# algebra fu'ivla

x1 is an algebra of type/describing x2

Lujvo synonym: snicmaci. Place structure parallel to that of cmaci.

## On gloss:

snicmaci in sense "The field of mathematics that studies symbolic variables and rules." on place 1
c1 is an algebra of type/describing c2

## In definition:

dzalenypi'i
x1 (li; often but not necessarily an integer) is a multiple of x2 (li; often but not necessarily an integer) by some integer, namely x3 (li; MUST be an integer in the structure; possibly, more than one input may be valid), in algebraic structure x4.
gu'au'i
mekso operator, variable arity - algebraic structure order of X1; OR: order of/(size of) period of element X1 in algebraic structure X2 under operator/of type X3
kau'o (exp!)
generic algebra unit en
pei'e'a
at-most-3-ary mekso operator: "integer exponent" for X1 divided by X2 in algebraic structure X3
po'i'oi
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)
pu'e'ei (exp!)
mekso binary operator: generate span; outputs span(X1, X= spanX; set of all (finite) sums of terms of form c v, where v is an element of algebraic structure X1 (wherein scalar multiplication and summation is defined), and c is a scalar belonging to ring X2.
aigne
x1 is an eigenvalue (or zero) of linear transformation/square matrix x2, associated with/'owning' all vectors in generalized eigenspace x3 (implies neither nondegeneracy nor degeneracy; default includes the zero vector) with 'eigenspace-generalization' power/exponent x4 (typically and probably by cultural default will be 1), with algebraic multiplicity (of eigenvalue) x5
epsi bu
digit/number: dual ε of dual number in linear algebra; square root of 0

## In notes:

soi'auroi (comp!)
almost never/nowhere (default: time sense)
kazmi
x1 (li) is the cardinality of set x2 (set)
fei'i (exp!)
mekso variable-arity (at most ternary) operator: number of prime divisors of number X1, counting with or without multiplicity according to the value X2 (1 xor 0 respectively; see note for equality to -1 and for default value), in structure X3.
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).
va'ei'a (exp!)
digit/number: Dom Hans van der Laan's plastic number ρ = 1.324717957244746025960908854…
vei'o (exp!)
binary mekso operator: form quotient space X1/X.
cmacistura
x1 is a mathematical structure defined on underlying structure/set/parts x2 with properties/rules/relations/operands/functions/substructures x3 in mathematics x4.