Difference between revisions of "Language/Multiple-languages/Vocabulary/Algebra"
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{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 科目 | |||
! cmn-Hans-CN: | ! cmn-Latn.Pinyin-CN: kēmù | ||
! cmn-Latn.Pinyin-CN: | ! deu-Latn-DE: Fach [n] | ||
! deu-Latn-DE: | ! eng-Latn-US: subject | ||
! fra-Latn-FR: | ! fra-Latn-FR: matière [f] | ||
! jpn-Jpan-JP: | ! jpn-Jpan-JP: 科目 | ||
! jpn-Hrkt-JP: | ! jpn-Hrkt-JP: か↑もく | ||
! rus-Cyrl-RU: | ! rus-Cyrl-RU: предме́т | ||
|- | |- | ||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| | | 抽象代数 | ||
| chōuxiàng dàishù | |||
| dàishù | | abstrakte Algebra | ||
| Algebra | | abstract algebra | ||
| algèbre | | algèbre générale, algèbre abstraite | ||
| | | 抽象代数学 | ||
| | | ちゅ↑うしょうだいす↓うがく | ||
| а́лгебра | | абстра́ктная а́лгебра, общая а́лгебра, вы́сшая а́лгебра | ||
|- | |- | ||
| | | 群论 | ||
| | | qún lùn | ||
| | | Gruppentheorie [f] | ||
| | | group theory | ||
| | | théorie [f] des groupes [m pl] | ||
| | | 群論 | ||
| | | ぐ↓んろん | ||
| | | тео́рия групп | ||
|- | |- | ||
| | | 环论 | ||
| | | huán lùn | ||
| | | Ringtheorie [f] | ||
| | | ring theory | ||
| | | théorie [f] des anneaux [m pl] | ||
| | | 環論 | ||
| | | か↑んろん | ||
| | | тео́рия коле́ц | ||
|- | |- | ||
| | | 范畴论 | ||
| fànchóu lùn | |||
| | | Kategorientheorie [f] | ||
| | | category theory | ||
| théorie [f] des | | théorie [f] des catégories [f pl] | ||
| | | 圏論 | ||
| | | け↑んろん | ||
| тео́рия | | тео́рия катего́рий | ||
|- | |- | ||
| | | 交换代数 | ||
| | | jiāohuàn dàishù | ||
| | | kommutative Algebra | ||
| | | commutative algebra | ||
| | | algèbre [f] commutative | ||
| | | 可換環論 | ||
| | | か↑かんか↓んろん | ||
| | | коммутати́вная а́лгебра | ||
|- | |- | ||
| | | 线性代数 | ||
| | | xiànxìng dàishù | ||
| | | lineare Algebra, Vektoralgebra [f] | ||
| linear algebra | |||
| | | algèbre [f] linéaire | ||
| | | 線型代数 | ||
| | | せ↑んけいだいす↓うがく | ||
| | | лине́йная а́лгебра | ||
|- | |- | ||
| | | 多重线性代数 | ||
| duōchóng xiànxìng dàishù | |||
| | | multilineare Algebra | ||
| | | multilinear algebra | ||
| algèbre [f] | | algèbre [f] multilinéaire | ||
| | | 多重線型代数 | ||
| | | た↑じゅうせんけいだいす↓う | ||
| | | полилине́йная а́лгебра | ||
|- | |- | ||
| | | 泛代数 | ||
| | | fàn dàishù | ||
| universelle Algebra, allgemeine Algebra | |||
| | | universal algebra, common algebra | ||
| algèbre [f] | | algèbre [f] universelle | ||
| | | 普遍代数学,一般代数学 | ||
| | | ふ↑へんだいすう↓がく,い↑っぱんだいすう↓がく | ||
| | | универса́льная а́лгебра | ||
|- | |- | ||
| | | 同调代数 | ||
| tóngdiào dàishù | |||
| | | homologische Algebra | ||
| | | homological algebra | ||
| algèbre [f] | | algèbre [f] homologique | ||
| | | ホモロジー代数学 | ||
| | | ホ↑モロジ↓ーだいす↑うがく | ||
| | | гомологи́ческая а́лгебра | ||
|- | |- | ||
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|} | |} | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
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| || | | || | ||
|- | |- | ||
| 代数方程 || | |||
| dàishù fāngchéng || | |||
| algebraische Gleichung || | |||
| algebraic equation || coefficient | | algebraic equation || coefficient | ||
| | | équation polynomiale, équation [f] algébrique || | ||
| | | 代数方程式 || | ||
| | | だ↑いす↓うほ↑うて↓いしき || | ||
| | | алгебраи́ческое уравне́ние || | ||
|- | |- | ||
| 代数式 || | |||
| dàishù shì || | |||
| algebraischer Ausdruck || | |||
| algebraic expression || expression <mathematical logic>; integer; constant; variable; algebraic operation | | algebraic expression || expression <mathematical logic>; integer; constant; variable; algebraic operation | ||
| expression [f] algébrique || | |||
| 代数式 || | |||
| だ↑いす↓うしき || | |||
| алгебраи́ческим выраже́нием || | |||
|- | |||
| 代数分式 || | |||
| dàishù fēnshì || | |||
| || | | || | ||
| | | algebraic fraction || fraction; algebraic expression | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| algebraic operation || operation <mathematical logic> | | algebraic operation || operation <mathematical logic> | ||
| || | | || | ||
| || | | || | ||
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| || | | || | ||
|- | |- | ||
| 最大值自变量点集 || | |||
| zuìdàzhí zìbiànliàng diǎn jí || | |||
| Argument [n] des Maximums [n] || | |||
| argument of the maximum || domain <mathematical logic>; maximum <mathematical analysis> | | argument of the maximum || domain <mathematical logic>; maximum <mathematical analysis> | ||
| | | argument [m] du maximum [m] || | ||
| | | 最大点作用素集合 || | ||
| | | さ↑いだいてんさ↓ようそしゅうごう || | ||
| | | аргуме́нт максимиза́ции || | ||
|- | |- | ||
| 最小值自变量点集 || | |||
| zuìxiǎozhí zìbiànliàng diǎn jí || | |||
| Argument [n] des Minimums [n] || | |||
| argument of the minimum || domain <mathematical logic>; minimum <mathematical analysis> | | argument of the minimum || domain <mathematical logic>; minimum <mathematical analysis> | ||
| | | argument [m] du minimum [m] || | ||
| | | 最小点作用素集合 || | ||
| | | さ↑いしょうてんさ↓ようそしゅうごう || | ||
