Difference between revisions of "GroebnerDegRevLex Command"
From GeoGebra Manual
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{{example| 1=<div><code><nowiki>GroebnerDegRevLex[{x^3-y-2,x^2+y+1}]</nowiki></code> yields {<math> y^{2} - x + 3 y + 3, x y + x + y + 2, x^{2} + y + 1 </math>}. | {{example| 1=<div><code><nowiki>GroebnerDegRevLex[{x^3-y-2,x^2+y+1}]</nowiki></code> yields {<math> y^{2} - x + 3 y + 3, x y + x + y + 2, x^{2} + y + 1 </math>}. | ||
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| − | ;GroebnerLex[ <List of Polynomials>, <List of Variables> ]: Computes the Gröbner basis of the list of the polynomials with respect to graded reverse lexicographical ordering of the variables (also known as ''total degree reverse lexicographic ordering'', ''degrevlex'' or ''grevlex'' ordering). | + | ;GroebnerLex[ <List of Polynomials>, <List of Variables> ]: Computes the Gröbner basis of the list of the polynomials with respect to graded reverse lexicographical ordering of the given variables (also known as ''total degree reverse lexicographic ordering'', ''degrevlex'' or ''grevlex'' ordering). |
{{example| 1=<div><code><nowiki>GroebnerDegRevLex[{x^3-y-2,x^2+y+1},{y,x}]</nowiki></code> yields {<math> x^{2} - y, y \; x - x, y^{2} - y </math>}. | {{example| 1=<div><code><nowiki>GroebnerDegRevLex[{x^3-y-2,x^2+y+1},{y,x}]</nowiki></code> yields {<math> x^{2} - y, y \; x - x, y^{2} - y </math>}. | ||
</div>}} | </div>}} | ||
{{Note| See also [[GroebnerLex Command|GroebnerLex]], [[GroebnerLexDeg Command|GroebnerLexDeg]] commands.}} | {{Note| See also [[GroebnerLex Command|GroebnerLex]], [[GroebnerLexDeg Command|GroebnerLexDeg]] commands.}} | ||
Revision as of 14:53, 8 May 2014
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This page is about a feature that is supported only in GeoGebra 5.0. |
- GroebnerDegRevLex[ <List of Polynomials> ]
- Computes the Gröbner basis of the list of the polynomials with respect to graded reverse lexicographical ordering of the variables (also known as total degree reverse lexicographic ordering, degrevlex or grevlex ordering).
Example:
GroebnerDegRevLex[{x^3-y-2,x^2+y+1}] yields { y^{2} - x + 3 y + 3, x y + x + y + 2, x^{2} + y + 1 }.
- GroebnerLex[ <List of Polynomials>, <List of Variables> ]
- Computes the Gröbner basis of the list of the polynomials with respect to graded reverse lexicographical ordering of the given variables (also known as total degree reverse lexicographic ordering, degrevlex or grevlex ordering).
Example:
GroebnerDegRevLex[{x^3-y-2,x^2+y+1},{y,x}] yields { x^{2} - y, y \; x - x, y^{2} - y }.
Note: See also GroebnerLex, GroebnerLexDeg commands.
