polynomial2 http://www.openmath.org/cd/polynomial2.ocd 2006-02-02 2004-07-09 1 0 experimental alg1 arith1 logic1 quant1 set1 setname1 setname2 relation1 fns1 interval1 integer1 polynomial1 This CD holds a collection of basic modular arithmetic for univariate polynomials over rings. The data structures for polynomials can be arithmetic expressions, for instance using the ring1.expression symbol, or DMP as in the CD polyd1. modulo_relation This symbol represents a univariate function, whose argument should be a polynomial. When applied to a polynomial m, it denotes the equivalence relation of being equal modulo m. modulo_relation(m)(a,b) is equivalent to eqmod(a,b,m). divides This symbol represents a bivariate Boolean function, whose arguments should be polynomials in the same polynomial ring. When applied to a and b, it denotes the property that a divides b. The polynomial a divides the polynomial b with the same coefficient ring as a if and only there is a polynomial q over this coefficient ring such that a * q = b. eqmod This symbol represents a Boolean valued trivariate function, whose arguments should be polynomials. When applied to polynomials a, b, m, it denotes the Boolean evalue of the assertion that a and b are equal modulo m. neqmod This symbol represents a Boolean valued trivariate function, whose arguments should be polynomials. When applied to polynomials a, b, m, it denotes the Boolean evalue of the assertion that a and b are not equal modulo m. class This symbol represents a bivariate function, whose arguments should be polynomials. If a, m are polynomials in a polynomial ring R[X], then class(a,m) denotes the residue class a mod m in the quotient ring R[X]/ (mR[X]).