ju'au
experimental cmavo semimathematical binary operator: named number base operator/interpreter Follows a number and is followed by a sumti string (introduced with appropriate gadri, multiple sumti strung together via connectives); scope terminates with the end of the sumti and/or with ke'e'au. The construct as a whole syntactically functions as a parenthetical so that mekso may be resumed immediately thereafter without any difficulty. This word attaches to/affects the immediately preceding macrodigit string extending from the last evaluated number, number operation, etc. or bracket to/until this word. The preceding number is semantically interpreted according to the description to which the following sumti refers. If a sequence is supplied as the following sumti, the preceding number is interpreted so that each digit, starting from the left (default: see next), is understood as a multiple of the corresponding value in the sequence under the ordering given (which may produce an invalid/illformed result; the placement of pi matters as well). If a single number is submitted (such as "li dau"), this word acts as ju'u; the number is interpreted according to the rules of mekso and is its own island for such interpretation (thus ju'u is needed to override a cultural/grammatical default interpretation, such as decimal, even if this is done within the mekso expression outside of and including the scope of this word). In this way, the sumti being (10^n)_n, which is a sequence, is the same as the sumti being just 10, but is very different from it being the sequence (10)_n. The original default for numeralposition/string reading/interpretation is from lefttoright, where a digit on the left in a pair of digits represents that multiple of a "later" term in the sequence as compared to right member of the pair; thus "23" in decimal means (2*(10^1)) + (3*(10^0)), which is twentythree. This default may be overridden via specification of the sequence (either its ordering, its domain being negated, or alteration to the base); alternatively, and perhaps more easily, the appearance of "la'e zoi jbo. ri'u bi'o zu'a .jbo" will always reverse it (this is a special input value with interpretation defined by this grammar); when reversed, "23" in decimal means (2*(10^0)) + (3*(10^1)), which is to say thirtytwo. Generally, this word overrides the default interpretation of a string of microdigits when computing the value of a macrodigit (see: ju'u'i). See also: ju'u, ju'u'i, pi'e.


ju'u'i
experimental cmavo longdigit interpretation specifier; macrodigit named base specifier When a string of multiple digits is on either side of pi'e, the string is to be interpreted as a single "macrodigit" in the longer numeric string; let the digits that compose it be called "microdigits" for clarity. By default, the macrodigit is interpreted as being written/expressed in some cultural or grammatical default (this default is overridden by ju'au if its specifying sumti requires an alternative interpretation for the value of the macrodigits), probably decimal the interpretation of the string of microdigits produces a number, x; the "pi'e" implies the denominator to be used in determining the fraction for which x is in the numerator and context or possibly a specified base determines its value in timekeeping, the interpretation is typically x/60 for certain macrodigits. However, the default for determining the value of x given a string of microdigits might be useful to override (for example, Tsohnai uses an overall factorial base but each macrodigit is written in balanced quinary); this word specifies the base used for interpreting the macrodigit from a string of microdigits. It is placed at the end of the string (possibly before the next "pi'e") and its scope of effect extends from there, through the string of microdigits, to either the beginning of the number as a whole or the most recent "pi'e" (whichsoever was more recently uttered). It is to be followed by a sumti (or multiple sumti strung together by connectives) and has its scope of specification terminate with that sumti; in this regard, it works syntactically and semantically exactly like ju'au. In fact, ju'au can be used outside of the number in order to specify the macrodigit interpretation instead of this word (for example, if its sumti were la .tsonais., this word would not be needed); however, if only a sequence were to have been given as the argument of ju'au (such as the factorial sequence) and if some base other than decimal were desired for the interpretation of each macrodigit from the string of microdigits, then this word would be used. If only one macrodigit appears in the number, then this word is equivalent to ju'au. In short, the scope of this word is one contiguous string of microdigits, and it influences their interpretation into a macrodigit value in the same way that ju'au does. However, if both ju'au and this word specify how to interpret a given string of microdigits in the same number (composed of macrodigits), this word overrides the interpretation specified by ju'au (but only for this macrodigit); thus, for example, a Tsohnai number can have each of its macrodigits be interpreted in balanced quinary except one, which the speaker specifies via this word, because they know the value but did not want to convert it to balanced quinary (because it may be too large or hard to do so easily), so they instead expressed it in decimal.


zoi'ai
experimental cmavo nonmekso quote/name substitution for ordered collection of prescriptions, descriptions, definitions, etc. Delimited nonmath/nonmekso quote (works like zoi in this respect). Treats the quote as a substitute for some formal collection of rules or mathematical description/definitions/notations; the exact meaning of the quote must be inferred as is the case with la or any quote; the quote is treated as a single block of text representative a single entity so described in only that case/context by the utterer; can be used to clarify the interpretation of text (convention specification; text need not be mathematical (in which case, it must be used in a metalinguistic scope)) or as an operand of certain mathematical operators (or, more generally perhaps, bridi). Might be useful for quoting names as descriptors for arguments of operands. For example: orderings, metrics, bases, densities, analytic properties, conventions, etc. can all be more easily described by a moniker than by a formal mathematical description. See also: ju'au, se'au, mau'au.
