def pyobject(self, ex, obj):
from mathics.core import expression
from mathics.core.expression import Number
if obj is None:
return expression.Symbol('Null')
elif isinstance(obj, (list, tuple)) or is_Vector(obj):
return expression.Expression('List', *(from_sage(item, self.subs) for item in obj))
elif isinstance(obj, Constant):
return expression.Symbol(obj._conversions.get('mathematica', obj._name))
elif is_Integer(obj):
return expression.Integer(str(obj))
elif isinstance(obj, sage.Rational):
rational = expression.Rational(str(obj))
if rational.value.denom() == 1:
return expression.Integer(rational.value.numer())
else:
return rational
elif isinstance(obj, sage.RealDoubleElement) or is_RealNumber(obj):
return expression.Real(str(obj))
elif is_ComplexNumber(obj):
real = Number.from_string(str(obj.real())).value
imag = Number.from_string(str(obj.imag())).value
return expression.Complex(real, imag)
elif isinstance(obj, NumberFieldElement_quadratic):
# TODO: this need not be a complex number, but we assume so!
real = Number.from_string(str(obj.real())).value
imag = Number.from_string(str(obj.imag())).value
return expression.Complex(real, imag)
else:
return expression.from_python(obj)
def substitute(self, expr):
from mathics.core import expression
index = len(self.subs)
self.subs.append(expr)
return expression.Expression(self.head_name, expression.Integer(index),
*expr.get_atoms())
def derivative(self, ex, operator):
params = operator.parameter_set()
counts = {}
for param in params:
if param in counts:
counts[param] += 1
else:
counts[param] = 1
new_params = []
for index, count in counts.items():
if len(new_params) <= index:
new_params.extend([0] * (index - len(new_params) + 1))
new_params[index] = count
f = self.create_symbol(repr(operator.function()))
return expression.Expression(expression.Expression('Derivative',
*(expression.Integer(count) for count in new_params)), f)
def _make_Integer(self, x):
return ma.Integer(x)
def convert_Number(self, node):
s = node.value
if s[0] == '-':
sign_prefix, s = s[0], s[1:]
sign = -1
else:
sign_prefix = ''
sign = 1
# fast exit
if s.isdigit():
return ma.Integer(sign * int(s))
# Look for base
s = s.split('^^')
if len(s) == 1:
base, s = 10, s[0]
else:
assert len(s) == 2
base, s = int(s[0]), s[1]
assert 2 <= base <= 36
# Look for mantissa
s = s.split('*^')
if len(s) == 1:
n, s = 0, s[0]
else:
# TODO: modify regex and provide error message if n not an int
n, s = int(s[1]), s[0]
# Look at precision ` suffix to get precision/accuracy
prec, acc = None, None
s = s.split('`', 1)
if len(s) == 1:
s, suffix = s[0], None
else:
s, suffix = s[0], s[1]
# Look for decimal point
if '.' not in s:
if suffix is None:
if n < 0:
return ma.Rational(sign * int(s, base), base**abs(n))
else:
return ma.Integer(sign * int(s, base) * (base**n))
else:
s = s + '.'
if base == 10:
man = s
if n != 0:
s = s + 'E' + str(n)
if suffix is None:
# MachineReal/PrecisionReal is determined by number of digits
# in the mantissa
d = len(man) - 2 # one less for decimal point
if d < reconstruct_digits(machine_precision):
result = float(sign_prefix + s)
else:
result = sympy.Float(str(sign_prefix + s), d)
elif suffix == '':
result = float(sign_prefix + s)
elif suffix.startswith('`'):
acc = float(suffix[1:])
x = float(s)
if x == 0:
prec10 = acc
else:
prec10 = acc + log10(x)
result = sympy.Float(str(sign_prefix + s), prec10)
else:
result = sympy.Float(str(sign_prefix + s), float(suffix))
if isinstance(result, float):
return ma.MachineReal(result)
elif isinstance(result, sympy.Float):
return ma.PrecisionReal(result)
# Put into standard form mantissa * base ^ n
s = s.split('.')
if len(s) == 1:
man = s[0]
else:
n -= len(s[1])
man = s[0] + s[1]
man = sign * int(man, base)
if n >= 0:
result = sympy.Integer(man * base**n)
else:
result = sympy.Rational(man, base**-n)
x = float(result)
# determine `prec10` the digits of precision in base 10
if suffix is None:
acc = len(s[1])
acc10 = acc * log10(base)
if x == 0:
prec10 = acc10
else:
prec10 = acc10 + log10(abs(x))
if prec10 < reconstruct_digits(machine_precision):
prec10 = None
elif suffix == '':
prec10 = None
elif suffix.startswith('`'):
acc = float(suffix[1:])
acc10 = acc * log10(base)
if x == 0:
prec10 = acc10
else:
prec10 = acc10 + log10(abs(x))
else:
prec = float(suffix)
prec10 = prec * log10(base)
if prec10 is None:
return ma.MachineReal(x)
else:
result = sympy.Float(result, prec10)
return ma.PrecisionReal(result)
def convert_Number(self, node):
s = node.value
if s[0] == '-':
sign_prefix, s = s[0], s[1:]
sign = -1
else:
sign_prefix = ''
sign = 1
# fast exit
if s.isdigit():
return ma.Integer(sign * int(s))
# Look for base
s = s.split('^^')
if len(s) == 1:
base, s = 10, s[0]
else:
assert len(s) == 2
base, s = int(s[0]), s[1]
assert 2 <= base <= 36
# Look for mantissa
s = s.split('*^')
if len(s) == 1:
n, s = 0, s[0]
else:
# TODO: modify regex and provide error message if n not an int
n, s = int(s[1]), s[0]
# Look at precision ` suffix to get precision/accuracy
prec, acc = None, None
s = s.split('`', 1)
if len(s) == 1:
suffix, s = None, s[0]
else:
suffix, s = s[1], s[0]
if suffix == '':
prec = machine_precision
elif suffix.startswith('`'):
acc = float(suffix[1:])
else:
if re.match('0+$', s) is not None:
return ma.Integer(0)
prec = float(suffix)
# Look for decimal point
if s.count('.') == 0:
if suffix is None:
if n < 0:
return ma.Rational(sign * int(s, base), base**abs(n))
else:
return ma.Integer(sign * int(s, base) * (base**n))
else:
s = s + '.'
if base == 10:
if n != 0:
s = s + 'E' + str(n) # sympy handles this
if acc is not None:
if float(s) == 0:
prec = 0.
else:
prec = acc + log10(float(s)) + n
# XXX
if prec is not None:
prec = dps(prec)
# return ma.Real(s, prec, acc)
return ma.Real(sign_prefix + s, prec)
else:
# Convert the base
assert isinstance(base, int) and 2 <= base <= 36
# Put into standard form mantissa * base ^ n
s = s.split('.')
if len(s) == 1:
man = s[0]
else:
n -= len(s[1])
man = s[0] + s[1]
man = sign * int(man, base)
if n >= 0:
result = ma.Integer(man * base**n)
else:
result = ma.Rational(man, base**-n)
if acc is None and prec is None:
acc = len(s[1])
acc10 = acc * log10(base)
prec10 = acc10 + log10(result.to_python())
if prec10 < 18:
prec10 = None
elif acc is not None:
acc10 = acc * log10(base)
prec10 = acc10 + log10(result.to_python())
elif prec is not None:
if prec == machine_precision:
prec10 = machine_precision
else:
prec10 = prec * log10(base)
# XXX
if prec10 is None:
prec10 = machine_precision
else:
prec10 = dps(prec10)
return result.round(prec10)