riemann roch spaces

as_covers/as_cover_class.sage

@@ -135,6 +135,18 @@ class as_cover:
                 dd += [jumps[place][i-1]*(p-1) + p*dd[i-1]]
         return dd[n]
     
+    def exponent_of_different_bis(self, place = 0):
+        jumps = self.jumps
+        n = self.height
+        p = self.characteristic
+        dd = [0]
+        for i in range(1, n+1):
+            if jumps[place][i-1] == 0:
+                dd += [dd[i-1]]
+            else:
+                dd += [(jumps[place][i-1]-1)*(p-1) + p*dd[i-1]]
+        return dd[n]
+    
     def holomorphic_differentials_basis(self, threshold = 8):
         from itertools import product
         x_series = self.x_series
@@ -545,3 +557,81 @@ class as_cover:
         n = AS.height
         F = AS.base_ring
         return as_group_action_matrices(F, AS.at_most_poles_forms(1), AS.group.gens, basis = AS.at_most_poles_forms(1))
+    
+    def riemann_roch_space(self, pole_orders, threshold = 8):
+        """ Find fcts with pole order in infty's at most pole_order from the given dictionary. The keys of the dictionary are pairs (place_at_infty, group element). The items are the poles orders at those places.
+        Threshold gives a bound on powers of x in the function. If you suspect that you haven't found all the functions, you may increase it."""
+        from itertools import product
+        x_series = self.x_series
+        y_series = self.y_series
+        z_series = self.z_series
+        delta = self.nb_of_pts_at_infty
+        p = self.characteristic
+        n = self.height
+        prec = self.prec
+        C = self.quotient
+        F = self.base_ring
+        m = C.exponent
+        r = C.polynomial.degree()
+        RxyzQ, Rxyz, x, y, z = self.fct_field
+        F = C.base_ring
+        Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
+        #Tworzymy zbiór S form z^i x^j y^k dx/y o waluacji >= waluacja z^(p-1)*dx/y
+        S = []
+        RQxyz = FractionField(Rxyz)
+        pr = [list(GF(p)) for _ in range(n)]
+        for i in range(0, threshold*r):
+            for j in range(0, m):
+                for k in product(*pr):
+                    eta = as_function(self, x^i * prod(z[i1]^(k[i1]) for i1 in range(n))*y^j)
+                    eta_exp = eta.expansion_at_infty()
+                    S += [(eta, eta_exp)]
+
+        forms = holomorphic_combinations_fcts(S, pole_orders[(0, self.group.one)])
+        print('iteration')
+        for i in range(delta):
+            for g in self.fiber(place = i):
+                if i!=0 or g != self.group.one:
+                    print('iteration')
+                    forms = [(omega, omega.group_action(g).expansion_at_infty(place = i)) for omega in forms]
+                    forms = holomorphic_combinations_fcts(forms, pole_orders[(i, g)])
+        return forms
+
+    def riemann_roch_space_forms(self, pole_orders, threshold = 8):
+        """ Find fcts with pole order in infty's at most pole_order from the given dictionary. The keys of the dictionary are pairs (place_at_infty, group element). The items are the poles orders at those places.
+        Threshold gives a bound on powers of x in the function. If you suspect that you haven't found all the functions, you may increase it."""
+        from itertools import product
+        x_series = self.x_series
+        y_series = self.y_series
+        z_series = self.z_series
+        delta = self.nb_of_pts_at_infty
+        p = self.characteristic
+        n = self.height
+        prec = self.prec
+        C = self.quotient
+        F = self.base_ring
+        m = C.exponent
+        r = C.polynomial.degree()
+        RxyzQ, Rxyz, x, y, z = self.fct_field
+        F = C.base_ring
+        Rt.<t> = LaurentSeriesRing(F, default_prec=prec)
+        #Tworzymy zbiór S form z^i x^j y^k dx/y o waluacji >= waluacja z^(p-1)*dx/y
+        S = []
+        RQxyz = FractionField(Rxyz)
+        pr = [list(GF(p)) for _ in range(n)]
+        for i in range(0, threshold*r):
+            for j in range(0, m):
+                for k in product(*pr):
+                    eta = heisenberg_form(self, x^i * prod(z[i1]^(k[i1]) for i1 in range(n))/y^j)
+                    eta_exp = eta.expansion_at_infty()
+                    S += [(eta, eta_exp)]
+
+        forms = holomorphic_combinations_forms(S, pole_orders[(0, (0, 0, 0))])
+        print('iteration')
+        for i in range(delta):
+            for g in self.fiber(place = i):
+                if i!=0 or g != self.group.one:
+                    print('iteration')
+                    forms = [(omega, omega.group_action(g).expansion_at_infty(place = i)) for omega in forms]
+                    forms = holomorphic_combinations_forms(forms, pole_orders[(i, g)])
+        return forms

elementary_covers/ith_magical_component.sage

@@ -1,6 +1,6 @@
-def ith_magical_component(omega, zvee, g):
+def ith_magical_component(omega, zvee, g, super=True):
     '''Given a form omega on AS cover, element g of group AS.group and normal basis element zmag, find the decomposition
     sum_g g(zmag) omega_g and return omega_g.'''
     z_vee_g = zvee.group_action(g)
     new_form = z_vee_g*omega
-    return new_form.trace()
+    return new_form.trace(super=super)