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se'o'e
experimental cmavo elliptical/generic/unspecific/vague selbri conversion Basically says 'in some (id est: at least one) ordering/permutation, these arguments and this selbri make sense [and I claim the produced sentence]'. The ordering may be complicated, or it could even be the case that multiple orderings work. Can be useful for when one does not quite remember or care about the exact definition of a brivla, including in sumti; can also be useful when the conversion is particularly complicated, when a desired terbri has a large index, or when multiple conversions are true; it is an allowed, if unhelpful, response to se'u'o.


ta'ei
experimental cmavo discursive: reconsideration of statement  continuing (on) in that line of thought/discussion Common English phrases that may (based on context) indicate reconsideration of what has been or was about to be said: reconsider, backpedal, "On second thought", second thinking, "Eh", "Never mind", "Forget that (all)", "I should not have said that", "Actually, ...", conversational Uturn, revise, retrace (with intent to brush aside/over, ignore, move in different direction of conversation), reevaluate, reweigh, review, rethink (that), emend/correct (with intent to avoid a certain path of discussion), etc.


cu'au
experimental cmavo universial famyma'o: terminates the most recently opened construct or clause. cu'au looks back for the most recently opened construct that has not been terminated, and emulates whatever famyma'o would terminate it. It can also be subscripted with xi, and will terminate that many times. Note that that means grammatical function is being put in a xi clause, so be careful when using it. Additionally, cu'au xi ro will terminate all the way up to the last sentencestarting word (.i mi klama lo zarci pe lo pendo be mi cu'au xi ro > .i mi klama lo zarci pe lo pendo be mi cu'aube'okuge'ukuvau). This will also terminate to sentences started in lu (will NOT emulate li'u UNLESS used multiple times), ni'o, and no'i. It will NOT emulate le'u. In addition to ro, it can be subscripted with da'a, which terminates to the sentence level, minus 1. In the previous example, this would just leave the vau remaining, and allow you to continue to add to the place structure of klama.


pau'a'u
experimental cmavo mekso operator: part of number/projection (one sense); the X2 part of X1 X1 can be a tensor, in which case the operator applies entrywise; X1 can be a function, in which case the operator applies pointwise. It extracts the part of the number that belongs to the structure X2 united with the singleton 0. X2 = R implies "real part"; X2 = i*R implies "imaginary part"; X2 = R+ implies "positive part"; X2 = R implies "negatige part". If X1 has no explicit value/projection in/along X2, then the output is 0. If 0 is X1 or X2, then the output is 0. X1 should really be a structure, not just a set.


pavysmi
lujvo x1 is the one(like) element/multiplicative identity of structure/ring x2; often is denoted by ' 1_R ' or ' I_R ' or by (when context is obvious) '1' or 'I', for structure/ring R (given by x2). Definition and rules may be specified in the second terbri; this definition does not suppose that the ring is not the 0ring (the trivial ring) with the mapping of all multiplications to 0 (in which case, the additive identity is also the multiplicative identity). The usage of "additive" and "multiplicative" in this context are defined by the ring. The n×n identity matrix over a given ring is an example of one such element. See also: nonsmi


bai'i
experimental cmavo mekso string operator (ternary): findandreplace; in string/text/word/sequence X1 formally replace X2 (ordered tuple of terms to be replaced) with X3 (ordered tuple of terms to be respectively substituted) X2 and X3 are ordered tuples of substrings/letters/characters/letterals/digits/numerals. The ith term in tuple X2 is replaced with the ith term in tuple X3; the replacements are executed simultaneously (thus, no overlap/contradiction can be allowed to arise in the substitution in particular, in X2)  alternatively, if there is overlap/conflict in/between the terms of X2, the replacements are performed in order of presentation (the ith term in X2 is replaced by the ith term in X3, and then the (i+1)th term in X2 is replaced with the (i+1)th term in X3, starting with the 1st term in each). X2 and X3 must have the same length/number of terms  alternatively, X3 cannot be longer/have more terms than X2; in this situation, the ith term of X2 is replaced with the ith term of X3 until and including when the last term of X3 is reached, after which point the remaining terms in X2 are not replaced at all. Use a permutation acting on X2 as the argument for X3 in order to rearrange the substrings of X1; if the alphabet is ordered, then operators can be applied to the letters in order to rotate through the alphabet. In particular, if X1 is a binary string (a word over an alphabet of two letters) and X2 is the 2tuple of the letters of that binary alphabet (length1 substrings), then without specification of X3, this operator defaults to bitwise binary negation (bit conjugation) wherein each letter in X1 is replaced by the unique other letter in the binary alphabet (otherwise, the replacement would be the identity/trivial replacement or just a formal substitution letterbyletter which does not really change the nature of the word). X1 and each entry in X2 and X3 should be quoted, match a necessary type (such as being a character), or be abstracted a level by symbolics. In general, the replacement is formal and the strings in X3 need not be over the same alphabet as the one over which X1 is written. This operator is useful for combinatorial lines and for expanding digits (such as, in a binary string, replacing each occurrence of "0" with "01" and each occurrence of "1" with "10"; note that the replacement is instantaneous and simultaneous for all terms of X2 and every occurrence of such terms in X1, thus this substitution is perfectly acceptable).


