Groebner Bases Applet

Instructions.

1. Write the generators in the text area labeled "Generators:", one polynomial per row. Write the polynomial as a series of monomials with coefficients before indeterminates. Use "^" for powers. Examples:
   
   

   -2*x1^3+x1*x2-1	OK
   1-x1*2/3-x2*5	NO
   1-2/3*x1-5*x2	OK
   y*(x-z)+(2x)^3	NO
   y*x-y*z+8*x^3	OK
   -2*(x-1)	NO
   -2*x+2	OK

   
   

2. Write the indeterminates you have used separated by blanks, in decreasing order. Examples:
   
   

   x y z t	means	x>y>z>t
   x1 x2 x3	means	x1>x2>x3
   x3 x2 x1	means	x3>x2>x1

   
   

3. Choose a monomial ordering among:
   
   

   LEX	Lexicographic
   GRLEX	Graded Lexicographic
   GREVLEX	Graded Reverse Lexicographic
   ELIM	kth-elimination order. You must specify k in the textfield on the right (1 is the default).

   
   

4. Tick the "detailed output" check box if you want the applet to print a detailed output of the steps actually performed to compute the basis. I think this is a nice option from a didactic point of view.
   
   
5. Click the "Compute" button to start the applet or "Clear" to clear all the fields.