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ja: use the Japanese names for the elementary functions and the parts of a complex number - #733

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ja: use the Japanese names for the elementary functions and the parts of a complex number#733
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yasumorishima:ja-elementary-functions

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The Japanese seed data reached the elementary functions and the complex-number
parts through machine translation, and most of the names came out as either a
different mathematical object or an ordinary Japanese word. This replaces them
with the terms Japanese mathematics actually uses.

Only strings change. No rule is added, removed, or restructured, and
audit-translations ja reports the same 28 rule differences before and after.

Names that were a different object

symbol was means now
tan 接線 the tangent line (a curve) タンジェント
sec 割線 the secant line (a curve) セカント
sec (terse) 探す the verb "to search" セカント
sinh 高分子正弦 高分子 is a macromolecule 双曲線正弦
cosh 高分子コサイン same 双曲線余弦
real-part 実際の部分 "the actual portion" 実部
imaginary-part 想像上の部分 "a portion someone imagined" 虚部
complex-conjugate 複雑なコンジュゲート 複雑な is "complicated" 複素共役
polar-coordinate 極の座標 "coordinate belonging to a pole" 極座標

Names that were not Japanese words at all

種目 (secant), アークシネ (arcsine), アルコシン (arccosine),
アーク-コタント (arccotangent), コタント (cotangent),
ピンチ (sinh, terse), タンチ (tanh), コシュネック (csch),
コタンチ (coth), シーメール (sech, terse — this one is an offensive word in
Japanese), フラクショナルパーツ (fractional part), アーグ (complex arg).

Terms used

All of them are the standard Japanese names and are the ones the Japanese
Wikipedia articles use:

  • trigonometric: 正弦 / 余弦 / 正接 / 正割 / 余割 / 余接
  • inverse trigonometric: 逆正弦 … 逆余接 (all six appear in 逆三角関数)
  • hyperbolic: 双曲線正弦 … 双曲線余接 (all six appear in 双曲線関数)
  • complex numbers: 実部, 虚部, 複素共役 (共役複素数 redirects to it), 偏角

The inverse hyperbolic functions keep katakana only. Japanese sources do not
use a 逆双曲線正弦 form, so there was nothing to put there; the change is limited
to spelling アークコッシュ as アークハイパーボリックコサイン.

Verbosity

definitions.yaml already used katakana: kanji for sine, cosecant and the
hyperbolic entries, so the rest of the block now follows it: terse says the
abbreviation the way it is read aloud (コサイン, タンジェント), medium and verbose
say the formal name (余弦, 正接).

The mi rules in general.yaml keep katakana in both branches, matching the
cos rule that was already there and sin, which — as in en — has no
verbosity test and always says サイン. Splitting only some of the six would make
one formula say サイン and 余弦 side by side.

Tests

22 assertions in tests/Languages/ja/ja.rs: the six trigonometric and six
hyperbolic functions as mi, one terse reading, the four complex-number
intents, and the six inverse trigonometric intents.

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