Deleting .py

sage/toric_topdata.sage

@@ -3,22 +3,23 @@ import logging
 import os
 import json
 from datetime import datetime, timezone
+import re
 
+# Logger
 logger = logging.getLogger(__name__)
-logging.basicConfig(level=logging.DEBUG)  # or logging.DEBUG to see both
+logging.basicConfig(level=logging.DEBUG)
 
 # For grep-commands
-import re 
-find_zs = re.compile('z\d+')
-find_ls = re.compile('l\d+')
-find_index_z = re.compile('\d+')
+find_zs = re.compile(r'z\d+')
+find_ls = re.compile(r'l\d+')
+find_index_z = re.compile(r'\d+')
 
 
 class Polytope:
     """
     Class representing a lattice polytope. Objects contain a list of defining points
     and a list of points in the convex hull of the polytope. Points inside codimension
-    are excluded from the convex hull and stored in a separate list.
+    one are excluded from the convex hull and stored in a separate list.
     """
 
     #############################
@@ -70,6 +71,8 @@ class ToricPolytope(Polytope):
     toric polytope describing the original family's ambient space.
 
     Example: For the mirror quintic, the vertices are e_1, ..., e_4, -e_1-...-e_4.
+
+    For CICYs, a nef-partition must be provided, defaulting to hypersurface if none given.
     """
 
     ##############################
@@ -111,7 +114,7 @@ class ToricPolytope(Polytope):
                 raise ValueError("Invalid nef partition: {}".format(nef_partition))
             self.nef_partition = nef_partition
         else:
-            self.nef_partition = [range(len(self.relevant_lattice_points) - 1)]  # Default to a trivial partition if none is provided
+            self.nef_partition = [list(range(len(self.relevant_lattice_points) - 1))]  # Default to a trivial partition if none is provided
 
     def set_Mori_cone(self, lvec = None):
         """
@@ -127,14 +130,13 @@ class ToricPolytope(Polytope):
                 raise ValueError("All rows in lvec must have the same length.")
             elif len(lvec[0]) != len(self.relevant_lattice_points):
                 raise ValueError("The length of the l-vectors is invalid.")
-            elif matrix(matrix(default_Mori_cone.rays()).stack(matrix(lvec))).rank() != matrix(default_Mori_cone.rays()).rank():
+            elif matrix(default_Mori_cone.rays()).stack(matrix(lvec)).rank() != matrix(default_Mori_cone.rays()).rank():
                 raise ValueError("The provided l-vectors are not in the linear span of the original Mori cone.")
             else:
                 self.Mori_cone = Cone(lvec)
         
         if len(matrix(self.Mori_cone.rays()).kernel().gens()) > 0:
             logger.warning("Non-simplicial Mori-cone encountered.")
-            logger.info("Using the first %d linearly independent vectors.", len(self.Mori_cone.rays()))
             self.Mori_cone = Cone(
                                 transpose(
                                     transpose(self.Mori_cone.rays())
@@ -144,7 +146,8 @@ class ToricPolytope(Polytope):
                                     ).kernel().gens()
                                 ).transpose()
                              )
-        
+            logger.info("Using the first %d linearly independent vectors.", len(self.Mori_cone.rays()))
+
         self.lvec = matrix(self.Mori_cone.rays())
 
     def __init__(
@@ -161,11 +164,22 @@ class ToricPolytope(Polytope):
 
         self.set_triangulation(no_triangulation)
         self.set_nef_partition(nef_partition)
+        self.cy_dimension = self.dimension - len(self.nef_partition)
 
         self.fan = self.triangulation.fan(self.origin)
         self.ToricVariety = ToricVariety(self.fan)
         self.set_Mori_cone(lvec = lvec)
 
+        self.model_name = model_name if model_name else "Unnamed Model"
+        
+        logger.info(
+            "Initialised %s: %s%d with h21 = %d.",
+            self.model_name,
+            "CY" if len(self.nef_partition) == 1 else "CICY",
+            self.cy_dimension,
+            len(list(self.lvec)),
+        )
+
     ###############################
     # Discriminant Computation
     ###############################
@@ -264,6 +278,7 @@ class ToricPolytope(Polytope):
         except:
             # In one-parameter cases there may be nothing to eliminate.
             polynomials = equation_system
+            logger.debug("No elimination needed for the equation system: %s", equation_system)
 
         try:
             if len(lambda_symbols) == 0:
@@ -295,20 +310,22 @@ class ToricPolytope(Polytope):
                 codim = total_relation_blocks - 1 - index
             discriminants.append([polynomial, codim])
 
