def testAccuracy(self):
self.lex_error('1.5``')
self.check('1.0``20', Real('1.0', p=20))
def out(z):
return Real(z)
def evaluate(self, evaluation):
return Real(-time.timezone / 3600.)
def apply_N(self, prec, evaluation):
'N[MachinePrecision, prec_]'
prec = get_precision(prec, evaluation)
if prec is not None:
return Real(machine_precision).round(prec)
def apply(self, image, x, y, evaluation):
'PixelValue[image_Image, {x_?RealNumberQ, y_?RealNumberQ}]'
return Real(image.pixels[int(y.to_python() - 1),
int(x.to_python() - 1)])
def apply(self, functions, x, start, stop, evaluation, options):
'Plot[functions_, {x_Symbol, start_, stop_}, OptionsPattern[Plot]]'
expr = Expression('Plot', functions,
Expression('List', x, start, stop),
*options_to_rules(options))
if functions.has_form('List', None):
functions = functions.leaves
else:
functions = [functions]
x = x.get_name()
try:
start = start.to_number(n_evaluation=evaluation)
except NumberError:
evaluation.message('Plot', 'plln', start, expr)
return
try:
stop = stop.to_number(n_evaluation=evaluation)
except NumberError:
evaluation.message('Plot', 'plln', stop, expr)
return
def eval_f(f, x_value):
value = dynamic_scoping(f.evaluate, {x: x_value}, evaluation)
value = chop(value).get_real_value()
return value
hue = 0.67
hue_pos = 0.236068
hue_neg = -0.763932
graphics = []
for index, f in enumerate(functions):
points = []
continuous = False
steps = 50
d = (stop - start) / steps
for index in range(steps + 1):
x_value = start + index * d
y = eval_f(f, Real(x_value))
if y is not None:
point = (x_value, y)
if continuous:
points[-1].append(point)
else:
points.append([point])
continuous = True
else:
continuous = False
graphics.append(Expression('Hue', hue, 0.6, 0.6))
graphics.append(
Expression(
'Line',
Expression(
'List',
*(Expression(
'List',
*(Expression('List', Real(x), Real(y))
for x, y in line)) for line in points))))
if index % 4 == 0:
hue += hue_pos
else:
hue += hue_neg
if hue > 1: hue -= 1
if hue < 0: hue += 1
return Expression('Graphics', Expression('List', *graphics),
*options_to_rules(options))
def eval_f(self, f, x_name, x_value, evaluation):
value = quiet_evaluate(f, {x_name: Real(x_value)}, evaluation, expect_list=True)
if value is None or len(value) != 2:
return None
return value
def apply(self, evaluation):
"TimeUsed[]"
# time.process_time() is better than
# time.clock(). See https://bugs.python.org/issue31803
return Real(time.process_time())
def testReal(self):
_test_group(Real(1.17361), Real(-1.42), Real(42.846195714), Real(42.846195714), Real(42.846195713))
def vertices():
for i in range(n):
phi = phi0 + pi2 * i / float(n)
yield Expression("List", Real(x + r * cos(phi)),
Real(y + r * sin(phi)))
def from_sympy(expr):
from mathics.builtin import sympy_to_mathics
from mathics.core.expression import (Symbol, Integer, Rational, Real,
Complex, String, Expression,
MachineReal)
from mathics.core.numbers import machine_precision
from sympy.core import numbers, function, symbol
if isinstance(expr, (tuple, list)):
return Expression('List', *[from_sympy(item) for item in expr])
if isinstance(expr, int):
return Integer(expr)
if isinstance(expr, float):
return Real(expr)
if isinstance(expr, complex):
return Complex(Real(expr.real), Real(expr.imag))
if isinstance(expr, six.string_types):
return String(expr)
if expr is None:
return Symbol('Null')
if isinstance(expr, sympy.Matrix):
if len(expr.shape) == 2 and (expr.shape[1] == 1):
# This is a vector (only one column)
# Transpose and select first row to get result equivalent to Mathematica
return Expression(
'List', *[from_sympy(item) for item in expr.T.tolist()[0]])
else:
return Expression(
'List',
*[[from_sympy(item) for item in row] for row in expr.tolist()])
if expr.is_Atom:
