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Date: Fri, 03 Jul 2015 14:05:52 -0700
To: webmaster@lojban.org, curtis289@att.net
Subject: [jvsw] Definition Edited At Word se'au -- By krtisfranks
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In jbovlaste, the user krtisfranks has edited a
definition of "se'au" in the language "English".

Differences:

5,5c5,5
< =09=09Produces the left application of the operation/function $a=3D=
=E2=80=A2$ on sequence $b=3Db(y)$, the terms of which are functions eva=
luated at (possibly dummy) values $y$ (multi-index), where each b(y) be=
longs to set $c$ (at the values of which the function b is evaluated), =
operation $a$ being applied thereto in order $d$ (rule prescription; sp=
ecifies order of &y&'s; note that the application is from the left). Th=
e steps at which $y$'s are taken can be specified by $c$ or by taking c=
omplicated (evaluated) expressions $z(y)$ instead of $y$ as arguments o=
f $b$. Notice that $d$ affects both $y$ (or $z(y)$) directly as well as=
 $b$ (less directly) by being established on $c$.  Output is in the for=
mat (for example: scalar, tensor, function, etc.) that the operation $a=
=3D=E2=80=A2$ yields. For Sigma/series summation notation ({si'i}), $a=
=3D+$, for Pi multiplication notation $a=3D*$, for functional power/ite=
rated composition of functions $a=3D=C2=B0$, for the Cartesian product =
of sets $a=3D=C3=97$ (preferred to "exponentiation of sets" notation li=
ke $A^n$). {mau'au} and {zai'ai} will be necessary for the proper use o=
f this word (particularly for specifying $a$); $d$ will be specified ex=
plicitly (possibly elsewhere) and/or via {zoi'ai}. See also: {ma'o'e}.
---
> =09=09Produces the left application of the operation/function $a=3D=
=E2=80=A2$ on sequence $b=3Db(y)$, the terms of which are functions eva=
luated at (possibly dummy) values $y$ (multi-index), where each b(y) be=
longs to set $c$ (at the values of which the function b is evaluated), =
operation $a$ being applied thereto in order $d$ (rule prescription; sp=
ecifies order of $y$'s; note that the application is from the left). Th=
e steps at which $y$'s are taken can be specified by $c$ or by taking c=
omplicated (evaluated) expressions $z(y)$ instead of $y$ as arguments o=
f $b$. Notice that $d$ affects both $y$ (or $z(y)$) directly as well as=
 $b$ (less directly) by being established on $c$.  Output is in the for=
mat (for example: scalar, tensor, function, etc.) that the operation $a=
=3D=E2=80=A2$ yields. If $b$ is a constant (at least with respect to th=
e argument $y$ being ranged over), then the operator $a$ is taken being=
 applied to $b$ for a number of times equal to the cardinality of $c$ (=
and, technically, in the order specified by $d$). If $c$ is explicitly =
created via use of {ce'o}, then the order is from the first term uttere=
d to the last term uttered, as uttered; $d$ need not be specified (if i=
t is, it overrides the order of utterance). For Sigma/series summation =
notation ({si'i}), $a=3D+$, for Pi multiplication notation $a=3D*$, for=
 functional power/iterated composition of functions $a=3D=C2=B0$, for t=
he Cartesian product of sets $a=3D=C3=97$ (preferred to "exponentiation=
 of sets" notation like $A^n$). {mau'au} and {zai'ai} will be necessary=
 for the proper use of this word (particularly for specifying $a$); $d$=
 will be specified explicitly (possibly elsewhere) and/or via {zoi'ai}.=
 See also: {ma'o'e}.
10a11,11
\n> =09=09Word: big operator, In Sense:=20
15,15d15
< =09=09Word: big operator, In Sense:=20
\n

Old Data:

=09Definition:
=09=09mathematical quinary operator; big operator: left sequence notati=
on/converter - operator a, sequence b, in set c, under ordering d

