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valsi du'a'o
type experimental cmavo
creator krtisfranks
time entered Thu Apr 7 02:42:39 2016

Definition #68579 - Preferred [edit]
selma'o VUhU
definition mekso binary operator: extract substructure/underlying set/endowing operator; the substructure (general sense; includes just operator, order, set, etc.) of X1 (structure; explicitly given by du'a'e) which is formed by collecting the ith entries of that du'a'e-tuple in order together into their own du'a'e-tuple (or by extracting them naked into the ambient environment if X2 is a singleton) for all i in set X2
notes Usually, a complicated structure will involve the underlying set. i is not a user-submission-accepting terbri; only X1 and X2 are. If X1 is not provided explicitly here by a du'a'e construct, then one must be inferred from context (the most recent definition; the order of things entries submitted to that construct is understood to apply here via direct formal substitution); otherwise, this word is undefined. Even though operators and orders must be submitted to de'a'e via zai'ai-mau'au quotes, they are extracted naked by this word (so that they can be used directly as evaluating operators in numerical expressions; thus, they must be requoted if that is desired/appropriate). Counting starts at 1. Thus, X2 being exactly the singleton of 1 will output the underlying set of X1.
gloss words
created by krtisfranks
vote information 1
time Thu Apr 7 02:42:40 2016
[View Comments For This Definition]


Example #1:

"li pe'o du'a'o pe'o du'a'e tau ry boi mau'au su'i zai'ai boi mau'au pi'i zai'ai ku'e boi pa ce tu'oi ku'e du li tau ry" = "(R,'+','*')_1 = R"; a ring (R, '+', '*') has an underlying set R of number (with no algebraic properties)

(by krtisfranks) [edit]

Example #2:

"li pe'o du'a'o pe'o du'a'e tau ry boi mau'au su'i zai'ai boi mau'au pi'i zai'ai ku'e boi ci ce pa ku'e du li pe'o du'a'e tau ry boi mau'au pi'i zai'ai ku'e" = "(R,'+','*')_(3,1) = (R, '*')"; a ring (R, '+', '*') has a multiplicative group substructure (R, '*') where '*' behaves as in the superstructure but knows nothing of '+'; notice that the order of the extracted elements (3,1) does not matter because we extract each element of the superstructure which is any of 3 or 1 and reconstruct them in the order forced upon us by the superstructure.

(by krtisfranks) [edit]

Example #3:

"li pa pe'o du'a'o pe'o du'a'e tau ry boi mau'au su'i zai'ai boi mau'au pi'i zai'ai ku'e boi re ce tu'oi ku'e du li pa su'i re" = "1 (R,'+','*')_(2) 2 = 1 + 2"; notice the abnormal structure of the utterance (with a lonely "pa" followed immediately by an operator which does not operate on it in the left-hand side), and the fact that the operator '+' is extracted from its quotes so as to act directly on 1 and 2; note that 1+2 must be defined for '+' (probably in (R,'+','*') ).

(by krtisfranks) [edit]

krtisfranksOpposite of {du'a'e}.[edit]
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