Solve Large Triangular Polynomial Systems

Equation solvers like Solve, Reduce, FindInstance and NSolve now use new, efficient methods for solving systems that consist of a zero-dimensional triangular set of polynomial equations and an arbitrary additional condition.

Shown are timings for finding the exact solutions of triangular systems of polynomial equations in variables. Each polynomial is dense of total degree 7 with randomly generated integer coefficients between and . The experiment was performed on an Intel Xeon 3.07 GHz 64-bit Linux system, with a time limit of 1 hour. The number at the bottom tells how many times faster Version 12 is than Version 11.

Here are the timings for the same systems as before, with an additional condition that the square of the Euclidean norm of the solution is at most 7.