name = None
if expr.is_Symbol:
name = six.text_type(expr)
if isinstance(expr, symbol.Dummy):
name = name + ('__Dummy_%d' % expr.dummy_index)
return Symbol(name, sympy_dummy=expr)
if is_Cn_expr(name):
return Expression('C', int(name[1:]))
if name.startswith(sympy_symbol_prefix):
name = name[len(sympy_symbol_prefix):]
if name.startswith(sympy_slot_prefix):
index = name[len(sympy_slot_prefix):]
return Expression('Slot', int(index))
elif expr.is_NumberSymbol:
name = six.text_type(expr)
if name is not None:
builtin = sympy_to_mathics.get(name)
if builtin is not None:
name = builtin.get_name()
return Symbol(name)
elif isinstance(expr, (numbers.Infinity, numbers.ComplexInfinity)):
return Symbol(expr.__class__.__name__)
elif isinstance(expr, numbers.NegativeInfinity):
return Expression('Times', Integer(-1), Symbol('Infinity'))
elif isinstance(expr, numbers.ImaginaryUnit):
return Complex(Integer(0), Integer(1))
elif isinstance(expr, numbers.Integer):
return Integer(expr.p)
elif isinstance(expr, numbers.Rational):
if expr.q == 0:
if expr.p > 0:
return Symbol('Infinity')
elif expr.p < 0:
return Expression('Times', Integer(-1), Symbol('Infinity'))
else:
assert expr.p == 0
return Symbol('Indeterminate')
return Rational(expr.p, expr.q)
elif isinstance(expr, numbers.Float):
if expr._prec == machine_precision:
return MachineReal(float(expr))
return Real(expr)
elif isinstance(expr, numbers.NaN):
return Symbol('Indeterminate')
elif isinstance(expr, function.FunctionClass):
return Symbol(six.text_type(expr))
elif expr.is_number and all([x.is_Number for x in expr.as_real_imag()]):
# Hack to convert 3 * I to Complex[0, 3]
return Complex(*[from_sympy(arg) for arg in expr.as_real_imag()])
elif expr.is_Add:
return Expression('Plus',
*sorted([from_sympy(arg) for arg in expr.args]))
elif expr.is_Mul:
return Expression('Times',
*sorted([from_sympy(arg) for arg in expr.args]))
elif expr.is_Pow:
return Expression('Power', *[from_sympy(arg) for arg in expr.args])
elif expr.is_Equality:
return Expression('Equal', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, SympyExpression):
return expr.expr
elif isinstance(expr, sympy.Piecewise):
args = expr.args
default = []
if len(args) > 0:
default_case, default_cond = args[-1]
if default_cond == sympy.true:
args = args[:-1]
if isinstance(default_case,
sympy.Integer) and int(default_case) == 0:
pass # ignore, as 0 default case is always implicit in Piecewise[]
else:
default = [from_sympy(default_case)]
return Expression(
'Piecewise',
Expression(
'List', *[
Expression('List', from_sympy(case), from_sympy(cond))
for case, cond in args
]), *default)
elif isinstance(expr, sympy.RootSum):
return Expression('RootSum', from_sympy(expr.poly),
from_sympy(expr.fun))
elif isinstance(expr, sympy.PurePoly):
coeffs = expr.coeffs()
monoms = expr.monoms()
result = []
for coeff, monom in zip(coeffs, monoms):
factors = []
if coeff != 1:
factors.append(from_sympy(coeff))
for index, exp in enumerate(monom):
if exp != 0:
slot = Expression('Slot', index + 1)
if exp == 1:
factors.append(slot)
else:
factors.append(
Expression('Power', slot, from_sympy(exp)))
if factors:
result.append(Expression('Times', *factors))
else:
result.append(Integer(1))
return Expression('Function', Expression('Plus', *result))
elif isinstance(expr, sympy.Lambda):
vars = [
sympy.Symbol('%s%d' % (sympy_slot_prefix, index + 1))
for index in range(len(expr.variables))
]
return Expression('Function', from_sympy(expr(*vars)))
elif expr.is_Function or isinstance(
expr,
(sympy.Integral, sympy.Derivative, sympy.Sum, sympy.Product)):
if isinstance(expr, sympy.Integral):
name = 'Integral'
elif isinstance(expr, sympy.Derivative):
name = 'Derivative'
else:
name = expr.func.__name__
if is_Cn_expr(name):
