See transition function in All languages combined, or Wiktionary
Download JSON data for transition function meaning in English (5.7kB)
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"kind": "topical",
"langcode": "en",
"name": "Theory of computing",
"orig": "en:Theory of computing",
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"A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state."
],
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"(computing theory) A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state."
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"translations": [
{
"_dis1": "93 7",
"code": "fi",
"lang": "Finnish",
"sense": "function from (state, input symbol) to state",
"word": "siirtymäfunktio"
},
{
"_dis1": "93 7",
"code": "de",
"lang": "German",
"sense": "function from (state, input symbol) to state",
"tags": [
"feminine"
],
"word": "Übergangsfunktion"
},
{
"_dis1": "93 7",
"code": "ro",
"lang": "Romanian",
"sense": "function from (state, input symbol) to state",
"tags": [
"feminine"
],
"word": "funcție de tranziție"
}
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Differential geometry",
"orig": "en:Differential geometry",
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"Mathematical analysis",
"Mathematics",
"Formal sciences",
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"name": "Functions",
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"examples": [
{
"ref": "2007, Dominic D. Joyce, Riemannian Holonomy Groups and Calibrated Geometry (Oxford graduate texts in mathematics), Oxford University Press, →LCCN, page 76",
"text": "If (U#x5F;1,#x5C;psi#x5F;1) and (U#x5F;2,#x5C;psi#x5F;2) are two complex charts, then the transition function is #x5C;psi#x5F;#x7B;12#x7D;#x3A;#x5C;psi#x5F;1(U#x5F;1#x5C;capU#x5F;2)#x5C;rightarrow#x5C;psi#x5F;2(U#x5F;1#x5C;capU#x5F;2), given by #x5C;psi#x5F;#x7B;12#x7D;#x3D;#x5C;psi#x5F;2#x5C;circ#x5C;psi#x5F;1#x7B;-1#x7D;. We say M is a complex manifold if it has an atlas of complex charts (U,#x5C;psi), such that all the transition functions are holomorphic, as maps from #x5C;mathbb#x7B;C#x7D;ᵐ to itself.",
"type": "quotation"
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"glosses": [
"A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed."
],
"id": "en-transition_function-en-noun-jVQkloDM",
"links": [
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"differential geometry",
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"(differential geometry) A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed."
],
"synonyms": [
{
"word": "transition map"
}
],
"translations": [
{
"_dis1": "10 90",
"code": "fi",
"lang": "Finnish",
"sense": "homeomorphism between subsets of images of overlapping coordinate charts",
"word": "transitiokuvaus"
},
{
"_dis1": "10 90",
"code": "de",
"lang": "German",
"sense": "homeomorphism between subsets of images of overlapping coordinate charts",
"tags": [
"feminine"
],
"word": "Übergangsfunktion"
},
{
"_dis1": "10 90",
"code": "de",
"lang": "German",
"sense": "homeomorphism between subsets of images of overlapping coordinate charts",
"tags": [
"masculine"
],
"word": "Kartenübergang"
},
{
"_dis1": "10 90",
"code": "de",
"lang": "German",
"sense": "homeomorphism between subsets of images of overlapping coordinate charts",
"tags": [
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],
"word": "Kartenwechsel"
}
]
}
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"word": "transition function"
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"A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state."
],
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"computing",
"computing#Noun"
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"(computing theory) A function from (state, input symbol) to state describing what state to move to on receiving a given input in a given state."
],
"topics": [
"computing",
"computing-theory",
"engineering",
"mathematics",
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"sciences"
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"examples": [
{
"ref": "2007, Dominic D. Joyce, Riemannian Holonomy Groups and Calibrated Geometry (Oxford graduate texts in mathematics), Oxford University Press, →LCCN, page 76",
"text": "If (U#x5F;1,#x5C;psi#x5F;1) and (U#x5F;2,#x5C;psi#x5F;2) are two complex charts, then the transition function is #x5C;psi#x5F;#x7B;12#x7D;#x3A;#x5C;psi#x5F;1(U#x5F;1#x5C;capU#x5F;2)#x5C;rightarrow#x5C;psi#x5F;2(U#x5F;1#x5C;capU#x5F;2), given by #x5C;psi#x5F;#x7B;12#x7D;#x3D;#x5C;psi#x5F;2#x5C;circ#x5C;psi#x5F;1#x7B;-1#x7D;. We say M is a complex manifold if it has an atlas of complex charts (U,#x5C;psi), such that all the transition functions are holomorphic, as maps from #x5C;mathbb#x7B;C#x7D;ᵐ to itself.",
"type": "quotation"
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"A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed."
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"(differential geometry) A homeomorphism that bijects between the subsets of the images of two overlapping coordinate charts that are shared in the preimage: For (U_1,φ₁) and (U_2,φ₂) coordinate charts with U_1∩U_2≠∅, the transition functions φ₁₂=φ₂∘φ₁⁻¹ and its inverse φ₂₁=φ₁∘φ₂⁻¹ may be constructed."
],
"synonyms": [
{
"word": "transition map"
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"translations": [
{
"code": "fi",
"lang": "Finnish",
"sense": "function from (state, input symbol) to state",
"word": "siirtymäfunktio"
},
{
"code": "de",
"lang": "German",
"sense": "function from (state, input symbol) to state",
"tags": [
"feminine"
],
"word": "Übergangsfunktion"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "function from (state, input symbol) to state",
"tags": [
"feminine"
],
"word": "funcție de tranziție"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "homeomorphism between subsets of images of overlapping coordinate charts",
"word": "transitiokuvaus"
},
{
"code": "de",
"lang": "German",
"sense": "homeomorphism between subsets of images of overlapping coordinate charts",
"tags": [
"feminine"
],
"word": "Übergangsfunktion"
},
{
"code": "de",
"lang": "German",
"sense": "homeomorphism between subsets of images of overlapping coordinate charts",
"tags": [
"masculine"
],
"word": "Kartenübergang"
},
{
"code": "de",
"lang": "German",
"sense": "homeomorphism between subsets of images of overlapping coordinate charts",
"tags": [
"masculine"
],
"word": "Kartenwechsel"
}
],
"wikipedia": [
"transition function"
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"word": "transition function"
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This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-05-05 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.
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