def construct_domain(obj, **args):
"""Construct a minimal domain for the list of coefficients. """
opt = build_options(args)
if isinstance(obj, dict):
monoms, coeffs = zip(*obj.items())
else:
coeffs = obj
coeffs = map(sympify, coeffs)
result = _construct_simple(coeffs, opt)
if result is not None:
if result is not False:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
else:
result = _construct_composite(coeffs, opt)
if result is not None:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
if isinstance(obj, dict):
return domain, dict(zip(monoms, coeffs))
else:
return domain, coeffs
def construct_domain(obj, **args):
"""Construct a minimal domain for the list of coefficients. """
opt = build_options(args)
if isinstance(obj, dict):
monoms, coeffs = zip(*obj.items())
else:
coeffs = obj
coeffs = map(sympify, coeffs)
result = _construct_simple(coeffs, opt)
if result is not None:
if result is not False:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
else:
result = _construct_composite(coeffs, opt)
if result is not None:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
if isinstance(obj, dict):
return domain, dict(zip(monoms, coeffs))
else:
return domain, coeffs
def sfield(exprs, *symbols, **options):
"""Construct a field deriving generators and domain
from options and input expressions.
Parameters
==========
exprs : py:class:`~.Expr` or sequence of :py:class:`~.Expr` (sympifiable)
symbols : sequence of :py:class:`~.Symbol`/:py:class:`~.Expr`
options : keyword arguments understood by :py:class:`~.Options`
Examples
========
>>> from sympy.core import symbols
>>> from sympy.functions import exp, log
>>> from sympy.polys.fields import sfield
>>> x = symbols("x")
>>> K, f = sfield((x*log(x) + 4*x**2)*exp(1/x + log(x)/3)/x**2)
>>> K
Rational function field in x, exp(1/x), log(x), x**(1/3) over ZZ with lex order
>>> f
(4*x**2*(exp(1/x)) + x*(exp(1/x))*(log(x)))/((x**(1/3))**5)
"""
single = False
if not is_sequence(exprs):
exprs, single = [exprs], True
exprs = list(map(sympify, exprs))
opt = build_options(symbols, options)
numdens = []
for expr in exprs:
numdens.extend(expr.as_numer_denom())
reps, opt = _parallel_dict_from_expr(numdens, opt)
if opt.domain is None:
# NOTE: this is inefficient because construct_domain() automatically
# performs conversion to the target domain. It shouldn't do this.
coeffs = sum([list(rep.values()) for rep in reps], [])
opt.domain, _ = construct_domain(coeffs, opt=opt)
_field = FracField(opt.gens, opt.domain, opt.order)
fracs = []
for i in range(0, len(reps), 2):
fracs.append(_field(tuple(reps[i:i + 2])))
if single:
return (_field, fracs[0])
else:
return (_field, fracs)
def sfield(exprs, *symbols, **options):
"""Construct a field deriving generators and domain
from options and input expressions.
Parameters
==========
exprs : :class:`Expr` or sequence of :class:`Expr` (sympifiable)
symbols : sequence of :class:`Symbol`/:class:`Expr`
options : keyword arguments understood by :class:`Options`
Examples
========
>>> from sympy.core import symbols
>>> from sympy.functions import exp, log
>>> from sympy.polys.fields import sfield
>>> x = symbols("x")
>>> K, f = sfield((x*log(x) + 4*x**2)*exp(1/x + log(x)/3)/x**2)
>>> K
Rational function field in x, exp(1/x), log(x), x**(1/3) over ZZ with lex order
>>> f
(4*x**2*(exp(1/x)) + x*(exp(1/x))*(log(x)))/((x**(1/3))**5)
"""
single = False
if not is_sequence(exprs):
exprs, single = [exprs], True
exprs = list(map(sympify, exprs))
opt = build_options(symbols, options)
numdens = []
for expr in exprs:
numdens.extend(expr.as_numer_denom())
reps, opt = _parallel_dict_from_expr(numdens, opt)
if opt.domain is None:
