Commit f732da80 by Peter Korcsok

### added basic sage scripts

parent 4f87353a
advanced.sage 0 → 100644
 def Partitions(List): """ Generates all proper partitions of List. """ if len(List)==0: yield [] return if len(List)==1: return for A in Subsets( List[:-1] ): if len(A) > 0: M = List[:-1] for a in A: M.remove(a) AA = A.list() + [List[-1]] for r in Partitions(M): yield r + [ AA ] # Partitions def Classes(Partition): """ Returns a list determining the class where the partition belongs. """ m = max([ max(p) for p in Partition]) Res = range(m + 1) for P in Partition: m = min(P) for p in P: Res[p] = m return Res # Classes def IsMinPartition(Part, Gamma): """ Returns True if given partition is lexicographically minimal in its class. """ X = Classes(Part) for r in [ GammaPartition(g, Part) for g in Gamma]: x = Classes(r) if x < X: return False return True # IsMinPartition def GammaPartition(Gamma, Partition): """ Applies permutation Gamma on Partition. """ Res = Set([]) for P in Partition: P_ = Set([Gamma[r]-1 for r in P]) Res = Res.union(Set([P_])) return Res # GammaPartition def PartitionClasses(Partitions, Gamma): """ Returns list of classes of partitions. """ Res = [] for Partition in Partitions: if IsMinPartition(Partition, Gamma): Res += [ Set([ GammaPartition(g, Partition) for g in Gamma ]) ] return Res # PartitionClasses def NTuples(n): """ Generates all n-tuples of {1, 2, 3, 4}^n. """ if n==0: yield [] return for t in NTuples(n-1): for i in [1, 2, 3, 4]: yield t + [i] # NTuples def CountTerminalValues(n): """ Counts all values of n terminals with - first item = 1, - sum of all items = 0. """ if n<=1: return 0 Count = 0 for t in NTuples(n-2): T = [1] + t s = Integers(5)(0) for i in T: s += i if s!=0: Count += 1 return Count # CountTerminalValues def TerminalValues(n): """ Generates all values of n terminals with - first item = 1, - sum of all items = 0. """ if n<=1: yield [] return for t in NTuples(n-2): T = [1] + t s = Integers(5)(0) for i in T: s += i if s!=0: yield T + [-s] # TerminalValues def Compatibility(Partition, TerminalValues): """ Returns 1 if the partition is compatible with values on terminals. """ for Class in Partition: s = Integers(5)(0) for Index in Class: s += TerminalValues[Index] if s!=0: return 0 return 1 # Compatibility def Chi(PartitionClasses, TerminalValues): """ Returns the vector of compatibility. """ return [sum(Compatibility(P, TerminalValues) for P in Part) for Part in PartitionClasses] # Chi def IsFlow(TerminalValues): """ Returns True if there exists a flow with given values on terminals. """ val = [ Integers(5)(i) for i in range(1,5) ] for Val in TerminalValues: val = [ v + Val for v in val if v + Val > 0 ] return len(val) > 0 # IsFlow def EncodeTerminalValues(Values): """ Encodes values of terminals into one number. """ if len(Values) == 1: return Integer(Values[-1] - 1) return 4 * EncodeTerminalValues(Values[:-1]) + Integer(Values[-1] - 1) # EncodeTerminalValues def GammaValues(Values, Gamma): """ Applies permutation Gamma on Values. """ Res = [] for i in range(len(Values)): Res += [ Values[Gamma[i] - 1] ] s = 1/Integers(5)(Res[0]) if s != 1: return [ i * s for i in Res] return Res # GammaValues def Generate(n, Buffer, Verbose, Save=True, Type=3): """ Generates the matrices M_n and M'_n and counts their ranks. If some matrix is too long the rank is computed by parts with matrix buffer of given size. The parameter Verbose determines the number of rows after that a progress message is printed. The parameter Save determines whether the result matrices are saved on disk. The parameter Type determines which matrices are generated: 1 - M_n, 2 - M'_n, 3 - both. """ from datetime import datetime print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "initiating..." G = DihedralGroup(n) Gamma = [ g.tuple() for g in G ] PartCls = PartitionClasses(Partitions(range(n)), Gamma) PartSml = [ range(n-2), [ n-2, n-1 ] ] Count = CountTerminalValues(n) Vals = TerminalValues(n) Used = [] for i in range(4^(n-1)): Used += [ False ] Mn = [] MMn = [] rn = 0 rrn = 0 proc = 0 verb = 0 print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processing terminal values..." for H in Vals: proc += 1 verb += 1 if verb >= Verbose: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processed", proc, "of", Count, "...", (100 * proc/Count).round(), "%" verb = 0 if Used[EncodeTerminalValues(H)]: continue Used[EncodeTerminalValues(H)] = True if IsFlow(H): X = Chi(PartCls, H) for G in Gamma: Used[EncodeTerminalValues(GammaValues(H, G))] = True if Type & 1 == 1: Mn += [ X ] rn += 1 if rn >= Buffer: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processed", proc, "of", Count, "...", (100 * proc/Count).round(), "%" print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for Mn overflow (", rn, ")..." M = Matrix(QQ, Mn) rn = M.rank() P, L, U = M.LU() Mn = [ U[i].list() for i in range(rn) ] print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for Mn completed (", rn, ")" if Type & 2 == 2: MMn += [ X ] rrn += 1 if rrn >= Buffer: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processed", proc, "of", Count, "...", (100 * proc/Count).round(), "%" print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for MMn overflow (", rrn, ")..." M = Matrix(QQ, MMn) rrn = M.rank() P, L, U = M.LU() MMn = [ U[i].list() for i in range(rrn) ] print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for MMn completed (", rrn, ")" continue if (Compatibility(PartSml, H) == 1) and IsFlow(H[:-2]): X = Chi(PartCls, H) for G in Gamma: Used[EncodeTerminalValues(GammaValues(H, G))] = True if Type & 2 == 2: MMn += [ X ] rrn += 1 if rrn >= Buffer: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processed", proc, "of", Count, "...", (100 * proc/Count).round(), "%" print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for MMn overflow (", rrn, ")..." M = Matrix(QQ, MMn) rrn = M.rank() P, L, U = M.LU() MMn = [ U[i].list() for i in range(rrn) ] print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for MMn completed (", rrn, ")" print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processing terminal values completed" Mn = Matrix(Mn) MMn = Matrix(MMn) if Save: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "saving the matrices..." s = "saves/advanced/" + datetime.now().strftime('%Y-%m-%d_%H-%M-%S') + "_" + n.str() + "_" if Type & 1 == 1: save(Mn, s + "1") if Type & 2 == 2: save(MMn, s + "2") print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "counting the ranks..." rn = Mn.rank() rrn = MMn.rank() print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "counting the ranks completed" return [ n, rn, rrn ] # Generate
basic.sage 0 → 100644
 def Partitions(List): """ Generates all proper partitions of List. """ if len(List)==0: return [ [] ] if len(List)==1: return [ ] Res = [] for A in Subsets( List[:-1] ): if len(A)>0: M = List[:-1] for a in A: M.remove(a) AA = A.list() + [List[-1]] Res += [ r + [ AA ] for r in Partitions(M) ] return Res # Partitions def NTuples(n): """ Generates all n-tuples of {1, 2, 3, 4}^n. """ if n==0: yield [] return for t in NTuples(n-1): for i in [1, 2, 3, 4]: yield t + [i] # NTuples def CountTerminalValues(n): """ Counts all values of n terminals with - first item = 1, - sum of all items = 0. """ if n<=1: return 0 Count = 0 for t in NTuples(n-2): T = [1] + t s = Integers(5)(0) for i in T: s += i if s!=0: Count += 1 return Count # CountTerminalValues def TerminalValues(n): """ Generates all values of n terminals with - first item = 1, - sum of all items = 0. """ if n<=1: yield [] return for t in NTuples(n-2): T = [1] + t s = Integers(5)(0) for i in T: s += i if s!=0: yield T + [-s] # TerminalValues def Compatibility(Partition, TerminalValues): """ Returns 1 if the partition is compatible with values on terminals. """ for Class in Partition: s = Integers(5)(0) for Index in Class: s += TerminalValues[Index] if s!=0: return 0 return 1 # Compatibility def Chi(Partitions, TerminalValues): """ Returns the vector of compatibility. """ return [Compatibility(P, TerminalValues) for P in Partitions] # Chi def IsFlow(TerminalValues): """ Returns True if there exists a flow with given values on terminals. """ val = [ Integers(5)(i) for i in range(1,5) ] for Val in TerminalValues: val = [ v + Val for v in val if v + Val > 0 ] return len(val) > 0 # IsFlow def Generate(n, Buffer, Verbose, Save=True, Type=3): """ Generates the matrices M_n and M_{C_n} and counts their ranks. If some matrix is too long the rank is computed by parts with matrix buffer of given size. The parameter Verbose determines the number of rows after that a progress message is printed. The parameter Save