polyd3 http://www.openmath.org/cd http://www.openmath.org/cd/polyd3.ocd 2006-04-01 2004-07-07 experimental 1 0 This CD contains conversions between different data structures for polynomials. first attempt collect This a binary function. Its first argument should be a DMP f, its second argument a list of positive integers L. When applied to f and L, it represents the DMP with coefficients from the poly_ring_d whose variables only have indices i for i not occurring in the list L, and whose monomials are built up from the variables indexed by the entries of L. list_to_poly_d This symbol is a function with two arguments. The first argument is a ring R and the second argument is a list L. The entries of L are elements of R or can be cast canconically onto elements of R. When applied to R and L, the symbol denotes the distributed (univariate) polynomial over R with terms (L[i-1],i) for i running over the indices of L (i=1, ..., length(L)). The polynomial X^2+4X+7 with integers coefficients can be represented, without recourse to X, by 741 Thus, the above expression is semantically equivalent to 70 41 12 poly_d_to_arith This symbol is a binary function. The first argument is a DMP and the second argument is a list of objects, typically variables or arithmetic expressions, at least as many as there are variables in the ring to which the DMP belongs. When applied to R and L, the symbol denotes the arithmetic expression that is the sum of the terms with the i-th variable of the ring of the DMP being substituted by the i-th expression or variable of the list L. This expression is very close to a substitute, or an application of the DMP, as viewed as a function, to as many arguments as there are variables. The polynomial X^2+4X+7 with integer coefficients has poly_d form 1 70 41 12 This expression represents 7 4 2 poly_d_named_to_arith This symbol is a unary function. Its argument is a DMP with named variables. When applied to R, the symbol denotes the arithmetic expression that is the sum of the terms. The polynomial X^2+4X+7 with integers coefficients has poly_d_named form 70 41 12 This expression represents 7 4 2