def __init__(self, name, conversions=None, latex=None, mathml="",
domain='complex'):
"""
EXAMPLES::
sage: from sage.symbolic.constants import Constant
sage: p = Constant('p')
sage: loads(dumps(p))
p
"""
self._conversions = conversions if conversions is not None else {}
self._latex = latex if latex is not None else name
self._mathml = mathml
self._name = name
self._domain = domain
for system, value in self._conversions.items():
setattr(self, "_%s_"%system, partial(self._generic_interface, value))
setattr(self, "_%s_init_"%system, partial(self._generic_interface_init, value))
from sage.libs.pynac.constant import PynacConstant
self._pynac = PynacConstant(self._name, self._latex, self._domain)
self._serial = self._pynac.serial()
constants_table[self._serial] = self
constants_name_table[self._name] = self
register_symbol(self.expression(), self._conversions)
def __init__(self,
name,
conversions=None,
latex=None,
mathml="",
domain='complex'):
"""
EXAMPLES::
sage: from sage.symbolic.constants import Constant
sage: p = Constant('p')
sage: loads(dumps(p))
p
"""
self._conversions = conversions if conversions is not None else {}
self._latex = latex if latex is not None else name
self._mathml = mathml
self._name = name
self._domain = domain
for system, value in self._conversions.items():
setattr(self, "_%s_" % system,
partial(self._generic_interface, value))
setattr(self, "_%s_init_" % system,
partial(self._generic_interface_init, value))
from sage.libs.pynac.constant import PynacConstant
self._pynac = PynacConstant(self._name, self._latex, self._domain)
self._serial = self._pynac.serial()
constants_table[self._serial] = self
constants_name_table[self._name] = self
register_symbol(self.expression(), self._conversions)
if m == 1:
return r"H_{%s}" % z
else:
return r"H_{{%s},{%s}}" % (z, m)
harmonic_number = Function_harmonic_number_generalized()
def _swap_harmonic(a, b):
return harmonic_number(b, a)
from sage.libs.pynac.pynac import register_symbol
register_symbol(_swap_harmonic, {'maxima': 'gen_harmonic_number'})
register_symbol(_swap_harmonic, {'maple': 'harmonic'})
class Function_harmonic_number(BuiltinFunction):
r"""
Harmonic number function, defined by:
.. MATH::
H_{n}=H_{n,1}=\sum_{k=1}^n\frac1k
H_{s}=\int_0^1\frac{1-x^s}{1-x}
See the docstring for :meth:`Function_harmonic_number_generalized`.
H_{x}
sage: latex(harmonic_number(x,2))
H_{{x},{2}}
"""
if m == 1:
return r"H_{%s}" % z
else:
return r"H_{{%s},{%s}}" % (z, m)
harmonic_number = Function_harmonic_number_generalized()
def _swap_harmonic(a,b): return harmonic_number(b,a)
from sage.libs.pynac.pynac import register_symbol
register_symbol(_swap_harmonic,{'maxima':'gen_harmonic_number'})
register_symbol(_swap_harmonic,{'maple':'harmonic'})
class Function_harmonic_number(BuiltinFunction):
r"""
Harmonic number function, defined by:
.. MATH::
H_{n}=H_{n,1}=\sum_{k=1}^n\frac1k
H_{s}=\int_0^1\frac{1-x^s}{1-x}
See the docstring for :meth:`Function_harmonic_number_generalized`.
This class exists as callback for ``harmonic_number`` returned by Maxima.
raise TypeError(
"Symbolic function psi takes at most 2 arguments (%s given)" %
(len(args) + 1))
return psi2(x, args[0], **kwds)
# We have to add the wrapper function manually to the symbol_table when we have
# two functions with different number of arguments and the same name
symbol_table['functions']['psi'] = psi
def _swap_psi(a, b):
return psi(b, a)
register_symbol(_swap_psi, {'giac': 'Psi'})
class Function_beta(GinacFunction):
def __init__(self):
r"""
Return the beta function. This is defined by
.. MATH::
\operatorname{B}(p,q) = \int_0^1 t^{p-1}(1-t)^{q-1} dt
for complex or symbolic input `p` and `q`.
Note that the order of inputs does not matter:
`\operatorname{B}(p,q)=\operatorname{B}(q,p)`.
