When an expression is here said to be "undefined," it means that, in the absence of external information about the interpretation of the expression, it is semantically void, meaningless, and/or nonsensical.
Mathematical operators take one or more operands, which are here referred to by an 'x' subscripted with a number.
Operators defined here as "unary" are defined as operating on their first operand that is not equal to tu'o (referred to as "the operand" within the respective definitions), regardless of where it occurs in the operand list.
See also: CLL section 18.16, example 16.3 and the paragraph before it, in which the operand of va'a is in the x_1 place; CLL section 18.14, example 14.1, in which the operand of va'a is in the x_2 place.
If all operands of an operator are tu'o, the value of the expression is equal to tu'o.
If an operand described in an operator's definition is missing from the operator's operand list and there is no default value given, the missing operand shall be interpreted as tu'o.
If one or more extra operands not described in an operator's definition are present in the operator's operand list, they affect the evaluation in an undefined or unspecified manner analogous to sumti attached to a selbri with do'e.
Lojban mathematical operators are defined in terms of conventional mathematical operators, and thus there is an implicit type system used in determining the value of an expression. Mekso operands may be of any of the following types:
number — a "number" production in the formal grammar, usually corresponding to an element of the complex plane
array — an array, vector, ordered list/set, or tuple of one or more mekso values, constructed using jo'i
matrix — a composition of one or more arrays of numbers, all of the same size, constructed using pi'a or sa'i
function
If an operator is applied to operands of a type which its definition does not address, the expression is undefined.
The operand tu'o is polymorphic; its type in an expression is determined by its surrounding context.