Difference between revisions of "GroebnerLex Command"
From GeoGebra Manual
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;GroebnerLex[ <List of Polynomials> ]: Computes the Gröbner basis of the list of the polynomials with respect to lexicographical ordering of the variables. | ;GroebnerLex[ <List of Polynomials> ]: Computes the Gröbner basis of the list of the polynomials with respect to lexicographical ordering of the variables. | ||
{{example| 1=<div><code><nowiki>GroebnerLex[{x^3-y-2,x^2+y+1}]</nowiki></code> yields {<math> y^{3} + 4 y^{2} + 7 y + 5, x - y^{2} - 3 y - 3 </math>}. | {{example| 1=<div><code><nowiki>GroebnerLex[{x^3-y-2,x^2+y+1}]</nowiki></code> yields {<math> y^{3} + 4 y^{2} + 7 y + 5, x - y^{2} - 3 y - 3 </math>}. | ||
+ | </div>}} | ||
+ | ;GroebnerLex[ <List of Polynomials>, <List of Variables> ]: Computes the Gröbner basis of the list of the polynomials with respect to lexicographical ordering of the given variables. | ||
+ | {{example| 1=<div><code><nowiki>GroebnerLex[{x^3-y-2,x^2+y+1},{y,x}]</nowiki></code> yields {<math> -x^{3} - x^{2} + 1, -y - x^{2} - 1 </math>}. | ||
</div>}} | </div>}} | ||
{{Note| See also [[GroebnerDegRevLex Command|GroebnerDegRevLex]], [[GroebnerLexDeg Command|GroebnerLexDeg]] commands.}} | {{Note| See also [[GroebnerDegRevLex Command|GroebnerDegRevLex]], [[GroebnerLexDeg Command|GroebnerLexDeg]] commands.}} |
Revision as of 13:29, 8 May 2014
This page is about a feature that is supported only in GeoGebra 5.0. |
- GroebnerLex[ <List of Polynomials> ]
- Computes the Gröbner basis of the list of the polynomials with respect to lexicographical ordering of the variables.
Example:
GroebnerLex[{x^3-y-2,x^2+y+1}]
yields { y^{3} + 4 y^{2} + 7 y + 5, x - y^{2} - 3 y - 3 }.
- GroebnerLex[ <List of Polynomials>, <List of Variables> ]
- Computes the Gröbner basis of the list of the polynomials with respect to lexicographical ordering of the given variables.
Example:
GroebnerLex[{x^3-y-2,x^2+y+1},{y,x}]
yields { -x^{3} - x^{2} + 1, -y - x^{2} - 1 }.
Note: See also GroebnerDegRevLex, GroebnerLexDeg commands.