-    def disc(self, only_strong_coupling=False, no_triangulation=0):
+    def disc(self, only_strong_coupling=False):
         """
         Computes the A-discriminant for the toric polytope (following Aspinwall, Plesser, Wang),
-        which gives the singular loci of the moduli space in Batyrev coordinates.
-
-        Parameters:
-        - only_strong_coupling: If True, only gives loci arising from edges (one-dimensional faces).
-        - no_triangulation: Index of the triangulation to use.
+        which gives the singular loci of the moduli space in Batyrev coordinates. There is an option
+        to only compute strong coupling discriminant factors, so those coming from dependencies
+        in one-dimensional faces.
 
         Returns:
         A list of tuples [disc_i, codim_i] of discriminant factors disc_i
         coming from a relation inside a face of codimension codim_i.
         """
 
+        logger.info("Computing discriminant for %s", self.model_name)
+        if only_strong_coupling:
+            logger.info("Restricting to strong-coupling loci (codimension-1 faces).")
+
         all_linear_dependencies_among_points = self._collect_linear_dependencies(only_strong_coupling)
         self._append_origin_weight(all_linear_dependencies_among_points)
         a_vars, z_vars, lambda_vars, a_row, mori_matrix = self._setup_discriminant_symbols()
@@ -344,6 +361,9 @@ class ToricPolytope(Polytope):
             # Insert an empty codimension-0 entry for compatibility with prior behavior.
             discriminants = [[]] + discriminants
 
+        logger.info("Found %d discriminant factors.", len(discriminants))
+        logger.info("Discriminant factors: %s", discriminants)
+
         return discriminants
 
     ##############################
@@ -482,7 +502,7 @@ class ToricPolytope(Polytope):
                 messages.append("Possible elliptic fibration in the divisor class dual to t{}.".format(i))
 
         if messages:
-            logger.info("\n\n--- Elliptic fibrations --------------------------\n" + "\n".join(messages))
+            logger.info("\n\n--- Elliptic fibrations --------------------------\n%s", "\n".join(messages))
 
         return messages
 
@@ -609,11 +629,7 @@ class ToricPolytope(Polytope):
     def _write_output_json(self, output):
         """
         Writes the given output dictionary (from _get_output, i.e. exactly what is
-        logged) to data/<model_name>.json (relative to the repository root), if a
-        model_name is given. Plain JSON, so it is directly loadable in Python
-        (json.load), C++ (e.g. nlohmann::json), or any other language without any
-        custom parsing code; lvec loads back as a plain list of lists, e.g. lvec[0].
-        """
+        logged) to data/<model_name>.json."""
         if not self.model_name:
             logger.info("No model_name given, skipping writing topological data to JSON.")
             return None
@@ -631,24 +647,9 @@ class ToricPolytope(Polytope):
 
     def topdata(self):
         """
-        Computes topological data for hypersurfaces and CICYs in toric ambient spaces.
-        For hypersurfaces, nef_partition should remain untouched (=0).
-        For CICYs with d polynomials, a nef_partition has to be supplied:
-        its format should be a list of d lists as in the examples below
-        which is a decomposition of the N points of $(polytope); the number
-        should corresponds to an enumeration of the points of $(polytope) with
-        the inner point omitted.
-
-        Conditions for possible fibrations are:
-            - elliptic:           if t_i^n = 0 and t_i^{n-1} != 0
-            - K3 (only 3-folds):  if c2.t_i = 24
-
-        Input:  - (for CICYs:) nef-partition
-                - (optional:) set of l-vectors to be used
-                - (optional:) index of triangulation
+        Computes topological data for hypersurfaces and CICYs in toric ambient spaces
+        and saves the result to /data/topdata/<model_name>.json if a model_name is provided.
         """
-        no_polys = len(self.nef_partition)
-        self.cy_dimension = self.dimension - no_polys
         # Each point gives a toric divisor, each "column" gives one linear relation
         self.no_divs = len(self.relevant_lattice_points) - self.dimension - 1
 
