NZMATH  1.2.0
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Public Member Functions | List of all members
nzmath.poly.formalsum.FormalSumContainerInterface Class Reference
Inheritance diagram for nzmath.poly.formalsum.FormalSumContainerInterface:
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Collaboration diagram for nzmath.poly.formalsum.FormalSumContainerInterface:
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Public Member Functions

def __iter__ (self)
 
def __getitem__ (self, base)
 
def __contains__ (self, base)
 
def __len__ (self)
 
def __eq__ (self, other)
 
def __hash__ (self)
 
def __ne__ (self, other)
 
def __nonzero__ (self)
 
def __hash__ (self)
 
def __add__ (self, other)
 
def __sub__ (self, other)
 
def __neg__ (self)
 
def __pos__ (self)
 
def __mul__ (self, other)
 
def __rmul__ (self, other)
 
def iterterms (self)
 
def itercoefficients (self)
 
def iterbases (self)
 
def terms (self)
 
def coefficients (self)
 
def bases (self)
 
def terms_map (self, func)
 
def coefficients_map (self, func)
 
def bases_map (self, func)
 
def construct_with_default (self, maindata)
 

Detailed Description

Interface of formal sum container.
Do not instantiate.

Definition at line 39 of file formalsum.py.

Member Function Documentation

◆ __add__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__add__ (   self,
  other 
) 
self + other

Reimplemented in nzmath.poly.uniutil.RingPolynomial, nzmath.poly.univar.SortedPolynomial, nzmath.poly.multiutil.RingPolynomial, and nzmath.poly.univar.BasicPolynomial.

Definition at line 121 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.construct_with_default(), and nzmath.poly.formalsum.FormalSumContainerInterface.iterterms().

◆ __contains__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__contains__ (   self,
  base 
) 
base in self

membership test.

Reimplemented in nzmath.poly.univar.SortedPolynomial, and nzmath.poly.univar.BasicPolynomial.

Definition at line 58 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.bases().

◆ __eq__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__eq__ (   self,
  other 
) 
self == other

This implementaion is not optimal for more structured
descendants.

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.univar.BasicPolynomial, nzmath.poly.formalsum.DictFormalSum, and nzmath.poly.univar.PolynomialInterface.

Definition at line 72 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.iterbases().

Referenced by nzmath.poly.multivar.TermIndices.__ne__(), nzmath.poly.ring.PolynomialRing.__ne__(), nzmath.quad.ReducedQuadraticForm.__ne__(), nzmath.ring.Ring.__ne__(), nzmath.poly.formalsum.FormalSumContainerInterface.__ne__(), nzmath.real.RealField.__ne__(), nzmath.ring.Ideal.__ne__(), and nzmath.prime.FactoredInteger.__ne__().

◆ __getitem__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__getitem__ (   self,
  base 
) 
Return the coefficient of specified base.
If there is no term of the base, return 0.

Reimplemented in nzmath.poly.multivar.BasicPolynomial, nzmath.poly.uniutil.RingPolynomial, nzmath.poly.univar.SortedPolynomial, nzmath.poly.univar.BasicPolynomial, nzmath.poly.formalsum.ListFormalSum, and nzmath.poly.formalsum.DictFormalSum.

Definition at line 51 of file formalsum.py.

◆ __hash__() [1/2]

def nzmath.poly.formalsum.FormalSumContainerInterface.__hash__ (   self)

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.univar.BasicPolynomial, nzmath.poly.multivar.BasicPolynomial, nzmath.poly.formalsum.DictFormalSum, and nzmath.poly.univar.PolynomialInterface.

Definition at line 92 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.iterbases().

Referenced by nzmath.poly.formalsum.FormalSumContainerInterface.__hash__().

◆ __hash__() [2/2]

def nzmath.poly.formalsum.FormalSumContainerInterface.__hash__ (   self) 
hash(self)

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.univar.BasicPolynomial, nzmath.poly.multivar.BasicPolynomial, nzmath.poly.formalsum.DictFormalSum, and nzmath.poly.univar.PolynomialInterface.

Definition at line 112 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.__hash__().

◆ __iter__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__iter__ (   self) 
Return the iterator.
It is an alias of iterterms.

Definition at line 44 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.iterterms().