be'ei'oi
experimental cmavo ternary mekso operator: x_{1}th Bergelson multiplicative interval with exponents bounded from above by function x_{2} and with sequence of shifts x_{3}, where exponents belong to set x_{4} x1 must be a positive integer. x2 must be a strictly monotonic increasing function mapping from all of the positive integers to a subset (not necessarily proper) thereof. x3 must be a sequence of natural numbers. x2 without context will default to the same value as x1 (it is simple linear on the set of positive integers), x3 without context will be a sequence all and only of 1's, x4 without context defaults to the set of all nonnegative integers. Let p_i be a prime for all i, with p_{1} = 2 and the ith prime (in the normal monotonic increasing order) being p_i. Let all other symbols match the aforementioned conditions. Represent the nth term of the sequence x3 by x3_n; represent the function in x2 being applied to the number m by x2(m). Then x1 be'ei'oi x2 boi x3 boi x4 produces the set of all numbers of the form x3_(x1) * (p_{1})^(e_{1}) *...* (p_(x1))^(e_(x1)), where e_j belongs to the intersection of the interval [0, x2(x1)] with x4.


ce'oi
experimental cmavo argument list separator: acts as a comma between arguments in an argument list supplied to a function. "ce'oi" is the word of choice to separate the arguments in bridi_{3}. Using ce'o there has obvious limitations when the selbri actually calls for a sequence. Obviously, ce'oi has issues too if the selbri can accept an argument list, but this can be circumvented more readily with ke...ke'e brackets than it can with ce'o. Consider ".i lo ka broda cu selbri fi ko'a ce'o ko'e". Without inspecting the type requirements of broda and the respective types of ko'a and ko'e, one cannot determine the meaning of the bridi. Furthermore, if one accepts nonstatic typing of sumti places, multiple correct answers can be given for a question asking what is the bridi_{1}. This would create ambiguity that is otherwise resolved by "ce'oi". See also ka, du'u, me'au


daigno
fu'ivla x_{1} (ordered list) is a sampling of entries of matrix/tensor x_{2} in which exactly one entry is sampled from each row and/or column (etc.) between entries x_{3} (list; default: the largest 'square'/'hypercubic' sampling possible in the entire tensor starting with the first entry, see notes) inclusively following selection procedure/rule/function/order x_{4} (default: diagonally, see notes), where the tensor/matrix is expressed in basis/under conditions x_{5} Entries of the list in x3 need not actually be sampled; the entries listed are merely to name the minimal and maximal indices between which the sampling may be drawn. Thus, the indices/labels specified are included in the range of sampling; id est: if the matrix entries listed belong to the ith row and jth column and the (i+n)th row and (j+m)th column respectively (for positive integers i,j,n,m), then the sampling will be conducted in all rows of number between (and including) i and i+n (yielding n+1 sampled rows) and in all columns of number between (and including) j and j+m (yielding m+1 sampled columns). The default diagonal sampling procedure for x4 is as follows: The first sampled entry has the minimum allowed (as specified in x3) indices. All latter sampled entries (by default) have indices of the immediately previous sampled entry each augmented by 1. (Which is to say that if the kth sampled entry has indices (x,y,...), in that order, then the (k+1)th sampled entry has indices (x+1,y+1,...), in that order and where each subsequent index would be the respective index of the kth sampled entry augmented by 1). The process terminates generally whenever exactly one entry is sampled from each of the rows, each of the columns, etc. of the tensor. In the default, the process terminates when at least one of the indices of a sampled entry of the tensor is as large as possible in the range specified by x3. Thus, in order to reconcile the general and the default termination conditions, the range specified by x3 must be compatible with both; id est: it must be a rdimensional hypercube of entries, so to speak, where r is the rank of tensor x2. The default for sampling range x3 is between and including the entry in the first row and first column (etc.) and the entry in the last row and last column (etc.) for an rdimensional hypercube tensor (meaning that each row, column, etc. of the tensor has exactly the same number of entries as the others). Generally, the default range begins with the entry of indices each minimal in the tensor (called 'the first entry') and extends to include ("draw") the maximal rdimensional hypercube of entries in the tensor with one vertex on the first entry; in other words, if the minimum of the set of maximal indices in the tensor is g, then the sampling range is every row between the first and the gth, every column between the first and the gth, etc. Generally, the sampling range must be an rdimensional orthotope of some positive size (that is to say: including at least one entry) no larger than the tensor itself, but with the freedom to place at most r of its vertices among the entries thereof; if the default sampling procedure x4 is being used, then the rdimensional orthotope must be an rdimensional hypercube. Generalizes to any tensor, but is only interesting for tensors of rank at least 1. Any mention of geometric terminology (such as mention of diagonals, orthotopes, etc.) in the definition or notes of this word should be interpreted cautiously and is not necessarily good Lojbanic practice; such terminology should not necessarily be emulated in practicing Lojbanic thought or speech. Not for use for geometric diagonals (such as between vertices); confer: digno.


