A null operator, in the sense that it returns all its arguments unchanged. Used as syntactic glue in poly-ary operators, such as to pass three arguments to a ternary operator in infix notation.
The n-ary operation of division. Divides the first argument by all subsequent ones in a left associative manner: x1 / x2 / x3 ...
The n-ary operation of multiplication. Multiplies all the arguments together in a left associative manner: x1 * x2 * x3 ...
The n-ary operation of addition. Adds all the arguments together in a left associative manner: x1 + x2 + x3 ...
The n-ary operation of subtraction. Takes the first argument as subtracts all subsequent ones in a left associative manner: x1 - x2 - x3 ...
This is the operator for subtraction. It is distinct from {va'a} which is the operator for negation, and also from {ni'u} which is a minus sign and is part of the number
The unary operation of inverting. It returns the reciprocal of the given number: 1 / x1
This is performs similar to {fi'u}. There are differences though. This is an operator and thus may take a mekso operand as an argument, whereas {fi'u} is part of PA and so is part a number.
This operator is a trinary operator that mimics scientific notation. It is designed so that arguments can be omitted to give magnitudes quickly. gei x1 x2 x3 = x_2 * (x_3 ^ x_1). x_3 defaults to 10; so gei x1 x2 = x2 * 10 ^ x1. x_2 defaults to 1; so gei x1 = 10 ^ x1
The binary operation that indicates the number base of its first argument: x1 is in base x2
For bases up to 16 Lojban has numerals you can use. But for bases greater than 16, use {pi'e} to separate the place values. {pi} is used as radix point in any base.
The binary operation that returns the ratio of its two arguments: the ratio of x1 to x2.
No examples in CLL and none turned up searching lojban.org
The binary operation of taking an nth root. The default is to take a square root. The x2-th root of x1.
The factorial function. The factorial of x1.
The definition could easily be expanded to non integer arguments by identification with a suitable modification of the gamma function (z! = \Gamma(z-1)). It depends how stringent the community wants to be with the initial definitions and how much they want to leave up to usage.
The unary operation giving the additive inverse of a number. For most people, this is a fancy way of saying the negative of a number.
This n-ary operator takes vectors as operands and forms them into the rows of a matrix. The matrix with rows x1, x2, x3, ...
8 | 1 | 6 |
3 | 5 | 7 |
4 | 9 | 2 |
The trinary operation of taking the definite integral of a function. The integral of x1 with respect to x2 over range x3
This definition should be extended somehow to accommodate indefinite integration. I suggest that indefinite integration should be the interpretation when x3 is omitted. I'm not sure whether the grammar is capable of polymorphic operators like this. Other options/ways to get this behaviour is to default x3 to no bi'o ty (recover indefinite integrals as parameter integrals), or make it the indefinite when x3 is filled with mo'e zi'o.
This definition is (rather sneakily) fully compatible with a Lebesgue definition of integration. Just give a measurable function as x1, a measure to x2 and measurable set to x3.
This n-ary operator takes vectors as operands and forms them into the columns of a matrix. The matrix with the columns x1, x2, x3, ...
8 | 1 | 6 |
3 | 5 | 7 |
4 | 9 | 2 |
The trinary operation of taking the derivative of a function. The derivative of x1 with respect to x2 of degree x3. The default value of x3 is 1.
The trinary operation which lays out the summation of an indexed sequence of expressions. Also known in mathematics as sigma notation. The sum of x1 in a variable x2 over range x3