arith1 http://www.openmath.org/cd/arith1.ocd 2003-04-01 official 2001-03-12 2 0 alg1 fns1 integer1 interval1 linalg2 logic1 quant1 relation1 set1 setname1 transc1 This CD defines symbols for common arithmetic functions. nl.tue.win.riaca.x.codec.core P. Perez lcm The symbol to represent the n-ary function to return the least common multiple of its arguments. gcd The symbol to represent the n-ary function to return the gcd (greatest common divisor) of its arguments. plus The symbol representing an n-ary commutative function plus. unary_minus This symbol denotes unary minus, i.e. the additive inverse. minus The symbol representing a binary minus function. This is equivalent to adding the additive inverse. times The symbol representing an n-ary multiplication function. divide This symbol represents a (binary) division function denoting the first argument right-divided by the second, i.e. divide(a,b)=a*inverse(b). It is the inverse of the multiplication function defined by the symbol times in this CD. power This symbol represents a power function. The first argument is raised to the power of the second argument. When the second argument is not an integer, powering is defined in terms of exponentials and logarithms for the complex and real numbers. This operator can represent general powering. abs A unary operator which represents the absolute value of its argument. The argument should be numerically valued. In the complex case this is often referred to as the modulus. root A binary operator which represents its first argument "lowered" to its n'th root where n is the second argument. This is the inverse of the operation represented by the power symbol defined in this CD. Care should be taken as to the precise meaning of this operator, in particular which root is represented, however it is here to represent the general notion of taking n'th roots. As inferred by the signature relevant to this symbol, the function represented by this symbol is the single valued function, the specific root returned is the one indicated by the first CMP. Note also that the converse of the second CMP is not valid in general. sum An operator taking two arguments, the first being the range of summation, e.g. an integral interval, the second being the function to be summed. Note that the sum may be over an infinite interval. product An operator taking two arguments, the first being the range of multiplication e.g. an integral interval, the second being the function to be multiplied. Note that the product may be over an infinite interval.