feat: add discriminant method to fmpz_poly, fmpq_poly, nmod_poly

Author: remyoudompheng

src/flint/test/test_all.py

@@ -3045,6 +3045,9 @@ def setbad(obj, i, val):
         assert x.resultant(x**10 - x**5 + 1) == S(1)
         assert (x - 1).resultant(x**5 + 1) == S(2)
 
+        assert (x**5 + 1).discriminant() == S(3125)
+        assert (x**5 + 1).resultant(5 * x**4) == S(3125)
+
         for k in range(-10, 10):
             assert x.resultant(x + S(k)) == S(k)
 

src/flint/types/fmpq_poly.pyi

@@ -73,6 +73,7 @@ class fmpq_poly(flint_poly[fmpq]):
     def truncate(self, n: int, /) -> fmpq_poly: ...
 
     def gcd(self, other: ifmpq_poly, /) -> fmpq_poly: ...
+    def discriminant(self) -> fmpq: ...
     def resultant(self, other: ifmpq_poly, /) -> fmpq: ...
     def xgcd(self, other: ifmpq_poly, /) -> tuple[fmpq_poly, fmpq_poly, fmpq_poly]: ...
 

src/flint/types/fmpq_poly.pyx

@@ -10,7 +10,8 @@ from flint.types.fmpz cimport any_as_fmpz
 
 from flint.flintlib.functions.fmpz cimport fmpz_is_zero
 from flint.flintlib.functions.fmpz cimport fmpz_set
-from flint.flintlib.functions.fmpq cimport fmpq_is_zero
+from flint.flintlib.functions.fmpz_poly cimport fmpz_poly_discriminant
+from flint.flintlib.functions.fmpq cimport fmpq_is_zero, fmpq_set_fmpz_frac
 from flint.flintlib.functions.fmpq_poly cimport *
 from flint.flintlib.functions.arith cimport arith_bernoulli_polynomial
 from flint.flintlib.functions.arith cimport arith_euler_polynomial
@@ -518,6 +519,34 @@ cdef class fmpq_poly(flint_poly):
         fmpq_poly_gcd(res.val, self.val, (<fmpq_poly>other).val)
         return res
 
+    def discriminant(self):
+        """
+        Return the discriminant of ``self``.
+
+            >>> f = fmpq_poly([1, 2, 3, 4, 5, 6])
+            >>> f.discriminant()
+            1037232
+            >>> f = fmpq_poly([1, 3, 5, 7, 9, 11, 13])
+            >>> f.discriminant()
+            -2238305839
+            >>> f = fmpq_poly([1, 3, 5, 7, 9, 11, 13], 10)
+            >>> f.discriminant()
+            -2238305839/10000000000
+
+        """
+        # There is no FLINT function for the discriminant of a fmpq_poly,
+        # we use the fact that disc(f/q) = disc(f)/q^(2d-2)
+        cdef fmpq res = fmpq.__new__(fmpq)
+        cdef fmpz rnum = fmpz.__new__(fmpz)
+        cdef fmpz rden = self.denom()**(2 * self.degree() - 2)
+
+        cdef fmpz_poly x = fmpz_poly.__new__(fmpz_poly)
+        fmpq_poly_get_numerator(x.val, self.val)
+        fmpz_poly_discriminant(rnum.val, x.val)
+        fmpq_set_fmpz_frac(res.val, rnum.val, rden.val)
+
+        return res
+
     def resultant(self, other):
         """
         Returns the resultant of *self* and *other*.

src/flint/types/fmpz_poly.pyi

@@ -62,6 +62,7 @@ class fmpz_poly(flint_poly[fmpz]):
 
     def gcd(self, other: ifmpz_poly, /) -> fmpz_poly: ...
     def content(self) -> fmpz: ...
+    def discriminant(self) -> fmpz: ...
     def resultant(self, other: ifmpz_poly, /) -> fmpz: ...
     def factor(self) -> tuple[fmpz, list[tuple[fmpz_poly, int]]]: ...
     def factor_squarefree(self) -> tuple[fmpz, list[tuple[fmpz_poly, int]]]: ...

src/flint/types/fmpz_poly.pyx

@@ -500,6 +500,22 @@ cdef class fmpz_poly(flint_poly):
         fmpz_poly_gcd(res.val, self.val, (<fmpz_poly>other).val)
         return res
 
+    def discriminant(self):
+        """
+        Return the discriminant of ``self``.
+
+            >>> f = fmpz_poly([1, 2, 3, 4, 5, 6])
+            >>> f.discriminant()
+            1037232
+            >>> f = fmpz_poly([1, 3, 5, 7, 9, 11, 13])
+            >>> f.discriminant()
+            -2238305839
+
+        """
+        cdef fmpz res = fmpz.__new__(fmpz)
+        fmpz_poly_discriminant(res.val, self.val)
+        return res
+
     def resultant(self, other):
         """
         Returns the resultant of *self* and *other*.

src/flint/types/nmod_poly.pyi

@@ -61,6 +61,7 @@ class nmod_poly(flint_poly[nmod]):
         self, e: int, modulus: inmod_poly, mod_rev_inv: inmod_poly | None = None
     ) -> nmod_poly: ...
     def gcd(self, other: inmod_poly) -> nmod_poly: ...
+    def discriminant(self) -> nmod: ...
     def resultant(self, other: inmod_poly) -> nmod: ...
     def xgcd(self, other: inmod_poly) -> tuple[nmod_poly, nmod_poly, nmod_poly]: ...
     def factor(

src/flint/types/nmod_poly.pyx

@@ -712,6 +712,22 @@ cdef class nmod_poly(flint_poly):
         nmod_poly_gcd(res.val, self.val, (<nmod_poly>other).val)
         return res
 
+    def discriminant(self):
+        """
+        Return the discriminant of ``self``.
+
+            >>> f = nmod_poly([1, 2, 3, 4, 5, 6], 65537)
+            >>> f.discriminant()
+            54177
+            >>> f = nmod_poly([1, 3, 5, 7, 9, 11, 13], 65537)
+            >>> f.discriminant()
+            44859
+
+        """
+        cdef nmod res = nmod(0, self.modulus())
+        res.val = nmod_poly_discriminant(self.val)
+        return res
+
     def resultant(self, other):
         """
         Returns the resultant of *self* and *other*.