panic("index out of range")
	}
	a.a[i*a.m+j] = x
}

func newMatrix(n, m int) *matrix {
	if !(0 <= n && 0 <= m) {
		panic("illegal matrix")
	}
	a := new(matrix)
	a.n = n
	a.m = m
	a.a = make([]*Rat, n*m)
	return a
}

func newUnit(n int) *matrix {
	a := newMatrix(n, n)
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			x := NewRat(0, 1)
			if i == j {