jednpa
fu'ivla x_{1} (event/state) is on Monday or the first day of a week x_{2} in system x_{3}. lo jednpa = lo se jefydeidetri be li pa. ex.) lo nu sanga ctuca mi cu jednpa ro loi re jeftu la gregoris (It's on Monday of every two weeks that I learn singing.) / mi'a kansa lo nunjmaji noi jednpa lo bavlamjeftu (We will attend the meeting on Monday of next week.) See also detri, detke'u, jeftu; jednpa, jednre, jednci, jednvo, jednmu, jednxa, jednze, jednbi, jednso, jedndau, jednfei, jedngai, jednjau, jednrei or jednxei, jednvai.


nacyzmarai
lujvo x_{1} (number) is the greatest element/maximum of the set (of numbers) x_{2} under (partial) ordering x_{3} x1 must be a set. If this word is being used as a function (max), common but lazy mathematical practice allows for speaking of "the maximum of a function" (including sequences) or to constrain the maximum with respect to certain variables, but these constraints can and properly ought to be incorporated into the definition of the set of which the maximum is being taken. This word is not limited to purely mathematical usage and the set can be defined loosely (such as in "the maximum number of people whom I permit to be invited" wherein the set x2 is understood to be the set of the possible acceptable numbers of guests allowed by the speaker). The maximum x1 must belong to set x2; compare with: mecraizmana'u (supremum). See also: nacmecrai.


se'u'o
experimental cmavo selbri conversion question Asks for the SE word that is intended (or at least makes the sentence true). Subscript a set of numbers that represent the order of terbri in question; the subscripted set can be a set of ordered or unordered tuples, specifying exactly which terbri may be exchanged. 'la .ralf. se'u'o xi li re ce li ci pi'u li re cebo li ci klama by boi cy' = 'Did Ralph come to B from C or to C from B?' (notably, 'Did B come to Ralph from C?' is not a possible option for answering the question). An answer is a SE string that is allowed by the selbri and by the subscripts; continuing the example, if the response is 'Ralph went to C from B', one would respond with '.i setese'. Any SE word works for the general question possibility (which is the unrestricted/nonsubscripted case). Essentially 'se'u'o xi sy' is equivalent to 'se xi li xo poi ke'a cmima sy' (where 'te' is basically understood as ' se xi li jo'i pa boi ci te'u ', etc.), but the answer can be a complicated ordered sequence/string of SE words; this word complements specifically fi'a in the typical/same way that SE complements FA. Typically, leaving the subscripted set vague or not completely free of every possible semantic or syntactic pathology is perfectly fine; syntax and practicality will typically restrict it enough for reasonable responses to be made. See also: re'au'e (which alone would be used in answering that 'Ralph goes to B from C' in the previous question).


