field3 http://www.openmath.org/cd http://www.openmath.org/cd/field3.ocd 2006-06-01 2004-06-01 1 1 experimental A CD of functions for basic constructions in field theory. Written by Arjeh M. Cohen 2004-02-25 free_field This symbol represents a binary function. The first argument should be a natural number p which is zero or a prime number, the second argument a list or a set L. When evaluated on such arguments p and L, the function represents the field of rational functions in L over the rationals if p = 0 and over the field of integers mod p if p is a prime. The rational function field Q(a,b) in the indeterminates a, b is 0 fraction_field This is a unary function. Its argument should be a domain (as in CD ring4). It denotes the fraction field of the domain. The rationals equals fraction_field(Integers) field_by_poly This symbol is a binary function whose first argument is a univariate polynomial ring R over a field, and whose second argument is an irreducible polynomial f in this polynomial ring R. So, when applied to R and f, the function has value the quotient ring R/(f). The finite field GF(2)[X]/(X^2+X+1) is represented by 2 10 11 12 or by 2 1 2