Index

A | B | C | D | E | F | G | H | I | K | L | M | N | O | P | Q | R | S | T | U | V | Z

A

absolute_norm() (sage.rings.ideal.Ideal_generic method)
Algebra (class in sage.rings.ring)
algebraic_closure() (sage.rings.ring.Field method)
ambient() (sage.rings.quotient_ring.QuotientRing_nc method)
AnInfinity (class in sage.rings.infinity)
apply_morphism() (sage.rings.ideal.Ideal_generic method)
associated_primes() (sage.rings.ideal.Ideal_generic method)

B

base_extend() (sage.rings.ring.Ring method)
base_ring() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.ideal.Ideal_generic method)

C

cardinality() (sage.rings.ring.Ring method)
category() (sage.rings.ideal.Ideal_generic method)
(sage.rings.ring.Ring method)
characteristic() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.quotient_ring.QuotientRing_nc method)
(sage.rings.ring.Algebra method)
class_group() (sage.rings.ring.PrincipalIdealDomain method)
class_number() (sage.rings.fraction_field.FractionField_1poly_field method)
CommutativeAlgebra (class in sage.rings.ring)
CommutativeRing (class in sage.rings.ring)
composite_field() (in module sage.rings.misc)
construction() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.quotient_ring.QuotientRing_nc method)
content() (sage.rings.ring.PrincipalIdealDomain method)
cover() (sage.rings.quotient_ring.QuotientRing_nc method)
cover_ring() (sage.rings.quotient_ring.QuotientRing_nc method)
Cyclic() (in module sage.rings.ideal)

D

DedekindDomain (class in sage.rings.ring)
defining_ideal() (sage.rings.quotient_ring.QuotientRing_nc method)
denominator() (sage.rings.fraction_field_element.FractionFieldElement method)
divides() (sage.rings.ideal.Ideal_principal method)
(sage.rings.ring.Field method)

E

Element (sage.rings.ideal_monoid.IdealMonoid_c attribute)
(sage.rings.quotient_ring.QuotientRing_nc attribute)
embedded_primes() (sage.rings.ideal.Ideal_generic method)
epsilon() (sage.rings.ring.Ring method)
EuclideanDomain (class in sage.rings.ring)
extension() (sage.rings.ring.CommutativeRing method)

F

Field (class in sage.rings.ring)
FieldIdeal() (in module sage.rings.ideal)
FiniteNumber (class in sage.rings.infinity)
fraction_field() (sage.rings.infinity.InfinityRing_class method)
(sage.rings.infinity.UnsignedInfinityRing_class method)
(sage.rings.ring.CommutativeRing method)
(sage.rings.ring.Field method)
FractionField() (in module sage.rings.fraction_field)
FractionField_1poly_field (class in sage.rings.fraction_field)
FractionField_generic (class in sage.rings.fraction_field)
FractionFieldElement (class in sage.rings.fraction_field_element)
FractionFieldElement_1poly_field (class in sage.rings.fraction_field_element)
frobenius_endomorphism() (sage.rings.ring.CommutativeRing method)
FrobeniusEndomorphism_generic (class in sage.rings.morphism)

G

gcd() (sage.rings.ideal.Ideal_pid method)
(sage.rings.ring.PrincipalIdealDomain method)
gen() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.ideal.Ideal_generic method)
(sage.rings.ideal.Ideal_principal method)
(sage.rings.infinity.InfinityRing_class method)
(sage.rings.infinity.UnsignedInfinityRing_class method)
(sage.rings.quotient_ring.QuotientRing_nc method)
gens() (sage.rings.ideal.Ideal_generic method)
(sage.rings.infinity.InfinityRing_class method)
(sage.rings.infinity.UnsignedInfinityRing_class method)
gens_reduced() (sage.rings.ideal.Ideal_generic method)

H

has_coerce_map_from() (sage.rings.homset.RingHomset_generic method)
has_standard_involution() (sage.rings.ring.Algebra method)

