Fixed database typo and removed unnecessary class identifier.

venv/Lib/site-packages/scipy/special/_precompute/utils.py

@@ -0,0 +1,44 @@
+from numpy.testing import suppress_warnings
+
+try:
+    import mpmath as mp  # type: ignore[import]
+except ImportError:
+    pass
+
+try:
+    # Can remove when sympy #11255 is resolved; see
+    # https://github.com/sympy/sympy/issues/11255
+    with suppress_warnings() as sup:
+        sup.filter(DeprecationWarning, "inspect.getargspec.. is deprecated")
+        from sympy.abc import x  # type: ignore[import]
+except ImportError:
+    pass
+
+
+def lagrange_inversion(a):
+    """Given a series
+
+    f(x) = a[1]*x + a[2]*x**2 + ... + a[n-1]*x**(n - 1),
+
+    use the Lagrange inversion formula to compute a series
+
+    g(x) = b[1]*x + b[2]*x**2 + ... + b[n-1]*x**(n - 1)
+
+    so that f(g(x)) = g(f(x)) = x mod x**n. We must have a[0] = 0, so
+    necessarily b[0] = 0 too.
+
+    The algorithm is naive and could be improved, but speed isn't an
+    issue here and it's easy to read.
+
+    """
+    n = len(a)
+    f = sum(a[i]*x**i for i in range(len(a)))
+    h = (x/f).series(x, 0, n).removeO()
+    hpower = [h**0]
+    for k in range(n):
+        hpower.append((hpower[-1]*h).expand())
+    b = [mp.mpf(0)]
+    for k in range(1, n):
+        b.append(hpower[k].coeff(x, k - 1)/k)
+    b = map(lambda x: mp.mpf(x), b)
+    return b