| | | аргуме́нт минимиза́ции || | ||
| | |- | ||
| | | 二项式 || | ||
| | | èrxiàng shì || | ||
| Binom [n] || | |||
| binomial || | |||
| binôme [m] || | |||
| 二項式 || | |||
| に↑こうしき || | |||
| бино́м, двучле́н || | |||
|- | |- | ||
| 系数 || | |||
| xì shù || | |||
| Koeffizient [n], Beizahl [f], Vorzahl [f] || | |||
| coefficient || multiplication <number theory>; expression <mathematical logic> | | coefficient || multiplication <number theory>; expression <mathematical logic> | ||
| | | coefficient [f] || | ||
| | | 係数 || | ||
| | | け↑いす↓う || | ||
| | | коэффицие́нт || | ||
|- | |- | ||
| 常数函数 || | |||
| chángshù hánshù || | |||
| konstante Funktion || | |||
| constant function || constant <number theory>; function | | constant function || constant <number theory>; function | ||
| fonction constante || | |||
| 定数関数 || | |||
| て↑いすうか↓んすう || | |||
| конста́нтная фу́нкция, постоя́нная фу́нкция || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| constant term || term <logic>; algebraic expression; constant | |||
| || | | || | ||
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|- | |- | ||
| 因变量 || | | 因变量 || | ||
| yīn biànliàng || | | yīn biànliàng || | ||
| abhängige Variable | | abhängige Variable || | ||
| | | dependent variable || fraction; operand <mathematical logic> | ||
| | | variable dépendante || | ||
| | | 従属変数 || | ||
| | | じ↑ゅうぞくへ↓んすう || | ||
| зави́симая переме́нная || | |||
|- | |- | ||
| 等式,方程 || | | 等式,方程 || | ||
| děng shì, fāngchéng || | | děng shì, fāngchéng || | ||
| Gleichung [f] || | | Gleichung [f] || | ||
| équation [f] | | equation || equality <mathematical logic>; expression <mathematical logic> | ||
| équation [f] || | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
|- | |- | ||
| 偶函数 || | |||
| ǒu hánshù || | |||
| gerade Funktion || | |||
| even function || function <mathematical logic>; line symmetry <geometry> | | even function || function <mathematical logic>; line symmetry <geometry> | ||
| fonction paire || | |||
| 偶関数 || | |||
| ぐ↑うかんす↓う || | |||
| чётная фу́нкция || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| identity || equality <mathematical logic> | | identity || equality <mathematical logic> | ||
| || | | || | ||
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|- | |- | ||
| 单位元,中立元 || | |||
| dānwèi yuán, zhōnglì yuán || | |||
| neutrales Element || | |||
| identity element, neutral element || set <mathematical logic>; binary operation <mathematical logic> | | identity element, neutral element || set <mathematical logic>; binary operation <mathematical logic> | ||
| | | élément [m] neutre, élément [m] identité || | ||
| | | 単位元,中立元 || | ||
| | | た↑んいげん,ちゅ↑うりつげん || | ||
| | | нейтра́льный элеме́нт || | ||
|- | |- | ||
| 自变量 || | | 自变量 || | ||
| zì biànliàng || | | zì biànliàng || | ||
| unabhängige Variable || | | unabhängige Variable || | ||
| | | independent variable || function <mathematical logic> | ||
| | | variable indépendante || | ||
| | | 独立変数 || | ||
| | | ど↑くりつへ↓んすう || | ||
| незави́симая переме́нная || | |||
|- | |- | ||
| 未定元 || | |||
| wèidìng yuán || | |||
| Unbestimmte [f] || | |||
| indeterminate || variable | | indeterminate || variable | ||
| | | indéterminée [f] || | ||
| | | 不定元 || | ||
| | | ふ↑ていげん || | ||
| | | неопределённый || | ||
|- | |- | ||
| 不等式 || | | 不等式 || | ||
| bùděng shì || | | bùděng shì || | ||
| Ungleichung [f] || | | Ungleichung [f] || | ||
| inéquation [f] | | inequation || inequality <mathematical logic> | ||
| inéquation [f] || | |||
| | | 不等式 || | ||
| | | ふ↑と↓うしき || | ||
| | | неуравне́ние || | ||
|- | |- | ||
| | | 代数分式 || | ||
| dàishù fēnshì || | |||
| || | | || | ||
| irrational fraction || algebraic fraction; polynomial; exponent | | irrational fraction || algebraic fraction; polynomial; exponent | ||
| || | | || | ||
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|- | |- | ||
| 不可约多项式 || | |||
| bùkěyuē duōxiàngshì || | |||
| irreduzibles Polynom || | |||
| irreducible polynomial || polynomial; factorization | | irreducible polynomial || polynomial; factorization | ||
| | | polynôme [m] irréductible || | ||
| | | 既約多項式 || | ||
| | | き↑やくたこ↓うしき || | ||
| | | неприводимый многочле́н || | ||
|- | |- | ||
| 一次方程 || | |||
| yīcì fāngchéng || | |||
| lineare Gleichung || | |||
| linear equation || equation; coefficient | | linear equation || equation; coefficient | ||
| équation linéaire || | |||
| 一次方程式 || | |||
| い↑ち↓じほ↑うて↓いしき || | |||
| лине́йное уравне́ние || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| left identity || identity element <mathematical logic> | |||
| || | | || | ||
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|- | |- | ||
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| monomial || variable; natural number | | monomial || variable; natural number | ||
| || | | || | ||
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|- | |- | ||
| 奇函数 || | |||
| jī hánshù || | |||