I

Ideal() (in module sage.rings.ideal)
ideal() (sage.rings.quotient_ring.QuotientRing_nc method)
(sage.rings.ring.Field method)
(sage.rings.ring.Ring method)
Ideal_fractional (class in sage.rings.ideal)
Ideal_generic (class in sage.rings.ideal)
ideal_monoid() (sage.rings.ring.CommutativeRing method)
(sage.rings.ring.Ring method)
Ideal_nc (class in sage.rings.noncommutative_ideals)
Ideal_pid (class in sage.rings.ideal)
Ideal_principal (class in sage.rings.ideal)
IdealMonoid() (in module sage.rings.ideal_monoid)
IdealMonoid_c (class in sage.rings.ideal_monoid)
IdealMonoid_nc (class in sage.rings.noncommutative_ideals)
im_gens() (sage.rings.morphism.RingHomomorphism_im_gens method)
InfinityRing_class (class in sage.rings.infinity)
integral_closure() (sage.rings.ring.DedekindDomain method)
(sage.rings.ring.Field method)
IntegralDomain (class in sage.rings.ring)
inverse_image() (sage.rings.morphism.RingHomomorphism method)
is_commutative() (sage.rings.infinity.InfinityRing_class method)
(sage.rings.quotient_ring.QuotientRing_nc method)
(sage.rings.ring.CommutativeAlgebra method)
(sage.rings.ring.CommutativeRing method)
(sage.rings.ring.Ring method)
is_CommutativeAlgebra() (in module sage.rings.commutative_algebra)
is_CommutativeRing() (in module sage.rings.commutative_ring)
is_DedekindDomain() (in module sage.rings.dedekind_domain)
is_EuclideanDomain() (in module sage.rings.euclidean_domain)
is_exact() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.ring.Ring method)
is_field() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.quotient_ring.QuotientRing_nc method)
(sage.rings.ring.Field method)
(sage.rings.ring.IntegralDomain method)
(sage.rings.ring.Ring method)
is_finite() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.ring.Ring method)
is_FractionField() (in module sage.rings.fraction_field)
is_FractionFieldElement() (in module sage.rings.fraction_field_element)
is_Ideal() (in module sage.rings.ideal)
is_identity() (sage.rings.morphism.RingHomomorphism_from_base method)
is_Infinite() (in module sage.rings.infinity)
is_injective() (sage.rings.morphism.RingHomomorphism method)
is_integral() (sage.rings.fraction_field_element.FractionFieldElement_1poly_field method)
is_integral_domain() (sage.rings.quotient_ring.QuotientRing_nc method)
(sage.rings.ring.IntegralDomain method)
(sage.rings.ring.Ring method)
is_IntegralDomain() (in module sage.rings.integral_domain)
is_integrally_closed() (sage.rings.ring.DedekindDomain method)
(sage.rings.ring.Field method)
(sage.rings.ring.IntegralDomain method)
is_maximal() (sage.rings.ideal.Ideal_generic method)
(sage.rings.ideal.Ideal_pid method)
is_noetherian() (sage.rings.quotient_ring.QuotientRing_nc method)
(sage.rings.ring.DedekindDomain method)
(sage.rings.ring.Field method)
(sage.rings.ring.NoetherianRing method)
(sage.rings.ring.PrincipalIdealDomain method)
(sage.rings.ring.Ring method)
is_one() (sage.rings.fraction_field_element.FractionFieldElement method)
is_primary() (sage.rings.ideal.Ideal_generic method)
is_prime() (sage.rings.ideal.Ideal_generic method)
(sage.rings.ideal.Ideal_pid method)
is_prime_field() (sage.rings.ring.Ring method)
is_principal() (sage.rings.ideal.Ideal_generic method)
(sage.rings.ideal.Ideal_principal method)
is_PrincipalIdealDomain() (in module sage.rings.principal_ideal_domain)
is_QuotientRing() (in module sage.rings.quotient_ring)
is_Ring() (in module sage.rings.ring)
is_ring() (sage.rings.ring.Ring method)
is_RingHomomorphism() (in module sage.rings.morphism)
is_RingHomset() (in module sage.rings.homset)
is_square() (sage.rings.fraction_field_element.FractionFieldElement method)
is_subring() (sage.rings.ring.Ring method)
is_trivial() (sage.rings.ideal.Ideal_generic method)
is_unit() (sage.rings.quotient_ring_element.QuotientRingElement method)
is_zero() (sage.rings.fraction_field_element.FractionFieldElement method)
(sage.rings.infinity.InfinityRing_class method)
(sage.rings.morphism.RingHomomorphism method)

K

Katsura() (in module sage.rings.ideal)
kernel() (sage.rings.morphism.RingHomomorphism_cover method)
krull_dimension() (sage.rings.ring.CommutativeRing method)
(sage.rings.ring.DedekindDomain method)
(sage.rings.ring.Field method)

L

lc() (sage.rings.quotient_ring_element.QuotientRingElement method)
lcm() (sage.rings.infinity.AnInfinity method)
less_than_infinity() (sage.rings.infinity.UnsignedInfinityRing_class method)
LessThanInfinity (class in sage.rings.infinity)
lift() (sage.rings.morphism.RingHomomorphism method)
(sage.rings.quotient_ring.QuotientRing_nc method)
(sage.rings.quotient_ring_element.QuotientRingElement method)
lifting_map() (sage.rings.quotient_ring.QuotientRing_nc method)
lm() (sage.rings.quotient_ring_element.QuotientRingElement method)
lt() (sage.rings.quotient_ring_element.QuotientRingElement method)

M

make_element() (in module sage.rings.fraction_field_element)
make_element_old() (in module sage.rings.fraction_field_element)
maximal_order() (sage.rings.fraction_field.FractionField_1poly_field method)
minimal_associated_primes() (sage.rings.ideal.Ideal_generic method)
MinusInfinity (class in sage.rings.infinity)
monomials() (sage.rings.quotient_ring_element.QuotientRingElement method)
morphism_from_cover() (sage.rings.morphism.RingHomomorphism_from_quotient method)

