Difference between revisions of "GroebnerLex Command"

From GeoGebra Manual
Jump to: navigation, search
Line 3: Line 3:
 
;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


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.
© 2024 International GeoGebra Institute