- matrices
- matrix
- matrix factorization
- monomials
- multivariate Bernstein subdivision solver
- multivariate polynomials
- multivariate resultants
- multivariate solvers
- polynomial solvers
- sparse matrices
- structured matrices
- Sturm sequences
- Sturm subdivision solver
- Sylvester matrices
- Toeplitz matrices
- univariate Aberth solver
- univariate Bezier subdivision solver
- univariate exclusion solver
- univariate polynomials
- univariate resultants
- univariate solvers
- vectors