@@ -731,7 +732,6 @@ class ToricPolytopeCICY(ToricPolytope):
 
     def __init__(self, CICY, no_triangulation=0, model_name=None, lvec=None):
         points, nef_partition = self._CICY_to_points(CICY)
-        print(points, nef_partition)
         super().__init__(
             points,
             no_triangulation=no_triangulation,

sage/toric_topdata.sage.py

@@ -1,348 +0,0 @@
-
-
-# This file was *autogenerated* from the file sage/toric_topdata.sage
-from sage.all_cmdline import *   # import sage library
-
-_sage_const_0 = Integer(0); _sage_const_1 = Integer(1); _sage_const_2 = Integer(2); _sage_const_8 = Integer(8); _sage_const_10 = Integer(10); _sage_const_4 = Integer(4); _sage_const_24 = Integer(24)### FUNCTIONS: ####
-# - pointstopoly: converts list of points to CY-polytope
-# - disc: computes discriminant for polytope
-# - topdata: computes all sorts of topological data for polytope
-# - CICYtopdata: computes topdata in the simple CICY format, e.g. [[3,3]] for two cubics in P5 or [[3,0,1],[0,3,1]] for the Tian--Yau manifold
-
-
-import numpy as np
-# For grep-commands
-import re
-findzs = re.compile('z\d+')
-findls = re.compile('l\d+')
-findindexz = re.compile('\d+')
-
-
-def pointstopoly(points):
-    # Takes a list of points and returns the points inside its convex hull while omitting points inside faces of co-dimension one
-    
-    global pcodim1 #points in co-dimension one
-    
-    zeros = [_sage_const_0  for i in range(len(points[_sage_const_0 ]))] #origin
-    pc = LatticePolytope(points) # all points
-    polytope = [list(m) for m in pc.points()]
-    pcodim1 = []
-    for f in pc.facets():
-        for i in f.interior_point_indices():
-            try:
-                polytope.remove([list(m) for m in f.points(i)][_sage_const_0 ]) # remove those inside codim1 faces
-                pcodim1.append([list(m) for m in f.points(i)][_sage_const_0 ]) # save omitted points in pcodim1
-            except:
-                pass
-    # Moving zeros to the end
-    polytope.remove(zeros)
-    polytope.append(zeros)
-    return polytope
-
-def disc(polytope, only_sc=False, no_triangulation=_sage_const_0 ):
-    # Takes a poltyope and returns a list of tuples [disc_i,codim_i] of discriminant factors disc_i coming from a relation inside a face of codimension codim_i
-    
-    global globalks, pc
-    pc = LatticePolytope(polytope)
-    dimp = len(polytope[_sage_const_0 ])
-    zeros = [_sage_const_0  for i in range(dimp)]
-    # Compute all relations in all faces
-    globalks = []
-    if only_sc:
-        pcfaces = pc.faces()[:-_sage_const_1 ]
-    else:
-        pcfaces = pc.faces()
-     
-    for facesofdim in pcfaces: # for each face-dimension
-        atdim = [] 
-        for face in facesofdim: # for each face of fixed dimension
-            atface = []
-            facepoints = [list(i) for i in matrix(face.points())]
-            try:
-                facepoints.remove(zeros)
-            except:
-                pass
-
-            for p in facepoints.copy():
-                try:
-                    if p not in polytope:
-                        facepoints.remove(p)       # remove points that were omitted for polytope
-                except:
-                    pass
-
-            rels = {str(i):polytope.index(i) for i in facepoints}       # dictionary for getting positions in relations correct
-            kernel = matrix(facepoints).kernel().gens()
-            for k in kernel:                                     # just formatting
-                globalk = [_sage_const_0  for i in range(len(polytope)-_sage_const_1 )]    # MAY HAVE TO BE ADAPTED FOR CASES WITH MORE VERTICES
-                for i in range(len(k)):
