Collaborative Research: A Software System for Algebraic Geometry Research

点击翻译按钮获取中文摘要

Stillman This is a collaborative project carreied out by Daniel R.Grayson and Michael E. Stillman. Macaulay 2 is a free computeralgebra system dedicated to the qualitative investigation ofsystems of polynomial equations in many variables. Theinvestigators continue development of Macaulay 2. They upgradeexisting algorithms, install more algorithms, develop and publishnew algorithms, implement new algorithms as they are discovered,add symbolic-numeric algorithm support, improve thedocumentation, and make systemic software changes that helpcontributors to write, test, and document code. Areas where newalgorithms can make an impact include the study of numericalsystems, fractions with specified types of denominators, idealfactorization, systems where the multiplication of the variablesdoesn't satisfy the commutative law, geometric optimization, theanalysis of observations of gene expression levels over time, andbioinformatics. Macaulay 2 is part of the infrastructure that supportsmathematical research involving systems of polynomial equationsin many variables. A measure of its impact is that at least 70research papers have cited Macaulay 2, at least sevenmathematicians have contributed code, and books and coursematerials are now using it. The experimental results found withMacaulay 2 are helping in the formulation and development oftractable conjectures. Now that the software is approachingmaturity, the investigators place more emphasis on recruitingdevelopers from the research community and on collaborations withother scientists on both mathematical and interdisciplinaryprojects that exploit Macaulay 2's capabilities. They introducegraduate students and postdocs to the use of computers inresearch mathematics through visits and a 5 day workshop inUrbana. The study of systems of polynomial equations has a longand distinguished history in pure and applied mathematics, withrecent impact on such fields as cryptography and robotics.Increasing computer power, combined with further development ofMacaulay 2, enables scientists to expand dramatically its scope.