return Expression(Expression('C', int(name[1:])),
*[from_sympy(arg) for arg in expr.args])
if name.startswith(sympy_symbol_prefix):
name = name[len(sympy_symbol_prefix):]
args = [from_sympy(arg) for arg in expr.args]
builtin = sympy_to_mathics.get(name)
if builtin is not None:
return builtin.from_sympy(name, args)
return Expression(Symbol(name), *args)
elif isinstance(expr, sympy.Tuple):
return Expression('List', *[from_sympy(arg) for arg in expr.args])
# elif isinstance(expr, sympy.Sum):
# return Expression('Sum', )
elif isinstance(expr, sympy.LessThan):
return Expression('LessEqual', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.StrictLessThan):
return Expression('Less', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.GreaterThan):
return Expression('GreaterEqual',
*[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.StrictGreaterThan):
return Expression('Greater', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.Unequality):
return Expression('Unequal', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.Equality):
return Expression('Equal', *[from_sympy(arg) for arg in expr.args])
elif expr is sympy.true:
return Symbol('True')
elif expr is sympy.false:
return Symbol('False')
else:
raise ValueError("Unknown SymPy expression: %s" % expr)
def testLowPrecision(self):
self.check('1.4`1', Real('1', p=1))
self.check('1.4`0', Real(0, p=0))
self.check('1.4`-5', Real(0, p=0))
def testPrecision(self):
self.check('1.`20', Real(1, p=20))
self.check('1.00000000000000000000000`', Real(1))
self.check('1.00000000000000000000000`30', Real(1, p=30))
def testLowAccuracy(self):
self.check('1.4``0', Real(0))
self.check('1.4``-20', Real(0))
def apply(self, items, evaluation):
'Power[items__]'
items_sequence = items.get_sequence()
if len(items_sequence) == 2:
x, y = items_sequence
else:
return Expression('Power', *items_sequence)
if y.get_int_value() == 1:
return x
elif x.get_int_value() == 1:
return x
elif y.get_int_value() == 0:
if x.get_int_value() == 0:
evaluation.message('Power', 'indet', Expression('Power', x, y))
return Symbol('Indeterminate')
else:
return Integer(1)
elif x.has_form('Power', 2) and isinstance(y, Integer):
return Expression('Power', x.leaves[0],
Expression('Times', x.leaves[1], y))
elif x.has_form('Times', None) and isinstance(y, Integer):
return Expression('Times', *[
Expression('Power', leaf, y) for leaf in x.leaves])
elif (isinstance(x, Number) and isinstance(y, Number) and
not (x.is_inexact() or y.is_inexact())):
sym_x, sym_y = x.to_sympy(), y.to_sympy()
try:
if sympy.re(sym_y) >= 0:
result = sym_x ** sym_y
else:
if sym_x == 0:
evaluation.message('Power', 'infy')
return Symbol('ComplexInfinity')
result = sympy.Integer(1) / (sym_x ** (-sym_y))
if isinstance(result, sympy.Pow):
result = result.simplify()
args = [from_sympy(expr) for expr in result.as_base_exp()]
result = Expression('Power', *args)
result = result.evaluate_leaves(evaluation)
return result
return from_sympy(result)
except ValueError:
return Expression('Power', x, y)
except ZeroDivisionError:
evaluation.message('Power', 'infy')
return Symbol('ComplexInfinity')
elif (isinstance(x, Number) and isinstance(y, Number) and
(x.is_inexact() or y.is_inexact())):
try:
prec = min_prec(x, y)
with mpmath.workprec(prec):
mp_x = sympy2mpmath(x.to_sympy(), prec)
mp_y = sympy2mpmath(y.to_sympy(), prec)
result = mp_x ** mp_y
if isinstance(result, mpmath.mpf):
return Real(str(result), prec)
elif isinstance(result, mpmath.mpc):
return Complex(str(result.real),
str(result.imag), prec)
except ZeroDivisionError:
evaluation.message('Power', 'infy')
return Symbol('ComplexInfinity')
else:
numerified_items = items.numerify(evaluation)
return Expression('Power', *numerified_items.get_sequence())
def testInstances(self):
