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Multilingual mathematics dictionary
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[ | |
{ "en" : "-", | |
"fr" : "-", | |
"de" : "-", | |
"it" : "-", | |
"terms" : [ | |
{ "key" : "term", | |
"fr" : { "txt" : "terme (m), (pré)facteur (m), coéffiecient (m)" }, | |
"en" : { "txt" : "term, (pre)factor, coefficient" }, | |
"de" : { "txt" : "Glied (m), (Vor)Faktor (m), Koeffizient (m)" }, | |
"it" : { "txt" : "termine (m), fattore (m), coefficiente (m)" } | |
}, | |
{ "key" : "lhs", | |
"fr" : { "txt" : "membre (m) de gauche/droite" }, | |
"en" : { "txt" : "left/right-hand side" }, | |
"de" : { "txt" : "linke/rechte Seite (f)" }, | |
"it" : { "txt" : "membro (m) di sinistra/destra" } | |
}, | |
{ "key" : "parenthesis", | |
"symbol" : "(\\;),\\;[\\;],\\;\\{\\;\\}", | |
"fr" : { "txt" : "parenthèse (f), crochet (m), accolade (f)" }, | |
"en" : { "txt" : "parenthesis, bracket, curly bracket" }, | |
"de" : { "txt" : "(runde) Klammer (f), eckige Klammer (f), Akkolade (f)" }, | |
"it" : { "txt" : "parentesa tonda (f), parentesa quadra (f), parentesa graffa (f)" } | |
}, | |
{ "key" : "preuve", | |
"fr" : { "txt" : "preuve (f)" }, | |
"en" : { "txt" : "proof" }, | |
"de" : { "txt" : "Beweis (m)" }, | |
"it" : { "txt" : "dimostrazione (f)" } | |
}, | |
{ "key" : "absurd", | |
"fr" : { "txt" : "raisonnement (m) par l'absurde, preuve (f) par contradiction" }, | |
"en" : { "txt" : "proof by contradiction" }, | |
"de" : { "txt" : "Widerspruchsbeweis (m)" }, | |
"it" : { "txt" : "dimostrazione (f) per assurdo, ragionamento (m) per assurdo" } | |
}, | |
{ "key" : "theorem", | |
"fr" : { "txt" : "théorème (m), corollaire (m), lemme (m), proposition (f), remarque (f)" }, | |
"en" : { "txt" : "theorem, corollary, lemma, proposition, remark" }, | |
"de" : { "txt" : "Satz (m) [Theorem (n)], Korollar (n), Lemma (n) [Hilfsatz (m)], Proposition (f), Bemerkung (f)" }, | |
"it" : { "txt" : "teorema (m), corollario (m), lemma (m), proposizione (f), osservazione (f)" } | |
}, | |
{ "key" : "equation", | |
"fr" : { "txt" : "équation (f)" }, | |
"en" : { "txt" : "equation" }, | |
"de" : { "txt" : "Gleichung (f)" }, | |
"it" : { "txt" : "equazione (f)" } | |
}, | |
{ "key" : "equality", | |
"fr" : { "txt" : "égalité, inégalité (f)" }, | |
"en" : { "txt" : "equation, inequality" }, | |
"de" : { "txt" : "Gleichung, Ungleichung (f)" }, | |
"it" : { "txt" : "uguaglianza, disuguaglianza (f)" } | |
}, | |
{ "key" : "existence", | |
"fr" : { "txt" : "existence (f), unicité (f)" }, | |
"en" : { "txt" : "existence, uniqueness" }, | |
"de" : { "txt" : "Existenz (f), Eindeutigkeit (f)" }, | |
"it" : { "txt" : "esistenza (f), unicità (f)" } | |
}, | |
{ "key" : "add", | |
"fr" : { "txt" : "additionner, soustraire, multiplier, diviser" }, | |
"en" : { "txt" : "add, subtract, multiply, divide" }, | |
"de" : { "txt" : "addieren, subtrahieren, multiplizieren, dividieren [durch etw. teilen]" }, | |
"it" : { "txt" : "sommare, sottrarre, moltiplicare, dividere" } | |
