Gröbner basis (Q2181): Difference between revisions

@@ Property / Freebase ID @@
+/m/01_0w0
@@ Property / Freebase ID: /m/01_0w0 / rank @@
+Normal rank
@@ Property / Freebase ID: /m/01_0w0 / reference @@
+stated in: Freebase Data Dumps
publication date: 28 October 2013Timestamp +2013-10-28T00:00:00Z
Timezone +00:00
Calendar Gregorian
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-Timestamp
++2013-10-28T00:00:00Z
-Timezone
++00:00
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+Gregorian
-Precision
+day
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@@ Property / subclass of @@
+generating set of a module
@@ Property / subclass of: generating set of a module / rank @@
+Normal rank
@@ Property / Stack Exchange tag @@
+https://stackoverflow.com/tags/groebner-basis
+Normal rank
@@ Property / Stack Exchange tag @@
+https://mathoverflow.net/tags/groebner-bases
+Normal rank
@@ Property / MathWorld ID @@
+GroebnerBasis
@@ Property / MathWorld ID: GroebnerBasis / rank @@
+Normal rank
@@ Property / MathWorld ID: GroebnerBasis / reference @@
+imported from Wikimedia project: English Wikipedia
@@ Property / named after @@
+Wolfgang Gröbner
@@ Property / named after: Wolfgang Gröbner / rank @@
+Normal rank
@@ Property / named after: Wolfgang Gröbner / qualifier @@
+named by: Bruno Buchberger
@@ Property / Library of Congress authority ID @@
+sh92005856
@@ Property / Library of Congress authority ID: sh92005856 / rank @@
+Normal rank
@@ Property / Library of Congress authority ID: sh92005856 / reference @@
+reference URL: https://github.com/JohnMarkOckerbloom/ftl/blob/master/data/wikimap
retrieved: 3 April 2019Timestamp +2019-04-03T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
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-Timestamp
++2019-04-03T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
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@@ Property / Bibliothèque nationale de France ID @@
+124219399
@@ Property / Bibliothèque nationale de France ID: 124219399 / rank @@
+Normal rank
@@ Property / IdRef ID @@
+033344299
@@ Property / IdRef ID: 033344299 / rank @@
+Normal rank
@@ Property / GND ID @@
+4276378-2
@@ Property / GND ID: 4276378-2 / rank @@
+Normal rank
@@ Property / FAST ID @@
@@ Property / FAST ID: 948675 / rank @@
+Normal rank
@@ Property / Microsoft Academic ID @@
+198082693
@@ Property / Microsoft Academic ID: 198082693 / rank @@
+Normal rank
@@ Property / Scholarpedia article ID @@
+Groebner_basis
@@ Property / Scholarpedia article ID: Groebner_basis / rank @@
+Normal rank
@@ Property / OpenAlex ID @@
+C198082693
@@ Property / OpenAlex ID: C198082693 / rank @@
+Normal rank
@@ Property / OpenAlex ID: C198082693 / reference @@
+stated in: OpenAlex
retrieved: 26 January 2022Timestamp +2022-01-26T00:00:00Z
Timezone +00:00
Calendar Gregorian
Precision 1 day
Before 0
After 0
reference URL: https://docs.openalex.org/download-snapshot/snapshot-data-format
-Timestamp
++2022-01-26T00:00:00Z
-Timezone
++00:00
-Calendar
+Gregorian
-Precision
+day
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 After
@@ Property / National Library of Israel J9U ID @@
+987007539439305171
@@ Property / National Library of Israel J9U ID: 987007539439305171 / rank @@
+Normal rank
@@ Property / National Library of Israel J9U ID: 987007539439305171 / reference @@
+stated in: National Library of Israel Names and Subjects Authority File
@@ Property / defining formula @@
+ ${\begin{aligned}{\mathfrak {I}}&=(G)\\(\operatorname {lm} (p)\colon p\in {\mathfrak {I}})&=(\operatorname {lm} (p)\colon p\in G)\\\operatorname {lm} \left(\sum _{A\subset I}p_{A}\prod _{i\in A}x_{i}\right)&{\stackrel {\mathrm {def} }{=}}\min _{\leq }\left\{\prod _{i\in A}x_{i}\colon p_{A}\neq 0\right\}\end{aligned}}$ 
\begin{aligned}\mathfrak I&=(G)\\(\operatorname{lm}(p)\colon p\in\mathfrak I)&=(\operatorname{lm}(p)\colon p\in G)\\\operatorname{lm}\left(\sum_{A\subset I}p_A\prod_{i\in A}x_i\right)&\stackrel{\mathrm{def}}=\min_\le\left\{\prod_{i\in A}x_i\colon p_A\ne0\right\}\end{aligned}
+Normal rank
@@ Property / in defining formula @@
+ ${\mathfrak {I}}$ 
\mathfrak I
@@ Property / in defining formula: ${\mathfrak {I}}$ / rank @@
+Normal rank
@@ Property / in defining formula: ${\mathfrak {I}}$ / qualifier @@
+symbol represents: ideal
@@ Property / in defining formula @@
+ $G$ 
G
@@ Property / in defining formula: $G$ / rank @@
+Normal rank
@@ Property / in defining formula: $G$ / qualifier @@
+symbol represents: Gröbner basis
@@ Property / in defining formula @@
+ $\leq$ 
\le
@@ Property / in defining formula: $\leq$ / rank @@
+Normal rank
@@ Property / in defining formula: $\leq$ / qualifier @@
+symbol represents: monomial order
@@ Property / ProofWiki ID @@
+Gröbner_Basis
@@ Property / ProofWiki ID: Gröbner_Basis / rank @@
+Normal rank
@@ Property / has part(s) @@
+polynomial
@@ Property / has part(s): polynomial / rank @@
+Normal rank