// NewD returns a fiber of type D_n, with n >= 4.
func NewD(n int) *Fiber {
//TODO(fs) should check d >= 4
i := strconv.Itoa(n)
contr := make([]*nt.Frac, 3) // no contr[3] as the two far components are symmetric
contr[0] = nt.NewFrac(0, 1)
contr[1] = nt.NewFrac(1, 1)
contr[2] = nt.NewFrac(n, 4)
return &Fiber{n + 2, n, 4, "D_" + i, contr}
}
// NewE returns a fiber of type E_n, with n=6,7 or 8.
func NewE(n int) *Fiber {
i := strconv.Itoa(n)
var contr []*nt.Frac
switch n {
case 6:
contr = []*nt.Frac{nt.NewFrac(0, 1), nt.NewFrac(4, 3)}
case 7:
contr = []*nt.Frac{nt.NewFrac(0, 1), nt.NewFrac(3, 2)}
case 8:
contr = []*nt.Frac{nt.NewFrac(0, 1)}
}
return &Fiber{2 + n, n, 9 - n, "E_" + i, contr}
}
func (c Config) walkHeightsIter(contr *nt.Frac, rest Config, inter []int, goal *nt.Frac) {
if len(rest) == 0 {
height := nt.NewFrac(4, 1)
height.Add(height, nt.NewFrac(2*zeroIntersection, 1)) // possible intersection with the zero-section
height.Sub(height, contr)
disc := nt.NewFrac(0, 1)
disc.Mul(height, nt.NewFrac(c.Disc(), 1))
if disc.Equal(goal) {
fmt.Println(c, "with inter=", inter, "contr=", contr, "d_T=", c.Disc(), "d_NS=", disc)
}
} else {
for i, v := range rest[0].Contrib() {
c.walkHeightsIter(nt.NewFrac(0, 1).Add(contr, v), rest[1:], append(inter, i), goal)
}
}
}
// NewA returns a fiber of type A_n.
func NewA(n int) *Fiber {
i := strconv.Itoa(n)
contr := make([]*nt.Frac, (n+1)/2+1) // A_n fibers are symmetric
for i := range contr {
contr[i] = nt.NewFrac(i*((n+1)-i), n+1)
}
return &Fiber{n + 1, n, n + 1, "A_" + i, contr}
}
// WalkHeights prints all possible ways a section may meet the given configuration
// to produce a lattice with discriminant d.
func (c Config) WalkHeights(d int) {
c.walkHeightsIter(nt.NewFrac(0, 1), c, []int{}, nt.NewFrac(d, 1))
}