This report addresses the problem of computing the parametrization of the intersection of deformable quadratic algebraic surfaces (quadrics) in projective space. It also presents an automatic method for describing the evolution in time of the topology of the intersection. The work is based on the results from [3, 4], which offer an exact parametrization of the intersection of two quadrics with ...

We determine necessary and sufficient conditions for a tubular surface to be swung, and viceversa. From these characterizations, we derive two symbolic algorithms. The first one decides whether a given implicit equation, of a tubular surface, admits a swung parametrization and, in the affirmative case, it outputs such a parametrization. The second one decides whether a given swung surface param...

A well-defined chirally split functional integrating the 2D chirally split diffeomorphism anomaly is exhibited on an arbitrary compact Riemann surface without boundary. The construction requires both the use of the Beltrami parametrisation of complex structures and the introduction of a background metric possibly subject to a Liouville equation. This formula reproduces in the flat case the so-c...

We give real Jacobian elliptic function parametrizations for a genuinely asymmetric biquadratic curve where the variables and parameters are real.

CL development and especially the development of tools for CL convergence checking is a time and cost consuming task. The development of flexible CL checkers by reusing existing resources is a great challenge for the CL community today. The article presents some theoretical reflections and lessons learnt in ongoing CL projects on the subject of customisation and parametrisation, trying to show ...

We look for complete four dimensional Einstein-Weyl spaces equipped with a Bianchi metric. Using the explicit 4-parameters expression of the distance obtained in a previous work for non-conformally-Einstein Einstein-Weyl structures, we show that four 1-parameter families of compact metrics exist : they are all of Bianchi IX type and conformally Kähler ; moreover, in agreement with general resul...

Given a parametrization of a curve we would like to find a ‘small’ parametrization of the same curve. Where small simply refers to the number of bits required to display the parametrization. In order to be practical we must accomplish our task quickly, since the result is an aesthetic result. Presented here is a largely heuristic algorithm which is quite practical and could be easily included i...