Add resultant tests and nmod_poly implementation

Author: rdbliss

src/flint/test/test_all.py

@@ -2834,6 +2834,36 @@ def setbad(obj, i, val):
         if type(p) == flint.fq_default_poly:
             assert raises(lambda: p.integral(), NotImplementedError)
 
+        # resultant checks.
+
+        if is_field and characteristic == 0:
+            # Check that the resultant of two cyclotomic polynomials is right.
+            # See Dresden's 2012 "Resultants of Cyclotomic Polynomials"
+            for m in range(1, 50):
+                for n in range(m + 1, 50):
+                    a = flint.fmpz_poly.cyclotomic(m)
+                    b = flint.fmpz_poly.cyclotomic(n)
+                    q, r = divmod(flint.fmpz(n), flint.fmpz(m))
+                    fs = q.factor()
+                    if r != 0 or len(fs) > 1:
+                        assert a.resultant(b) == 1
+                    else:
+                        prime = fs[0][0]
+                        tot = flint.fmpz(m).euler_phi()
+                        assert a.resultant(b) == prime**tot
+
+        x = P([0, 1])
+        # Flint does not implement resultants over GF(q) for nonprime q, so we
+        # there's nothing for us to check.
+        if composite_characteristic or type(x) == flint.fq_default_poly:
+            pass
+        else:
+            assert x.resultant(x) == 0
+            assert x.resultant(x**2 + x - x) == 0
+
+            for k in range(-10, 10):
+                assert x.resultant(x + S(k)) == S(k)
+                assert x.resultant(x**10 - x**5 + 1) == S(1)
 
 def _all_mpolys():
     return [
@@ -2869,7 +2899,6 @@ def _all_mpolys():
         ),
     ]
 
-
 def test_mpolys():
     for P, get_context, S, is_field, characteristic in _all_mpolys():
 

src/flint/types/fmpz_poly.pyx

@@ -450,7 +450,6 @@ cdef class fmpz_poly(flint_poly):
         fmpz_poly_resultant_modular(res.val, self.val, (<fmpz_poly>other).val)
         return res
 
-
     def factor(self):
         """
         Factors self into irreducible factors, returning a tuple

src/flint/types/nmod_poly.pyx

@@ -621,6 +621,26 @@ cdef class nmod_poly(flint_poly):
         nmod_poly_gcd(res.val, self.val, (<nmod_poly>other).val)
         return res
 
+    def resultant(self, other):
+        """
+        Returns the resultant of *self* and *other*.
+
+            >>> f = nmod_poly([1, 2, 3], 3)
+            >>> g = nmod_poly([1, 0, 1], 3)
+            >>> f.resultant(f)
+            0
+            >>> f.resultant(g)
+            2
+
+        """
+        cdef ulong res
+        other = any_as_nmod_poly(other, (<nmod_poly>self).val.mod)
+        if other is NotImplemented:
+            raise TypeError("cannot convert input to nmod_poly")
+
+        res = nmod_poly_resultant(self.val, (<nmod_poly>other).val)
+        return res
+
     def xgcd(self, other):
         cdef nmod_poly res1, res2, res3
         other = any_as_nmod_poly(other, (<nmod_poly>self).val.mod)