obliczanie dzialania na dR chyba dziala

sage/as_covers/as_cech_class.sage

@@ -44,6 +44,10 @@ class as_cech:
     def coordinates(self, threshold=10, basis = 0):
         '''Find coordinates of self in the de Rham cohomology basis. Threshold is an argument passed to AS.de_rham_basis().'''
         AS = self.curve
+        C = AS.quotient
+        m = C.exponent
+        r = C.polynomial.degree()
+        n = AS.height
         RxyzQ, Rxyz, x, y, z = AS.fct_field
         if basis == 0:
             basis = [AS.holomorphic_differentials_basis(), AS.cohomology_of_structure_sheaf_basis(), AS.de_rham_basis(threshold=threshold)]
@@ -54,7 +58,6 @@ class as_cech:
         f_products = []
         for f in coh_basis:
             f_products += [[omega.serre_duality_pairing(f) for omega in holo_diffs]]
-        print(f_products)
         product_of_fct_and_omegas = []
         fct = self.f
         product_of_fct_and_omegas = [omega.serre_duality_pairing(fct) for omega in holo_diffs]
@@ -63,26 +66,29 @@ class as_cech:
         coh_coordinates = V.coordinates(product_of_fct_and_omegas) #coeficients of self in the basis elts coming from cohomology of OX
         for i in range(AS.genus()):
             self -= coh_coordinates[i]*dR[i+AS.genus()]
+        coh_coordinates = AS.genus()*[0] + list(coh_coordinates)
+        if self.f.function not in Rxyz:
             #We remove now from f the summands which are obviously regular at infty
-        print(self, [])
-        f_num = numerator(self.f.function)
-        f_den = denominator(self.f.function)
-        v_f_den = as_function(AS, f_den).valuation()
-        for a in f_num.monomials():
-            if as_function(AS, a).valuation() >= v_f_den:
-                self.f.function -= f_num.monomial_coefficient(a)*a/f_den
-        f_num = numerator(self.f.function)
-        f_den = denominator(self.f.function)
-        quo, rem = f_num.quo_rem(f_den)
-        if as_function(AS, rem/f_den).valuation() >= 0:
-            self.f = as_function(AS, quo)
-            hol_form = self.omega0 - self.f.diffn() #now this should be a holomorphic form
-            hol_form = as_form(AS, as_reduction(AS, hol_form.form))
-            print('hol_form', hol_form)
-            return hol_form.coordinates() + coh_coordinates
-        print(self, [omega.serre_duality_pairing(self.f) for omega in holo_diffs])
-        raise ValueError('I arrived at a form (omega, 0), in which omega is not regular on U0. I hoped this wouldn t happen.')
-        
+            pr = [list(GF(p)) for _ in range(n)]
+            S = []
+            from itertools import product
+            for i in range(0, threshold*r):
+                for j in range(0, m):
+                    for k in product(*pr):
+                        g = (AS.x)^i*prod((AS.z[i1])^(k[i1]) for i1 in range(n))*(AS.y)^j
+                        S += [(g, g.expansion_at_infty())]
+            S += [(self.f, self.f.expansion_at_infty())]
+            fcts = holomorphic_combinations_fcts(S, 0)
+            for g in fcts:
+                if g.function not in Rxyz:
+                    for a in F:
+                        if (self.f.function - a*g.function in Rxyz):
+                            self.f.function = self.f.function - a*g.function
+                            return vector(coh_coordinates)+vector(self.coordinates(threshold=threshold, basis = basis))
+        else:
+            self.omega0 -= self.f.diffn()
+            return vector(coh_coordinates) + vector(list(self.omega0.coordinates())+AS.genus()*[0])
+        raise ValueError("Increase threshold.")
         
     def group_action(self, g):
         AS = self.curve

sage/as_covers/as_cover_class.sage

@@ -335,7 +335,6 @@ class as_cover:
 
     def lift_to_de_rham(self, fct, threshold = 30):
         '''Given function fct, find form eta regular on affine part such that eta - d(fct) is regular in infty. (Works for one place at infty now)'''
-        print(fct)
         from itertools import product
         x_series = self.x_series
         y_series = self.y_series