eliminate

Usage:

eliminate(v,J)
Inputs:
- v, a ring element or a list, a variable or list of variables of a polynomial ring R
- J, an ideal, in the ring R
Outputs:
- an ideal, generated by the elements of J not involving the variables v

Description

If the ideal J is homogeneous, then an effort is made to use the Hilbert function to speed up the computation.

i1 : R = ZZ/101[x,a,b,c,d]	  

o1 = R

o1 : PolynomialRing

i2 : f = x^2+a*x+b

      2
o2 = x  + x*a + b

o2 : R

i3 : g = x^2+c*x+d

      2
o3 = x  + x*c + d

o3 : R

i4 : time eliminate(x,ideal(f,g))
 -- used 0.0029927s (cpu); 0.00310875s (thread); 0s (gc)

                      2    2             2           2
o4 = ideal(a*b*c - b*c  - a d + a*c*d - b  + 2b*d - d )

o4 : Ideal of R

i5 : time ideal resultant(f,g,x)
 -- used 0.00144958s (cpu); 0.00184757s (thread); 0s (gc)

                        2    2             2           2
o5 = ideal(- a*b*c + b*c  + a d - a*c*d + b  - 2b*d + d )

o5 : Ideal of R

i6 : sylvesterMatrix(f,g,x)

o6 = {-3} | 1 a b 0 |
     {-2} | 0 1 a b |
     {-3} | 1 c d 0 |
     {-2} | 0 1 c d |

             4      4
o6 : Matrix R  <-- R

i7 : discriminant(f,x)

        2
o7 = - a  + 4b

o7 : R

One may also switch the order of arguments: the ideal being the first argument. This usage has been deprecated, and should no longer be used.

Caveat

The ring R should not be a quotient ring, or a non-commutative ring. Additionally, it would be nice to be able to use a DegreeLimit, or to be able to interrupt the computation.

Ways to use eliminate:

eliminate(List,Ideal)
eliminate(RingElement,Ideal)

For the programmer

The object eliminate is a method function.

The source of this document is in Elimination.m2:213:0.

eliminate

Description

Caveat

See also

Ways to use eliminate:

For the programmer