-                    globalk[rels[str(facepoints[i])]] = k[i]
-                atdim.append(globalk)
-        globalks.append([[i[j] for j in range(len(i))] for i in np.unique(np.matrix(atdim),axis=_sage_const_0 )])
-    for atdim in globalks: # inserting weight for innter point
-        for k in atdim:
-            if len(k)>_sage_const_0 :
-                k.append(-sum(k))
-    # Computing discriminants 
-    pc = PointConfiguration(polytope)
-    pc_star =  pc.restrict_to_star_triangulations(zeros)
-    pc_star_and_fine=pc_star.restrict_to_fine_triangulations()
-    if(len(pc_star_and_fine.triangulations_list())==_sage_const_0 ):
-        print("No fine star triangulation!")
-        return _sage_const_0 
-    if(len(pc_star_and_fine.triangulations_list())>_sage_const_1 ):
-        print("More than one fine star triangulation! (",len(pc_star_and_fine.triangulations_list()),")")
-    triangulation=pc_star_and_fine.triangulations_list()[no_triangulation]
-    fan=triangulation.fan(zeros)
-    X=ToricVariety(fan)
-    ls = [l for l in X.Mori_cone().rays()]
-    if (len(matrix(ls).kernel().gens())>_sage_const_0 ):
-        print("Non-simplicical Mori-cone")
-
-    As = [var("a_{}".format(u), latex_name="a_{{}}".format(u)) for u in (ellipsis_iter(_sage_const_1 ,Ellipsis,len(ls)))]
-    z = var('z', n=len(ls)+_sage_const_1 , latex_name='z') # z[0] is superfluous
-    l = var('l', n=len(ls)+_sage_const_1 , latex_name='l') # l[0] is superfluous
-    #globalks.reverse()
-    globalks = [k for k in globalks if k not in ([[]],)]
-    discs = []
-    for i,atdim in enumerate(globalks):
-        solsys = []
-        for kindex in range(len(atdim)):
-            sol=solve((matrix(As)*matrix(ls)-matrix(atdim[kindex])).list(),matrix(As).list())
-            zindex = [abs(i.subs(sol)) for i in As].index(_sage_const_1 ) +_sage_const_1 
-            solsys.append(z[zindex]-prod([sum([atdim[j][i]*l[j] for j in range(len(atdim))])**(atdim[kindex][i]) for i in range(len(atdim[_sage_const_0 ]))]))
-            lambdas = list(set(findls.findall(str(solsys))))
-            lambdas.sort()
-        try:
-            pol = maxima.eliminate(solsys,[eval(i) for i in lambdas[_sage_const_1 :]]).sage()
-            if pol[_sage_const_0 ]==_sage_const_0 :
-                pol = maxima.eliminate(solsys,[eval(i) for i in lambdas[:-_sage_const_1 ]]).sage()
-                reversesolve = True
-            else:
-                reversesolve = False
-        except:  # this is just for 1-parameter cases where there is nothing to solve
-            pol = solsys
-            pass
-        try:
-            if not reversesolve:
-                pol = [i/l0**(i.degree(l0)) for i in pol]
-            else:
-                pol = [i/eval(lambdas[-_sage_const_1 ])**(i.degree(eval(lambdas[-_sage_const_1 ]))) for i in pol]
-        except:
-            pass
-        for poli in pol:
-            if (poli not in [a[_sage_const_0 ] for a in discs] and poli!=_sage_const_0 ):
-                if only_sc:
-                    discs.append([poli,len(globalks)-i]) # account for offset
-                else:
-                    discs.append([poli,len(globalks)-_sage_const_1 -i])
-                
-    if only_sc: #insert an empty list for the codimension 0 face discriminant
-        discstmp = discs
-        discstmp.reverse()
-        discstmp.append([])
-        discstmp.reverse()
-        discs = discstmp
-    return discs
-
-def topdata(polytope, nef_partition=_sage_const_0 , lvec=_sage_const_0 , no_triangulation=_sage_const_0 , returnvars=False):
-    # Computes topological data for hypersurfaces and CICYs in toric ambient spaces.
-    # For hypersurfaces, nef_partition should remain untouched (=0).