◆ __len__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__len__ (   self) 
Return the number of data entries.

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.multivar.BasicPolynomial, nzmath.poly.formalsum.DictFormalSum, and nzmath.poly.univar.BasicPolynomial.

Definition at line 66 of file formalsum.py.

◆ __mul__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__mul__ (   self,
  other 
) 
self * other

Only scalar multiplication is defined.

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.formalsum.DictFormalSum, nzmath.poly.multivar.BasicPolynomial, and nzmath.poly.univar.BasicPolynomial.

Definition at line 157 of file formalsum.py.

◆ __ne__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__ne__ (   self,
  other 
) 
self != other

Definition at line 96 of file formalsum.py.

References nzmath.group.Group.__eq__(), nzmath.poly.formalsum.FormalSumContainerInterface.__eq__(), nzmath.factor.misc.FactoredInteger.__eq__(), nzmath.imaginary.Complex.__eq__(), nzmath.poly.array.ArrayPoly.__eq__(), nzmath.group.GroupElement.__eq__(), nzmath.matrix.Matrix.__eq__(), nzmath.intresidue.IntegerResidueClass.__eq__(), nzmath.finitefield.FinitePrimeField.__eq__(), nzmath.imaginary.ComplexField.__eq__(), nzmath.poly.array.ArrayPolyMod.__eq__(), nzmath.module.Module.__eq__(), nzmath.permute.Permute.__eq__(), nzmath.intresidue.IntegerResidueClassRing.__eq__(), nzmath.algfield.NumberField.__eq__(), nzmath.finitefield.ExtendedFieldElement.__eq__(), nzmath.permute.ExPermute.__eq__(), nzmath.permute.PermGroup.__eq__(), nzmath.finitefield.ExtendedField.__eq__(), and nzmath.matrix.MatrixRing.__eq__().

◆ __neg__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__neg__ (   self) 
-self

Reimplemented in nzmath.poly.formalsum.ListFormalSum, nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.DictFormalSum, nzmath.poly.univar.BasicPolynomial, and nzmath.poly.multivar.PolynomialInterface.

Definition at line 145 of file formalsum.py.

◆ __nonzero__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__nonzero__ (   self) 
Return True, if self has some nonzero coefficients.
False, otherwise.

Definition at line 102 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.itercoefficients().

◆ __pos__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__pos__ (   self) 
+self

Reimplemented in nzmath.poly.formalsum.ListFormalSum, nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.DictFormalSum, nzmath.poly.univar.BasicPolynomial, and nzmath.poly.multivar.PolynomialInterface.

Definition at line 151 of file formalsum.py.

◆ __rmul__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__rmul__ (   self,
  other 
) 
other * self

This method is invoked only when type of other does not
support multiplication with FormalSumContainerInterface

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.formalsum.DictFormalSum, nzmath.poly.multivar.BasicPolynomial, and nzmath.poly.univar.BasicPolynomial.

Definition at line 165 of file formalsum.py.

◆ __sub__()

def nzmath.poly.formalsum.FormalSumContainerInterface.__sub__ (   self,
  other 
) 
self - other

Reimplemented in nzmath.poly.uniutil.RingPolynomial, nzmath.poly.univar.SortedPolynomial, nzmath.poly.multiutil.RingPolynomial, and nzmath.poly.univar.BasicPolynomial.

Definition at line 133 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.construct_with_default(), and nzmath.poly.formalsum.FormalSumContainerInterface.iterterms().

◆ bases()

def nzmath.poly.formalsum.FormalSumContainerInterface.bases (   self) 
Return a list of all bases.

Definition at line 204 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.iterbases().

Referenced by nzmath.poly.formalsum.FormalSumContainerInterface.__contains__().

◆ bases_map()

def nzmath.poly.formalsum.FormalSumContainerInterface.bases_map (   self,
  func 
) 
Create a new formal sum container by applying func to each
base.

Definition at line 229 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.terms_map().

Referenced by nzmath.poly.univar.PolynomialInterface.downshift_degree(), and nzmath.poly.univar.PolynomialInterface.upshift_degree().

◆ coefficients()

def nzmath.poly.formalsum.FormalSumContainerInterface.coefficients (   self) 
Return a list of all coefficients.

