groebner

manipulate and solve systems of multivariate polynomial equations by computing the groebner basis
4K Downloads
Updated 2 Nov 2010

View License

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.

Cite As

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

MATLAB Release Compatibility
Created with R2009a
Compatible with any release
Platform Compatibility
Windows macOS Linux
Categories
Find more on Polynomials in Help Center and MATLAB Answers

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
Version Published Release Notes
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