syngular.field
- class syngular.field.Field(*args)
A class representing number fields.
- property I
- property characteristic
- property digits
- epsilon(shape=(1,))
- property i
- property is_algebraically_closed
- property j
- property name
- property one
- random(shape=(1,))
- random_element(*args, **kwargs)
- random_square()
- set(*args)
(name, characteristic, digits)
- property singular_notation
- sqrt(val)
- property tollerance
- property zero
- property ε
syngular.ring
- class syngular.ring.Ring(field, variables, ordering)
- property field
- property ordering
Monomial ordering
- random_point(field, seed=None)
Returns a random numerical point in the given field on the zero ideal of the ring.
- test_valid_ring()
- unit_ideal()
Returns the unit ideal ⟨1⟩ in the ring.
- univariate_slice(field, extra_approximate_constraints=(), indepSet=None, seed=None, verbose=False)
- property variables
- zero_ideal()
Returns the zero ideal ⟨0⟩ in the ring.
syngular.qring
- syngular.qring.QRing
alias of
QuotientRing
syngular.ideal
- class syngular.ideal.Ideal(ring, generators)
- property codim
- property codims
- delete_cached_properties()
- property dim
- property dims
- eliminate(var_range)
- property generators
- generators_eval(**kwargs)
- get_groebner_basis(reduced=False, algorithm='slimgb')
- property groebner_basis
- guess_indep_set()
Guesses an independent set, you can provide codim_upper_bound attribute to help.
- property indepSet
- property indepSets
- static intersection(*args)
Intersection of Ideals - wrapper around & operator for chained intersection.
- property is_unit_ideal
- property leadGBmonomials
Gives the leading monomials of the Groebner basis polynomials.
- property minbase
- property primary_decomposition
- property radical
Returns the radical of the ideal.
- reduce(other)
Remainder of division, i.e. reduction.
- property reduced_groebner_basis
- saturation(other)
Saturation of ideals (self : other^∞), returns both saturation ideal and saturation index.
- saturation_index(other)
Saturation of ideals (self : other^∞), returns only the saturation index.
- squash()
- squoosh()
- test_valid_ideal()
- to_full_ring()
- to_qring(other)
- syngular.ideal.monomial_to_exponents(variables, monomial)
Converts a monomial in the variables of a polynomial ring into a numpy.array of exponents.
- syngular.ideal.reduce(poly, ideal)
Module contents
- class syngular.Field(*args)
A class representing number fields.
- property I
- property characteristic
- property digits
- epsilon(shape=(1,))
- property i
- property is_algebraically_closed
- property j
- property name
- property one
- random(shape=(1,))
- random_element(*args, **kwargs)
- random_square()
- set(*args)
(name, characteristic, digits)
- property singular_notation
- sqrt(val)
- property tollerance
- property zero
- property ε
- class syngular.Ideal(ring, generators)
- property codim
- property codims
- delete_cached_properties()
- property dim
- property dims
- eliminate(var_range)
- property generators
- generators_eval(**kwargs)
- get_groebner_basis(reduced=False, algorithm='slimgb')
- property groebner_basis
- guess_indep_set()
Guesses an independent set, you can provide codim_upper_bound attribute to help.
- property indepSet
- property indepSets
- static intersection(*args)
Intersection of Ideals - wrapper around & operator for chained intersection.
- property is_unit_ideal
- property leadGBmonomials
Gives the leading monomials of the Groebner basis polynomials.
- property minbase
- property primary_decomposition
- property radical
Returns the radical of the ideal.
- reduce(other)
Remainder of division, i.e. reduction.
- property reduced_groebner_basis
- saturation(other)
Saturation of ideals (self : other^∞), returns both saturation ideal and saturation index.
- saturation_index(other)
Saturation of ideals (self : other^∞), returns only the saturation index.
- squash()
- squoosh()
- test_valid_ideal()
- to_full_ring()
- to_qring(other)
- class syngular.Monomial(*_)
A FrozenMultiset representation of a Monomial. Positive integer multiplicities represent powers.
- as_exps_list(ring)
Converts the monomial into an array of exponents w.r.t. variables in ring.
- property exps
- property invs
- subs(values_dict)
- tolist()
- property variables
- class syngular.Polynomial(coeffs_and_monomials, field)
Generalization of the concept of Multiset where multiplicities are in an arbitrary Field and the elements are Monomials.
- property coeffs
- property coeffs_and_monomials
- property field
- property lead_monomial
- property lead_term
- property lexps
- property linvs
- property monomials
- rationalise()
- reduce()
Merges equal monomials
- subs(base_point, field=None)
- property variables
- syngular.QRing
alias of
QuotientRing
- class syngular.Ring(field, variables, ordering)
- property field
- property ordering
Monomial ordering
- random_point(field, seed=None)
Returns a random numerical point in the given field on the zero ideal of the ring.
- test_valid_ring()
- unit_ideal()
Returns the unit ideal ⟨1⟩ in the ring.
- univariate_slice(field, extra_approximate_constraints=(), indepSet=None, seed=None, verbose=False)
- property variables
- zero_ideal()
Returns the zero ideal ⟨0⟩ in the ring.
- class syngular.RingPoint(ring, field, seed=None, val=None)
Represents a numerical or semi-numerical point on a variety within the space defiend by the ring. Generalizes the idea of a phase space point from particle physics.
- copy() a shallow copy of D
- singular_variety(directions_or_ideal=None, valuations=(), seed=None, verbose=False)
- subs(myDict)
- univariate_slice(extra_approximate_constraints=(), indepSet=None, seed=None, verbose=False)
- exception syngular.SingularException
- class syngular.TemporarySetting(module_or_module_name, setting_name, new_value)