We consider Presburger arithmetic extended by infinity. For this we give an effective quantifier elimination and decision procedure which implies also the completeness of our exten...
Programmable shading provides artistic control over materials and geometry, but the black box nature of shaders makes some rendering optimizations difficult to apply. In many case...
Petrik Clarberg, Robert Toth, Jon Hasselgren, Toma...
We explicit the link between the computer arithmetic problem of providing correctly rounded algebraic functions and some diophantine approximation issues. This allows to get bounds...
or representation theory of groups), and even borrows abstract geometrical concepts like Euler characteristic or Grothendieck ring. However, the most stimulating for proof complexi...
We propose a new number representation and arithmetic for the elements of the ring of integers modulo p. The socalled Polynomial Modular Number System (PMNS) allows for fast polyn...
Jean-Claude Bajard, Laurent Imbert, Thomas Plantar...