See symplectic on Wiktionary
Download JSON data for symplectic meaning in All languages combined (14.0kB)
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"ref": "1995, V. I. Arnold, “Some remarks on symplectic monodromy of Milnor fibrations”, in Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder, editors, The Floer Memorial Volume, Birkhäuser Verlag, page 99",
"text": "There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.",
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"text": "1997, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau, Structure of Dynamical Systems: A Symplectic View of Physics, Springer Science & Business Media (Birkhäuser)."
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"text": "2003, Fabrizio Catanese, Gang Tian (editors), Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E Summer School, Springer, Lecture Notes in Mathematics No. 1938."
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"text": "2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde, editors, Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society:",
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"ref": "2003, Maung Min-Oo, “The Dirac Operator in Geometry and Physics”, in Steen Markvorsen, Maung Min-Oo, editors, Global Riemannian Geometry: Curvature and Topology, Springer, page 72",
"text": "In symplectic geometry, there is a notion of fibrations #x5C;pi#x3A;P#x5C;rightarrowM with a symplectic manifold F as fiber, where the structure group is the group of (exact) Hamiltonian symplectomorphisms of the fiber. These are called symplectic fibrations. If the base manifold (M,#x5C;omega#x5F;M) is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space P.",
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"bilinear form"
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[
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"alternating"
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[
"nondegenerate",
"nondegenerate"
]
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"(mathematics, multilinear algebra, of a bilinear form) That is alternating and nondegenerate."
],
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"of a bilinear form"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
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{
"categories": [
"en:Mathematics"
],
"glosses": [
"That is equipped with an alternating nondegenerate bilinear form."
],
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"mathematics",
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[
"vector space",
"vector space"
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"alternating",
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[
"nondegenerate",
"nondegenerate"
],
[
"bilinear form",
"bilinear form"
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],
"qualifier": "multilinear algebra",
"raw_glosses": [
"(mathematics, multilinear algebra, of a vector space) That is equipped with an alternating nondegenerate bilinear form."
],
"raw_tags": [
"of a vector space"
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"English terms with quotations",
"Quotation templates to be cleaned",
"en:Mathematics"
],
"examples": [
{
"ref": "1995, V. I. Arnold, “Some remarks on symplectic monodromy of Milnor fibrations”, in Helmut Hofer, Clifford H. Taubes, Alan Weinstein, Eduard Zehnder, editors, The Floer Memorial Volume, Birkhäuser Verlag, page 99",
"text": "There exist interesting and unexplored relations between symplectic geometry and the theory of critical points of holomorphic functions.",
"type": "quotation"
},
{
"text": "1997, C. H. Cushman-de Vries (translator), Richard H. Cushman, Gijs M. Tuynman (translation editors), Jean-Marie Souriau, Structure of Dynamical Systems: A Symplectic View of Physics, Springer Science & Business Media (Birkhäuser)."
},
{
"text": "2003, Fabrizio Catanese, Gang Tian (editors), Symplectic 4-Manifolds and Algebraic Surfaces: Lectures given at the C.I.M.E Summer School, Springer, Lecture Notes in Mathematics No. 1938."
},
{
"text": "2003, Yakov Eliashberg, Boris A. Khesin, François Lalonde, editors, Symplectic and Contact Topology: Interactions and Perspectives, American Mathematical Society:",
"type": "quotation"
},
{
"ref": "2003, Maung Min-Oo, “The Dirac Operator in Geometry and Physics”, in Steen Markvorsen, Maung Min-Oo, editors, Global Riemannian Geometry: Curvature and Topology, Springer, page 72",
"text": "In symplectic geometry, there is a notion of fibrations #x5C;pi#x3A;P#x5C;rightarrowM with a symplectic manifold F as fiber, where the structure group is the group of (exact) Hamiltonian symplectomorphisms of the fiber. These are called symplectic fibrations. If the base manifold (M,#x5C;omega#x5F;M) is also symplectic, there is a weak coupling construction, originally due to Thurston, of defining a symplectic structure on the total space P.",
"type": "quotation"
}
],
"glosses": [
"Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form."
],
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"mathematics",
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[
"geometry",
"geometry"
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"differentiable",
"differentiable"
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[
"manifold",
"manifold"
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[
"closed",
"closed"
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[
"nondegenerate",
"nondegenerate"
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[
"bilinear form",
"bilinear form"
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],
"raw_glosses": [
"(mathematics) Of or pertaining to (the geometry of) a differentiable manifold equipped with a closed nondegenerate bilinear form."
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"glosses": [
"That moves in the same direction as a system of synchronized waves."
],
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[
"synchronized",
"synchronized"
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"wave",
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],
"tags": [
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},
{
"categories": [
"en:Mineralogy",
"en:Petrology"
],
"glosses": [
"Of or pertaining to a symplectite; symplectitic."
],
"links": [
[
"petrology",
"petrology"
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[
"mineralogy",
"mineralogy"
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[
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[
"symplectitic",
"symplectitic#English"
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],
"raw_glosses": [
"(petrology, mineralogy) Of or pertaining to a symplectite; symplectitic."