N

natural_map() (sage.rings.homset.RingHomset_generic method)
ngens() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.ideal.Ideal_generic method)
(sage.rings.infinity.InfinityRing_class method)
(sage.rings.infinity.UnsignedInfinityRing_class method)
(sage.rings.quotient_ring.QuotientRing_nc method)
NoetherianRing (class in sage.rings.ring)
norm() (sage.rings.ideal.Ideal_generic method)
numerator() (sage.rings.fraction_field_element.FractionFieldElement method)

O

O() (in module sage.rings.big_oh)
one() (sage.rings.ring.Ring method)
order() (sage.rings.ring.Ring method)

P

parameter() (sage.rings.ring.EuclideanDomain method)
PlusInfinity (class in sage.rings.infinity)
power() (sage.rings.morphism.FrobeniusEndomorphism_generic method)
primary_decomposition() (sage.rings.ideal.Ideal_generic method)
prime_subfield() (sage.rings.ring.Field method)
principal_ideal() (sage.rings.ring.Ring method)
PrincipalIdealDomain (class in sage.rings.ring)
pushforward() (sage.rings.morphism.RingHomomorphism method)
Python Enhancement Proposals
PEP 3141

Q

quo() (sage.rings.ring.Ring method)
quotient() (sage.rings.ring.Ring method)
quotient_ring() (sage.rings.ring.Ring method)
QuotientRing() (in module sage.rings.quotient_ring)
QuotientRing_generic (class in sage.rings.quotient_ring)
QuotientRing_nc (class in sage.rings.quotient_ring)
QuotientRingElement (class in sage.rings.quotient_ring_element)

R

random_element() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.ring.Ring method)
reduce() (sage.rings.fraction_field_element.FractionFieldElement method)
(sage.rings.ideal.Ideal_generic method)
(sage.rings.ideal.Ideal_pid method)
(sage.rings.quotient_ring_element.QuotientRingElement method)
register_sage_classes() (in module sage.rings.numbers_abc)
residue_field() (sage.rings.ideal.Ideal_pid method)
retract() (sage.rings.quotient_ring.QuotientRing_nc method)
Ring (class in sage.rings.ring)
ring() (sage.rings.fraction_field.FractionField_generic method)
(sage.rings.ideal.Ideal_generic method)
(sage.rings.ideal_monoid.IdealMonoid_c method)
ring_of_integers() (sage.rings.fraction_field.FractionField_1poly_field method)
RingHomomorphism (class in sage.rings.morphism)
RingHomomorphism_coercion (class in sage.rings.morphism)
RingHomomorphism_cover (class in sage.rings.morphism)
RingHomomorphism_from_base (class in sage.rings.morphism)
RingHomomorphism_from_quotient (class in sage.rings.morphism)
RingHomomorphism_im_gens (class in sage.rings.morphism)
RingHomset() (in module sage.rings.homset)
RingHomset_generic (class in sage.rings.homset)
RingHomset_quo_ring (class in sage.rings.homset)
RingMap (class in sage.rings.morphism)
RingMap_lift (class in sage.rings.morphism)

S

sage.rings.big_oh (module)
sage.rings.commutative_algebra (module)
sage.rings.commutative_ring (module)
sage.rings.dedekind_domain (module)
sage.rings.euclidean_domain (module)
sage.rings.fraction_field (module)
sage.rings.fraction_field_element (module)
sage.rings.homset (module)
sage.rings.ideal (module)
sage.rings.ideal_monoid (module)
sage.rings.infinity (module)
sage.rings.integral_domain (module)
sage.rings.misc (module)
sage.rings.morphism (module)
sage.rings.noncommutative_ideals (module)
sage.rings.numbers_abc (module)
sage.rings.principal_ideal_domain (module)
sage.rings.quotient_ring (module)
sage.rings.quotient_ring_element (module)
sage.rings.ring (module)
side() (sage.rings.noncommutative_ideals.Ideal_nc method)
SignError
sqrt() (sage.rings.infinity.FiniteNumber method)
(sage.rings.infinity.MinusInfinity method)
(sage.rings.infinity.PlusInfinity method)
support() (sage.rings.fraction_field_element.FractionFieldElement_1poly_field method)

T

term_order() (sage.rings.quotient_ring.QuotientRing_nc method)
test_comparison() (in module sage.rings.infinity)
test_signed_infinity() (in module sage.rings.infinity)

U

underlying_map() (sage.rings.morphism.RingHomomorphism_from_base method)
unit_ideal() (sage.rings.ring.Ring method)
UnsignedInfinity (class in sage.rings.infinity)
UnsignedInfinityRing_class (class in sage.rings.infinity)

V

valuation() (sage.rings.fraction_field_element.FractionFieldElement method)
variables() (sage.rings.quotient_ring_element.QuotientRingElement method)

Z

zero() (sage.rings.ring.Ring method)
zero_ideal() (sage.rings.ring.Ring method)
zeta() (sage.rings.ring.Ring method)
zeta_order() (sage.rings.ring.Ring method)