## Fermat

### Summary

Fermat is a super calculator – computer algebra system, in which the basic items being computed can be rational numbers, modular numbers, elements of finite fields, multivariable polynomials, multivariable rational functions, or multivariable polynomials modulo other polynomials. Fermat is available for Mac OS, Windows, Unix, and Linux. It is shareware.

The basic “ground ring” F is the field of rational numbers. One may choose to work modulo a specified integer n, thereby changing the ground ring F from Q to Z/n. On top of this may be attached any number of unevaluated variables t_1, t_2, .. t_n., thereby creating the polynomial ring F[t_1, t_2, .. t_n] and its quotient field, the rational functions. Further, polynomials p, q, .. can be chosen to mod out with, creating the quotient ring F(t_1, t_2, ..)/[p, q, ...]. It is possible to allow Laurent polynomials. Once the computational ring is established in this way, all computations are of elements of this ring.

### Authors

Dr. Robert H. Lewis

### Vendor

http://www.bway.net/~lewis

### Links

### Status

incomplete information or not officially approved by the authors### Aims and scope

### Mathematical Classification

### Keywords

- arbitrary long integers
- arithmetic
- calculator
- complex numbers
- computer algebra
- determinants
- diagonal matrices
- finite fields
- fractions
- graphics
- integers
- Laurent polynomials
- matrices
- matrices over polynomial rings
- matrix
- matrix algebra
- matrix computation
- matrix inverse
- modular numbers
- multivariable polynomials
- multivariate rational function arithmetic
- normalization
- numerical calculations
- polynomial computation
- polynomial rings
- polynomials
- polynomials modulo polynomials
- quolynomials
- quotient rings
- rational functions
- rational numbers
- real numbers
- rings
- sparse matrices
- submatrices
- symbolic calculations