Definition at line 198 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.itercoefficients().

◆ coefficients_map()

def nzmath.poly.formalsum.FormalSumContainerInterface.coefficients_map (   self,
  func 
) 
Create a new formal sum container by applying func to each
coefficient.

Definition at line 222 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.terms_map().

Referenced by nzmath.poly.formalsum.DictFormalSum.rscalar_mul(), nzmath.poly.formalsum.ListFormalSum.rscalar_mul(), nzmath.poly.uniutil.DivisionProvider.scalar_exact_division(), nzmath.poly.uniutil.PseudoDivisionProvider.scalar_exact_division(), nzmath.poly.formalsum.DictFormalSum.scalar_mul(), and nzmath.poly.formalsum.ListFormalSum.scalar_mul().

◆ construct_with_default()

def nzmath.poly.formalsum.FormalSumContainerInterface.construct_with_default (   self,
  maindata 
) 
Create a new formal sum container of the same class with self,
with given only the maindata and use copy of self's data if
necessary.

Reimplemented in nzmath.poly.univar.PolynomialInterface, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.multivar.BasicPolynomial, and nzmath.poly.formalsum.DictFormalSum.

Definition at line 236 of file formalsum.py.

Referenced by nzmath.poly.formalsum.FormalSumContainerInterface.__add__(), nzmath.poly.univar.BasicPolynomial.__add__(), nzmath.poly.univar.SortedPolynomial.__add__(), nzmath.poly.uniutil.DivisionProvider.__divmod__(), nzmath.poly.uniutil.DivisionProvider.__floordiv__(), nzmath.poly.multivar.PolynomialInterface.__neg__(), nzmath.poly.univar.BasicPolynomial.__neg__(), nzmath.poly.formalsum.DictFormalSum.__neg__(), nzmath.poly.univar.SortedPolynomial.__neg__(), nzmath.poly.formalsum.ListFormalSum.__neg__(), nzmath.poly.multivar.PolynomialInterface.__pos__(), nzmath.poly.univar.BasicPolynomial.__pos__(), nzmath.poly.formalsum.DictFormalSum.__pos__(), nzmath.poly.univar.SortedPolynomial.__pos__(), nzmath.poly.formalsum.ListFormalSum.__pos__(), nzmath.poly.univar.BasicPolynomial.__pow__(), nzmath.poly.multivar.BasicPolynomial.__pow__(), nzmath.poly.univar.SortedPolynomial.__pow__(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.__pow__(), nzmath.poly.formalsum.FormalSumContainerInterface.__sub__(), nzmath.poly.univar.BasicPolynomial.__sub__(), nzmath.poly.univar.SortedPolynomial.__sub__(), nzmath.poly.uniutil.DivisionProvider._populate_reduced(), nzmath.poly.multivar.BasicPolynomial.combine_similar_terms(), nzmath.poly.univar.PolynomialInterface.differentiate(), nzmath.poly.uniutil.DivisionProvider.mod(), nzmath.poly.uniutil.DivisionProvider.mod_pow(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_divmod(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_floordiv(), nzmath.poly.uniutil.PseudoDivisionProvider.monic_mod(), nzmath.poly.multivar.BasicPolynomial.partial_differentiate(), nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_divmod(), nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_floordiv(), nzmath.poly.uniutil.PseudoDivisionProvider.pseudo_mod(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.pthroot(), nzmath.poly.univar.PolynomialInterface.ring_mul(), nzmath.poly.multivar.BasicPolynomial.ring_mul(), nzmath.poly.uniutil.FinitePrimeFieldPolynomial.ring_mul(), nzmath.poly.univar.SortedPolynomial.ring_mul_karatsuba(), nzmath.poly.uniutil.KaratsubaProvider.ring_mul_karatsuba(), nzmath.poly.univar.PolynomialInterface.scalar_mul(), nzmath.poly.multivar.BasicPolynomial.scalar_mul(), nzmath.poly.univar.SortedPolynomial.scalar_mul(), nzmath.poly.uniutil.OrderProvider.shift_degree_to(), nzmath.poly.uniutil.OrderProvider.split_at(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.split_same_degrees(), nzmath.poly.univar.BasicPolynomial.square(), nzmath.poly.multivar.BasicPolynomial.square(), nzmath.poly.univar.SortedPolynomial.square(), nzmath.poly.uniutil.FinitePrimeFieldPolynomial.square(), nzmath.poly.uniutil.KaratsubaProvider.square_karatsuba(), nzmath.poly.univar.PolynomialInterface.term_mul(), nzmath.poly.multivar.BasicPolynomial.term_mul(), nzmath.poly.univar.PolynomialInterface.terms_map(), and nzmath.poly.formalsum.FormalSumContainerInterface.terms_map().

