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What is SINGULAR? SINGULAR is a specialized computer algebra system for polynomial computations with emphasize on the needs of commuta-tive algebra, algebraic geometry, and singularity theory. SINGULAR's main computational objects are polynomials, ideals and modules over a large variety of rings, including important non-commutative rings. SINGULAR features(More)
BACKGROUND Approximately 30% of schizophrenic patients defined as treatment refractory significantly improve with clozapine. However, clozapine produces agranulocytosis in approximately 1% to 2% of patients in the United States. The mechanism of clozapine-induced agranulocytosis has not been established, but evidence suggests an immune-mediated mechanism.(More)
Systems of polynomial equations arise throughout mathematics, engineering, and the sciences. It is therefore a fundamental problem both in mathematics and in application areas to find the solution sets of polynomial systems. The focus of this paper is to compare two fundamentally different approaches to computing and representing the solutions of polynomial(More)
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, and then use Farey sequences for rational reconstruction. Successively enlarging the set of primes if needed, this method is guaranteed to work if we restrict ourselves to " good "(More)