}, | |
{ "key" : "factor", | |
"fr" : { "txt" : "factoriser, développer, réduire, combiner" }, | |
"en" : { "txt" : "factor, expand, reduce, combine" }, | |
"de" : { "txt" : "faktorisieren, ausmultiplizieren, kürzen, combinieren" }, | |
"it" : { "txt" : "scomporre [fattorizzare], sviluppare, ridurre, -" } | |
}, | |
{ "key" : "cancel", | |
"fr" : { "txt" : "s'annuler" }, | |
"en" : { "txt" : "cancel" }, | |
"de" : { "txt" : "sich aufheben" }, | |
"it" : { "txt" : "annularsi" } | |
} | |
] | |
}, | |
{ "en":"logic", | |
"fr":"logique", | |
"de":"Logik", | |
"it":"logica", | |
"terms" : [ | |
{ "key": "exists", | |
"symbol" : "\\exists", | |
"fr" : { "txt" : "il existe" }, | |
"en" : { "txt" : "there exists" }, | |
"de" : { "txt" : "es gibt, es existiert" }, | |
"it" : { "txt" : "esiste" } | |
}, | |
{ "key":"exists_unique", | |
"symbol" : "\\exists!", | |
"fr" : { "txt" : "il existe un(e) unique" }, | |
"en" : { "txt" : "there exists a unique" }, | |
"de" : { "txt" : "es gibt genau ein" }, | |
"it" : { "txt" : "esiste ed è unico/a" } | |
}, | |
{ "key":"no_exists", | |
"symbol" : "\\nexists", | |
"fr" : { "txt" : "il n'existe pas" }, | |
"en" : { "txt" : "there does not exist" }, | |
"de" : { "txt" : "es gibt kein" }, | |
"it" : { "txt" : "non esiste" } | |
}, | |
{ "key":"for_all", | |
"symbol" : "\\forall", | |
"fr" : { "txt" : "pour tout(e)" }, | |
"en" : { "txt" : "for all" }, | |
"de" : { "txt" : "für alle" }, | |
"it" : { "txt" : "per ogni" } | |
}, | |
{ "key":"implies", | |
"symbol" : "A \\Rightarrow B", | |
"fr" : { "txt" : "A implique B" }, | |
"en" : { "txt" : "A implies B" }, | |
"de" : { "txt" : "von A folgt B" }, | |
"it" : { "txt" : "A implica B" } | |
}, | |
{ "key":"equivalent", | |
"symbol" : "A \\Leftrightarrow B", | |
"fr" : { "txt" : "A est équivalent à B" }, | |
"en" : { "txt" : "A is equivalent to B" }, | |
"de" : { "txt" : "A ist äquivalent zu B" }, | |
"it" : { "txt" : "A è equivalente a B" } | |
}, | |
{ "key" : "converse", | |
"fr" : { "txt" : "réciproque (f)" }, | |
"en" : { "txt" : "converse" }, | |
"de" : { "txt" : "Umkehrung (f)" }, | |
"it" : { "txt" : "inversa (f)" } | |
}, | |
{ "key" : "contrapositive", | |
"fr" : { "txt" : "contraposée (f)" }, | |
"en" : { "txt" : "contrapositive" }, | |
"de" : { "txt" : "Kontraposition (f)" }, | |
"it" : { "txt" : "contronominale (f)" } | |
} | |
] | |
}, | |
{ "en":"analysis", | |
"fr":"analyse", | |
"de":"Analysis", | |
"it":"analisi", | |
"terms" : [ | |
{ "key":"function", | |
"fr" : { "txt" : "fonction (f), application (f)" }, | |
"en" : { "txt" : "function, map" }, | |
"de" : { "txt" : "Funktion (f), Abbildung (f)" }, | |
"it" : { "txt" : "funzione (f), applicazione (f), mappa (f)" } | |
}, | |
{ "key" : "trigonometric_functions", | |
"symbol" : "\\sin,\\;\\cos,\\;\\tan", | |
"fr" : { "txt" : "sinus (m), cosinus (m), tangente (f)" }, | |
"en" : { "txt" : "sine, cosine, tangent" }, | |
"de" : { "txt" : "Sinus (m), Kosinus (m), Tangens (m)" }, | |