# NOTE: this is inefficient because construct_domain() automatically
# performs conversion to the target domain. It shouldn't do this.
coeffs = sum([list(rep.values()) for rep in reps], [])
opt.domain, _ = construct_domain(coeffs, opt=opt)
_field = FracField(opt.gens, opt.domain, opt.order)
fracs = []
for i in range(0, len(reps), 2):
fracs.append(_field(tuple(reps[i:i+2])))
if single:
return (_field, fracs[0])
else:
return (_field, fracs)
def _sort_gens(gens, **args):
"""Sort generators in a reasonably intelligent way. """
opt = build_options(args)
gens_order, wrt = {}, None
if opt is not None:
gens_order, wrt = {}, opt.wrt
for i, gen in enumerate(opt.sort):
gens_order[gen] = i + 1
def order_key(gen):
gen = str(gen)
if wrt is not None:
try:
return (-len(wrt) + wrt.index(gen), gen, 0)
except ValueError:
pass
name, index = _re_gen.match(gen).groups()
if index:
index = int(index)
else:
index = 0
try:
return (gens_order[name], name, index)
except KeyError:
pass
try:
return (_gens_order[name], name, index)
except KeyError:
pass
return (_max_order, name, index)
try:
gens = sorted(gens, key=order_key)
except TypeError: # pragma: no cover
pass
return tuple(gens)
def _sort_gens(gens, **args):
"""Sort generators in a reasonably intelligent way. """
opt = build_options(args)
gens_order, wrt = {}, None
if opt is not None:
gens_order, wrt = {}, opt.wrt
for i, gen in enumerate(opt.sort):
gens_order[gen] = i + 1
def order_key(gen):
gen = str(gen)
if wrt is not None:
try:
return (-len(wrt) + wrt.index(gen), gen, 0)
except ValueError:
pass
name, index = _re_gen.match(gen).groups()
if index:
index = int(index)
else:
index = 0
try:
return ( gens_order[name], name, index)
except KeyError:
pass
try:
return (_gens_order[name], name, index)
except KeyError:
pass
return (_max_order, name, index)
try:
gens = sorted(gens, key=order_key)
except TypeError: # pragma: no cover
pass
return tuple(gens)
def construct_domain(obj, **args):
"""Construct a minimal domain for the list of coefficients. """
opt = build_options(args)
if hasattr(obj, '__iter__'):
if isinstance(obj, dict):
if not obj:
monoms, coeffs = [], []
else:
monoms, coeffs = list(zip(*list(obj.items())))
else:
coeffs = obj
else:
coeffs = [obj]
coeffs = list(map(sympify, coeffs))
result = _construct_simple(coeffs, opt)
if result is not None:
if result is not False:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
else:
if opt.composite is False:
result = None
else:
result = _construct_composite(coeffs, opt)
if result is not None:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
if hasattr(obj, '__iter__'):
if isinstance(obj, dict):
return domain, dict(list(zip(monoms, coeffs)))
else:
return domain, coeffs
else:
return domain, coeffs[0]
def construct_domain(obj, **args):
"""Construct a minimal domain for the list of coefficients. """
opt = build_options(args)
if hasattr(obj, '__iter__'):
if isinstance(obj, dict):
if not obj:
monoms, coeffs = [], []
else:
monoms, coeffs = list(zip(*list(obj.items())))
else:
coeffs = obj
else:
coeffs = [obj]
coeffs = list(map(sympify, coeffs))
result = _construct_simple(coeffs, opt)
if result is not None:
if result is not False:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
else:
if opt.composite is False:
result = None
else:
result = _construct_composite(coeffs, opt)
if result is not None:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
if hasattr(obj, '__iter__'):
if isinstance(obj, dict):
return domain, dict(list(zip(monoms, coeffs)))
else:
return domain, coeffs
else:
return domain, coeffs[0]
def dict_from_expr(expr, **args):
"""Transform an expression into a multinomial form. """
rep, opt = _dict_from_expr(expr, build_options(args))
return rep, opt.gens
def parallel_dict_from_expr(exprs, **args):
"""Transform expressions into a multinomial form. """
reps, opt = _parallel_dict_from_expr(exprs, build_options(args))
return reps, opt.gens
def dict_from_expr(expr, **args):
"""Transform an expression into a multinomial form. """
rep, opt = _dict_from_expr(expr, build_options(args))
return rep, opt.gens
def parallel_dict_from_expr(exprs, **args):
"""Transform expressions into a multinomial form. """
reps, opt = _parallel_dict_from_expr(exprs, build_options(args))
return reps, opt.gens
def construct_domain(obj, **args):
"""Construct a minimal domain for a list of expressions.