],
"tags": [
"not-comparable"
],
"topics": [
"chemistry",
"geography",
"geology",
"mineralogy",
"natural-sciences",
"petrology",
"physical-sciences"
]
}
],
"sounds": [
{
"ipa": "/sɪmˈplɛktɪk/"
},
{
"rhymes": "-ɛktɪk"
}
],
"wikipedia": [
"Hermann Weyl",
"The Classical Groups"
],
"word": "symplectic"
}
{
"categories": [
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"English adjectives",
"English countable nouns",
"English entries with incorrect language header",
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"English uncomparable adjectives",
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],
"etymology_templates": [
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"args": {
"1": "en",
"2": "complex"
},
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"name": "m"
},
{
"args": {
"1": "en",
"2": "grc",
"3": "συμπλεκτικός"
},
"expansion": "Ancient Greek συμπλεκτικός (sumplektikós)",
"name": "der"
},
{
"args": {
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{
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"2": "σύν"
},
"expansion": "σύν (sún)",
"name": "m"
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{
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"1": "grc",
"2": "πλεκτικός"
},
"expansion": "πλεκτικός (plektikós)",
"name": "m"
},
{
"args": {
"1": "grc",
"2": "πλέκω"
},
"expansion": "πλέκω (plékō)",
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},
{
"args": {
"1": "en",
"2": "complex"
},
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"name": "m"
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{
"args": {
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"3": "",
"4": "braided together"
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{
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"args": {
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"2": "plectere",
"3": "",
"4": "to weave, braid"
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"expansion": "plectere (“to weave, braid”)",
"name": "m"
}
],
"etymology_text": "A calque of complex, coined by Hermann Weyl in his 1939 book The Classical Groups: Their Invariants and Representations. From Ancient Greek συμπλεκτικός (sumplektikós), from συμ (sum) (variant of σύν (sún)), + πλεκτικός (plektikós) (from πλέκω (plékō)); modelled on complex (from Latin complexus (“braided together”), from com- (“together”) + plectere (“to weave, braid”)).\nThe symplectic group has previously been called the line complex group.",
"forms": [
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"form": "symplectics",
"tags": [
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"args": {},
"expansion": "symplectic (plural symplectics)",
"name": "en-noun"
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"lang": "English",
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"pos": "noun",
"senses": [
{
"categories": [
"English terms with quotations",
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"examples": [
{
"ref": "1967, Journal of Mathematics and Mechanics, volume 16, number 1, Indiana University, page 339",
"text": "The structure of stable symplectics on finite dimensional spaces has been studied by Krein [8], Gelfand & Lidskii [9], and Moser [10] in work of considerable practical importance.",
"type": "quotation"
}
],
"glosses": [
"A symplectic bilinear form, manifold, geometry, etc."
],
"links": [
[
"mathematics",
"mathematics"
]
],
"raw_glosses": [
"(mathematics) A symplectic bilinear form, manifold, geometry, etc."
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"English terms with quotations",
"en:Ichthyology"
],
"examples": [
{
"ref": "1914, The Philippine Journal of Science, Volume 9, page 27",
"text": "The symplectics (9) consist of a somewhat curved central triangular portion with the base upward, and anteriorly and posteriorly from this extends a wing-like process.",
"type": "quotation"
},
{
"ref": "1965, Agra University Journal of Research: Science, Volume 14, page 71",
"text": "The symplectics (Fig. 8, sym) are thin slender bones placed vertically in between the quadrates and the hyomandibulars.",
"type": "quotation"
},
{
"ref": "1967, Tyson R. Roberts, Studies on the Osteology and Phylogeny of Characoid Fishes, page 59",
"text": "In many teleosts, on the other hand, including the catfishes, the symplectics have been entirely lost.",
"type": "quotation"
}
],
"glosses": [
"A bone in the teleostean fishes that forms the lower ossification of the suspensorium, and which articulates below with the quadrate bone by which it is firmly held."
],
"links": [
[
"ichthyology",
"ichthyology"
],
[
"bone",
"bone"
],
[
"teleostean",
"teleostean"
],
[
"fish",
"fish"
],
[
"ossification",
"ossification"
],
[
"suspensorium",
"suspensorium"
],
[
"articulate",
"articulate"
],
[
"quadrate bone",
"quadrate bone"
]
],
"raw_glosses": [
"(ichthyology) A bone in the teleostean fishes that forms the lower ossification of the suspensorium, and which articulates below with the quadrate bone by which it is firmly held."
],
"topics": [
"biology",
"ichthyology",
"natural-sciences",
"zoology"
]
}
],
"sounds": [
{
"ipa": "/sɪmˈplɛktɪk/"
},
{
"rhymes": "-ɛktɪk"
}
],
"wikipedia": [
"Hermann Weyl",
"The Classical Groups"
],
"word": "symplectic"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.