| This applet computes the reduced Groebner basis of a polynomial
ideal in Q[x1,
x2,
..., xn]. Instructions.
- 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 |
- 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 |
- 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). |
- Tick off 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.
- Click the "Compute"
button to start the applet or "Clear"
to clear all the fields.
|
|
