## 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. }