# duplicate instantiations of same content (like Integer 5) to test for potential instantiation randomness.
_test_group(list(map(lambda f: (f(), f()),
(lambda: Integer(5), lambda: Rational(5, 2), lambda: Real(5.12345678),
lambda: Complex(5, 2), lambda: String('xy'), lambda: Symbol('xy')))))
def from_sympy(expr):
from mathics.builtin import sympy_to_mathics
from mathics.core.expression import (Symbol, Integer, Rational, Real,
Complex, String, Expression)
from sympy.core import numbers, function, symbol
if isinstance(expr, (tuple, list)):
return Expression('List', *[from_sympy(item) for item in expr])
if isinstance(expr, int):
return Integer(expr)
if isinstance(expr, float):
return Real(expr)
if isinstance(expr, complex):
return Complex(expr.real, expr.imag)
if isinstance(expr, str):
return String(expr)
if expr is None:
return Symbol('Null')
if isinstance(expr, sympy.Matrix):
return Expression(
'List', *[
Expression('List', *[from_sympy(item) for item in row])
for row in expr.tolist()
])
if expr.is_Atom:
name = None
if expr.is_Symbol:
name = unicode(expr)
if isinstance(expr, symbol.Dummy):
name = name + ('__Dummy_%d' % expr.dummy_index)
return Symbol(name, sympy_dummy=expr)
if ((
not name.startswith(sympy_symbol_prefix) or # noqa
name.startswith(sympy_slot_prefix))
and name.startswith('C')):
return Expression('C', int(name[1:]))
if name.startswith(sympy_symbol_prefix):
name = name[len(sympy_symbol_prefix):]
if name.startswith(sympy_slot_prefix):
index = name[len(sympy_slot_prefix):]
return Expression('Slot', int(index))
elif expr.is_NumberSymbol:
name = unicode(expr)
if name is not None:
builtin = sympy_to_mathics.get(name)
if builtin is not None:
name = builtin.get_name()
return Symbol(name)
elif isinstance(expr, (numbers.Infinity, numbers.ComplexInfinity)):
return Symbol(expr.__class__.__name__)
elif isinstance(expr, numbers.NegativeInfinity):
return Expression('Times', Integer(-1), Symbol('Infinity'))
elif isinstance(expr, numbers.ImaginaryUnit):
return Complex(0, 1)
elif isinstance(expr, numbers.Integer):
return Integer(expr.p)
elif isinstance(expr, numbers.Rational):
if expr.q == 0:
if expr.p > 0:
return Symbol('Infinity')
elif expr.p < 0:
return Expression('Times', Integer(-1), Symbol('Infinity'))
else:
assert expr.p == 0
return Symbol('Indeterminate')
return Rational(expr.p, expr.q)
elif isinstance(expr, numbers.Float):
return Real(expr)
elif isinstance(expr, numbers.NaN):
return Symbol('Indeterminate')
elif isinstance(expr, function.FunctionClass):
return Symbol(unicode(expr))
elif expr.is_number and all([x.is_Number for x in expr.as_real_imag()]):
# Hack to convert 3 * I to Complex[0, 3]
return Complex(*[from_sympy(arg) for arg in expr.as_real_imag()])