###############################################################################
from __future__ import print_function
from __future__ import absolute_import
import math
from functools import partial
from sage.rings.infinity import (infinity, minus_infinity, unsigned_infinity)
constants_table = {}
constants_name_table = {}
constants_name_table[repr(infinity)] = infinity
constants_name_table[repr(unsigned_infinity)] = unsigned_infinity
constants_name_table[repr(minus_infinity)] = minus_infinity
from sage.libs.pynac.pynac import register_symbol, I
register_symbol(infinity, {'maxima': 'inf'})
register_symbol(minus_infinity, {'maxima': 'minf'})
register_symbol(unsigned_infinity, {'maxima': 'infinity'})
register_symbol(I, {'mathematica': 'I'})
def unpickle_Constant(class_name, name, conversions, latex, mathml, domain):
"""
EXAMPLES::
sage: from sage.symbolic.constants import unpickle_Constant
sage: a = unpickle_Constant('Constant', 'a', {}, 'aa', '', 'positive')
sage: a.domain()
'positive'
sage: latex(a)
aa
gamma(4/3)
sage: gamma(4/3, 1)._mathematica_().sage() # indirect doctest, optional - mathematica
gamma(4/3, 1)
sage: mathematica('Gamma[4/3, 0, 1]').sage() # indirect doctest, optional - mathematica
gamma(4/3) - gamma(4/3, 1)
"""
if not args or len(args) > 3:
raise TypeError("Mathematica function Gamma takes 1 to 3 arguments"
" (%s given)" % (len(args)))
elif len(args) == 3:
return gamma_inc(args[0], args[1]) - gamma_inc(args[0], args[2])
else:
return gamma(*args)
register_symbol(_mathematica_gamma, dict(mathematica='Gamma'))
class Function_psi1(GinacFunction):
def __init__(self):
r"""
The digamma function, `\psi(x)`, is the logarithmic derivative of the
gamma function.
.. MATH::
\psi(x) = \frac{d}{dx} \log(\Gamma(x)) = \frac{\Gamma'(x)}{\Gamma(x)}
EXAMPLES::
sage: from sage.functions.gamma import psi1
# http://www.gnu.org/licenses/
###############################################################################
import math
from functools import partial
from sage.rings.infinity import (infinity, minus_infinity, unsigned_infinity)
from sage.structure.richcmp import richcmp_method, op_EQ, op_GE, op_LE
constants_table = {}
constants_name_table = {}
constants_name_table[repr(infinity)] = infinity
constants_name_table[repr(unsigned_infinity)] = unsigned_infinity
constants_name_table[repr(minus_infinity)] = minus_infinity
from sage.libs.pynac.pynac import register_symbol, I
register_symbol(infinity, {'maxima': 'inf'})
register_symbol(minus_infinity, {'maxima': 'minf'})
register_symbol(unsigned_infinity, {'maxima': 'infinity'})
register_symbol(I, {'mathematica': 'I'})
register_symbol(True, {
'giac': 'true',
'mathematica': 'True',
'maxima': 'true'
})
register_symbol(False, {
'giac': 'false',
'mathematica': 'False',
'maxima': 'false'
})
gamma(4/3)
sage: gamma(4/3, 1)._mathematica_().sage() # indirect doctest, optional - mathematica
gamma(4/3, 1)
sage: mathematica('Gamma[4/3, 0, 1]').sage() # indirect doctest, optional - mathematica
gamma(4/3) - gamma(4/3, 1)
"""
if not args or len(args) > 3:
raise TypeError("Mathematica function Gamma takes 1 to 3 arguments"
" (%s given)" % (len(args)))
elif len(args) == 3:
return gamma_inc(args[0], args[1]) - gamma_inc(args[0], args[2])
else:
return gamma(*args)
register_symbol(_mathematica_gamma, dict(mathematica='Gamma'))
class Function_psi1(GinacFunction):
def __init__(self):
r"""
The digamma function, `\psi(x)`, is the logarithmic derivative of the
gamma function.
.. MATH::
\psi(x) = \frac{d}{dx} \log(\Gamma(x)) = \frac{\Gamma'(x)}{\Gamma(x)}
EXAMPLES::
sage: from sage.functions.gamma import psi1
from __future__ import print_function
from __future__ import absolute_import
import math
from functools import partial
from sage.rings.infinity import (infinity, minus_infinity,
unsigned_infinity)
constants_table = {}
constants_name_table = {}
constants_name_table[repr(infinity)] = infinity
constants_name_table[repr(unsigned_infinity)] = unsigned_infinity
constants_name_table[repr(minus_infinity)] = minus_infinity
from sage.libs.pynac.pynac import register_symbol, I
register_symbol(infinity, {'maxima':'inf'})
register_symbol(minus_infinity, {'maxima':'minf'})
register_symbol(unsigned_infinity, {'maxima':'infinity'})
register_symbol(I, {'mathematica':'I'})
def unpickle_Constant(class_name, name, conversions, latex, mathml, domain):
"""
EXAMPLES::
sage: from sage.symbolic.constants import unpickle_Constant
sage: a = unpickle_Constant('Constant', 'a', {}, 'aa', '', 'positive')
sage: a.domain()
'positive'
sage: latex(a)
aa
