A binary form F(t0,t1) = a0 t0n+n a1 t0n-1 t1+1/2 n (n-1) a2 t0n-2 t12+ … +n an-1 t0 t1n-1+an t1n can be identified with the list {a0,a1,...,an} of its coefficients, and also with the ideal of the corresponding point of ℙn. The method switch when applied to a binary form returns the list of its coefficients; when applied to a list of coefficients returns the ideal of the corresponding point; when applied to the ideal of a point returns the corresponding binary form.
i1 : F = randomBinaryForm 9 9 8 7 2 6 3 5 4 4 5 3 6 2 7 o1 = 162t + 18t t + 81t t + 18t t + 36t t + 27t t + 54t t + 27t t + 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 ------------------------------------------------------------------------ 8 9 63t t + 28t 0 1 1 o1 : QQ[t , t ] 0 1 |
i2 : L = switch F 9 3 2 3 9 3 o2 = {162, 2, -, --, -, --, --, -, 7, 28} 4 14 7 14 14 4 o2 : List |
i3 : I = switch L o3 = ideal (4t - t , 112t - 3t , 392t - 9t , 392t - 3t , 98t - t , 392t 8 9 7 9 6 9 5 9 4 9 3 ------------------------------------------------------------------------ - 3t , 112t - 9t , 14t - t , 14t - 81t ) 9 2 9 1 9 0 9 o3 : Ideal of QQ[t , t , t , t , t , t , t , t , t , t ] 0 1 2 3 4 5 6 7 8 9 |
i4 : switch I 9 8 7 2 6 3 5 4 4 5 3 6 2 7 o4 = 162t + 18t t + 81t t + 18t t + 36t t + 27t t + 54t t + 27t t + 0 0 1 0 1 0 1 0 1 0 1 0 1 0 1 ------------------------------------------------------------------------ 8 9 63t t + 28t 0 1 1 o4 : QQ[t , t ] 0 1 |
i5 : oo == F o5 = true |