elif expr.is_Add:
return Expression('Plus',
*sorted([from_sympy(arg) for arg in expr.args]))
elif expr.is_Mul:
return Expression('Times',
*sorted([from_sympy(arg) for arg in expr.args]))
elif expr.is_Pow:
return Expression('Power', *[from_sympy(arg) for arg in expr.args])
elif expr.is_Equality:
return Expression('Equal', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, SympyExpression):
# print "SympyExpression: %s" % expr
return expr.expr
elif isinstance(expr, sympy.RootSum):
return Expression('RootSum', from_sympy(expr.poly),
from_sympy(expr.fun))
elif isinstance(expr, sympy.PurePoly):
coeffs = expr.coeffs()
monoms = expr.monoms()
result = []
for coeff, monom in zip(coeffs, monoms):
factors = []
if coeff != 1:
factors.append(from_sympy(coeff))
for index, exp in enumerate(monom):
if exp != 0:
slot = Expression('Slot', index + 1)
if exp == 1:
factors.append(slot)
else:
factors.append(
Expression('Power', slot, from_sympy(exp)))
if factors:
result.append(Expression('Times', *factors))
else:
result.append(Integer(1))
return Expression('Function', Expression('Plus', *result))
elif isinstance(expr, sympy.Lambda):
vars = [
sympy.Symbol('%s%d' % (sympy_slot_prefix, index + 1))
for index in range(len(expr.variables))
]
return Expression('Function', from_sympy(expr(*vars)))
elif expr.is_Function or isinstance(
expr,
(sympy.Integral, sympy.Derivative, sympy.Sum, sympy.Product)):
if isinstance(expr, sympy.Integral):
name = 'Integral'
elif isinstance(expr, sympy.Derivative):
name = 'Derivative'
else:
name = expr.func.__name__
if name.startswith(sympy_symbol_prefix):
name = name[len(sympy_symbol_prefix):]
args = [from_sympy(arg) for arg in expr.args]
builtin = sympy_to_mathics.get(name)
if builtin is not None:
name = builtin.get_name()
args = builtin.from_sympy(args)
return Expression(Symbol(name), *args)
elif isinstance(expr, sympy.Tuple):
return Expression('List', *[from_sympy(arg) for arg in expr.args])
# elif isinstance(expr, sympy.Sum):
# return Expression('Sum', )
elif isinstance(expr, sympy.LessThan):
return Expression('LessEqual', [from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.StrictLessThan):
return Expression('Less', [from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.GreaterThan):
return Expression('GreaterEqual',
[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.StrictGreaterThan):
return Expression('Greater', [from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.Unequality):
return Expression('Unequal', [from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.Equality):
return Expression('Equal', [from_sympy(arg) for arg in expr.args])
else:
raise ValueError("Unknown SymPy expression: %s" % expr)
def evaluate(self, evaluation) -> Real:
# Make this be whatever the latest Mathematica release is,
# assuming we are trying to be compatible with this.
return Real(self.value)
def eval_f(self, f, x_name, x_value, evaluation):
value = quiet_evaluate(f, {x_name: Real(x_value)}, evaluation)
if value is None:
return None
return (x_value, value)
def from_sympy(expr):
from mathics.builtin import sympy_to_mathics
from mathics.core.expression import (Symbol, Integer, Rational, Real,
Complex, String, Expression,
MachineReal)
from mathics.core.numbers import machine_precision
if isinstance(expr, (tuple, list)):
return Expression('List', *[from_sympy(item) for item in expr])
if isinstance(expr, int):
return Integer(expr)
if isinstance(expr, float):
return Real(expr)
if isinstance(expr, complex):
return Complex(Real(expr.real), Real(expr.imag))
if isinstance(expr, str):
return String(expr)
if expr is None:
return Symbol('Null')
if isinstance(expr, sympy.Matrix) or isinstance(expr,
sympy.ImmutableMatrix):
if len(expr.shape) == 2 and (expr.shape[1] == 1):
# This is a vector (only one column)
# Transpose and select first row to get result equivalent to Mathematica
return Expression(
'List', *[from_sympy(item) for item in expr.T.tolist()[0]])
else:
return Expression(
'List',
*[[from_sympy(item) for item in row] for row in expr.tolist()])
if isinstance(expr, sympy.MatPow):
return Expression('MatrixPower', from_sympy(expr.base),
from_sympy(expr.exp))
if expr.is_Atom:
name = None
if expr.is_Symbol:
name = str(expr)
if isinstance(expr, sympy.Dummy):
name = name + ('__Dummy_%d' % expr.dummy_index)
return Symbol(name, sympy_dummy=expr)
if is_Cn_expr(name):
return Expression('C', int(name[1:]))
if name.startswith(sympy_symbol_prefix):
name = name[len(sympy_symbol_prefix):]
if name.startswith(sympy_slot_prefix):
index = name[len(sympy_slot_prefix):]
return Expression('Slot', int(index))
elif expr.is_NumberSymbol:
name = str(expr)
if name is not None:
builtin = sympy_to_mathics.get(name)
if builtin is not None:
name = builtin.get_name()
return Symbol(name)
elif isinstance(
expr,
(sympy.core.numbers.Infinity, sympy.core.numbers.ComplexInfinity)):
return Symbol(expr.__class__.__name__)
elif isinstance(expr, sympy.core.numbers.NegativeInfinity):
return Expression('Times', Integer(-1), Symbol('Infinity'))
elif isinstance(expr, sympy.core.numbers.ImaginaryUnit):
return Complex(Integer(0), Integer(1))
elif isinstance(expr, sympy.Integer):
return Integer(int(expr))
elif isinstance(expr, sympy.Rational):
numerator, denominator = map(int, expr.as_numer_denom())
if denominator == 0:
if numerator > 0:
return Symbol('Infinity')
elif numerator < 0:
return Expression('Times', Integer(-1), Symbol('Infinity'))
else:
assert numerator == 0
return Symbol('Indeterminate')
return Rational(numerator, denominator)
elif isinstance(expr, sympy.Float):
if expr._prec == machine_precision:
return MachineReal(float(expr))
return Real(expr)
elif isinstance(expr, sympy.core.numbers.NaN):
return Symbol('Indeterminate')
elif isinstance(expr, sympy.core.function.FunctionClass):
return Symbol(str(expr))
elif expr is sympy.true:
return Symbol('True')
elif expr is sympy.false:
return Symbol('False')
elif expr.is_number and all([x.is_Number for x in expr.as_real_imag()]):
# Hack to convert 3 * I to Complex[0, 3]
return Complex(*[from_sympy(arg) for arg in expr.as_real_imag()])
elif expr.is_Add:
return Expression('Plus',
*sorted([from_sympy(arg) for arg in expr.args]))
elif expr.is_Mul:
return Expression('Times',
*sorted([from_sympy(arg) for arg in expr.args]))
elif expr.is_Pow:
return Expression('Power', *[from_sympy(arg) for arg in expr.args])
elif expr.is_Equality:
