not using sqrt_poly anymore

Author: fchapoton

src/sage/modular/abvar/homology.py

@@ -54,10 +54,9 @@
 from sage.modular.hecke.all import HeckeModule_free_module
 from sage.rings.all import Integer, ZZ, QQ, CommutativeRing
 
-from .abvar import sqrt_poly
-
 # TODO: we will probably also need homology that is *not* a Hecke module.
 
+
 @richcmp_method
 class Homology(HeckeModule_free_module):
     """
@@ -371,7 +370,7 @@ def _repr_(self):
             sage: J0(23).integral_homology()._repr_()
             'Integral Homology of Abelian variety J0(23) of dimension 2'
         """
-        return "Integral Homology of %s"%self.abelian_variety()
+        return "Integral Homology of %s" % self.abelian_variety()
 
     def hecke_matrix(self, n):
         """
@@ -410,6 +409,7 @@ def hecke_polynomial(self, n, var='x'):
         f = (M.hecke_polynomial(n, var)**2).change_ring(ZZ)
         return f
 
+
 class RationalHomology(Homology_abvar):
     r"""
     The rational homology `H_1(A,\QQ)` of a modular
@@ -446,7 +446,7 @@ def _repr_(self):
             sage: J0(23).rational_homology()._repr_()
             'Rational Homology of Abelian variety J0(23) of dimension 2'
         """
-        return "Rational Homology of %s"%self.abelian_variety()
+        return "Rational Homology of %s" % self.abelian_variety()
 
     def hecke_matrix(self, n):
         """
@@ -486,19 +486,14 @@ def hecke_polynomial(self, n, var='x'):
             (x + 2) * (x^2 - 2)
         """
         f = self.hecke_operator(n).matrix().characteristic_polynomial(var)
-        return sqrt_poly(f)
-
-        #n = Integer(n)
-        #M = self.abelian_variety().modular_symbols(sign=1)
-        #f = M.hecke_polynomial(n, var)**2
-        #return f
+        _, poly = f.is_square(True)
+        return poly
 
 
 class Homology_over_base(Homology_abvar):
     r"""
     The homology over a modular abelian variety over an arbitrary base
-    commutative ring (not `\ZZ` or
-    `\QQ`).
+    commutative ring (not `\ZZ` or `\QQ`).
     """
     def __init__(self, abvar, base_ring):
         r"""
@@ -537,7 +532,7 @@ def _repr_(self):
             sage: H._repr_()
             'Homology with coefficients in Finite Field of size 5 of Abelian variety J0(23) of dimension 2'
         """
-        return "Homology with coefficients in %s of %s"%(self.base_ring(), self.abelian_variety())
+        return "Homology with coefficients in %s of %s" % (self.base_ring(), self.abelian_variety())
 
     def hecke_matrix(self, n):
         """
@@ -590,10 +585,6 @@ def __init__(self, ambient, submodule):
         if not isinstance(ambient, Homology_abvar):
             raise TypeError("ambient must be the homology of a modular abelian variety")
         self.__ambient = ambient
-        #try:
-        #    if not submodule.is_submodule(ambient):
-        #        raise ValueError, "submodule must be a submodule of the ambient homology group"
-        #except AttributeError:
         submodule = ambient.free_module().submodule(submodule)
         self.__submodule = submodule
         HeckeModule_free_module.__init__(
@@ -744,5 +735,3 @@ def rank(self):
             [2, 4]
         """
         return self.__submodule.rank()
-
-