+ Solve a simple least squares problem over `[-\pi, \pi]`::
+
+ sage: a = -pi
+ sage: b = pi
+ sage: def inner_product(v1, v2):
+ ....: return integrate(v1*v2, x, a, b)
+ sage: def norm(v):
+ ....: return sqrt(inner_product(v,v))
+ sage: def project(basis, v):
+ ....: return sum( inner_product(v, b)*b/norm(b)**2
+ ....: for b in basis)
+ sage: f = sin(x)
+ sage: legendre_basis = [ legendre_p(k, x, a, b) for k in range(4) ]
+ sage: proj = project(legendre_basis, f)
+ sage: proj.simplify_trig()
+ 5/2*(7*(pi^2 - 15)*x^3 - 3*(pi^4 - 21*pi^2)*x)/pi^6
+