Loïc Pottier

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We present in this paper an algorithm which is a natural extension in dimension n of the Euclidean algorithm computing the greatest common divisor of two integers. Let H be a sub-group of Z“, given by a system of generators. This algorithm computes the union of bases of all monoids obtained as intersection of H with the 2n orthants of Zn . As a consequence,(More)
We describe a tool that combines a general purpose theorem prover and an off-theshelf interface for dynamic geometry drawing to enhance man-machine interaction involving geometrical proofs. With our tool, we can edit the statements of geometrical theorems, construct and verify their proofs with the theorem prover, and visualize the statements using the(More)
This paper describes current results of Ofr (Optical Formula Recognition), a system for extracting and understanding mathematical expressions in documents. Such a tool could be really useful to be able to re-use knowledge in scientific books which are not available in electronic form. We currently also study use of this system for direct input of formulas(More)
This paper presents an approach for the recognition of on-line handwritten mathematical expressions. The Hidden Markov Model (HMM) based system makes use of simultaneous segmentation and recognition capabilities, avoiding a crucial segmentation during pre-processing. With the segmentation and recognition results, obtained from the HMMrecognizer, it is(More)
This paper concerns space-time trade-oos for the reverse mode of auu tomatic diierentiation on the straight-line programs with nested loops. In the rst part we consider the problem of reversing a nite sequence given by u n+1 = f(u n), which can model a certain class of nite loops. We show an optimal time strategy for this problem, the number of available(More)
We describe how we connected three programs that compute Gröbner bases [1] to Coq [11], to do automated proofs on algebraic, geometrical and arithmetical expressions. The result is a set of Coq tactics and a certificate mechanism 1. The programs are: F4 [5], GB [4], and gbcoq [10]. F4 and GB are the fastest (up to our knowledge) available programs that(More)