Sage: System for Algebra and Geometry Experimentation

Abstract

SAGE is a framework for number theory, algebra, and geometry computationthat is initially being designed for computing with elliptic curves and modularforms. The current implementation is primarily due to William Stein. It is opensource and freely available under the terms of the GNU General Public License(GPL).SAGE is a Python library with a customized interpreter. It is written inPython, C++, and C (via Pyrex). Python is an open source object-orientedinterpreted language, with a large number of libraries, e.g., for numerical analysis,which are available to users of SAGE. Python can also be accessed in library modefrom C/C++ programs.SAGE will provides an interface to several important open source libraries,including Cremona’s MWRANK library for computing with elliptic curves, thePARI library for number theory, and Shoup’s number theory library NTL. Thereis also a tentative plan to incorporate an interface to SINGULAR (for commuta-tive algebra) and GAP (for group theory).The design of SAGE is heavily influenced by the carefully thought out andmature class structure of the closed source computer algebra program MAGMA.When possible, classes have similar names, constructors, and print representationsas in MAGMA, and similar functions are available. However, SAGE is not meantto be an exact clone of MAGMA.