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

random(shape=(1,))

random_element(*args, **kwargs)

set(*args): (name, characteristic, digits)

property singular_notation

sqrt(val)

property tollerance

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.

property variables

zero_ideal(): Returns the zero ideal ⟨0⟩ in the ring.

syngular.qring

syngular.qring.QRing: alias of QuotientRing

class syngular.qring.QuotientRing(ring, ideal)

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)

property groebner_basis

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.

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