po'i'oi VUhU experimental cmavo

mekso at-most-3-ary operator: convert to polynomial; X1 (ordered list of algebraic structure (probably field) elements) forms the (ordered list of) coefficients of a polynomial/Laurent-like series with respect to indeterminate X2 under ordering rule X3 (default for finite list: the first entry is the coefficient of the highest-degree term and each subsequent entry is the next lesser-degree coefficient via counting by ones and wherein the last entry is the constant term)

In English, there is no good way to distinguish between x2 + 2x as a function and as a number; typical notation would demand that it is a number but abuse must be adopted since no easy alternative exists for its expression as a function (such as when it is being defined; mapping notation is one of the best options, but is cumbersome). Lojban now allows for such functionality: just apply this word to the ordered list (1,2,0) and do not fill the second terbri (X2: the indeterminate). This word can also be viewed as creating an object in a ring. Termination of the list is extremely important; under normal interpretations, list entries can themselves have operations applied internally; moreover, multiple indetermimates can be introduced by careful application of this word to a list wherein each entry is itself treated as a polynomial. The last entry in X1 must be 'constant' term (when understood as a function), so care must be taken to explicitly mention an appropriate number of zeroes. See also: "cpolinomi'a", "po'i'ei".


In notes:

po'i'ei (exp!)
n-ary mekso operator: for an input of ordered list of ordered pairs ((X1, Y, it outputs formal generalized rational function (x - X1)^Y in the adjoined indeterminate (here: x).
cpolinomi'a
x1 is a formal polynomial with coefficients x2 (ordered list) of degree x3 (li; nonnegative integer) over structure/ring x4 (to which coefficients x2 all belong) and in indeterminant x5.