-    # For CICYs with d polynomials, a nef_partition has to be supplied:
-    # its format should be a list of d lists as in the examples below
-    # which is a decomposition of the N points of $(polytope); the number
-    # should corresponds to an enumeration of the points of $(polytope) with
-    # the inner point omitted.
-
-    # Conditions for possible fibrations are:
-    #         - elliptic:           if t_i^n = 0 and t_i^{n-1} != 0
-    #         - K3 (only 3-folds):  if c2.t_i = 24
-
-    # input:  - array of points in polytope
-    #         - (for CICYs:) nef-partition
-    #         - (optional:) set of l-vectors to be used
-    #         - (optional:) index of triangulation
-
-    # output: - Mori-cone generators
-    #         - Intersection rings of CY and ambient space
-    #         - Topological data
-    #         - Possible fibrations
-    #         - GLOBALS: triangulation and Mori-cone generators
-
-    global triangulation, lall, MoriMatrix, fan, X, Ydualform, J, D
-
-    pc = PointConfiguration(polytope)
-
-    dimp=len(polytope[_sage_const_0 ]) # dimension of polytope
-    if( nef_partition == _sage_const_0 ):
-        no_polys = _sage_const_1 
-        nef_partition = [[i for i in range(len(polytope)-_sage_const_1 )]] # trivial partition
-    else:
-        if( sorted(flatten(nef_partition)) != [ i for i in range(len(polytope)-_sage_const_1 )] ):
-            print("Nef-partition not valid!")
-        no_polys = len(nef_partition)
-    zeros=zero_vector(dimp)
-
-    pc_star =  pc.restrict_to_star_triangulations(zeros)
-    pc_star_and_fine=pc_star.restrict_to_fine_triangulations()
-    if(len(pc_star_and_fine.triangulations_list())==_sage_const_0 ):
-        print("No fine star triangulation!")
-        return _sage_const_0 
-    if(len(pc_star_and_fine.triangulations_list())>_sage_const_1 ):
-        print("More than one fine star triangulation! (",len(pc_star_and_fine.triangulations_list()),")")
-    triangulation=pc_star_and_fine.triangulations_list()[no_triangulation]
-    fan=triangulation.fan(zeros)
-    X=ToricVariety(fan)
-
-    # Change l-vectors if given:
-    if lvec==_sage_const_0 :
-        lall=matrix(X.Mori_cone().rays())
-    else:
-        lall=lvec
-    nodivs = len(polytope)-dimp-_sage_const_1 
-    MoriMatrix=matrix([[-sum([lall[j][i] for i in part]) for part in nef_partition] for j in range(nodivs)]), lall[:,:-_sage_const_1 ]
-    # Check whether Mori-cone is simplicial and continue with first $(nodivs) vectors
-    if ( lall.dimensions()[_sage_const_0 ] > nodivs ):
-        print("Non-simplicial Kähler-cone! (",lall.dimensions()[_sage_const_0 ]," > ",nodivs,")")
-        print("Picking ",nodivs," linearly independent vectors.")
-        l = transpose(transpose(lall)*(matrix(transpose(matrix(lall.kernel().gens())).kernel().gens()).transpose()))
-        MoriMatrix=matrix([[-sum([l[j][i] for i in part]) for part in nef_partition] for j in range(nodivs)]), l[:,:-_sage_const_1 ]
-    else:
-        l = lall
-
-    HH=X.cohomology_ring()
-    D = [HH(X.divisor(i)) for i in (ellipsis_range(_sage_const_0 ,Ellipsis,len(polytope)-_sage_const_2 ))]
-    zs = list(set(findzs.findall(str(D)))) # gives the $(nodivs) z-variables present in divisor classes
-    # Find Kähler-cone generators as duals to l-vectors:
-    Bsinv=l.matrix_from_columns([eval(m) for m in sorted(list(findindexz.findall(str(zs))))])
-    if (Bsinv.det()==_sage_const_0 ):
-        print("l-vectors not independent in divisor basis. Pick them manually with ``lvec=...''")
-        return
-    Bs = transpose(Bsinv**(-_sage_const_1 ))
-    J = Bs*vector([D[i] for i in list(set([eval(i) for i in findindexz.findall(str(findzs.findall(str(D))))]))])