◆ iterbases()

def nzmath.poly.formalsum.FormalSumContainerInterface.iterbases (   self) 
iterator for degrees.

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.multivar.BasicPolynomial, nzmath.poly.formalsum.DictFormalSum, and nzmath.poly.univar.BasicPolynomial.

Definition at line 186 of file formalsum.py.

Referenced by nzmath.poly.formalsum.FormalSumContainerInterface.__eq__(), nzmath.poly.formalsum.FormalSumContainerInterface.__hash__(), nzmath.poly.formalsum.FormalSumContainerInterface.bases(), and nzmath.poly.multivar.PolynomialInterface.total_degree().

◆ itercoefficients()

def nzmath.poly.formalsum.FormalSumContainerInterface.itercoefficients (   self) 
iterator for coefficients.

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.multivar.BasicPolynomial, nzmath.poly.formalsum.DictFormalSum, and nzmath.poly.univar.BasicPolynomial.

Definition at line 180 of file formalsum.py.

Referenced by nzmath.poly.formalsum.FormalSumContainerInterface.__nonzero__(), nzmath.poly.univar.BasicPolynomial.__pow__(), nzmath.poly.univar.SortedPolynomial.__pow__(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.__pow__(), nzmath.poly.uniutil.DivisionProvider._populate_reduced(), nzmath.poly.formalsum.FormalSumContainerInterface.coefficients(), nzmath.poly.uniutil.ContentProvider.content(), nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.distinct_degree_factorization(), nzmath.poly.multiutil.RingElementProvider.getRing(), nzmath.poly.uniutil.RingElementProvider.getRing(), and nzmath.poly.uniutil.PrimeCharacteristicFunctionsProvider.split_same_degrees().

◆ iterterms()

def nzmath.poly.formalsum.FormalSumContainerInterface.iterterms (   self) 
iterator for (degree, coefficient) pairs.

Reimplemented in nzmath.poly.univar.SortedPolynomial, nzmath.poly.formalsum.ListFormalSum, nzmath.poly.multivar.BasicPolynomial, nzmath.poly.formalsum.DictFormalSum, and nzmath.poly.univar.BasicPolynomial.

Definition at line 174 of file formalsum.py.

Referenced by nzmath.poly.formalsum.FormalSumContainerInterface.__add__(), nzmath.poly.univar.PolynomialInterface.__eq__(), nzmath.poly.univar.PolynomialInterface.__hash__(), nzmath.poly.formalsum.FormalSumContainerInterface.__iter__(), nzmath.poly.formalsum.FormalSumContainerInterface.__sub__(), nzmath.poly.formalsum.FormalSumContainerInterface.terms(), and nzmath.poly.uniutil.DomainPolynomial.to_field_polynomial().

◆ terms()

def nzmath.poly.formalsum.FormalSumContainerInterface.terms (   self) 
Return a list of terms as (base, coefficient) pairs.

Definition at line 192 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.iterterms().

Referenced by nzmath.poly.uniutil.RingPolynomial.__repr__(), and nzmath.poly.univar.BasicPolynomial.square().

◆ terms_map()

def nzmath.poly.formalsum.FormalSumContainerInterface.terms_map (   self,
  func 
) 
Create a new formal sum container by applying func to each
term.  func must be a function taking 2 arguments.

Reimplemented in nzmath.poly.univar.PolynomialInterface.

Definition at line 210 of file formalsum.py.

References nzmath.poly.formalsum.FormalSumContainerInterface.construct_with_default().

Referenced by nzmath.poly.formalsum.FormalSumContainerInterface.bases_map(), and nzmath.poly.formalsum.FormalSumContainerInterface.coefficients_map().

The documentation for this class was generated from the following file: