Chapter 18: lojbau mekso: Mathematical Expressions in Lojban

18. Using Lojban resources within mekso

The following cmavo are discussed in this section:

```   na'u    NAhU    selbri to operator
ni'e    NIhE    selbri to operand
mo'e    MOhE    sumti to operand
te'u    TEhU    terminator for all three
```

One of the mekso design goals requires the ability to make use of Lojban's vocabulary resources within mekso to extend the built-in cmavo for operands and operators. There are three relevant constructs: all three share the elidable terminator “te'u” (which is also used to terminate vectors marked with “jo'i”).

The cmavo “na'u” makes a selbri into an operator. In general, the first place of the selbri specifies the result of the operator, and the other unfilled places specify the operands:

```✥18.1    li na'u tanjo te'u
vei pai fe'i re [ve'o] du li ci'i
the-number the-operator tangent
( pi / 2 ) = the-number infinity
tan(pi/2) = ¥
```

“tanjo” is the gismu for “x1 is the tangent of x2”, and the “na'u” here makes it into an operator which is then used in forethought.

The cmavo “ni'e” makes a selbri into an operand. The x1 place of the selbri generally represents a number, and therefore is often a “ni” abstraction, since “ni” abstractions represent numbers. The “ni'e” makes that number available as a mekso operand. A common application is to make equations relating pure dimensions:

```✥18.2    li ni'e ni clani [te'u] pi'i
ni'e ni ganra [te'u] pi'i
ni'e ni condi te'u
du li ni'e ni canlu
the-number quantity-of length times
quantity-of width times
quantity-of depth
equals the-number quantity-of volume.
Length × Width × Depth = Volume
```

The cmavo “mo'e” operates similarly to “ni'e”, but makes a sumti (rather than a selbri) into an operand. This construction is useful in stating equations involving dimensioned numbers:

```✥18.3    li mo'e re ratcu su'i mo'e re ractu
du li mo'e vo danlu
the-number two rats plus two rabbits
equals the-number four animals
2 rats + 2 rabbits = 4 animals.
```

Another use is in constructing Lojbanic versions of so-called “folk quantifiers”, such as “a pride of lions”:

```✥18.4    mi viska vei mo'e lo'e lanzu ve'o cinfo
I see ( the-typical family )-number-of lions.
I see a pride of lions.
```