"it" : { "txt" : "seno (m), coseno (m), tangente (f)" } | |
}, | |
{ "key" : "trigonometric_functions_2", | |
"symbol" : "\\arcsin,\\;\\arccos,\\;\\arctan", | |
"fr" : { "txt" : "arcsinus (m), arccosinus (m), arctangente (f)" }, | |
"en" : { "txt" : "arcsine, arccosine, arctangent" }, | |
"de" : { "txt" : "Arkussinus (m), Arkuskosinus (m), Arkusangens (m)" }, | |
"it" : { "txt" : "arcseno (m), arccoseno (m), arctangente (f)" } | |
}, | |
{ "key" : "infinity", | |
"symbol" : "\\pm \\infty", | |
"fr" : { "txt" : "(plus/moins) infini" }, | |
"en" : { "txt" : "(plus/minus) infinity" }, | |
"de" : { "txt" : "(plus/minus) unendlich" }, | |
"it" : { "txt" : "(più/meno) infinito" } | |
}, | |
{ "key":"hat_tilda_bar", | |
"symbol" : "\\hat{f},\\;\\tilde{f},\\;\\bar{f}", | |
"fr" : { "txt" : "f chapeau, f tilde, f barre" }, | |
"en" : { "txt" : "f hat, f tilda, f bar" }, | |
"de" : { "txt" : "f Dach, f Tilde [Schlange], ?" }, | |
"it" : { "txt" : "f cappuccio, f tilda, f barra" } | |
}, | |
{ "key":"derivative", | |
"symbol" : "\\frac{df}{dx}(x_0)", | |
"fr" : { "txt" : "dérivée de f (par rapport à x) (au point x zero)" }, | |
"en" : { "txt" : "derivative of f (with respect to x) (at x naught)" }, | |
"de" : { "txt" : "Ableitung for f (bezüglich x) (?)" } | |
}, | |
{ "key":"prime", | |
"symbol" : "f',\\;f'',\\;f'''", | |
"fr" : { "txt" : "f prime, f seconde, f tièrce" }, | |
"en" : { "txt" : "f prime, f double prime, ?" }, | |
"de" : { "txt" : "f Strich, ?, ?" } | |
}, | |
{ "key":"dot", | |
"symbol" : "\\dot{f},\\;\\ddot{f}", | |
"fr" : { "txt" : "f point, f deux points" }, | |
"en" : { "txt" : "f dot, f double dot, ?" }, | |
"de" : { "txt" : "?, ?, ?" } | |
}, | |
{ "key":"integral", | |
"symbol" : "\\int f(x) dx,\\; \\int_a^b,\\; \\int_\\Omega", | |
"fr" : { "txt" : "intégrale (f) de f par rapport à x, intégrale de a à b, intégrale sur omega" }, | |
"en" : { "txt" : "integral of f with respect to x, integral from a to b, integral over omega" }, | |
"de" : { "txt" : "Integral (n) von f (?), ?, ?" } | |
}, | |
{ "key" : "integration_parts", | |
"fr" : { "txt" : "intégration par parties" }, | |
"en" : { "txt" : "integration by parts" }, | |
"de" : { "txt" : "partielle Integration" }, | |
"it" : { "txt" : "integrazione per parti" } | |
}, | |
{ "key" : "gradient", | |
"symbol" : "\\nabla u,\\;Du,\\;\\Delta u \\left(\\nabla^2 u\\right),\\;Hu\\left(D^2u\\right)", | |
"fr" : { "txt" : "gradient (m), laplacien (m), jacobienne (f), hessienne (f) de u" }, | |
"en" : { "txt" : "gradient, laplacian, jacobian, hessian of u" }, | |
"de" : { "txt" : "Gradient [Gradienten] (m), Laplace-Operator (m), Jacobi-Matrix (f), Hesse-Matrix (f) von u" }, | |
"it" : { "txt" : "gradiente (m), laplaciano (m), jacobiana (f), hessiana (f) di u" } | |
}, | |
{ "key" : "weak_solution", | |
"fr" : { "txt" : "solution lisse, classique, forte, faible (f)" }, | |
"en" : { "txt" : "smooth, classical, strong, weak solution" }, | |
"de" : { "txt" : "glatt, klassiche, starke, schwache Lösung (f)" }, | |
"it" : { "txt" : "soluzione liscia, classica, forte, debole (f)" } | |
} | |
] | |
}, | |
{ "en" : "topology", | |
"fr" : "topologie", | |
"de" : "Topologie", | |
"it" : "topologia", | |
"terms" : [ | |
{ "key":"interior", | |
"symbol" : "\\mathring{A}", | |
"fr" : { "txt" : "intérieur de A" } | |
}, | |
{ "key":"closure", | |
"symbol" : "\\bar{A}", | |
"fr" : { "txt" : "fermeture [adhérence] de A" }, | |
"en" : { "txt" : "closure of A"}, | |
"de" : { "txt" : "abgeschlossene Hülle [Abschließung, Abschluss] von A"}, | |
"it" : { "txt" : "chiusura (f) di A" } | |
}, | |
{ "key":"boundary", | |
"symbol" : "\\partial A", | |
"fr" : { "txt" : "frontière (f) de A" }, | |
"en" : { "txt" : "boundary of A" }, | |
"de" : { "txt" : "Rand (m) von A" }, | |
"it" : { "txt" : "frontiera (f) di A" } | |
}, | |
{ "key" : "ball", | |
"symbol" : "B_r(x),\\; \\overline{B_r(x)}", | |
"fr" : { "txt" : "boule ouverte (fermée) de centre x et de rayon r" }, | |
"en" : { "txt" : "open (closed) ball of radius r centered in x" }, | |
"de" : { "txt" : "offene (abgeschlossene) Kugel (f) mit Mittelpunkt a und Radius r" }, | |
"it" : { "txt" : "palla (f) aperta (chuisa) di raggio r centrata in x" } | |
}, | |
{ "key" : "neighbourhood", | |
"fr" : { "txt" : "voisinage (m)" }, | |
"en" : { "txt" : "neighbourhood" }, | |
"de" : { "txt" : "Umgebung (f)" }, | |
"it" : { "txt" : "intorno (m)" } | |
}, | |
{ "key" : "limit", | |
"symbol" : "\\lim", | |
"fr" : { "txt" : "limite (f)" }, | |
"en" : { "txt" : "limit" }, | |
"de" : { "txt" : "Limes (m), Grenzwert (m)" }, | |
"it" : { "txt" : "limite (m)" } | |
}, | |
{ "key" : "sequence", | |
"fr" : { "txt" : "suite (f), sous-suite (f), série (f)" }, | |
"en" : { "txt" : "sequence, subsequence, series" }, | |
"de" : { "txt" : "Folge (f), Teilfolge (f), Reihe (f)" }, | |
"it" : { "txt" : "successione (f), sottosuccessione (f), serie (f)" } | |
}, | |
{ "key" : "convergence", | |
"fr" : { "txt" : "converger, suite convergente, divergente" }, | |
"en" : { "txt" : "converge, converging, diverging sequence" }, | |
"de" : { "txt" : "konvergieren, konvergente, divergente Folge" }, | |
"it" : { "txt" : "convergere, successione convergente, divergente" } | |
}, | |
{ "key" : "compactness", | |
"fr" : { "txt" : "compacité (f), compact, relativement compact [précompact]" }, | |
"en" : { "txt" : "compactness, compact, relatively compact [precompact]" }, | |
"de" : { "txt" : "Kompaktheit, kompakt, relativ kompakt [präkompakt]" }, | |
"it" : { "txt" : "compattezza, compatto, relativamente compatto [precompatto]" } | |
}, | |
{ "key" : "connex", | |
"fr" : { "txt" : "connexe, connexe par arcs, simplement connexe" }, | |
"en" : { "txt" : "connected, path-connected, simply connected" }, | |
"de" : { "txt" : "zusammenhängend, wegzusammenhängend, einfach zusammenhängend" }, | |
"it" : { "txt" : "connesso, connesso per cammini, semplicemente connesso" } | |
} | |
] | |
}, | |
{ "en" : "algebra", | |
"fr" : "algèbre", | |
