See p-adic on Wiktionary
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "p",
"3": "adic"
},
"expansion": "p + -adic",
"name": "suffix"
}
],
"etymology_text": "From p + -adic. The letter p follows common number theory usage in representing an arbitrary prime number; the suffix -adic signals that properties of the number p (generally, those due to its being prime, and specifically those of a specified p) are fundamental to the theory and determine the properties of the resulting construction.",
"head_templates": [
{
"args": {
"1": "-",
"head": "p-adic"
},
"expansion": "p-adic (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms containing italics",
"parents": [
"Terms containing italics",
"Terms by orthographic property",
"Terms by lexical property"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms suffixed with -adic",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Entries with translation boxes",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with DISPLAYTITLE conflicts",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Catalan translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with French translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Italian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Polish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Portuguese translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Romanian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Number theory",
"orig": "en:Number theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"derived": [
{
"word": "p-adic absolute value"
},
{
"word": "p-adic norm"
},
{
"word": "p-adic number"
},
{
"word": "p-adic order"
},
{
"word": "p-adic ordinal"
},
{
"word": "p-adic ultrametric"
}
],
"examples": [
{
"ref": "1995, Alain Escassut, Analytic Elements in P-adic Analysis, World Scientific, page v:",
"text": "The theory of p'''-adic analytic functions in domains other than simple disks is not very well known yet, although such kind of functions happens to intervene in questions linked to p'''-adic functional analysis, number theory, and others.",
"type": "quote"
},
{
"text": "1997, Fernando Q. Gouvêa, p-adic Numbers: An Introduction, Springer, 2nd Edition, page 60,\nDefinition 3.3.3 The ring of p'''-adic integers is the valuation ring\nZ ₚ=x∈ Q ₚ:|x|ₚ<1."
},
{
"ref": "2007, Nguyen Minh Cheung, Nguyen Van Co, Le Quang Thuan, §12: Harmonic Analysis Over P-adic Field I: Some Equations and Singular Field Operators, N. M. Chuong, Yu V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (editors), Harmonic, Wavelet and P-adic Analysis, World Scientific, page 272, The paper is organized as follows",
"text": "2. Preliminaries\n3. A p'''-adic Cauchy problem\n4. The p'''-adic Hilbert transform\n5. The boundaries in the p'''-adic space L^q\n[…]"
}
],
"glosses": [
"Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers."
],
"id": "en-p-adic-en-adj-k3jWjy7j",
"links": [
[
"number theory",
"number theory"
],
[
"p-adic number",
"p-adic number"
]
],
"raw_glosses": [
"(number theory) Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers."
],
"related": [
{
"word": "ℓ-adic cohomology"
},
{
"word": "p-adic Riemann zeta function"
}
],
"synonyms": [
{
"sense": "of, etc., p-adic numbers",
"word": "ℓ-adic"
}
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "Translations",
"word": "p-àdic"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "p-adinen"
},
{
"code": "fr",
"lang": "French",
"sense": "Translations",
"word": "p-adique"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"word": "p-adisch"
},
{
"code": "it",
"lang": "Italian",
"sense": "Translations",
"word": "p-adico"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"word": "p-adyczny"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "Translations",
"word": "p-ádico"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "Translations",
"word": "p-adic"
},
{
"code": "es",
"lang": "Spanish",
"sense": "Translations",
"word": "p-ádico"
}
],
"wikipedia": [
"Weil cohomology theory"
]
}
],
"word": "p-adic"
}
{
"derived": [
{
"word": "p-adic absolute value"
},
{
"word": "p-adic norm"
},
{
"word": "p-adic number"
},
{
"word": "p-adic order"
},
{
"word": "p-adic ordinal"
},
{
"word": "p-adic ultrametric"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "p",
"3": "adic"
},
"expansion": "p + -adic",
"name": "suffix"
}
],
"etymology_text": "From p + -adic. The letter p follows common number theory usage in representing an arbitrary prime number; the suffix -adic signals that properties of the number p (generally, those due to its being prime, and specifically those of a specified p) are fundamental to the theory and determine the properties of the resulting construction.",
"head_templates": [
{
"args": {
"1": "-",
"head": "p-adic"
},
"expansion": "p-adic (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"word": "ℓ-adic cohomology"
},
{
"word": "p-adic Riemann zeta function"
}
],
"senses": [
{
"categories": [
"English adjectives",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English terms containing italics",
"English terms suffixed with -adic",
"English terms with quotations",
"English uncomparable adjectives",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with DISPLAYTITLE conflicts",
"Pages with entries",
"Terms with Catalan translations",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Italian translations",
"Terms with Polish translations",
"Terms with Portuguese translations",
"Terms with Romanian translations",
"Terms with Spanish translations",
"Translation table header lacks gloss",
"en:Number theory"
],
"examples": [
{
"ref": "1995, Alain Escassut, Analytic Elements in P-adic Analysis, World Scientific, page v:",
"text": "The theory of p'''-adic analytic functions in domains other than simple disks is not very well known yet, although such kind of functions happens to intervene in questions linked to p'''-adic functional analysis, number theory, and others.",
"type": "quote"
},
{
"text": "1997, Fernando Q. Gouvêa, p-adic Numbers: An Introduction, Springer, 2nd Edition, page 60,\nDefinition 3.3.3 The ring of p'''-adic integers is the valuation ring\nZ ₚ=x∈ Q ₚ:|x|ₚ<1."
},
{
"ref": "2007, Nguyen Minh Cheung, Nguyen Van Co, Le Quang Thuan, §12: Harmonic Analysis Over P-adic Field I: Some Equations and Singular Field Operators, N. M. Chuong, Yu V. Egorov, A. Khrennikov, Y. Meyer, D. Mumford (editors), Harmonic, Wavelet and P-adic Analysis, World Scientific, page 272, The paper is organized as follows",
"text": "2. Preliminaries\n3. A p'''-adic Cauchy problem\n4. The p'''-adic Hilbert transform\n5. The boundaries in the p'''-adic space L^q\n[…]"
}
],
"glosses": [
"Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers."
],
"links": [
[
"number theory",
"number theory"
],
[
"p-adic number",
"p-adic number"
]
],
"raw_glosses": [
"(number theory) Of, pertaining to, (ultimately) derived from or defined in the context of p-adic numbers."
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"number-theory",
"sciences"
],
"wikipedia": [
"Weil cohomology theory"
]
}
],
"synonyms": [
{
"sense": "of, etc., p-adic numbers",
"word": "ℓ-adic"
}
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "Translations",
"word": "p-àdic"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "Translations",
"word": "p-adinen"
},
{
"code": "fr",
"lang": "French",
"sense": "Translations",
"word": "p-adique"
},
{
"code": "de",
"lang": "German",
"sense": "Translations",
"word": "p-adisch"
},
{
"code": "it",
"lang": "Italian",
"sense": "Translations",
"word": "p-adico"
},
{
"code": "pl",
"lang": "Polish",
"sense": "Translations",
"word": "p-adyczny"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "Translations",
"word": "p-ádico"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "Translations",
"word": "p-adic"
},
{
"code": "es",
"lang": "Spanish",
"sense": "Translations",
"word": "p-ádico"
}
],
"word": "p-adic"
}
Download raw JSONL data for p-adic meaning in All languages combined (3.9kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.