CoCoA is a Macintosh system for doing Computations in Commutative Algebra. It runs on any Macintosh with at least 512K of RAM, but it takes advantage of any additional available memory; it runs also under .i.MultiFinder; (even though it is not yet capable of performing computations in the background). It is written in Pascal (apart from a few Ôglue routinesÕ in assembler); the release 1.0b of the system consists of about 24,000 lines of code.
CoCoA has been designed for offering the maximum ease of use and flexibility to the mathematician with little or no knowledge of computers. It is capable of performing simple and sophisticated operations on multivariate polynomial rings and on various data connected with them (ideals, modules, matrices, rational functions); polynomials may have coefficients either in the field Q of rational numbers or in the residue ring Zp. A current limit of the system is that the numerator and denominator of the coefficients in Q must not exceed 2311Ê=2147483648, and the integer p for Zp must not exceed 215-1 = 32767.
Every operation (sometimes called computation) is performed within the Ô.i.current ring;Õ, which the user can easily set up and change by just pulling down a menu and editing some values; the advanced user has also the possibility of changing the values of some special parameters; the meaning of these parameters can be nevertheless safely ignored by most users.
The user can open up to eight windows (standard textÐediting Macintosh windows) in which data can be entered in a format which has been chosen to be very close to the usual mathematical notation. Several kinds of computations can be performed on the entered data and the results can be stored for later use. If the user modifies the ring, then the already entered or computed data can be easily transferred to the new ring (when that makes sense).
The system is capable of performing the basic operations on polynomials and rational functions (sums, products, powers, derivatives), on ideals (sums, products, powers), on modules (sums) and on matrices (sums, products, powers, determinants) as well as more advanced operations like intersection and division of ideals, computing Hilbert functions and Poincar series of ideals, syzygies and free resolutions of ideals or modules, resultant of two polynomials, elimination and substitution of variables, etc.
(159.87 KiB / 163.71 KB)
Version 1.0c / compressed w/ Stuffit
Emulating this? It should run fine under: Basilisk II