=09Notes:
=09=09Produces the left application of the operation/function $a=3D=E2=
=80=A2$ on sequence $b=3Db(y)$, the terms of which are functions evalua=
ted at (possibly dummy) values $y$ (multi-index), where each b(y) belon=
gs to set $c$ (at the values of which the function b is evaluated), ope=
ration $a$ being applied thereto in order $d$ (rule prescription; speci=
fies order of &y&'s; note that the application is from the left). The s=
teps at which $y$'s are taken can be specified by $c$ or by taking comp=
licated (evaluated) expressions $z(y)$ instead of $y$ as arguments of $=
b$. Notice that $d$ affects both $y$ (or $z(y)$) directly as well as $b=
$ (less directly) by being established on $c$.  Output is in the format=
 (for example: scalar, tensor, function, etc.) that the operation $a=3D=
=E2=80=A2$ yields. For Sigma/series summation notation ({si'i}), $a=3D+=
$, for Pi multiplication notation $a=3D*$, for functional power/iterate=
d composition of functions $a=3D=C2=B0$, for the Cartesian product of s=
ets $a=3D=C3=97$ (preferred to "exponentiation of sets" notation like $=
A^n$). {mau'au} and {zai'ai} will be necessary for the proper use of th=
is word (particularly for specifying $a$); $d$ will be specified explic=
itly (possibly elsewhere) and/or via {zoi'ai}. See also: {ma'o'e}.

=09Jargon:
=09=09

=09Gloss Keywords:
=09=09Word: iteration, In Sense: serial operator
=09=09Word: sequence notation, In Sense:=20
=09=09Word: serial operator notation, In Sense:=20
=09=09Word: series notation, In Sense:=20
=09=09Word: big operator, In Sense:=20

=09Place Keywords:


New Data:

=09Definition:
=09=09mathematical quinary operator; big operator: left sequence notati=
on/converter - operator a, sequence b, in set c, under ordering d

=09Notes:
=09=09Produces the left application of the operation/function $a=3D=E2=
=80=A2$ on sequence $b=3Db(y)$, the terms of which are functions evalua=
ted at (possibly dummy) values $y$ (multi-index), where each b(y) belon=
gs to set $c$ (at the values of which the function b is evaluated), ope=
ration $a$ being applied thereto in order $d$ (rule prescription; speci=
fies order of $y$'s; note that the application is from the left). The s=
teps at which $y$'s are taken can be specified by $c$ or by taking comp=
licated (evaluated) expressions $z(y)$ instead of $y$ as arguments of $=
b$. Notice that $d$ affects both $y$ (or $z(y)$) directly as well as $b=
$ (less directly) by being established on $c$.  Output is in the format=
 (for example: scalar, tensor, function, etc.) that the operation $a=3D=
=E2=80=A2$ yields. If $b$ is a constant (at least with respect to the a=
rgument $y$ being ranged over), then the operator $a$ is taken being ap=
plied to $b$ for a number of times equal to the cardinality of $c$ (and=
, technically, in the order specified by $d$). If $c$ is explicitly cre=
ated via use of {ce'o}, then the order is from the first term uttered t=
o the last term uttered, as uttered; $d$ need not be specified (if it i=
s, it overrides the order of utterance). For Sigma/series summation not=
ation ({si'i}), $a=3D+$, for Pi multiplication notation $a=3D*$, for fu=
nctional power/iterated composition of functions $a=3D=C2=B0$, for the =
Cartesian product of sets $a=3D=C3=97$ (preferred to "exponentiation of=
 sets" notation like $A^n$). {mau'au} and {zai'ai} will be necessary fo=
r the proper use of this word (particularly for specifying $a$); $d$ wi=
ll be specified explicitly (possibly elsewhere) and/or via {zoi'ai}. Se=
e also: {ma'o'e}.

=09Jargon:
=09=09

=09Gloss Keywords:
=09=09Word: big operator, In Sense:=20
=09=09Word: iteration, In Sense: serial operator
=09=09Word: sequence notation, In Sense:=20
=09=09Word: serial operator notation, In Sense:=20
=09=09Word: series notation, In Sense:=20

=09Place Keywords:


You can go to <http://jbovlaste.lojban.org/dict/se'au> to see it.