Schützenberger-like products in non-free monoids
Semi-algebraic complexity-additive complexity of diagonalization of quadratic forms.
We study matrix calculations such as diagonalization of quadratic forms under the aspect of additive complexity and relate these complexities to the complexity of matrix multiplication. While in Bürgisser et al. (1991) for multiplicative complexity the customary thick path existence argument was sufficient, here for additive complexity we need the more delicate finess of the real spectrum (cf. Bochnak et al. (1987), Becker (1986), Knebusch and Scheiderer (1989)) to obtain a complexity relativization....
Shift equivalence of P-finite sequences.
Signed bits and fast exponentiation
An exact analysis is given of the benefits of using the non-adjacent form representation for integers (rather than the binary representation), when computing powers of elements in a group in which inverting is easy. By counting the number of multiplications for a random exponent requiring a given number of bits in its binary representation, we arrive at a precise version of the known asymptotic result that on average one in three signed bits in the non-adjacent form is non-zero. This shows that...
Simple groups in computational group theory.
Software for the algorithmic work with orthogonal polynomials and special functions.
Solving conics over function fields
Let be a field whose characteristic is not and . We give a simple algorithm to find, given , a nontrivial solution in (if it exists) to the equation . The algorithm requires, in certain cases, the solution of a similar equation with coefficients in ; hence we obtain a recursive algorithm for solving diagonal conics over (using existing algorithms for such equations over ) and over .
Solving word equations
Some properties of min-wise independent families and groups of permutations.
Spécialisation de la suite de Sturm
Spécialisation de la suite de Sturm et sous-résultants (I)
Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions
This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra of the symmetric group over a field of characteristic 0 (or ). The goal is to obtain a constructive version of the isomorphism where is a partition of and counts the standard tableaux of shape ....
Subalgebra bases and recognizable properties.
Sufficient conditions for the existence of a center in polynomial systems of arbitrary degree.
In this paper, we consider polynomial systems of the form x' = y + P(x, y), y' = -x + Q(x, y), where P and Q are polynomials of degree n wihout linear part.For the case n = 3, we have found new sufficient conditions for a center at the origin, by proposing a first integral linear in certain coefficient of the system. The resulting first integral is in the general case of Darboux type.By induction, we have been able to generalize these results for polynomial systems of arbitrary degree.
Sur le nombre de registres nécessaires à l'évaluation d'une expression arithmétique
Symbolic computation of variational symmetries in optimal control
Symbolic Derivation Without Using Expression Trees
Systolic arrays to solve algebraic equations by Bernoulli's method.