aigne
fu'ivla x_{1} is an eigenvalue (or zero) of linear transformation/square matrix x_{2}, associated with/'owning' all vectors in generalized eigenspace x_{3} (implies neither nondegeneracy nor degeneracy; default includes the zero vector) with 'eigenspacegeneralization' power/exponent x_{4} (typically and probably by cultural default will be 1), with algebraic multiplicity (of eigenvalue) x_{5} For any eigenvector v in generalized eigenspace x_{3} of linear transformation x_{2} for eigenvalue x_{1}, where I is the identity matrix/transformation that works/makes sense in the context, the following equation is satisfied: ((x_{2}  x_{1} I)^x_{4})v = 0. When the argument of x_{4} is 1, the generalized eigenspace x_{3} is simply a strict/simple/basic eigenspace; this is the typical (and probable cultural default) meaning of this word. x_{4} will typically be restricted to integer values k > 0. x_{2} should always be specified (at least implicitly by context), for an eigenvalue does not mean much without the linear transformation being known. However, since one usually knows the said linear transformation, and since the basic underlying relationship of this word is "eigenness", the eigenvalue is given the primary terbri (x_{1}). When filling x_{3} and/or x_{4}, x_{2} and x_{1} (in that order of importance) should already be (at least contextually implicitly) specified. x_{3} is the set of all eigenvectors of linear transformation x_{2}, endowed with all of the typical operations of the vector space at hand. The default includes the zero vector (else the x_{3} eigenspace is not actually a vector space); normally in the context of mathematics, the zero vector is not considered to be an eigenvector, but by this definition it is included. Thus, a Lojban mathematician would consider the zero vector to be an (automatic) eigenvector of the given (in fact, any) linear transformation (particularly ones represented by a square matrix in a given basis). This is the logically most basic definition, but is contrary to typical mathematical culture. This word implies neither nondegeneracy nor degeneracy of eigenspace x_{3}. In other words there may or may not be more than one linearly independent vector in the eigenspace x_{3} for a given eigenvalue x_{1} of linear transformation x_{2}. x_{3} is the unique generalized eigenspace of x_{2} for given values of x_{1} and x_{4}. x_{1} is not necessarily the unique eigenvalue of linear transformation x_{2}, nor is its multiplicity necessarily 1 for the same. Beware when converting the terbri structure of this word. In fact, the set of all eigenvalues for a given linear transformation x_{2} will include scalar zero (0); therefore, any linear transformation with a nontrivial set of eigenvalues will have at least two eigenvalues that may fill in terbri x_{1} of this word. The 'eigenvalue' of zero for a proper/nice linear transformation will produce an 'eigenspace' that is equivalent to the entire vector space at hand. If x_{3} is specified by a set of vectors, the span of that set should fully yield the entire eigenspace of the linear transformation x_{2} associated with eigenvalue x_{1}, however the set may be redundant (linearly dependent); the zero vector is automatically included in any vector space. A multidimensional eigenspace (that is to say a vector space of eigenvectors with dimension strictly greater than 1) for fixed eigenvalue and linear transformation (and generalization exponent) is degenerate by definition. The algebraic multiplicity x_{5} of the eigenvalue does not entail degeneracy (of eigenspace) if greater than 1; it is the integer number of occurrences of a given eigenvalue x_{1} in the multiset of eigenvalues (spectrum) of the given linear transformation/square matrix x_{2}. In other words, the characteristic polynomial can be factored into linear polynomial primes (with root x_{1}) which are exponentiated to the power x_{5} (the multiplicity; notably, not x_{4}). For x_{4} > x_{5}, the eigenspace is trivial. x_{2} may not be diagonalizable. The scalar zero (0) is a naturally permissible argument of x_{1} (unlike some cultural mathematical definitions in English). Eigenspaces retain the operations and properties endowing the vectorspaces to which they belong (as subspaces). Thus, an eigenspace is more than a set of objects: it is a set of vectors such that that set is endowed with vectorspace operators and properties. Thus klesi alone is insufficient. But the set underlying eigenspace x_{3} is a type of klesi, with the property of being closed under linear transformation x_{2} (up to scalar multiplication). The vector space and basis being used are not specified by this word. Use this word as a seltau in constructions such as "eigenket", "eigenstate", etc. (In such cases, te aigne is recommended for the typical English usages of such terms. Use zei in lujvo formed by these constructs. The term "eigenvector" may be rendered as cmima be le te aigne). See also gei'ai, klesi, daigno
