def prepare_indeterminates(names, ctx, coeffring=None):
"""
From space separated names of indeterminates, prepare variables
representing the indeterminates. The result will be stored in ctx
dictionary.
The variables should be prepared at once, otherwise wrong aliases
of variables may confuse you in later calculation.
If an optional coeffring is not given, indeterminates will be
initialized as integer coefficient polynomials.
Example:
>>> prepare_indeterminates("X Y Z", globals())
>>> Y
UniqueFactorizationDomainPolynomial({(0, 1, 0): 1})
"""
split_names = names.split()
number_of_variables = len(split_names)
if coeffring is None:
coeffring = uniutil.init_coefficient_ring({1:1})
for i, name in enumerate(split_names):
e_i = tuple([0] * i + [1] + [0] * (number_of_variables - i - 1))
ctx[name] = polynomial({e_i: 1}, coeffring, number_of_variables)
def __init__(self, coefficients, **kwds):
"""
Initialize the polynomial.
Required argument:
- coefficients: initializer for polynomial coefficients
Keyword arguments should include:
- coeffring: domain
- number_of_variables: the number of variables
"""
if "number_of_variables" not in kwds:
coefficients = dict(coefficients)
for i in coefficients.keys():
kwds["number_of_variables"] = len(i)
break
multivar.BasicPolynomial.__init__(self, coefficients, **kwds)
NestProvider.__init__(self)
PseudoDivisionProvider.__init__(self)
RingElementProvider.__init__(self)
coeffring = None
if "coeffring" in kwds:
coeffring = kwds["coeffring"]
else:
coeffring = uniutil.init_coefficient_ring(self._coefficients)
if coeffring is not None:
self.set_coefficient_ring(coeffring)
else:
raise TypeError("argument `coeffring' is required")
if "order" in kwds:
order = kwds["order"]
else:
order = termorder.lexicographic_order
OrderProvider.__init__(self, order)
def prepare_indeterminates(names, ctx, coeffring=None):
"""
From space separated names of indeterminates, prepare variables
representing the indeterminates. The result will be stored in ctx
dictionary.
The variables should be prepared at once, otherwise wrong aliases
of variables may confuse you in later calculation.
If an optional coeffring is not given, indeterminates will be
initialized as integer coefficient polynomials.
Example:
>>> prepare_indeterminates("X Y Z", globals())
>>> Y
UniqueFactorizationDomainPolynomial({(0, 1, 0): 1})
"""
split_names = names.split()
number_of_variables = len(split_names)
if coeffring is None:
coeffring = uniutil.init_coefficient_ring({1:1})
for i, name in enumerate(split_names):
e_i = tuple([0] * i + [1] + [0] * (number_of_variables - i - 1))
ctx[name] = polynomial({e_i: 1}, coeffring, number_of_variables)
def __init__(self, coefficients, **kwds):
"""
Initialize the polynomial.
Required argument:
- coefficients: initializer for polynomial coefficients
Keyword arguments should include:
- coeffring: domain
- number_of_variables: the number of variables
"""
if "number_of_variables" not in kwds:
coefficients = dict(coefficients)
for i in coefficients.iterkeys():
kwds["number_of_variables"] = len(i)
break
multivar.BasicPolynomial.__init__(self, coefficients, **kwds)
NestProvider.__init__(self)
PseudoDivisionProvider.__init__(self)
RingElementProvider.__init__(self)
coeffring = None
if "coeffring" in kwds:
coeffring = kwds["coeffring"]
else:
coeffring = uniutil.init_coefficient_ring(self._coefficients)
if coeffring is not None:
self.set_coefficient_ring(coeffring)
else:
raise TypeError("argument `coeffring' is required")
if "order" in kwds:
order = kwds["order"]
else:
order = termorder.lexicographic_order
OrderProvider.__init__(self, order)
def MultiVariableSparsePolynomial(coefficient, variable, coeffring=None):
"""
MultiVariableSparsePolynomial(coefficient, variable [,coeffring])
- coefficient has to be a dictionary of form {(i1,...,ik): c}
- variable has to be a list of character strings.
- coeffring has to be, if specified, an object inheriting ring.Ring.
This function is provided for backward compatible way of defining
multivariate polynomial. The variable names are ignored, but
their number is used.
"""
if not isinstance(variable, list) or not isinstance(coefficient, dict):
raise ValueError("You must input MultiVariableSparsePolynomial(dict, list) but (%s, %s)." % (coefficient.__class__, variable.__class__))
if coeffring is None:
coeffring = uniutil.init_coefficient_ring(coefficient)
return polynomial(coefficient, coeffring=coeffring, number_of_variables=len(variable))
def MultiVariableSparsePolynomial(coefficient, variable, coeffring=None):
"""
MultiVariableSparsePolynomial(coefficient, variable [,coeffring])
- coefficient has to be a dictionary of form {(i1,...,ik): c}
- variable has to be a list of character strings.
- coeffring has to be, if specified, an object inheriting ring.Ring.
This function is provided for backward compatible way of defining
multivariate polynomial. The variable names are ignored, but
their number is used.
"""
if not isinstance(variable, list) or not isinstance(coefficient, dict):
raise ValueError("You must input MultiVariableSparsePolynomial(dict, list) but (%s, %s)." % (coefficient.__class__, variable.__class__))
if coeffring is None:
coeffring = uniutil.init_coefficient_ring(coefficient)
return polynomial(coefficient, coeffring=coeffring, number_of_variables=len(variable))
