lojbo jufsisku
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Total: 66 result(s)
obsolete cmavo mekso 4-nary operator: spherical harmonics on colatitudinal/polar angle a and azimuthal/longitudinal angle b of unassociated order c and associated order d. Usually denoted Y^m_l (\theta, \phi). The Condon-Shortley phase must be prepended to the definition. The normalization is chosen so that the integral over all (solid) angles of Y^m_l(\Omega) conj(Y^n_k(\Omega) = \delta(m,n) \delta(l,k).
experimental cmavo mekso (n+1)-ary operator: q-analog converter - the ath analog of b (quoted operator) applied to operands c, d, ... Quote operator b with mau'au (and terminate it). The result is the q-analog of that operator (defined according to context if necessary), where q=a, which is then applied to operands of b in order (as defined for b).
experimental cmavo x1 is a number/value such that the abstraction is true, under mathematical system x2; x1 binds to ke'a within the abstraction Essentially a specialized version of poi'i for use with predicated mathematical statements (as an alternative to mekso). See also ke'a.
experimental cmavo mekso operator: power set - produces the set of all subsets of set A that are of (any) size (that is) b [a nonnegative integer or transfinite/infinite number] Possibly also could be used as a nonlogical "connective" of sorts. For accessing more than one cardinality in b, use modifiers ("less than"/"greater than") or vague numbers; default: «su'e ro», which outputs the set of all subsets of A; thus, the unary operator is just the standard power set operator.
lujvo x1 is a scalar in structure/set x2 with properties (potentially including magnitude, etc. in a given metric and coordinate system) x3; x1 is a simple number; x1 is a number that lacks In some interpretations, for example, complex numbers may be scalars; in others (including mekso in a sense), they can be treated as two-component vectors (in which case "direction in the complex plane" and magnitude can be noted in properties x3).
experimental cmavo non-logical connective (mekso set operator): regardless Primary motivation is to allow for an analog of .u using non-logical connectives of the form of set operators (in the same analogy that related set intersection to logical AND). .krtisfranks. is not sure that this word even fulfills a heretofore unsatisfied logical role, let alone is necessary or practically useful/desirable.
experimental cmavo mekso clausal referent bracket initializer Works with words of selma'o NOIhA. Within a mekso expression, any sequence of words/any subexpression between this word and the (immediate/very) next unmatched member of selma'o NOIhA are consolidated into (one whole and indivisible (for the sake of the clause) entity which acts as reference of the clause introduced by the same member of NOIhA, thus overriding the default attachment of NOIhA cmavo to the word immediately preceding them in a mekso expression. A member of NOIhA is considered "unmatched" if and only if the number of intervening additional uses of this word is less than or equal to the number of members of NOIhA uttered after the usage of this word being considered. The bracketed expression is considered to be a whole and single unit that can only be referenced together and in its single entirety; the bracketed expression is considered to be formal and remains unevaluated for the purposes of the reference/clause- thus, any reference to its evaluated result must be made by modifying ke'a. See also: noi'a, poi'a.
experimental cmavo mekso ternary operator: positive super-logarithm; the super-logarithm (inverse operator of hyper-operator with respect to "height" of power tower) of a with base b and of order c-2 c is a nonnegative number (currently, must be an integer). Currently, b must be a positive integer in order to be well-defined. c=3 produces the normal/standard/simple logarithm; c=4 produces slog. See also: te'au'u, fe'au'u, dei'au'o.
experimental cmavo mekso n-ary operator: append contravariant (upper) indices to tensor Terminated by te'oi'oi. Takes ordered input (A, X_1, X_2, …, X_(n-1)), where A is a tensor and X_i is an index with an understood (or elsewhere defined) ordered domain. It appends/assigns X_i to be the ith contravariant index of A, which is usually designated as a superscript in the ith position to the right of A. See also: ni'a'au. It is probable that Einstein summation notation will be conventionally in effect.
experimental cmavo non-logical connective/mekso operator - variable arity: X1 \ X2 Ordered: 'x1 kei'i x2' is not generally the same as/equivalent to 'x2 kei'i x1'. If X1 is not explicitly specified, it is taken to be some universal set in the discourse (of which all other mentioned sets are subsets, at the least); in this case, the word operates more as the set (absolute) complement. When X1 is specified, it represents the set relative complement. Somewhat analogous to logical NOT (just as intersection is analogous to logical AND, union is analogous to logical AND-OR). The preferred description/name in English is "set (theoretic) exclusion".
experimental cmavo mekso n-ary operator: append covariant (lower) indices to tensor Terminated by te'oi'oi. Takes ordered input (A, X_1, X_2, …, X_(n-1)), where A is a tensor and X_i is an index with an understood (or elsewhere defined) ordered domain. It appends/assigns X_i to be the ith covariant index of A, which is usually designated as a subscript in the ith position to the right of A. See also: ga'u'au. It is probable that Einstein summation notation will be conventionally in effect.
cmavo-compound mekso operator: plus or minus with order important, (((a±b)±c)±...±z) Strictly not "positive or negative" (if order matters, use ma'ufa'uni'u instead for that purpose). Subscript fa'u when multiple such operators (including "positive or negative" and others) are in use but are applied independently. This word is more useful and more general in mathematics than su'ijavu'u is, but is perhaps/arguably less general(ly useful) in Lojban, syntactically speaking, since not all statements have multiple occurrences of fa'u that may be linked.
cmavo-compound mekso operator: plus or minus, (((a±b)±c)±...±z) Strictly not "positive or negative" (which is ma'ujani'u vel sim.). This word is general but could easily be replaced by su'ijonaivu'u when the two options are not equivalent (usually when none of the operands are 0). Not preferred in complicated expressions wherein order of operations is important: see su'ifa'uvu'u or su'ifa'u'aivu'u.
experimental cmavo mekso ternary operator: Knuth up-arrow notation: a \textasciicircum{}…\textasciicircum{} b with c-2 arrows ("\textasciicircum{}") initially, evaluated from right to left; the cth hyperoperator on a by b c must be a nonnegative integer. c=0 is the lowest-order hyperoperator in the structure. Thus, for integers: c=0 is succession of/on b (in which case a can be omitted or be any number), c=1 is addition, c=2 is multiplication, c=3 is exponentiation, c=4 is tetration, etc. Notice that right-grouping is in effect for all c; thus x*(y*z) is calculated, rather than (x*y)*z.
experimental cmavo mekso unary operator: the set of all fixed points of function a The output is an (unordered) set of all of the fixed/stationary/self-mapping points of the input function a; in other words, it the set of all x that are in the domain of a such that a(x) = x. Beware that a may have a larger range than intended (for example, e^x makes sense even for some matrix-valued x). Use mau'au for quoting a.
experimental cmavo mekso convention default specification/definition (explicit) This word is followed by a list of rules. The rules specify the convention by which mekso or mathematical expressions (of various kinds) are to be interpreted. Such conventions are taken to remain in effect until the end of the discourse, until repealed, or if the come to conflict with subsequent rules so marked; in the lattermost case, the subsequent rule takes precedent and the earlier rules that are in conflict with it are ignored only in the most minimal domain of application possible (for example, a rule saying "left composition of functions is denoted by "°" in all cases" could be followed by a rule saying "when a linear transformation can be represented by a matrix, left composition of two such functions is equivalent to left multiplication of their corresponding matrices and so their left composition may be represented simply by juxtaposition as is typical with/for multiplication" with result being that "°" is to be used for all left compositions of functions except when both functions being composed are linear transformations admitting matrix representations, in which case "°" could be used but adjacency alone is sufficient to denote their left composition). Collections of rules (ordered in increasing precedence) can be named and referenced by such name expressed instead of those rules at length (such as calling a (specific) rather simple set of rules defining the order of operations ".pemas."). See also: xau'o'o.