return a
}

func newHilbert(n int) *matrix {
	a := newMatrix(n, n)
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			a.set(i, j, NewRat(1, int64(i+j+1)))
		}
	}
	return a
}

func newInverseHilbert(n int) *matrix {
	a := newMatrix(n, n)
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			x1 := new(Rat).SetInt64(int64(i + j + 1))
			x2 := new(Rat).SetInt(new(Int).Binomial(int64(n+i), int64(n-j-1)))