Explanation
===========
Given a list of normal SymPy expressions (of type :py:class:`~.Expr`)
``construct_domain`` will find a minimal :py:class:`~.Domain` that can
represent those expressions. The expressions will be converted to elements
of the domain and both the domain and the domain elements are returned.
Parameters
==========
obj: list or dict
The expressions to build a domain for.
**args: keyword arguments
Options that affect the choice of domain.
Returns
=======
(K, elements): Domain and list of domain elements
The domain K that can represent the expressions and the list or dict
of domain elements representing the same expressions as elements of K.
Examples
========
Given a list of :py:class:`~.Integer` ``construct_domain`` will return the
domain :ref:`ZZ` and a list of integers as elements of :ref:`ZZ`.
>>> from sympy import construct_domain, S
>>> expressions = [S(2), S(3), S(4)]
>>> K, elements = construct_domain(expressions)
>>> K
ZZ
>>> elements
[2, 3, 4]
>>> type(elements[0]) # doctest: +SKIP
<class 'int'>
>>> type(expressions[0])
<class 'sympy.core.numbers.Integer'>
If there are any :py:class:`~.Rational` then :ref:`QQ` is returned
instead.
>>> construct_domain([S(1)/2, S(3)/4])
(QQ, [1/2, 3/4])
If there are symbols then a polynomial ring :ref:`K[x]` is returned.
>>> from sympy import symbols
>>> x, y = symbols('x, y')
>>> construct_domain([2*x + 1, S(3)/4])
(QQ[x], [2*x + 1, 3/4])
>>> construct_domain([2*x + 1, y])
(ZZ[x,y], [2*x + 1, y])
If any symbols appear with negative powers then a rational function field
:ref:`K(x)` will be returned.
>>> construct_domain([y/x, x/(1 - y)])
(ZZ(x,y), [y/x, -x/(y - 1)])
Irrational algebraic numbers will result in the :ref:`EX` domain by
default. The keyword argument ``extension=True`` leads to the construction
of an algebraic number field :ref:`QQ(a)`.
>>> from sympy import sqrt
>>> construct_domain([sqrt(2)])
(EX, [EX(sqrt(2))])
>>> construct_domain([sqrt(2)], extension=True) # doctest: +SKIP
(QQ<sqrt(2)>, [ANP([1, 0], [1, 0, -2], QQ)])
See also
========
Domain
Expr
"""
opt = build_options(args)
if hasattr(obj, '__iter__'):
if isinstance(obj, dict):
if not obj:
monoms, coeffs = [], []
else:
monoms, coeffs = list(zip(*list(obj.items())))
else:
coeffs = obj
else:
coeffs = [obj]
coeffs = list(map(sympify, coeffs))
result = _construct_simple(coeffs, opt)
if result is not None:
if result is not False:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
else:
if opt.composite is False:
result = None
else:
result = _construct_composite(coeffs, opt)
if result is not None:
domain, coeffs = result
else:
domain, coeffs = _construct_expression(coeffs, opt)
if hasattr(obj, '__iter__'):
if isinstance(obj, dict):
return domain, dict(list(zip(monoms, coeffs)))
else:
return domain, coeffs
else:
return domain, coeffs[0]