Group theory in SAGE
David Joyner, David Kohel · Contemporary mathematics - American Mathematical Society · 2008
In rough design, SAGE is implemented using a categorical frame-work, with methods for objects, methods for their elements, and meth-ods for their morphisms. Currently, SAGE has the ability to deal with abelian groups, permutation groups, and matrix groups over a finite field. This paper will present an overview of the implementations of the group-theoretical algorithms in SAGE, with some examples. We conclude with some possible future directions. SAGE is a general purpose computer algebra system started in 2005 which includes (among many other packages) GAP, for group theory, Maxima, for symbolic computation, Pari, for number theory, and Singular, for multivari-ate polynomial computations and commutative algebra. SAGE uses Python as its interpretive language. This paper will restrict itself to presenting an overview of the implementations of the group-theoretical algorithms in SAGE.