remove comment and add inverse_mod

Author: GiacomoPope

src/flint/test/test_all.py

@@ -3986,7 +3986,6 @@ def test_fq_default_poly():
         # pow_mod
         assert f.pow_mod(2, g) == (f*f) % g
         assert raises(lambda: f.pow_mod(2, "AAA"), TypeError)
-
         assert raises(lambda: f.complex_roots(), DomainError)
 
         # compose errors
@@ -3995,6 +3994,16 @@ def test_fq_default_poly():
         assert raises(lambda: f.compose_mod(g, "A"), TypeError)
         assert raises(lambda: f.compose_mod(g, R_test.zero()), ZeroDivisionError)
 
+        # inverse_mod
+        f = R_test.random_element()
+        while True:
+            h = R_test.random_element()
+            if f.gcd(h).is_one():
+                break
+        g = f.inverse_mod(h)
+        assert f.mul_mod(g, h).is_one()
+        assert raises(lambda: f.inverse_mod(2*f), ValueError)
+
         # series
         f_non_square = R_test([nqr, 1, 1, 1])
         f_zero = R_test([0, 1, 1, 1])

src/flint/types/fq_default_poly.pyx

@@ -169,9 +169,6 @@ cdef class fq_default_poly_ctx:
         ``True``, ensures the output is monic. If ``irreducible`` is
         ``True``, ensures that the output is irreducible.
 
-        TODO: there is currently no fq_defualt_poly method for testing that
-        a polynomial is irreducible?!
-
             >>> R = fq_default_poly_ctx(163, 3)
             >>> f = R.random_element()
             >>> f.degree() <= 3
@@ -1316,6 +1313,23 @@ cdef class fq_default_poly(flint_poly):
 
         return (G, S, T)
 
+    def inverse_mod(self, other):
+        """
+        Returns the inverse of ``self`` modulo ``other``
+
+            >>> R = fq_default_poly_ctx(163)
+            >>> f = R([123, 129, 63, 14, 51, 76, 133])
+            >>> h = R([139, 9, 35, 154, 87, 120, 24])
+            >>> g = f.inverse_mod(h)
+            >>> g
+            41*x^5 + 121*x^4 + 47*x^3 + 41*x^2 + 6*x + 5
+            >>> assert f.mul_mod(g, h).is_one()
+        """
+        G, S, _ = self.xgcd(other)
+        if not G.is_one():
+            raise ValueError(f"polynomial has no inverse modulo {other = }")
+        return S
+
     # ====================================
     # Derivative
     # ====================================