See toric on Wiktionary
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See Toric variety on Wikipedia.Wikipedia" ], "id": "en-toric-en-adj-48k9xIbM", "links": [ [ "torus", "torus" ], [ "toroidal", "toroidal" ], [ "symmetry", "symmetry" ], [ "combinatorial", "combinatorial" ], [ "algebraic geometry", "algebraic geometry" ], [ "variety", "variety" ], [ "algebraic torus", "algebraic torus" ], [ "group action", "group action" ], [ "embedding", "embedding" ], [ "map", "map" ], [ "Toric variety", "w:Toric variety" ] ], "raw_glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "(geometry and algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.", "(algebraic geometry, of a variety) Containing an algebraic torus as a dense subset, such that the group action of the torus on itself extends to the whole space; or, the embedding map taking the torus into the space. See Toric variety on Wikipedia.Wikipedia" ], "raw_tags": [ "of a variety" ], "topics": [ "algebra", "algebraic-geometry", "geometry", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Curves", "orig": "en:Curves", "parents": [ "Shapes", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Geometry", "orig": "en:Geometry", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "14 40 14 20 12", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "15 40 15 19 11", "kind": "other", "name": "English terms suffixed with -ic", "parents": [], "source": "w+disamb" }, { "_dis": "18 29 18 18 18", "kind": "other", "name": "Entries with translation boxes", "parents": [], "source": "w+disamb" }, { "_dis": "15 42 14 22 6", "kind": "other", "name": "Pages with 1 entry", "parents": [], "source": "w+disamb" }, { "_dis": "13 43 13 20 11", "kind": "other", "name": "Pages with entries", "parents": [], "source": "w+disamb" }, { "_dis": "20 36 15 16 13", "kind": "other", "name": "Terms with Czech translations", "parents": [], "source": "w+disamb" }, { "_dis": "16 35 16 16 16", "kind": "other", "name": "Terms with French translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 41 14 17 14", "kind": "other", "name": "Terms with Italian translations", "parents": [], "source": "w+disamb" }, { "_dis": "15 40 14 17 14", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" }, { "_dis": "14 44 13 18 12", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" } ], "glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.", "(Narrowly) A compact smooth toric variety. (Broadly) Quasitoric: a closed, real, even-dimensional smooth manifold equipped with an effective, smooth action by an algebraic torus whose orbits are simple complex polytopes and such that the action is locally the same as a faithful real representation of the group." ], "id": "en-toric-en-adj-wziX2K2p", "links": [ [ "torus", "torus" ], [ "toroidal", "toroidal" ], [ "symmetry", "symmetry" ], [ "combinatorial", "combinatorial" ], [ "geometry", "geometry" ], [ "manifold", "manifold" ], [ "compact", "compact" ], [ "smooth", "smooth" ], [ "Quasitoric", "quasitoric" ], [ "closed", "closed" ], [ "real", "real" ], [ "smooth manifold", "smooth manifold" ], [ "effective", "effective" ], [ "action", "group action" ], [ "algebraic torus", "algebraic torus" ], [ "orbit", "orbit" ], [ "simple", "simple" ], [ "complex", "complex" ], [ "polytope", "polytope" ], [ "locally", "locally" ], [ "faithful", "faithful" ], [ "representation", "representation" ] ], "qualifier": "generalizing the case of toric varieties", "raw_glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "(geometry and algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.", "(geometry, of a manifold, generalizing the case of toric varieties) (Narrowly) A compact smooth toric variety. (Broadly) Quasitoric: a closed, real, even-dimensional smooth manifold equipped with an effective, smooth action by an algebraic torus whose orbits are simple complex polytopes and such that the action is locally the same as a faithful real representation of the group." ], "raw_tags": [ "of a manifold" ], "topics": [ "algebra", "geometry", "mathematics", "sciences" ], "translations": [ { "_dis1": "15 38 15 18 15", "code": "cs", "lang": "Czech", "sense": "Translations", "word": "torický" }, { "_dis1": "15 38 15 18 15", "code": "fr", "lang": "French", "sense": "Translations", "word": "torique" }, { "_dis1": "15 38 15 18 15", "code": "it", "lang": "Italian", "sense": "Translations", "word": "torico" }, { "_dis1": "15 38 15 18 15", "code": "pl", "lang": "Polish", "sense": "Translations", "word": "armilarny" }, { "_dis1": "15 38 15 18 15", "code": "es", "lang": "Spanish", "sense": "Translations", "word": "tórico" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebraic geometry", "orig": "en:Algebraic geometry", "parents": [ "Algebra", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Curves", "orig": "en:Curves", "parents": [ "Shapes", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.", "Any of several generalizations of the notion of toric varieties to stacks: the stack quotient of a toric variety by its torus; the stack quotient of a toric variety by a subgroup of its torus." ], "id": "en-toric-en-adj-xH2q49FI", "links": [ [ "torus", "torus" ], [ "toroidal", "toroidal" ], [ "symmetry", "symmetry" ], [ "combinatorial", "combinatorial" ], [ "algebraic geometry", "algebraic geometry" ], [ "stack", "stack" ], [ "quotient", "quotient" ] ], "raw_glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "(geometry and algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.", "(algebraic geometry, of a stack) Any of several generalizations of the notion of toric varieties to stacks: the stack quotient of a toric variety by its torus; the stack quotient of a toric variety by a subgroup of its torus." ], "raw_tags": [ "of a stack" ], "topics": [ "algebra", "algebraic-geometry", "geometry", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "kind": "topical", "langcode": "en", "name": "Curves", "orig": "en:Curves", "parents": [ "Shapes", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.", "Generated by differences of monomials." ], "id": "en-toric-en-adj-4Rb1~tS3", "links": [ [ "torus", "torus" ], [ "toroidal", "toroidal" ], [ "symmetry", "symmetry" ], [ "combinatorial", "combinatorial" ], [ "commutative algebra", "commutative algebra" ], [ "ideal", "ideal" ], [ "Generated", "generate" ], [ "difference", "difference" ], [ "monomial", "monomial" ] ], "qualifier": "commutative algebra", "raw_glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "(geometry and algebra) Which, in any of several technical senses, admits a high degree of symmetry, allowing combinatorial methods to be used in its study.", "(commutative algebra, of an ideal) Generated by differences of monomials." ], "raw_tags": [ "of an ideal" ], "topics": [ "algebra", "geometry", "mathematics", "sciences" ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Curves", "orig": "en:Curves", "parents": [ "Shapes", "Geometry", "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "A particular topological quantum error correcting code; see Toric code on Wikipedia.Wikipedia" ], "id": "en-toric-en-adj-RghvIlH8", "links": [ [ "torus", "torus" ], [ "toroidal", "toroidal" ], [ "topological", "topological" ], [ "code", "code" ], [ "Toric code", "w:Toric code" ] ], "qualifier": "error correction", "raw_glosses": [ "Pertaining to or shaped like a torus, or a section of a torus; toroidal.", "(error correction) A particular topological quantum error correcting code; see Toric code on Wikipedia.Wikipedia" ] } ], "sounds": [ { "ipa": "/tɒɹɪk/", "tags": [ "Received-Pronunciation" ] }, { "ipa": "/tɔːɹɪk/", "tags": [ "Received-Pronunciation" ] }, { "ipa": "/tɔɹɪk/", "tags": [ "General-American" ] }, { "ipa": "/tɑɹɪk/", "tags": [ "New-York-City", "Philadelphia" ] }, { "rhymes": "-ɒɹɪk" }, { "rhymes": "-ɔːɹɪk" } ], "wikipedia": [ "Toric section" ], "word": "toric" }
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