Coverage for /usr/lib/python3/dist-packages/sympy/combinatorics/group_constructs.py: 17%

1from sympy.combinatorics.perm_groups import PermutationGroup 

2from sympy.combinatorics.permutations import Permutation 

3from sympy.utilities.iterables import uniq 

4 

5_af_new = Permutation._af_new 

6 

7 

8def DirectProduct(*groups): 

9 """ 

10 Returns the direct product of several groups as a permutation group. 

11 

12 Explanation 

13 =========== 

14 

15 This is implemented much like the __mul__ procedure for taking the direct 

16 product of two permutation groups, but the idea of shifting the 

17 generators is realized in the case of an arbitrary number of groups. 

18 A call to DirectProduct(G1, G2, ..., Gn) is generally expected to be faster 

19 than a call to G1*G2*...*Gn (and thus the need for this algorithm). 

20 

21 Examples 

22 ======== 

23 

24 >>> from sympy.combinatorics.group_constructs import DirectProduct 

25 >>> from sympy.combinatorics.named_groups import CyclicGroup 

26 >>> C = CyclicGroup(4) 

27 >>> G = DirectProduct(C, C, C) 

28 >>> G.order() 

29 64 

30 

31 See Also 

32 ======== 

33 

34 sympy.combinatorics.perm_groups.PermutationGroup.__mul__ 

35 

36 """ 

37 degrees = [] 

38 gens_count = [] 

39 total_degree = 0 

40 total_gens = 0 

41 for group in groups: 

42 current_deg = group.degree 

43 current_num_gens = len(group.generators) 

44 degrees.append(current_deg) 

45 total_degree += current_deg 

46 gens_count.append(current_num_gens) 

47 total_gens += current_num_gens 

48 array_gens = [] 

49 for i in range(total_gens): 

50 array_gens.append(list(range(total_degree))) 

51 current_gen = 0 

52 current_deg = 0 

53 for i in range(len(gens_count)): 

54 for j in range(current_gen, current_gen + gens_count[i]): 

55 gen = ((groups[i].generators)[j - current_gen]).array_form 

56 array_gens[j][current_deg:current_deg + degrees[i]] = \ 

57 [x + current_deg for x in gen] 

58 current_gen += gens_count[i] 

59 current_deg += degrees[i] 

60 perm_gens = list(uniq([_af_new(list(a)) for a in array_gens])) 

61 return PermutationGroup(perm_gens, dups=False)