Exemple #1
0
// 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}
}
Exemple #2
0
// 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}
}
Exemple #3
0
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)
		}
	}
}
Exemple #4
0
// 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}
}
Exemple #5
0
// 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))
}