path: root/math/vinci/pkg-descr



The volume is one of the central properties of a convex body, and volume
computation is involved in many hard problems. Applications range from rather
classical ones as in convex optimisation to problems in remote fields like
algebraic geometry where the number of common roots of polynomials can be
related to a special polytope volume.

Part of the fascination of the subject stems from the discrepancy between the
intuitive notion of "volume" and the actual hardness of computing it. Despite
this discouraging complexity - algorithms in general need exponential time in
the input dimension - steadily growing computer power enables us to attack
problems of practical interest.

Vinci is an easy to install C package that implements several algorithms for
volume computation. It is the fruit of a research project carried out at the
end of the 1990s at the IFOR (Institute for Operations Research) of the ETH
Zurich.
The volume is one of the central properties of a convex body, and volume
computation is involved in many hard problems. Applications range from rather
classical ones as in convex optimisation to problems in remote fields like
algebraic geometry where the number of common roots of polynomials can be
related to a special polytope volume.

Part of the fascination of the subject stems from the discrepancy between the
intuitive notion of "volume" and the actual hardness of computing it. Despite
this discouraging complexity - algorithms in general need exponential time in
the input dimension - steadily growing computer power enables us to attack
problems of practical interest.

Vinci is an easy to install C package that implements several algorithms for
volume computation. It is the fruit of a research project carried out at the
end of the 1990s at the IFOR (Institute for Operations Research) of the ETH
Zurich.