| ungerade Funktion || | |||
| odd function || function <mathematical logic>; point symmetry <geometry> | | odd function || function <mathematical logic>; point symmetry <geometry> | ||
| fonction impaire || | |||
| 奇関数 || | |||
| き↑か↓んすう || | |||
| нечётная фу́нкция || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| parameter || | |||
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|- | |- | ||
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| partial fraction decomposition, partial fraction expansion || algebraic fraction; polynomial | |||
| || | | || | ||
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|- | |- | ||
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| polynomial || expression <mathematical logic>; coefficient; indeterminate | |||
| || | | || | ||
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|- | |- | ||
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| || | | || | ||
| || | | || | ||
| polynomial function || polynomial; function <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
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| quadratic equation || equation; coefficient | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
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| || | | || | ||
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| rational function || algebraic fraction; polynomial | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
| | | 可约多项式 || | ||
| kěyuē duōxiàngshì || | |||
| reduzibles Polynom || | |||
| reducible polynomial || polynomial; factorization | |||
| polynôme [m] réductible || | |||
| 可約多項式 || | |||
| か↑やくたこ↓うしき || | |||
| приводимый многочле́н || | |||
|- | |||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| right identity || identity element <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
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| solution || equation | |||
| || | | || | ||
| || | | || | ||
Line 431: | Line 427: | ||
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|- | |- | ||
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| || | | || | ||
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| square || exponentiation <number theory> | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
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| || | | || | ||
| || | | || | ||
| system of equations, simultaneous equations || finite set <mathematical logic>; equation | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
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| unknown || variable | |||
| || | | || | ||
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|- | |- | ||
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| variable || mathematical object <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| zero; root || domain; solution | | zero; root || domain; solution | ||
| || | | || | ||
| || | | || | ||
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|} | |} | ||
== Abstract Algebra == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 515: | Line 502: | ||
| || | | || | ||
|- | |- | ||
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| || | | || | ||
| || | | || | ||
| algebraic structure || underlying set; arity; identity | |||
| || | | || | ||
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|- | |- | ||
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| || | | || | ||
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| arity || argument <mathematical logic>; operand <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
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|- | |- | ||
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| Boolean domain || set; tautology <logic>; falsity <logic> | |||
| || | | || | ||
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|- | |- | ||
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| direct product || Cartesian product <mathematical logic> | |||
| || | | || | ||
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Line 551: | Line 538: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| field || set <mathematical logic>; basic operations <number theory>; rational number <number theory> | |||
| || | | || | ||
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|- | |- | ||
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| inverse element || set <mathematical logic>; additive inverse <number theory>; multiplicative inverse <number theory> | |||
| || | | || | ||
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|- | |- | ||
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| underlying set, carrier set || empty set <mathematical logic> | |||
| || | | || | ||
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Line 588: | Line 575: | ||
|} | |} | ||
=== Group Theory === | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 608: | Line 595: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Cayley table || finite group | |||
