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- from sympy.core.function import Add, ArgumentIndexError, Function
- from sympy.core.singleton import S
- from sympy.functions.elementary.trigonometric import cos, sin
- def _cosm1(x, *, evaluate=True):
- return Add(cos(x, evaluate=evaluate), -S.One, evaluate=evaluate)
- class cosm1(Function):
- """ Minus one plus cosine of x, i.e. cos(x) - 1. For use when x is close to zero.
- Helper class for use with e.g. scipy.special.cosm1
- See: https://docs.scipy.org/doc/scipy/reference/generated/scipy.special.cosm1.html
- """
- nargs = 1
- def fdiff(self, argindex=1):
- """
- Returns the first derivative of this function.
- """
- if argindex == 1:
- return -sin(*self.args)
- else:
- raise ArgumentIndexError(self, argindex)
- def _eval_rewrite_as_cos(self, x, **kwargs):
- return _cosm1(x)
- def _eval_evalf(self, *args, **kwargs):
- return self.rewrite(cos).evalf(*args, **kwargs)
- def _eval_simplify(self, x, **kwargs):
- candidate = _cosm1(x.simplify(**kwargs))
- if candidate != _cosm1(x, evaluate=False):
- return candidate
- else:
- return cosm1(x)
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