Multilingual mathematics dictionary

d.json

[
  { "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" }
      }
    ]
  }
]