SIGSAM

The Weyl group of a root system coming from the Lie theory is defined to be the group generated by reflections with respect to the roots. We have three series of finite Weyl groups and five exceptional Weyl groups. For the Weyl groups of classical and ...

A method of finding residue integrals for systems of non-algebraic equations containing analytic functions is presented. Such integrals are connected to the power sums of roots for a certain system of equations. The described approach can be used for ...

When users analyze symbolically physical phenomena, software products which partially help them write a symbolic equation to the phenomena are available. In electric engineering, there are a few software products which compute symbolically voltages and ...

Arithmetic operations with high degrees of precision are needed for an increasing number of applications. We propose an exact real arithmetic system that achieves adaptive precision using lazy infinite lists of floating-point values.

Finding roots of polynomials with coefficients in a finite field is a special instance of the polynomial factorization problem. The most well known algorithm for factoring and root-finding is the Cantor-Zassenhaus algorithm. It is a Las Vegas algorithm ...

We present an efficient decision procedure for positivity on a class of holonomic sequences satisfying recurrences of arbitrary order.

Suppose that we seek to factor a multivariate polynomial a ε R = Z[x₁, ..., x_n] and a = fg with f, g in R. The multivariate Hensel lifting algorithm (MHL) developed by Wang [1] uses a prime number p and an ideal I = 〈x₂ − α₂, ..., x_n − α_n〉 of Z_p[x₁, ...,...

Indefinite integration means that given f in some set we want to find g from possibly larger set such that f = g'. When f and g are required to be elementary functions due to work of among others Risch, Rothstein, Trager, Bronstein (see [1] for ...

The Hilbert function, its generating function and the Hilbert polynomial of a graded ring K[x₁, ..., x_k] have been extensively studied since the famous paper of Hilbert: Ueber die Theorie der algebraischen Formen ([Hilbert, 1890]). In particular, the ...

Multivariate polynomials over finite fields have found applications in Public Key Cryptography (PKC) where the hardness to find solutions provides the "one-way function" indispensable to such cryptosystems. Several schemes for both encryption and ...