groebner

Version 1.5.0.0 (9,93 KB) von Ben Petschel
manipulate and solve systems of multivariate polynomial equations by computing the groebner basis
4.5
(6)
4K Downloads
Aktualisiert 2. Nov 2010

Lizenz anzeigen

Example: simplify the system of equations
{x^2+2xy^2=0, xy+2y^3=1}

>> groebner({'x^2+2*x*y^2','x*y+2*y^3-1'},'lex',{'x','y'})

returns {'y^3-0.5','x'}

Solve equations:

>> polynsolve({'x^2+2*x*y^2','x*y+2*y^3-1'},'',{'x','y'})

returns [0, -0.3969 + 0.6874i; 0, -0.3969 - 0.6874i; 0, 0.7937]

>> polynsolve({'x^2-x','x*y-1'},'',{'x','y'})

returns [1, 1]

>> polynsolve({'x^2-x','x*y'},'',{'x','y'})

returns [0, NaN; 1, 0]

(infinite possibilities represented by NaN)

NOTE: calculation of Groebner bases in floating-point arithmetic can be numerically unstable. See the help text for more details.

Zitieren als

Ben Petschel (2024). groebner (https://www.mathworks.com/matlabcentral/fileexchange/24478-groebner), MATLAB Central File Exchange. Abgerufen .

Kompatibilität der MATLAB-Version
Erstellt mit R2009a
Kompatibel mit allen Versionen
Plattform-Kompatibilität
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Version Veröffentlicht Versionshinweise
1.5.0.0

fixed a few bugs that were introduced with the last update
1.4.0.0

changed polynomial representation from N-d array to rectangular array for more efficient memory usage when there are many variables
1.3.0.0

fixed bug in handling polynomials with >=3 variables; allowed spaces in polynomial strings
1.2.0.0

added polynsolve.m for explicitly solving the equations; removed ord='revlex' as it is not a well-ordering.
1.1.0.0

tweaked reduction algorithm; added grlex and revlex options for monomial ordering
1.0.0.0