return Expression('Equal', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, SympyExpression):
return expr.expr
elif isinstance(expr, sympy.Piecewise):
args = expr.args
return Expression(
'Piecewise',
Expression(
'List', *[
Expression('List', from_sympy(case), from_sympy(cond))
for case, cond in args
]))
elif isinstance(expr, SympyPrime):
return Expression('Prime', from_sympy(expr.args[0]))
elif isinstance(expr, sympy.RootSum):
return Expression('RootSum', from_sympy(expr.poly),
from_sympy(expr.fun))
elif isinstance(expr, sympy.PurePoly):
coeffs = expr.coeffs()
monoms = expr.monoms()
result = []
for coeff, monom in zip(coeffs, monoms):
factors = []
if coeff != 1:
factors.append(from_sympy(coeff))
for index, exp in enumerate(monom):
if exp != 0:
slot = Expression('Slot', index + 1)
if exp == 1:
factors.append(slot)
else:
factors.append(
Expression('Power', slot, from_sympy(exp)))
if factors:
result.append(Expression('Times', *factors))
else:
result.append(Integer(1))
return Expression('Function', Expression('Plus', *result))
elif isinstance(expr, sympy.CRootOf):
try:
e, i = expr.args
except ValueError:
return Expression('Null')
try:
e = sympy.PurePoly(e)
except:
pass
return Expression('Root', from_sympy(e), i + 1)
elif isinstance(expr, sympy.Lambda):
vars = [
sympy.Symbol('%s%d' % (sympy_slot_prefix, index + 1))
for index in range(len(expr.variables))
]
return Expression('Function', from_sympy(expr(*vars)))
elif expr.is_Function or isinstance(
expr,
(sympy.Integral, sympy.Derivative, sympy.Sum, sympy.Product)):
if isinstance(expr, sympy.Integral):
name = 'Integral'
elif isinstance(expr, sympy.Derivative):
name = 'Derivative'
margs = []
for arg in expr.args:
# parse (x, 1) ==> just x for test_conversion
# IMHO this should be removed in future versions
if isinstance(arg, sympy.Tuple):
if arg[1] == 1:
margs.append(from_sympy(arg[0]))
else:
margs.append(from_sympy(arg))
else:
margs.append(from_sympy(arg))
builtin = sympy_to_mathics.get(name)
return builtin.from_sympy(name, margs)
elif isinstance(expr, sympy.sign):
name = 'Sign'
else:
name = expr.func.__name__
if is_Cn_expr(name):
return Expression(Expression('C', int(name[1:])),
*[from_sympy(arg) for arg in expr.args])
if name.startswith(sympy_symbol_prefix):
name = name[len(sympy_symbol_prefix):]
args = [from_sympy(arg) for arg in expr.args]
builtin = sympy_to_mathics.get(name)
if builtin is not None:
return builtin.from_sympy(name, args)
return Expression(Symbol(name), *args)
elif isinstance(expr, sympy.Tuple):
return Expression('List', *[from_sympy(arg) for arg in expr.args])
# elif isinstance(expr, sympy.Sum):
# return Expression('Sum', )
elif isinstance(expr, sympy.LessThan):
return Expression('LessEqual', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.StrictLessThan):
return Expression('Less', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.GreaterThan):
return Expression('GreaterEqual',
*[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.StrictGreaterThan):
return Expression('Greater', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.Unequality):
return Expression('Unequal', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.Equality):
return Expression('Equal', *[from_sympy(arg) for arg in expr.args])
elif isinstance(expr, sympy.O):
if expr.args[0].func == sympy.core.power.Pow:
[var, power] = [from_sympy(arg) for arg in expr.args[0].args]
o = Expression('O', var)
return Expression('Power', o, power)
else:
return Expression('O', from_sympy(expr.args[0]))
else:
raise ValueError(
"Unknown SymPy expression: {} (instance of {})".format(
expr, str(expr.__class__)))
def t_number(self, t):
r'''
