Ideas.Text.OpenMath.Dictionary.Arith1

Documentation

arith1List :: [Symbol]

List of symbols defined in arith1 dictionary

lcmSymbol :: Symbol

The symbol to represent the n-ary function to return the least common multiple of its arguments.

gcdSymbol :: Symbol

The symbol to represent the n-ary function to return the gcd (greatest common divisor) of its arguments.

plusSymbol :: Symbol

The symbol representing an n-ary commutative function plus.

unaryMinusSymbol :: Symbol

This symbol denotes unary minus, i.e. the additive inverse.

minusSymbol :: Symbol

The symbol representing a binary minus function. This is equivalent to adding the additive inverse.

timesSymbol :: Symbol

The symbol representing an n-ary multiplication function.

divideSymbol :: Symbol

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.

powerSymbol :: Symbol

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.

absSymbol :: Symbol

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.

rootSymbol :: Symbol

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.

sumSymbol :: Symbol

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.

productSymbol :: Symbol

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.