Removed some commented code, changed README.md

2 files changed, 0 insertions, 183 deletions

diff --git a/parameters_Q4_new.sage b/parameters_Q4_new.sage
deleted file mode 100644
index 554cc0a..0000000
--- a/parameters_Q4_new.sage
+++ /dev/null
@@ -1,60 +0,0 @@
-# Returns the l-dvisibility parameters of G over Q, given a good basis gb of G,
-# as a list of pairs (di,hi).
-def parameters_Q( gb, l ):
-    ret = []
-    for i in range( len( gb ) ):
-        for j in gb[i]:
-            ret.append( (i,0) )
-    return ret
-
-# Computes the l-divisibility parameters of G over Q4, given a good basis gb
-# over Q for G. Returns a list of pairs (di,hi).
-# If l is odd it just uses the good basis given to compute the parameters.
-# If l=2, it uses the results of PST-2.
-def parameters_Q4_new( gb, l ):
-    if l != 2:
-        return parameters_Q( gb, l )
-    else:
-        # Converts from "good basis format" to simple list
-        b = []
-        for x in gb:
-            b += x
-    
-        M = exponent_matrix( b )
-
-        # Thanks to my terrible notation, the elements of b are what are called
-        # g_i in the article, while the elements of bb will be the b_i's.
-        bb = [ abs(b[i]) ^ (2^(-divisibility(M[i],2))) for i in range(len(b)) ]
-
-        # Computing a combination of bb elements of the form 2 * square.
-        MM = exponent_matrix( bb + [2] ).change_ring( GF( 2 ) ) 
-
-        for a in MM.kernel().basis():
-            if a[-1] != 0:
-                # the vector a[0:-1] gives the coefficients for a combination
-                # of the b_i's of the form 2 * square
-                
-                # Basis elements that actually appear in the combination
-                c = [ b[i] for i in range(len(a[0:-1])) if a[i] != 0 ]
-
-                # Return the parameters, changing only the ones fo the element
-                # of highest divisibility that appears in the combination.
-                ret = []
-                div_max = -1
-                ind_max = -1
-                for i in range(len(b)):
-                    ret.append( (divisibility(M[i],2), 1-max(0,sgn(b[i]))) )
-                    if a[i] != 0 and ret[i][0] > div_max:
-                        div_max = ret[i][0]
-                        ind_max = i
-                d1, h1 = ret[ind_max]
-                if d1 == 1:
-                    h1 = 1 - h1
-                elif d1 == 0:
-                    h1 = 2
-                ret[ind_max] = ( d1+1, h1 )
-
-                return ret
-
-        return parameters_Q( gb, 2 )
-
diff --git a/parameters_Q4_old.sage b/parameters_Q4_old.sage
deleted file mode 100644
index d96fd8c..0000000
--- a/parameters_Q4_old.sage
+++ /dev/null
@@ -1,123 +0,0 @@
-# Computes the l-divisibility parameters of G over Q4, given a good basis gb
-# over Q for G. Returns a list of pairs (di,hi).
-# If l is odd it just uses the good basis given to compute the parameters.
-def parameters_Q4( gb, l ):
-    # Converts from "good basis format" to simple list
-    b = []
-    for x in gb:
-        b += x
-    ret = []
-    
-    if l != 2:
-        for i in range( len( gb ) ):
-            for j in gb[i]:
-                ret.append( (i,0) )
-        return ret
-    else:
-        R.<y> = PolynomialRing( QQ )
-        pol = R(y^2+1)
-        Q4.<eye> = NumberField( pol ) # I already use i for other things
-
-        # Factorize basis elements over Q4 and so on.
-        d = []
-        B = []
-        h = []
-        ideals_list = set()
-        M = [] # Exponent matrix of the Bi's
-
-        # Pre-process to find all ideals appearing in the factorization and fix
-        # a chosen generator for each of them. This is important in order to
-        # compute the "sign" (h-parameter) of an element with respect to it Bi.
-        for g in b:
-            factorization_list = list( Q4.ideal(g).factor() )
-            ideals_list |= set( [ x[0] for x in factorization_list ] )
-        ideals_list = list( ideals_list )
-        # Chooses a generator of each principal ideal in the list
-        irreducibles_list = [ J.gens_reduced()[0] for J in ideals_list ]
-
-        # Compute the Q4-parameters of the given basis b. Also computes the
-        # exponent matrix of the Bi's 
-        for g in b:
-            factorization_list = list( Q4.ideal(g).factor() )
-            exps = [ x[1] for x in factorization_list ]
-            d.append( divisibility( exps, l ) )
-            Bg = 1
-            for j in range(len(factorization_list)):
-                a = 0
-                for i in range( len( ideals_list ) ):
-                    if ideals_list[i] == factorization_list[j][0]:
-                        a = irreducibles_list[i]
-                        break
-                Bg *= a ^ (exps[j]/(l^d[-1]))
-            B.append(Bg)
-            u = g / (Bg^(l^d[-1]))
-            if not u.is_unit():
-                print "Error: g is not the right power of the computed Bg."
-                print "g:", g, ", Bg:", Bg, ", exponent:", l^d[-1]
-            if u == 1:
-                h.append( 0 )
-            elif u == -1:
-                h.append( 1 )
-            else:
-                h.append( 2 ) 
-
-        # Make the exponent matrix M (for now as a list of rows)
-        for g in B:
-            row = [0] * len(ideals_list)
-            for i in range(len(ideals_list)):
-                I = ideals_list[i]
-                ee = 1
-                while (I^ee).divides(g):
-                    ee += 1
-                row[i] = ee-1
-            M.append(row)
-
-        # If the Bi's are not strongly independent, apply the algorithm (only
-        # once) to produce a new basis. The new basis has maximal parameters.
-        coeffs = find_combination( matrix(M), l )
-        if coeffs != []:
-
-            maxi = -1
-            maxd = -1
-            for i in range(len(d)):
-                if d[i] > maxd and coeffs[i] != 0:
-                    maxd = d[i]
-                    maxi = i
-
-            x = [(a/coeffs[maxi]).lift() for a in coeffs] # Now a vector of int
-
-            new_element = 1
-            for i in range(len(d)):
-                new_element *= b[i]^( x[i] * l^(d[maxi]-d[i]) )
-        
-            b[maxi] = new_element
-
-            # Compute new B, d and so on.
-            factorization_list = list( Q4.ideal(b[maxi]).factor() )
-            exps = [ x[1] for x in factorization_list ]
-            d[maxi] = divisibility( exps, l )
-            Bg = 1
-
-            for j in range(len(factorization_list)):
-                a = 0
-                for i in range( len( ideals_list ) ):
-                    if ideals_list[i] == factorization_list[j][0]:
-                        a = irreducibles_list[i]
-                        break
-                Bg *= a ^ (exps[j]/(l^d[maxi]))
-            B[maxi] = Bg
-            M[maxi] = [ x[1] for x in list( Q4.ideal(Bg).factor() ) ]
-            u = b[maxi] / (Bg^(l^d[maxi]))
-            if not u.is_unit():
-                print "Error: new element is not the right power of B."
-                print "New el.:", b[maxi], ", B:", Bg, ", exponent:", l^d[maxi]
-            if u == 1:
-                h[maxi] = 0
-            elif u == -1:
-                h[maxi] = 1
-            else:
-                h[maxi] = 2 
-            
-        return [(d[i],h[i]) for i in range(len(d))]
-
-