Difference between revisions of "GroebnerLexDeg Command"

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{{command|logical}}
 
{{command|logical}}
 
;GroebnerLexDeg[ <List of Polynomials> ]: Computes the Gröbner basis of the list of the polynomials with respect to graded lexicographical ordering of the variables (also known as ''grlex'', ''tdeg'', ''lexdeg'', ''total degree lexicographic ordering'' or ''elimination ordering'').
 
;GroebnerLexDeg[ <List of Polynomials> ]: Computes the Gröbner basis of the list of the polynomials with respect to graded lexicographical ordering of the variables (also known as ''grlex'', ''tdeg'', ''lexdeg'', ''total degree lexicographic ordering'' or ''elimination ordering'').
:{{example| 1=<div><code><nowiki>GroebnerLexDeg[{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>}.</div>}}
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{{example| 1=<div><code><nowiki>GroebnerLexDeg[{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>}.</div>}}
 
;GroebnerLexDeg[ <List of Polynomials>, <List of Variables> ]: Computes the Gröbner basis of the list of the polynomials with respect to graded lexicographical ordering of the given variables (also known as ''grlex'', ''tdeg'', ''lexdeg'', ''total degree lexicographic ordering'' or ''elimination ordering'').
 
;GroebnerLexDeg[ <List of Polynomials>, <List of Variables> ]: Computes the Gröbner basis of the list of the polynomials with respect to graded lexicographical ordering of the given variables (also known as ''grlex'', ''tdeg'', ''lexdeg'', ''total degree lexicographic ordering'' or ''elimination ordering'').
:{{example| 1=<div><code><nowiki>GroebnerLexDeg[{x^3 - y -2, x^2 + y + 1},{y, x}]</nowiki></code> yields {<math> x^{2} + y + 1, -y x - y - x - 2, y^{2} + 3 y - x + 3 </math>}.</div>}}
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{{example| 1=<div><code><nowiki>GroebnerLexDeg[{x^3 - y -2, x^2 + y + 1},{y, x}]</nowiki></code> yields {<math> x^{2} + y + 1, -y x - y - x - 2, y^{2} + 3 y - x + 3 </math>}.</div>}}
 
{{Note| See also [[GroebnerDegRevLex Command|GroebnerDegRevLex]] and [[GroebnerLex Command|GroebnerLex]] commands.}}
 
{{Note| See also [[GroebnerDegRevLex Command|GroebnerDegRevLex]] and [[GroebnerLex Command|GroebnerLex]] commands.}}

Revision as of 09:42, 9 May 2014


GroebnerLexDeg[ <List of Polynomials> ]
Computes the Gröbner basis of the list of the polynomials with respect to graded lexicographical ordering of the variables (also known as grlex, tdeg, lexdeg, total degree lexicographic ordering or elimination ordering).
Example:
GroebnerLexDeg[{x^3 - y - 2, x^2 + y + 1}] yields { -y^{2} + x - 3 y - 3, -x y - x - y - 2, x^{2} + y + 1}.
GroebnerLexDeg[ <List of Polynomials>, <List of Variables> ]
Computes the Gröbner basis of the list of the polynomials with respect to graded lexicographical ordering of the given variables (also known as grlex, tdeg, lexdeg, total degree lexicographic ordering or elimination ordering).
Example:
GroebnerLexDeg[{x^3 - y -2, x^2 + y + 1},{y, x}] yields { x^{2} + y + 1, -y x - y - x - 2, y^{2} + 3 y - x + 3 }.
Note: See also GroebnerDegRevLex and GroebnerLex commands.
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