Difference between revisions of "GroebnerLex Command"
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|logical}} | <noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|logical}} | ||
==CAS Syntax== | ==CAS Syntax== | ||
| − | ;GroebnerLex | + | ;GroebnerLex( <List of Polynomials> ): Computes the Gröbner basis of the list of the polynomials with respect to lexicographical ordering of the variables (also known as ''lex'', ''plex'' or ''pure lexical'' ordering). |
:{{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>}} | :{{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 | + | ;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 (also known as ''lex'', ''plex'' or ''pure lexical'' ordering). |
:{{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>}} | :{{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>}} | ||
{{Note| See also [[GroebnerDegRevLex Command|GroebnerDegRevLex]] and [[GroebnerLexDeg Command|GroebnerLexDeg]] commands.}} | {{Note| See also [[GroebnerDegRevLex Command|GroebnerDegRevLex]] and [[GroebnerLexDeg Command|GroebnerLexDeg]] commands.}} | ||
Revision as of 17:17, 7 October 2017
CAS Syntax
- GroebnerLex( <List of Polynomials> )
- Computes the Gröbner basis of the list of the polynomials with respect to lexicographical ordering of the variables (also known as lex, plex or pure lexical ordering).
- 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 (also known as lex, plex or pure lexical ordering).
- 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 and GroebnerLexDeg commands.
