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""" |
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Contains the base class for series |
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Made using sequences in mind |
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""" |
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from sympy.core.expr import Expr |
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from sympy.core.singleton import S |
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from sympy.core.cache import cacheit |
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class SeriesBase(Expr): |
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"""Base Class for series""" |
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@property |
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def interval(self): |
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"""The interval on which the series is defined""" |
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raise NotImplementedError("(%s).interval" % self) |
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@property |
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def start(self): |
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"""The starting point of the series. This point is included""" |
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raise NotImplementedError("(%s).start" % self) |
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@property |
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def stop(self): |
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"""The ending point of the series. This point is included""" |
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raise NotImplementedError("(%s).stop" % self) |
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@property |
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def length(self): |
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"""Length of the series expansion""" |
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raise NotImplementedError("(%s).length" % self) |
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@property |
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def variables(self): |
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"""Returns a tuple of variables that are bounded""" |
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return () |
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@property |
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def free_symbols(self): |
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""" |
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This method returns the symbols in the object, excluding those |
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that take on a specific value (i.e. the dummy symbols). |
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""" |
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return ({j for i in self.args for j in i.free_symbols} |
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.difference(self.variables)) |
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@cacheit |
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def term(self, pt): |
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"""Term at point pt of a series""" |
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if pt < self.start or pt > self.stop: |
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raise IndexError("Index %s out of bounds %s" % (pt, self.interval)) |
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return self._eval_term(pt) |
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def _eval_term(self, pt): |
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raise NotImplementedError("The _eval_term method should be added to" |
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"%s to return series term so it is available" |
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"when 'term' calls it." |
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% self.func) |
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def _ith_point(self, i): |
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""" |
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Returns the i'th point of a series |
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If start point is negative infinity, point is returned from the end. |
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Assumes the first point to be indexed zero. |
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Examples |
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======== |
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TODO |
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""" |
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if self.start is S.NegativeInfinity: |
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initial = self.stop |
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step = -1 |
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else: |
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initial = self.start |
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step = 1 |
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return initial + i*step |
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def __iter__(self): |
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i = 0 |
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while i < self.length: |
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pt = self._ith_point(i) |
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yield self.term(pt) |
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i += 1 |
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def __getitem__(self, index): |
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if isinstance(index, int): |
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index = self._ith_point(index) |
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return self.term(index) |
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elif isinstance(index, slice): |
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start, stop = index.start, index.stop |
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if start is None: |
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start = 0 |
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if stop is None: |
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stop = self.length |
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return [self.term(self._ith_point(i)) for i in |
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range(start, stop, index.step or 1)] |
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