Massively Parallel Modular Algorithms for the Image of Rational Maps
Computations over the rational numbers frequently encounter the issue of intermediate coefficient growth. Modular methods provide a solution to this problem by applying the algorithm under consideration modulo a number of primes and then lifting the modular results to the rationals. In this talk, we present a novel, massively parallel framework for modular computations with polynomial data, which is able to cover a broad spectrum of applications in commutative algebra and algebraic geometry. In particular, we give an example of how to apply the framework in birational geometry when computing the image of a rational map. Efficient algorithms in birational geometry are, for example, essential for an algorithmic approach for the Mori minimal model program. Addressing the technical foundations of the approach, the talk will also discuss the concept of separating coordination and computation, as well as its use in computer algebra.