borderbasix is a package for computing border basis and for solving zero-dimensional systems. Different types of coefficients can be used for the border basis computation: modular arithmetic, rational numbers, floating point numbers, ... The output of border basis computation is a monomial basis of the quotient algebra and the tables of multiplication by the variables in this basis, when the system is zero-dimensional. The roots of the system are deduced from the eigenvectors of the tables of multiplication. When the coefficients are rational or floating point numbers, the roots are computed over the complex numbers.
The package is written in C++. It contains classes for the manipulation of multivariate polynomials, for computing border bases and for solving zero-dimensional polynomial systems via eigenvalue/eigenvector computation. The classes are templated by the coefficient type. Different types of coefficients can be used: modular arithmetic, rational numbers, floating point numbers, ...