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.