| || | | || | ||
| || | | || | ||
Line 617: | Line 604: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| group || set <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
Line 626: | Line 613: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| finite group || underlying set; finite set <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
Line 635: | Line 622: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| normal subgroup, invariant subgroup || subgroup; conjugation | |||
| || | | || | ||
| || | | || | ||
Line 644: | Line 631: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| open interval || interval | |||
| || | | || | ||
| || | | || | ||
Line 653: | Line 640: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| semigroup || algebraic structure; associative property | |||
| || | | || | ||
| || | | || | ||
Line 662: | Line 649: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| subgroup || group; binary operation <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
Line 681: | Line 668: | ||
|} | |} | ||
=== Ring Theory === | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 701: | Line 688: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| ring || | |||
| || | | || | ||
| || | | || | ||
Line 720: | Line 707: | ||
|} | |} | ||
== Commutative Algebra == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 750: | Line 737: | ||
|} | |} | ||
== Linear Algebra == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 770: | Line 757: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| basis || linear combination | |||
| || | | || | ||
| || | | || | ||
Line 779: | Line 766: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| characteristic equation || characteristic polynomial | |||
| || | | || | ||
| || | | || | ||
Line 788: | Line 775: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| characteristic polynomial || square matrix; eigenvalue; matrix similarity; zero | |||
| || | | || | ||
| || | | || | ||
Line 797: | Line 784: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| conjugate matrix, Hermitian matrix || conjugate transpose | |||
| || | | || | ||
| || | | || | ||
Line 806: | Line 793: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| conjugate transpose, Hermitian transpose || complex conjugate <mathematical logic>; transpose | |||
| || | | || | ||
| || | | || | ||
Line 815: | Line 802: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| diagonal matrix || matrix; main diagonal | |||
| || | | || | ||
| || | | || | ||
Line 824: | Line 811: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| identity matrix || square matrix; main diagonal | |||
| || | | || | ||
| || | | || | ||
Line 833: | Line 820: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| invertible matrix, nonsingular matrix || identity matrix | |||
| || | | || | ||
| || | | || | ||
Line 842: | Line 829: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| linear combination || expression <mathematical logic>; coefficient; vector space | |||
| || | | || | ||
| || | | || | ||
Line 851: | Line 838: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| linear dependence || linear combination | |||
| || | | || | ||
| || | | || | ||
Line 860: | Line 847: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| linear independence || linear combination | |||
| || | | || | ||
| || | | || | ||
Line 869: | Line 856: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| linear mapping || vector addition; scalar multiplication | |||
| || | | || | ||
| || | | || | ||
Line 878: | Line 865: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| linear transformation || linear mapping | |||
| || | | || | ||
| || | | || | ||
Line 887: | Line 874: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| binary matrix, logical matrix, relation matrix, Boolean matrix || matrix; Boolean domain | |||
| || | | || | ||
| || | | || | ||
Line 896: | Line 883: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| like terms || term <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
Line 905: | Line 892: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| lower triangular matrix || triangular matrix | |||
| || | | || | ||
| || | | || | ||
Line 914: | Line 901: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| main diagonal || matrix; diagonal <geometry> | |||
| || | | || | ||
| || | | || | ||
Line 923: | Line 910: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| matrix || rectangle <geometry>; expression <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
Line 932: | Line 919: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| matrix addition || matrix; addition <number theory> | |||
| || | | || | ||
| || | | || | ||
Line 941: | Line 928: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| matrix of ones || matrix | |||
| || | | || | ||
| || | | || | ||