determines whether the result matrices are saved on disk. The parameter Type determines which matrices are generated: 1 - M_n, 2 - M_{C_n}, 3 - both. """ from datetime import datetime print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "initiating..." Count = CountTerminalValues(n) Parts = Partitions(range(n)) Vals = TerminalValues(n) Mn = [] MCn = [] rn = 0 rCn = 0 proc = 0 verb = 0 print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processing terminal values..." for V in Vals: proc += 1 verb += 1 chi = False if Type & 1 == 1: X = Chi(Parts, V) chi = True Mn += [ X ] rn += 1 if rn >= Buffer: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processed", proc, "of", Count, "...", (100 * proc/Count).round(), "%" print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for Mn overflow (", rn, ")..." M = Matrix(QQ, Mn) rn = M.rank() P, L, U = M.LU() Mn = [ U[i].list() for i in range(rn) ] print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for Mn completed (", rn, ")" if Type & 2 == 2: if IsFlow(V): if not chi: X = Chi(Parts, V) MCn += [ X ] rCn += 1 if rCn >= Buffer: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processed", proc, "of", Count, "...", (100 * proc/Count).round(), "%" print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for MCn overflow (", rCn, ")..." M = Matrix(QQ, MCn) rCn = M.rank() P, L, U = M.LU() MCn = [ U[i].list() for i in range(rCn) ] print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "buffer for MCn completed (", rCn, ")" if verb >= Verbose: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processed", proc, "of", Count, "...", (100 * proc/Count).round(), "%" verb = 0 print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "processing terminal values completed" Mn = Matrix(Mn) MCn = Matrix(MCn) if Save: print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "saving the matrices..." s = "saves/basic/" + datetime.now().strftime('%Y-%m-%d_%H-%M-%S') + "_" + n.str() + "_" if Type & 1 == 1: save(Mn, s + "1") if Type & 2 == 2: save(MCn, s + "2") print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "counting the ranks..." rn = Mn.rank() rCn = MCn.rank() print datetime.now().strftime('%Y-%m-%d %H:%M:%S'), "counting the ranks completed" return [ n, rn, rCn ] # Generate
pairs.sage 0 → 100644
 def Partitions(List): """ Generates all proper partitions of List. """ if len(List)==0: yield [] return if len(List)==1: return for A in Subsets( List[:-1] ): if len(A) > 0: M = List[:-1] for a in A: M.remove(a) AA = A.list() + [List[-1]] for r in Partitions(M): yield r + [ AA ] # Partitions def Classes(Partition): """ Returns a list determining the class where the partition belongs. """ m = max([ max(p) for p in Partition]) Res = range(m + 1) for P in Partition: m = min(P) for p in P: Res[p] = m return Res # Classes def IsMinPartition(Part, Gamma): """ Returns True if given partition is lexicographically minimal in its class. """ X = Classes(Part) for r in [ GammaPartition(g, Part) for g in Gamma]: x = Classes(r) if x < X: return False return True # IsMinPartition def GammaPartition(Gamma, Partition): """ Applies permutation Gamma on Partition. """ Res = Set([]) for P in Partition: P_ = Set([Gamma[r]-1 for r in P]) Res = Res.union(Set([P_])) return Res # GammaPartition def PartitionClasses(Partitions, Gamma): """ Returns list of classes of partitions. """ Res = [] for Partition in Partitions: if IsMinPartition(Partition, Gamma): Res += [ Set([ GammaPartition(g, Partition) for g in Gamma ]) ] return Res # PartitionClasses def NTuples(n): """ Generates all n-tuples of {1, 2, 3, 4}^n. """ if n==0: yield [] return for t in NTuples(n-1): for i in [1, 2, 3, 4]: yield t + [i] # NTuples def CountTerminalValues(n): """ Counts all values of n terminals with - first item = 1, - sum of all items = 0. """ if n<=1: return 0 Count = 0 for t in NTuples(n-2): T = [1] + t s = Integers(5)(0) for i in T: s += i if s!=0: Count += 1 return Count # CountTerminalValues def TerminalValues(n): """ Generates all values of n terminals with - first item = 1, - sum of all items = 0. """ if n<=1: yield [] return for t in NTuples(n-2): T = [1] + t s = Integers(5)(0) for i in T: s += i if s!=0: yield T + [-s] # TerminalValues def Compatibility(Partition, TerminalValues): """ Returns 1 if the partition is compatible with values on terminals.