"de" : "Algebra", | |
"it" : "algebra", | |
"terms" : [ | |
{ "key" : "matrix", | |
"symbol" : "M_{n\\times m}", | |
"fr" : { "txt" : "matrice (f)" }, | |
"en" : { "txt" : "matrix" }, | |
"de" : { "txt" : "Matrix (f)" }, | |
"it" : { "txt" : "matrice (f)" } | |
}, | |
{ "key" : "polynom", | |
"symbol" : "\\mathcal{P}_n[X]", | |
"fr" : { "txt" : "polynôme (m)" }, | |
"en" : { "txt" : "polynomial" }, | |
"de" : { "txt" : "Polynom (n)" }, | |
"it" : { "txt" : "polinomio (m)" } | |
}, | |
{ "key" : "space", | |
"fr" : { "txt" : "espace, sous-espace (m)" }, | |
"en" : { "txt" : "space, subspace" }, | |
"de" : { "txt" : "Raum, Unter-/Teilraum (m)" }, | |
"it" : { "txt" : "spazio, sottospazio (m)" } | |
}, | |
{ "key" : "vector_space", | |
"fr" : { "txt" : "espace vectoriel, euclidien, de Hilbert, de Banach, métrique, topologique" }, | |
"en" : { "txt" : "vector, Euclidean, Hilbert, Banach, metric, topological space" }, | |
"de" : { "txt" : "Vector-, Euklidischer, Hilbert-, Banach-, Topologischer, Metrischer Raum" }, | |
"it" : { "txt" : "spazio vettoriale, euclideo, di Hilbert, di Banach, metrico, topologico" } | |
}, | |
{ "key" : "rank", | |
"fr" : { "txt" : "rang (m), degré (m), ordre (m) de M" }, | |
"en" : { "txt" : "rank, degree, order of M" }, | |
"de" : { "txt" : "Rang (m), Grad (m), Ordnung (f) von M" }, | |
"it" : { "txt" : "rango (m), grado (m), ordine (m), di M" } | |
}, | |
{ "key" : "injective", | |
"fr" : { "txt" : "injective, surjective, bijective, inversible" }, | |
"en" : { "txt" : "injective, surjective, bijective, invertible" }, | |
"de" : { "txt" : "injektiv, surjektiv, bijektiv, invertierbar" }, | |
"it" : { "txt" : "iniettiva, suriettiva, biiettiva, invertibile" } | |
}, | |
{ "key":"inverse", | |
"symbol" : "f^{-1}", | |
"fr" : { "txt" : "la (fonction) réciproque de f" }, | |
"en" : { "txt" : "the inverse of f" }, | |
"de" : { "txt" : "die Umkehrfunktion [inverse Funktion] von f" }, | |
"it" : { "txt" : "la funzione inversa di f" } | |
}, | |
{ "key" : "image", | |
"symbol" : "f(A)", | |
"fr" : { "txt" : "image (f) de A par f" }, | |
"en" : { "txt" : "image" }, | |
"de" : { "txt" : "Bild (n) [-menge (f), -bereich (m)] von A unter f" }, | |
"it" : { "txt" : "immagine (m) di A tramite f" } | |
}, | |
{ "key":"preimage", | |
"symbol" : "f^{-1}(A)", | |
"fr" : { "txt" : "image réciproque (f) de A par f" }, | |
"en" : { "txt" : "preimage of A under f" }, | |
"de" : { "txt" : "Urbild (n) von A unter f" }, | |
"it" : { "txt" : "controimmagine (m) di A tramite f" } | |
} | |
] | |
}, | |
{ "en" : "set theory", | |
"fr" : "théorie des ensembles", | |
"de" : "Mengelehre", | |
"it" : "teoria degli insiemi", | |
"terms" : [ | |
{ "key": "set", | |
"fr" : { "txt" : "ensemble, sous-ensemble (m)" }, | |
"en" : { "txt" : "set, subset" }, | |
"de" : { "txt" : "Menge, Teilmenge (f)" }, | |
"it" : { "txt" : "insieme, sottoinsieme (m)" } | |
}, | |
{ "key": "numbers", | |
"symbol" : "\\mathbb{N}, \\mathbb{Z}, \\mathbb{Q}, \\mathbb{R}, \\mathbb{C}", | |