-    # Hyperplane divisor class:
-    Ydualform = product([sum([HH(D[p]) for p in part]) for part in nef_partition])
-
-    # Tuple lists for computations below
-    TupleListCY = UnorderedTuples(range(nodivs),dimp-no_polys)
-    TupleListCYordered = Tuples(range(nodivs),dimp-no_polys) # for intersection ring multiplicities must be included
-    TupleListAm = UnorderedTuples(range(nodivs),dimp)
-
-    # Find intersection numbers on CY and on ambient space:
-    intCY = [list((tl,X.integrate(Ydualform*product([J[tl[j]] for j in range(dimp-no_polys)])))) for tl in TupleListCY]
-    intAm = [list((tl,X.integrate(product([J[tl[j]] for j in range(dimp)])))) for tl in TupleListAm]
-
-    # Form intersection ring on CY:
-    t = var('t', n=nodivs, latex_name='t')
-    intring = sum([product([t[index] for index in tl])*X.integrate(Ydualform*product([J[tl[j]] for j in range(dimp-no_polys)])) for tl in TupleListCYordered])
-    intringnomults = sum([product([t[index] for index in tl])*X.integrate(Ydualform*product([J[tl[j]] for j in range(dimp-no_polys)])) for tl in set([tuple(sorted(i)) for i in TupleListCYordered])])
-    # Compute Chern-character for topological data:
-    var(findzs.findall(str([J[i] for i in range(nodivs)])))                    # Introduces all z in Kähler-forms as variables...
-    zs = [eval(z) for z in findzs.findall(str([J[i] for i in range(nodivs)]))] # ... and puts them into a vector.
-    tsubs=solve([lift(J[i])==t[i] for i in range(nodivs)],zs)       # Finds substitution rule for zs in terms Kähler-cone generators
-    cc = (product([_sage_const_1 +eval(str((lift(d)))).subs(tsubs[_sage_const_0 ]) for d in D]))/(product([_sage_const_1 +sum([eval(str(lift(HH(D[p])))) for p in part]) for part in nef_partition]).subs(tsubs[_sage_const_0 ]))    # Adjunction-formula
-    
-    print('--- Toric divisors (ambient space) -----------')
-    print(D)
-    print('\n--- Kähler cone generators (ambient space) --- ')
-    print(J)
-    print('\n--- Mori-cone-generators (ambient space) ------')
-    for j in range(nodivs):
-        print(MoriMatrix[_sage_const_0 ][j],MoriMatrix[_sage_const_1 ][j])
-
-    print('\n--- Intersection on CY ------------------------')
-    Ccy=[product([t[iden[_sage_const_0 ][i]] for i in range(dimp-no_polys)])==iden[_sage_const_1 ] for iden in intCY]
-    print(Ccy)
-    print('\nR = ',intring)
-    print('\nR (no multiplicities) = ',intringnomults)
-
-    print('\n--- Intersection in ambient space -------------')
-    Cam=[product([t[iden[_sage_const_0 ][i]] for i in range(dimp)])==iden[_sage_const_1 ] for iden in intAm]
-    print(Cam)
-
-    print('\n--- Topological data --------------------------')
-    #print((product([1+lift(d) for d in D]))/(product([1+sum([lift(HH(D[p])) for p in part]) for part in nef_partition])))
-    chi = X.integrate(Ydualform*(product([_sage_const_1 +lift(d) for d in D]))/(product([_sage_const_1 +sum([lift(HH(D[p])) for p in part]) for part in nef_partition])))
-    print('chi = ',chi)
-
-    c = var('c')
-    if( round((cc).subs({t:c*t for t in t}).taylor(c,_sage_const_0 ,_sage_const_1 ).coefficient(c,_sage_const_1 ).subs({t[i]:_sage_const_1  for i in range(nodivs)}),_sage_const_8 ) != _sage_const_0 ):
-        return "First Chern-class not zero!"
-
-    # Print Chern classes:
-    cJ = [[_sage_const_0 ]]*(dimp-no_polys)
-    for i in range(_sage_const_2 ,dimp-no_polys):
-        print('\nc',i,' = ',(cc).subs({t:c*t for t in t}).taylor(c,_sage_const_0 ,i).coefficient(c,i))
-        TupleListi = UnorderedTuples(range(nodivs),i)
-        TupleListz = UnorderedTuples(range(nodivs),dimp-no_polys-i)