Line 950: | Line 937: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| matrix multiplication || matrix; multiplication <number theory>; addition <number theory> | |||
| || | | || | ||
| || | | || | ||
Line 959: | Line 946: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| matrix similarity || invertible matrix | |||
| || | | || | ||
| || | | || | ||
Line 968: | Line 955: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| proportional function || proportionality <number theory>; function <mathematical logic> | |||
| || | | || | ||
| || | | || | ||
Line 977: | Line 964: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| rotation matrix || linear transformation; rotation <geometry> | |||
| || | | || | ||
| || | | || | ||
Line 986: | Line 973: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| skew-Hermitian matrix, anti-Hermitian matrix || Hermitian matrix | |||
| || | | || | ||
| || | | || | ||
Line 995: | Line 982: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| square matrix || matrix; square <geometry> | |||
| || | | || | ||
| || | | || | ||
Line 1,004: | Line 991: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| system of linear equations; linear system || linear equation | |||
| || | | || | ||
| || | | || | ||
Line 1,013: | Line 1,000: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| transformation matrix || linear transformation; matrix | |||
| || | | || | ||
| || | | || | ||
Line 1,022: | Line 1,009: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| translation matrix || translation <geometry>; matrix | |||
| || | | || | ||
| || | | || | ||
Line 1,031: | Line 1,018: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| transpose || reflection <geometry>; main diagonal | |||
| || | | || | ||
| || | | || | ||
Line 1,040: | Line 1,027: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| triangular matrix || square matrix; triangle <geometry> | |||
| || | | || | ||
| || | | || | ||
Line 1,049: | Line 1,036: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| upper triangular matrix || triangular matrix | |||
| || | | || | ||
| || | | || | ||
Line 1,070: | Line 1,057: | ||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
|+ theorem in linear algebra | |+ theorem in linear algebra | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,079: | Line 1,066: | ||
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| theorem in linear algebra || | |||
| || | | || | ||
| || | | || | ||
Line 1,097: | Line 1,084: | ||
| || | | || | ||
|- | |- | ||
| || | | || | ||
| || | | || | ||
| || | | || | ||
| Cayley–Hamilton theorem || characteristic polynomial; identity matrix; determinant; scalar; ring | |||
| || | | || | ||
| || | | || | ||
Line 1,125: | Line 1,112: | ||
|} | |} | ||
== Multilinear Algebra == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,155: | Line 1,142: | ||
|} | |} | ||
== Universal Algebra == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | |||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,185: | Line 1,172: | ||
|} | |} | ||
== Homological Algebra == | |||
{| class="wikitable sortable" | {| class="wikitable sortable" | ||
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提 | ||
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí | ||
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f] | ||
! eng-Latn-US: concept !! eng-Latn-US: prerequisite | ! eng-Latn-US: concept !! eng-Latn-US: prerequisite | ||
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m] | ||
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提 | ||
Line 1,246: | Line 1,202: | ||
|} | |} | ||
<center> | |||
https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Quadratic_function_graph_key_values.svg/480px-Quadratic_function_graph_key_values.svg.png | |||
</center> | |||
{{Sci-Tech-Index-Menu}} | |||
==Other Lessons== | |||
* [[Language/Multiple-languages/Vocabulary/Category-Theory|Category Theory]] | |||
* [[Language/Multiple-languages/Vocabulary/Mechanics|Mechanics]] | |||
* [[Language/Multiple-languages/Vocabulary/Animal-sounds-in-many-languages|Animal sounds in many languages]] | |||
* [[Language/Multiple-languages/Vocabulary/Common-Han-Characters-with-⾡|Common Han Characters with ⾡]] | |||
* [[Language/Multiple-languages/Vocabulary/Machine-Element|Machine Element]] | |||
* [[Language/Multiple-languages/Vocabulary/Body-in-many-languages|Body in many languages]] | |||
* [[Language/Multiple-languages/Vocabulary/Mathematical-Logic|Mathematical Logic]] | |||
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]] | |||
* [[Language/Multiple-languages/Vocabulary/Greetings-in-All-Languages|Greetings in All Languages]] | |||
* [[Language/Multiple-languages/Vocabulary/Greetings-General-greeting|Greetings General greeting]] | |||
<span links></span> |
Latest revision as of 13:15, 27 March 2023
Hello polyglots, 😀
On this page you will find a part of the Sci–Tech Index, a project for science and technology learners.
cmn-Hans-CN: 科目 | cmn-Latn.Pinyin-CN: kēmù | deu-Latn-DE: Fach [n] | eng-Latn-US: subject | fra-Latn-FR: matière [f] | jpn-Jpan-JP: 科目 | jpn-Hrkt-JP: か↑もく | rus-Cyrl-RU: предме́т |
---|---|---|---|---|---|---|---|
抽象代数 | chōuxiàng dàishù | abstrakte Algebra | abstract algebra | algèbre générale, algèbre abstraite | 抽象代数学 | ちゅ↑うしょうだいす↓うがく | абстра́ктная а́лгебра, общая а́лгебра, вы́сшая а́лгебра |
群论 | qún lùn | Gruppentheorie [f] | group theory | théorie [f] des groupes [m pl] | 群論 | ぐ↓んろん | тео́рия групп |
环论 | huán lùn | Ringtheorie [f] | ring theory | théorie [f] des anneaux [m pl] | 環論 | か↑んろん | тео́рия коле́ц |
范畴论 | fànchóu lùn | Kategorientheorie [f] | category theory | théorie [f] des catégories [f pl] | 圏論 | け↑んろん | тео́рия катего́рий |
交换代数 | jiāohuàn dàishù | kommutative Algebra | commutative algebra | algèbre [f] commutative | 可換環論 | か↑かんか↓んろん | коммутати́вная а́лгебра |
线性代数 | xiànxìng dàishù | lineare Algebra, Vektoralgebra [f] | linear algebra | algèbre [f] linéaire | 線型代数 | せ↑んけいだいす↓うがく | лине́йная а́лгебра |
多重线性代数 | duōchóng xiànxìng dàishù | multilineare Algebra | multilinear algebra | algèbre [f] multilinéaire | 多重線型代数 | た↑じゅうせんけいだいす↓う | полилине́йная а́лгебра |
泛代数 | fàn dàishù | universelle Algebra, allgemeine Algebra | universal algebra, common algebra | algèbre [f] universelle | 普遍代数学,一般代数学 | ふ↑へんだいすう↓がく,い↑っぱんだいすう↓がく | универса́льная а́лгебра |
同调代数 | tóngdiào dàishù | homologische Algebra | homological algebra | algèbre [f] homologique | ホモロジー代数学 | ホ↑モロジ↓ーだいす↑うがく | гомологи́ческая а́лгебра |
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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代数方程 | dàishù fāngchéng | algebraische Gleichung | algebraic equation | coefficient | équation polynomiale, équation [f] algébrique | 代数方程式 | だ↑いす↓うほ↑うて↓いしき | алгебраи́ческое уравне́ние | |||||||
代数式 | dàishù shì | algebraischer Ausdruck | algebraic expression | expression <mathematical logic>; integer; constant; variable; algebraic operation | expression [f] algébrique | 代数式 | だ↑いす↓うしき | алгебраи́ческим выраже́нием | |||||||
代数分式 | dàishù fēnshì | algebraic fraction | fraction; algebraic expression | ||||||||||||
algebraic operation | operation <mathematical logic> | ||||||||||||||
最大值自变量点集 | zuìdàzhí zìbiànliàng diǎn jí | Argument [n] des Maximums [n] | argument of the maximum | domain <mathematical logic>; maximum <mathematical analysis> | argument [m] du maximum [m] | 最大点作用素集合 | さ↑いだいてんさ↓ようそしゅうごう | аргуме́нт максимиза́ции | |||||||
最小值自变量点集 | zuìxiǎozhí zìbiànliàng diǎn jí | Argument [n] des Minimums [n] | argument of the minimum | domain <mathematical logic>; minimum <mathematical analysis> | argument [m] du minimum [m] | 最小点作用素集合 | さ↑いしょうてんさ↓ようそしゅうごう | аргуме́нт минимиза́ции | |||||||
二项式 | èrxiàng shì | Binom [n] | binomial | binôme [m] | 二項式 | に↑こうしき | бино́м, двучле́н | ||||||||
系数 | xì shù | Koeffizient [n], Beizahl [f], Vorzahl [f] | coefficient | multiplication <number theory>; expression <mathematical logic> | coefficient [f] | 係数 | け↑いす↓う | коэффицие́нт | |||||||
常数函数 | chángshù hánshù | konstante Funktion | constant function | constant <number theory>; function | fonction constante | 定数関数 | て↑いすうか↓んすう | конста́нтная фу́нкция, постоя́нная фу́нкция | |||||||
constant term | term <logic>; algebraic expression; constant | ||||||||||||||
因变量 | yīn biànliàng | abhängige Variable | dependent variable | fraction; operand <mathematical logic> | variable dépendante | 従属変数 | じ↑ゅうぞくへ↓んすう | зави́симая переме́нная | |||||||
等式,方程 | děng shì, fāngchéng | Gleichung [f] | equation | equality <mathematical logic>; expression <mathematical logic> | équation [f] | ||||||||||
偶函数 | ǒu hánshù | gerade Funktion | even function | function <mathematical logic>; line symmetry <geometry> | fonction paire | 偶関数 | ぐ↑うかんす↓う | чётная фу́нкция | |||||||
