Returns the list of all the saturated strongly stable ideals defining subschemes of \mathbb{P}^{n} or Proj S with Hilbert polynomial hp or d.
i1 : QQ[t]; |
i2 : S = QQ[x,y,z,w]; |
i3 : stronglyStableIdeals(4*t, S) 5 4 2 2 4 5 2 2 4 2 3 o3 = {ideal (x, y , y z ), ideal (x*z, x*y, x , y z, y ), ideal (x*y, x , x*z , y ), ideal (x*y, x , y )} o3 : List |
i4 : stronglyStableIdeals(4*t, 4) 5 4 2 2 4 5 2 2 4 2 3 o4 = {ideal (x , x , x x ), ideal (x x , x x , x , x x , x ), ideal (x x , x , x x , x ), ideal (x x , x , x )} 0 1 1 2 0 2 0 1 0 1 2 1 0 1 0 0 2 1 0 1 0 1 o4 : List |
i5 : hp = hilbertPolynomial(oo#0) o5 = - 4*P + 4*P 0 1 o5 : ProjectiveHilbertPolynomial |
i6 : stronglyStableIdeals(hp, S) 5 4 2 2 4 5 2 2 4 2 3 o6 = {ideal (x, y , y z ), ideal (x*z, x*y, x , y z, y ), ideal (x*y, x , x*z , y ), ideal (x*y, x , y )} o6 : List |
i7 : stronglyStableIdeals(hp, 4) 5 4 2 2 4 5 2 2 4 2 3 o7 = {ideal (x , x , x x ), ideal (x x , x x , x , x x , x ), ideal (x x , x , x x , x ), ideal (x x , x , x )} 0 1 1 2 0 2 0 1 0 1 2 1 0 1 0 0 2 1 0 1 0 1 o7 : List |
i8 : stronglyStableIdeals(5, S) 5 2 4 2 3 2 2 2 3 o8 = {ideal (y, x, z ), ideal (x, y*z, y , z ), ideal (x, y , z , y*z ), ideal (y*z, x*z, y , x*y, x , z )} o8 : List |
i9 : stronglyStableIdeals(5, 4) 5 2 4 2 3 2 2 2 3 o9 = {ideal (x , x , x ), ideal (x , x x , x , x ), ideal (x , x , x , x x ), ideal (x x , x x , x , x x , x , x )} 1 0 2 0 1 2 1 2 0 1 2 1 2 1 2 0 2 1 0 1 0 2 o9 : List |
The object stronglyStableIdeals is a method function with options.