"fr" : { "txt" : "entiers naturels, entiers, rationels, réels, complexes" }, | |
"en" : { "txt" : "naturals, integers, rationals, reals, complex numbers" }, | |
"de" : { "txt" : "natürliche (Zahlen), ganze, rationale, reelle, komplexe" }, | |
"it" : { "txt" : "naturali, interi, razionali, reali, complessi" } | |
}, | |
{ "key":"empty_set", | |
"symbol" : "\\emptyset", | |
"fr" : { "txt" : "ensemble vide" }, | |
"en" : { "txt" : "empty set" }, | |
"de" : { "txt" : "Leermenge" }, | |
"it" : { "txt" : "insieme vuoto" } | |
}, | |
{ "key":"complement", | |
"symbol" : "A^c", | |
"fr" : { "txt" : "complément (f) de A" }, | |
"en" : { "txt" : "complement of A" }, | |
"de" : { "txt" : "Komplement (n) von A" }, | |
"it" : { "txt" : "complemento (assoluto) (m) di A" } | |
}, | |
{ "key":"subset", | |
"symbol" : "A \\subset B", | |
"fr" : { "txt" : "A est inclus dans B, A est sous-ensemble de B" }, | |
"en" : { "txt" : "A is a subset of B" }, | |
"de" : { "txt" : "A ist eine Teilmenge von B" }, | |
"it" : { "txt" : "A è sottoinsieme di B" } | |
}, | |
{ "key":"intersection", | |
"symbol" : "A \\cap B", | |
"fr" : { "txt" : "intersection (f) de A et B" }, | |
"en" : { "txt" : "intersection of A and B" }, | |
"de" : { "txt" : "(Durch)schnitt (m) von A und B" }, | |
"it" : { "txt" : "intersezione (f) di A e B" } | |
}, | |
{ "key":"union", | |
"symbol" : "A \\cup B", | |
"fr" : { "txt" : "union de A et B, A union B" }, | |
"en" : { "txt" : "union of A and B, A union B" }, | |
"de" : { "txt" : "Vereinigung (f) von A und B, A vereinigt mit B"}, | |
"it" : { "txt" : "unione di A e B" } | |
}, | |
{ "key":"difference", | |
"symbol" : "A \\setminus B", | |
"fr" : { "txt" : "A privé de B" }, | |
"en" : { "txt" : "A minus B" }, | |
"de" : { "txt": "Differenz(menge) von A und B"}, | |
"it" : { "txt": "differenza tra A e B"} | |
}, | |
{ "key":"symmetric_difference", | |
"symbol" : "A \\Delta B", | |
"fr" : { "txt" : "différence symétrique entre A et B" }, | |
"en" : { "txt" : "symmetric difference of A and B" }, | |
"de" : { "txt" : "symmetrische Differenz von A und B" }, | |
"it" : { "txt" : "differenza simmetrica di A e B" } | |
}, | |
{ "key":"cartesian_product", | |
"symbol" : "A \\times B", | |
"fr" : { "txt" : "produit cartésien de A et B" }, | |
"en" : { "txt" : "cartesian product of A and B" }, | |
"de" : { "txt" : "kartesisches Produkt von A und B" }, | |
"it" : { "txt" : "prodotto cartesiano di A e B" } | |
}, | |
{ "key":"cardinality", | |
"symbol" : "|A|", | |
"fr" : { "txt" : "cardinal de A" }, | |
"en" : { "txt" : "cardinality (size) of A" }, | |
"de" : { "txt": "Mächtigkeit (Kardinalität) von A"}, | |
"it" : { "txt": "cardinalità (cardinale) di A"} | |
}, | |
{ "key":"a in A", | |
"symbol" : "a \\in A", | |
"fr" : { "txt" : "a élément de A" }, | |
"en" : { "txt" : "a element of A, a in A" }, | |
"de" : { "txt" : "a Element von A" }, | |
"it" : { "txt" : "a elemento di A" } | |
} | |
] | |
} | |
] |
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