identity | equality <mathematical logic> | ||||||||||||||
单位元,中立元 | dānwèi yuán, zhōnglì yuán | neutrales Element | identity element, neutral element | set <mathematical logic>; binary operation <mathematical logic> | élément [m] neutre, élément [m] identité | 単位元,中立元 | た↑んいげん,ちゅ↑うりつげん | нейтра́льный элеме́нт | |||||||
自变量 | zì biànliàng | unabhängige Variable | independent variable | function <mathematical logic> | variable indépendante | 独立変数 | ど↑くりつへ↓んすう | незави́симая переме́нная | |||||||
未定元 | wèidìng yuán | Unbestimmte [f] | indeterminate | variable | indéterminée [f] | 不定元 | ふ↑ていげん | неопределённый | |||||||
不等式 | bùděng shì | Ungleichung [f] | inequation | inequality <mathematical logic> | inéquation [f] | 不等式 | ふ↑と↓うしき | неуравне́ние | |||||||
代数分式 | dàishù fēnshì | irrational fraction | algebraic fraction; polynomial; exponent | ||||||||||||
不可约多项式 | bùkěyuē duōxiàngshì | irreduzibles Polynom | irreducible polynomial | polynomial; factorization | polynôme [m] irréductible | 既約多項式 | き↑やくたこ↓うしき | неприводимый многочле́н | |||||||
一次方程 | yīcì fāngchéng | lineare Gleichung | linear equation | equation; coefficient | équation linéaire | 一次方程式 | い↑ち↓じほ↑うて↓いしき | лине́йное уравне́ние | |||||||
left identity | identity element <mathematical logic> | ||||||||||||||
monomial | variable; natural number | ||||||||||||||
奇函数 | jī hánshù | ungerade Funktion | odd function | function <mathematical logic>; point symmetry <geometry> | fonction impaire | 奇関数 | き↑か↓んすう | нечётная фу́нкция | |||||||
parameter | |||||||||||||||
partial fraction decomposition, partial fraction expansion | algebraic fraction; polynomial | ||||||||||||||
polynomial | expression <mathematical logic>; coefficient; indeterminate | ||||||||||||||
polynomial function | polynomial; function <mathematical logic> | ||||||||||||||
quadratic equation | equation; coefficient | ||||||||||||||
rational function | algebraic fraction; polynomial | ||||||||||||||
可约多项式 | kěyuē duōxiàngshì | reduzibles Polynom | reducible polynomial | polynomial; factorization | polynôme [m] réductible | 可約多項式 | か↑やくたこ↓うしき | приводимый многочле́н | |||||||
right identity | identity element <mathematical logic> | ||||||||||||||
solution | equation | ||||||||||||||
square | exponentiation <number theory> | ||||||||||||||
system of equations, simultaneous equations | finite set <mathematical logic>; equation | ||||||||||||||
unknown | variable | ||||||||||||||
variable | mathematical object <mathematical logic> | ||||||||||||||
zero; root | domain; solution | ||||||||||||||
Abstract Algebra[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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algebraic structure | underlying set; arity; identity | ||||||||||||||
arity | argument <mathematical logic>; operand <mathematical logic> | ||||||||||||||
Boolean domain | set; tautology <logic>; falsity <logic> | ||||||||||||||
direct product | Cartesian product <mathematical logic> | ||||||||||||||
field | set <mathematical logic>; basic operations <number theory>; rational number <number theory> | ||||||||||||||
inverse element | set <mathematical logic>; additive inverse <number theory>; multiplicative inverse <number theory> | ||||||||||||||
underlying set, carrier set | empty set <mathematical logic> | ||||||||||||||
Group Theory[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Cayley table | finite group | ||||||||||||||
group | set <mathematical logic> | ||||||||||||||
finite group | underlying set; finite set <mathematical logic> | ||||||||||||||
normal subgroup, invariant subgroup | subgroup; conjugation | ||||||||||||||
open interval | interval | ||||||||||||||
