hypergeon0 http://www.math.kobe-u.ac.jp/OCD/hypergeon0.tfb 2003-11-11 experimental 2002-11-11, 2003-11-30 1 1 arith1 linalg1 linalg4 linalg5 quant1 relation1 set1 This CD defines some supplementary symbols necessary for hypergeon1 and hypergeon2 (hypergeometric series of n variables). These symbols may be included in CD's linalg, logic, poly, and set. plus_part The argument is a vector. It replaces negative elements in the vector to zero. minus_part The argument is a vector. It replaces positive elements in the vector to zero and negative elements to their absolute values. $u = u_{+} - u_{-}$ kernel It returns the kernel of the map defined by a matrix in a specified domain. $\kernel(D,A) = \{ x \in D | A x = 0 \}$ 1 where The word "where" is often used in mathematical expressions to set variables or to say side conditions. CDname logic1.implies can be used for these purposes, but "where" will be more intuitive and more friendly expression for authors. $x^n=x x x \where{n=3}$ 3 multi_power multi_power is for using the multi-index notation. $x^e = \prod_{i=1}^n x_i ^ {e_i}$ 1 cartesian_product_n the cartesian product of n copies of the first argument. Binary function. $Z^m \times Z^n = Z^{m+n}$