Coverage for /usr/lib/python3/dist-packages/sympy/series/series_class.py: 42%

1""" 

2Contains the base class for series 

3Made using sequences in mind 

4""" 

5 

6from sympy.core.expr import Expr 

7from sympy.core.singleton import S 

8from sympy.core.cache import cacheit 

9 

10 

11class SeriesBase(Expr): 

12 """Base Class for series""" 

13 

14 @property 

15 def interval(self): 

16 """The interval on which the series is defined""" 

17 raise NotImplementedError("(%s).interval" % self) 

18 

19 @property 

20 def start(self): 

21 """The starting point of the series. This point is included""" 

22 raise NotImplementedError("(%s).start" % self) 

23 

24 @property 

25 def stop(self): 

26 """The ending point of the series. This point is included""" 

27 raise NotImplementedError("(%s).stop" % self) 

28 

29 @property 

30 def length(self): 

31 """Length of the series expansion""" 

32 raise NotImplementedError("(%s).length" % self) 

33 

34 @property 

35 def variables(self): 

36 """Returns a tuple of variables that are bounded""" 

37 return () 

38 

39 @property 

40 def free_symbols(self): 

41 """ 

42 This method returns the symbols in the object, excluding those 

43 that take on a specific value (i.e. the dummy symbols). 

44 """ 

45 return ({j for i in self.args for j in i.free_symbols} 

46 .difference(self.variables)) 

47 

48 @cacheit 

49 def term(self, pt): 

50 """Term at point pt of a series""" 

51 if pt < self.start or pt > self.stop: 

52 raise IndexError("Index %s out of bounds %s" % (pt, self.interval)) 

53 return self._eval_term(pt) 

54 

55 def _eval_term(self, pt): 

56 raise NotImplementedError("The _eval_term method should be added to" 

57 "%s to return series term so it is available" 

58 "when 'term' calls it." 

59 % self.func) 

60 

61 def _ith_point(self, i): 

62 """ 

63 Returns the i'th point of a series 

64 If start point is negative infinity, point is returned from the end. 

65 Assumes the first point to be indexed zero. 

66 

67 Examples 

68 ======== 

69 

70 TODO 

71 """ 

72 if self.start is S.NegativeInfinity: 

73 initial = self.stop 

74 step = -1 

75 else: 

76 initial = self.start 

77 step = 1 

78 

79 return initial + i*step 

80 

81 def __iter__(self): 

82 i = 0 

83 while i < self.length: 

84 pt = self._ith_point(i) 

85 yield self.term(pt) 

86 i += 1 

87 

88 def __getitem__(self, index): 

89 if isinstance(index, int): 

90 index = self._ith_point(index) 

91 return self.term(index) 

92 elif isinstance(index, slice): 

93 start, stop = index.start, index.stop 

94 if start is None: 

95 start = 0 

96 if stop is None: 

97 stop = self.length 

98 return [self.term(self._ith_point(i)) for i in 

99 range(start, stop, index.step or 1)]