semigroup | algebraic structure; associative property | ||||||||||||||
subgroup | group; binary operation <mathematical logic> | ||||||||||||||
Ring Theory[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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ring | |||||||||||||||
Commutative Algebra[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Linear Algebra[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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basis | linear combination | ||||||||||||||
characteristic equation | characteristic polynomial | ||||||||||||||
characteristic polynomial | square matrix; eigenvalue; matrix similarity; zero | ||||||||||||||
conjugate matrix, Hermitian matrix | conjugate transpose | ||||||||||||||
conjugate transpose, Hermitian transpose | complex conjugate <mathematical logic>; transpose | ||||||||||||||
diagonal matrix | matrix; main diagonal | ||||||||||||||
identity matrix | square matrix; main diagonal | ||||||||||||||
invertible matrix, nonsingular matrix | identity matrix | ||||||||||||||
linear combination | expression <mathematical logic>; coefficient; vector space | ||||||||||||||
linear dependence | linear combination | ||||||||||||||
linear independence | linear combination | ||||||||||||||
linear mapping | vector addition; scalar multiplication | ||||||||||||||
linear transformation | linear mapping | ||||||||||||||
binary matrix, logical matrix, relation matrix, Boolean matrix | matrix; Boolean domain | ||||||||||||||
like terms | term <mathematical logic> | ||||||||||||||
lower triangular matrix | triangular matrix | ||||||||||||||
main diagonal | matrix; diagonal <geometry> | ||||||||||||||
matrix | rectangle <geometry>; expression <mathematical logic> | ||||||||||||||
matrix addition | matrix; addition <number theory> | ||||||||||||||
matrix of ones | matrix | ||||||||||||||
matrix multiplication | matrix; multiplication <number theory>; addition <number theory> | ||||||||||||||
matrix similarity | invertible matrix | ||||||||||||||
proportional function | proportionality <number theory>; function <mathematical logic> | ||||||||||||||
rotation matrix | linear transformation; rotation <geometry> | ||||||||||||||
skew-Hermitian matrix, anti-Hermitian matrix | Hermitian matrix | ||||||||||||||
square matrix | matrix; square <geometry> | ||||||||||||||
system of linear equations; linear system | linear equation | ||||||||||||||
transformation matrix | linear transformation; matrix | ||||||||||||||
translation matrix | translation <geometry>; matrix | ||||||||||||||
transpose | reflection <geometry>; main diagonal | ||||||||||||||
triangular matrix | square matrix; triangle <geometry> | ||||||||||||||
upper triangular matrix | triangular matrix | ||||||||||||||
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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theorem in linear algebra | |||||||||||||||
Cayley–Hamilton theorem | characteristic polynomial; identity matrix; determinant; scalar; ring | ||||||||||||||
Multilinear Algebra[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Universal Algebra[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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Homological Algebra[edit | edit source]
cmn-Hans-CN: 概念 | cmn-Hans-CN: 前提 | cmn-Latn.Pinyin-CN: gàiniàn | cmn-Latn.Pinyin-CN: qiántí | deu-Latn-DE: Begriff [m] | deu-Latn-DE: Voraussetzung [f] | eng-Latn-US: concept | eng-Latn-US: prerequisite | fra-Latn-FR: concept [m] | fra-Latn-FR: préalable [m] | jpn-Jpan-JP: 概念 | jpn-Jpan-JP: 前提 | jpn-Hrkt-JP: が↓いねん | jpn-Hrkt-JP: ぜ↑んてい | rus-Cyrl-RU: конце́пция | rus-Cyrl-RU: предпосы́лка |
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