Coverage for local/lib/python2.7/site-packages/sage/symbolic/constants_c.pyx : 54%
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""" The constant `e` """
#***************************************************************************** # Copyright (C) 2008 William Stein <wstein@gmail.com> # Copyright (C) 2008 Burcin Erocal <burcin@erocal.org> # Copyright (C) 2009 Mike Hansen <mhansen@gmail.com> # # This program is free software: you can redistribute it and/or modify # it under the terms of the GNU General Public License as published by # the Free Software Foundation, either version 2 of the License, or # (at your option) any later version. # http://www.gnu.org/licenses/ #*****************************************************************************
from __future__ import absolute_import, division, print_function
from sage.symbolic.expression cimport Expression from sage.symbolic.ring import SR
# keep exp(1) for fast access # this is initialized in the constructor of the class E below to prevent # circular imports while loading the library
# Note, the nearest IEEE 754 value of e is NOT the same as the correctly # rounded decimal value of e. # The numerical value of e = 2.71828182845904523536... # Correctly rounded decimal number = 2.7182818284590452 # Nearest IEEE 754 format number = 2.7182818284590451 # Value returned on some or all AMD/Intel CPUs = 2.7182818284590451 # On Sun Blade 1000 with SPARC processors = 2.7182818284590455
cdef object exp_one
cdef class E(Expression): def __init__(self): r""" Dummy class to represent base of the natural logarithm.
The base of the natural logarithm ``e`` is not a constant in GiNaC/Sage. It is represented by ``exp(1)``.
This class provides a dummy object that behaves well under addition, multiplication, etc. and on exponentiation calls the function ``exp``.
EXAMPLES:
The constant defined at the top level is just ``exp(1)``::
sage: e.operator() exp sage: e.operands() [1]
Arithmetic works::
sage: e + 2 e + 2 sage: 2 + e e + 2 sage: 2*e 2*e sage: e*2 2*e sage: x*e x*e sage: var('a,b') (a, b) sage: t = e^(a+b); t e^(a + b) sage: t.operands() [a + b]
Numeric evaluation, conversion to other systems, and pickling works as expected. Note that these are properties of the :func:`exp` function, not this class::
sage: RR(e) 2.71828182845905 sage: R = RealField(200); R Real Field with 200 bits of precision sage: R(e) 2.7182818284590452353602874713526624977572470936999595749670 sage: em = 1 + e^(1-e); em e^(-e + 1) + 1 sage: R(em) 1.1793740787340171819619895873183164984596816017589156131574 sage: maxima(e).float() 2.718281828459045 sage: t = mathematica(e) # optional - mathematica sage: t # optional - mathematica E sage: float(t) # optional - mathematica 2.718281828459045...
sage: loads(dumps(e)) e
sage: float(e) 2.718281828459045... sage: e.__float__() 2.718281828459045... sage: e._mpfr_(RealField(100)) 2.7182818284590452353602874714 sage: e._real_double_(RDF) # abs tol 5e-16 2.718281828459045 sage: import sympy sage: sympy.E == e # indirect doctest True
TESTS::
sage: t = e^a; t e^a sage: t^b (e^a)^b sage: SR(1).exp() e
Testing that it works with matrices (see :trac:`4735`)::
sage: m = matrix(QQ, 2, 2, [1,0,0,1]) sage: e^m [e 0] [0 e] """ global exp_one exp_one = SR.one().exp() Expression.__init__(self, SR, exp_one)
def __pow__(left, right, dummy): """ Call the `exp` function when taking powers of `e`.
EXAMPLES::
sage: var('a,b') (a, b) sage: t = e^a; t e^a sage: t.operator() exp sage: t.operands() [a]
This applies to the unit argument as well::
sage: u = SR(1).exp()^a; u e^a sage: u.operator() exp sage: u.operands() [a]
It also works with matrices (see :trac:`4735`)::
sage: m = matrix(QQ, 2, 2, [1,0,0,1]) sage: e^m [e 0] [0 e] sage: A = matrix(RDF, [[1,2],[3,4]]) sage: e^A # rel tol 1e-15 [51.968956198705044 74.73656456700327] [112.10484685050491 164.07380304920997] """ return exp_one.exp() else:
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