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 0.027996 seconds
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 0.001999 seconds
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 = {0} | b 0 d 0 |
{1} | a b c d |
{2} | 1 a 1 c |
{3} | 0 1 0 1 |
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.