-        cJ[i] = [sum([((cc).subs({t:c*t for t in t}).taylor(c,_sage_const_0 ,i).coefficient(c,i)).coefficient(product([t[i] for i in tupl]))*((product([t[j] for j in tuplz])*product([t[i] for i in tupl])).subs(Ccy)) for tupl in TupleListi]) for tuplz in TupleListz]
-        print('integrated: '+str([cJ[i][j]*product([t[k] for k in TupleListz[j]]) for j in range(len(TupleListz))]))
-    print('\nc',dimp-no_polys,' = ',(cc).subs({t:c*t for t in t}).taylor(c,_sage_const_0 ,dimp-no_polys).coefficient(c,dimp-no_polys))
-    
-    msg = ""
-    # elliptic:
-    ## Indicates whether J_i^n==0 with J_i^(n-1)!=0 for n-folds and some J_i
-    for i in range(nodivs):
-        for intn in intCY:
-            if( intn[_sage_const_0 ] == [i]*(dimp-no_polys) and intn[_sage_const_1 ] == _sage_const_0 ):
-                if not(all([round((t[i]**(dimp-no_polys-_sage_const_1 )*t[j]).subs(Ccy),_sage_const_10 ) == _sage_const_0  for j in range(nodivs) if j != i]) ):
-                    msg += "Possible elliptic fibration in cycle dual to t"+str(i)+".\n"
-
-    # K3 for 3-folds
-    ## Indicates whether c2.J_i =24 for some J_i
-    if( dimp+_sage_const_1 -no_polys == _sage_const_4 ):
-        TupleList2 = UnorderedTuples(range(nodivs),_sage_const_2 )
-        for j in range(nodivs):
-            if( sum([((cc).subs({t:c*t for t in t}).taylor(c,_sage_const_0 ,_sage_const_2 ).coefficient(c,_sage_const_2 )).coefficient(product([t[i] for i in tupl]))*((product([t[i] for i in tupl])*t[j]).subs(Ccy)) for tupl in TupleList2]) == _sage_const_24  ):
-                msg += "Possible K3-fibration in divisor t"+str(j)+".\n"
-
-    if( msg != "" ):
-        print('\n--- Fibrations --------------------------------')
-        print(msg)
-    if returnvars:
-        return str([(MoriMatrix[_sage_const_0 ][j],MoriMatrix[_sage_const_1 ][j]) for j in range(nodivs)]).replace("(","{").replace(")","}").replace("[","{").replace("]","}") # might return more in the future if necessary
-    
-    
-def CICYtopdata(CICY,justdata=False,justmori=False, lvec=_sage_const_0 ):
-    # Input: a list l with entries l[i,j] that give the weight in the 
-    #        ambient projective space i of polynomial j.
-    #        E.g. (P^3| 3 1)
-    #             (P^2| 2 0)
-    #        corresponds to the list ((3,1),(2,0))
-    
-    ambients=(np.array(CICY).transpose()).sum(axis=_sage_const_0 )-_sage_const_1 
-    if ambients in ZZ:
-        ambients=[ambients]
-    dimp=sum(ambients)
-    polytope=identity_matrix(int(dimp))
-    zeros=[_sage_const_0 ]*dimp
-    polytope=polytope.insert_row(_sage_const_0 ,zeros)
-    
-    offset=_sage_const_0 
-    for i in range(len(ambients)):
-        newrow=[_sage_const_0 ]*dimp
-        entry=[]
-        for j in range(ambients[i]):
-            newrow[offset]=-_sage_const_1 
-            offset+=_sage_const_1 
-            entry.append(offset)
-        polytope=polytope.insert_row(sum([ambients[n]+_sage_const_1  for n in (ellipsis_range(_sage_const_0 ,Ellipsis,i))]),newrow)
-    
-    partition=[]
-    eqs=matrix(CICY).transpose()
-    counters=[_sage_const_0 ]*len(ambients)
-    for eq in eqs:
-        part=[]
-        for j in range(len(eq)):
-            part.append([sum([ambients[m]+_sage_const_1  for m in (ellipsis_range(_sage_const_0 ,Ellipsis,(j-_sage_const_1 )))])+counters[j]+a for a in (ellipsis_range(_sage_const_0 ,Ellipsis,(eq[j]-_sage_const_1 )))])
-            counters[j]+=len(part[j])
-        partition.append(flatten(part))
-    
-    if justdata:
-        return [list(polytope),partition]
-    elif justmori:
-        moricone((list(polytope)))
-    else:
-        topdata(list(polytope),nef_partition=partition,lvec=lvec)
-
-topdata(pointstopoly([(_sage_const_1 ,_sage_const_0 ),(_sage_const_0 ,_sage_const_1 ),(-_sage_const_1 ,-_sage_const_1 )]))
-