poly1p http://www.math.kobe-u.ac.jp/OCD/poly1p.tfb 2003-08-08 experimental 2002-08-08 1 0 linalg1p poly1p set1p logic1p arith1 fns1 interval1 linalg1 linalg4 relation1 set1 This CD defines symbols for concerning multi-index and indexed variables. multi_power multi_power is for using the multi-index notation. $\prod_{i=1}^n x_i ^ {e_i}$ poly1p.multi_power(x,e) ~relation1.eq~ arith1.product( interval1.integer_interval(1,linalg4.size(x)), OMLBIND( OMBVAR(i), arith1.power(linalg1.vector_selector(i,x), linalg1.vector_selector(i,e)))); index index returns the index of a given indexed variable. indexed_variable indexed_variable(x,i) returns the variable x_i index(indexed_variable(x,i)) = i index(indexed_variable(x,i)) ~relation1.eq~ i; index(indexed_variable(x,[1,2])) = [1,2] index(indexed_variable(x,linalg2.vector(1,2))) ~relation1.eq~ linalg2.vector(1,2); vector_of_indexed_variables vector_of_indexed_variables(x,n) returns the vector of variables (x_1, ..., x_n). vector_of_indexed_variables(x,[m,n]) returns the vector of variables (x_{1,1}, ..., x_{m,n}). Any vector of numbers can be given as an argument. i-th element of vector_of_indexed_variable(x,n) is indexed_variable(x,i) linalg1.vector_selector(i,vector_of_indexed_variables(x,n)) ~relation1.eq~ indexed_variable(x,i); sorted_set_of_indexed_variables sorted_set_of_indexed_variables(x,s) returns the vector of variables indexed by the sorted set s. m-element of sorted_set_of_indexed_variables(x,s) is indexed_variable(x,m) set1p.index_set_selector(m,sorted_set_of_indexed_variables(x,s)) ~relation1.eq~ indexed_variable(x,m);