See algebraic function in All languages combined, or Wiktionary
Download JSON data for algebraic function meaning in English (4.9kB)
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"text": "Quite often, algebraic functions are algebraic expressions using a finite number of terms and involving only the algebraic operations addition, subtraction, multiplication, division, and raising to a fractional power. Some algebraic functions, however, cannot be expressed by such finite expressions.",
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"text": "The value of an algebraic function at an algebraic number is always an algebraic number.",
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"text": "1989, Manuel Bronstein, An Algorithm for the Integration of Elementary Functions, James H. Davenport (editor), EUROCAL '87: European Conference on Computer Algebra, Proceedings, Springer, LNCS 378, page 491,\nTrager (1984) recently gave a new algorithm for the indefinite integration of algebraic functions."
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"text": "1992, A. A. Goldberg, V. A. Pyana, Uniqueness Theorems for Algebraic Functions, A. B. Sossinsky (translation editor), Boris Yakovlevich Levin (editor), Entire and Subharmonic Functions, American Mathematical Society, page 199,\nIt is known that the algebraic function w=w(z) enables one to determine the polynomial P(z,w) up to a constant factor."
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"text": "1993, Goro Kato (translator), Kenkichi Iwasawa, Algebraic Functions, American Mathematical Society, page xiv,\nRiemann provided a clear picture of many difficult topics. His most significant contribution, rather than his construction of a Riemann surface from an algebraic function, was to derive the existence of algebraic functions as he built his theory based on the concept of a Riemann surface."
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"Informally, any function expressible using (only) the operations of addition, subtraction, multiplication, division and raising to a rational power; more precisely, any continuous function definable as the root of some polynomial equation."
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"(algebraic geometry) Informally, any function expressible using (only) the operations of addition, subtraction, multiplication, division and raising to a rational power; more precisely, any continuous function definable as the root of some polynomial equation."
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"sense": "function definable as the root of some polynomial equation",
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},
{
"text": "1992, A. A. Goldberg, V. A. Pyana, Uniqueness Theorems for Algebraic Functions, A. B. Sossinsky (translation editor), Boris Yakovlevich Levin (editor), Entire and Subharmonic Functions, American Mathematical Society, page 199,\nIt is known that the algebraic function w=w(z) enables one to determine the polynomial P(z,w) up to a constant factor."
},
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"text": "1993, Goro Kato (translator), Kenkichi Iwasawa, Algebraic Functions, American Mathematical Society, page xiv,\nRiemann provided a clear picture of many difficult topics. His most significant contribution, rather than his construction of a Riemann surface from an algebraic function, was to derive the existence of algebraic functions as he built his theory based on the concept of a Riemann surface."
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"sense": "function definable as the root of some polynomial equation",
"tags": [
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"word": "algebraická funkce"
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{
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"sense": "function definable as the root of some polynomial equation",
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{
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"sense": "function definable as the root of some polynomial equation",
"tags": [
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"sense": "function definable as the root of some polynomial equation",
"tags": [
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"word": "função algébrica"
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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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