( (?# Two possible forms depending on whether base is specified)
(\d+\^\^([a-zA-Z0-9]+\.?[a-zA-Z0-9]*|[a-zA-Z0-9]*\.?[a-zA-Z0-9]+))
| (\d+\.?\d*|\d*\.?\d+)
)
(``?(\+|-)?(\d+\.?\d*|\d*\.?\d+)|`)? (?# Precision / Accuracy)
(\*\^(\+|-)?\d+)? (?# Exponent)
'''
s = t.value
# 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:
t.value = Integer(0)
return t
prec = float(suffix)
# Look for decimal point
if s.count('.') == 0:
if suffix is None:
if n < 0:
t.value = Rational(int(s, base), base**abs(n))
else:
t.value = Integer(int(s, base) * (base**n))
return t
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)
t.value = Real(s, prec)
#t.value = Real(s, prec, acc)
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 = int(man, base)
if n >= 0:
result = Integer(man * base**n)
else:
result = 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)
t.value = result.round(prec10)
return t
def testReal(self):
_test_group(MachineReal(1.17361), MachineReal(-1.42),
MachineReal(42.846195714), MachineReal(42.846195714),
MachineReal(42.846195713), Real('42.846195713', 18),
Real('-1.42', 3))
def apply_real(self, x, evaluation):
'Precision[x_Real]'
return Real(dps(x.get_precision()))
def testAcrossTypes(self):
_test_group(Integer(1), Rational(1, 1), Real(1),
Complex(Integer(1), Integer(1)), String('1'), Symbol('1'))
def apply(self, image, evaluation):
'ImageAspectRatio[image_Image]'
dim = image.dimensions()
return Real(dim[1] / float(dim[0]))
def apply_N(self, precision, evaluation):
'N[E, precision_]'
precision = get_precision(precision, evaluation)
if precision is not None:
return Real(sympy.E.n(dps(precision)), p=precision)
def out(z):
return Real(z, precision)
def apply(self, evaluation):
'SessionTime[]'
return Real(time.time() - START_TIME)
def apply(self, evaluation):
'TimeUsed[]'
return Real(time.clock()) # TODO: Check this for windows
def find_root_secant(f, x0, x, opts, evaluation) -> (Number, bool):
region = opts.get("$$Region", None)
if not type(region) is list:
if x0.is_zero:
region = (Real(-1), Real(1))
else:
xmax = 2 * x0.to_python()
xmin = -2 * x0.to_python()
if xmin > xmax:
region = (Real(xmax), Real(xmin))
else:
region = (Real(xmin), Real(xmax))
maxit = opts["System`MaxIterations"]
x_name = x.get_name()
if maxit.sameQ(Symbol("Automatic")):
maxit = 100
else:
maxit = maxit.evaluate(evaluation).get_int_value()
x0 = from_python(region[0])
x1 = from_python(region[1])
f0 = dynamic_scoping(lambda ev: f.evaluate(evaluation), {x_name: x0},
evaluation)
f1 = dynamic_scoping(lambda ev: f.evaluate(evaluation), {x_name: x1},
evaluation)
if not isinstance(f0, Number):
return x0, False
if not isinstance(f1, Number):
return x0, False
f0 = f0.to_python(n_evaluation=True)
f1 = f1.to_python(n_evaluation=True)
count = 0
while count < maxit:
if f0 == f1:
x1 = Expression(
"Plus",
x0,
Expression(
"Times",
Real(0.75),
Expression("Plus", x1, Expression("Times", Integer(-1),
x0)),
),
)
x1 = x1.evaluate(evaluation)
f1 = dynamic_scoping(lambda ev: f.evaluate(evaluation),
{x_name: x1}, evaluation)
if not isinstance(f1, Number):
return x0, False
f1 = f1.to_python(n_evaluation=True)
continue
inv_deltaf = from_python(1.0 / (f1 - f0))
num = Expression(
"Plus",
Expression("Times", x0, f1),
Expression("Times", x1, f0, Integer(-1)),
)
x2 = Expression("Times", num, inv_deltaf)
x2 = x2.evaluate(evaluation)
f2 = dynamic_scoping(lambda ev: f.evaluate(evaluation), {x_name: x2},
evaluation)
if not isinstance(f2, Number):
return x0, False
f2 = f2.to_python(n_evaluation=True)
f1, f0 = f2, f1
x1, x0 = x2, x1
if x1 == x0 or abs(f2) == 0:
break
count = count + 1
else:
evaluation.message("FindRoot", "maxiter")
return x0, False
return x0, True