+ The first few polynomials shifted to [0,1] are known to be::
+
+ sage: p0 = 1
+ sage: p1 = 2*x - 1
+ sage: p2 = 6*x^2 - 6*x + 1
+ sage: p3 = 20*x^3 - 30*x^2 + 12*x - 1
+ sage: bool(legendre_p(0, x, 0, 1) == p0)
+ True
+ sage: bool(legendre_p(1, x, 0, 1) == p1)
+ True
+ sage: bool(legendre_p(2, x, 0, 1) == p2)
+ True
+ sage: bool(legendre_p(3, x, 0, 1) == p3)
+ True
+
+ The zeroth polynomial is an element of the ring that we're working
+ in::
+
+ sage: legendre_p(0, MatrixSpace(ZZ, 2)([1, 2, -4, 7]))
+ [1 0]
+ [0 1]
+