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refine the category of Gaussian integers #38937

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refine the category of Gaussian integers #38937

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cd52d16
refine the category of Gaussian integers
fchapoton Nov 7, 2024
6d02aa0
Merge branch 'develop' into refine_gaussian
fchapoton Dec 10, 2024
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22 changes: 20 additions & 2 deletions src/sage/rings/number_field/order.py
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Original file line number Diff line number Diff line change
Expand Up @@ -2942,12 +2942,21 @@ def GaussianIntegers(names='I', latex_name='i'):
x^2 + 1
sage: GaussianIntegers().basis()
[1, I]

TESTS::

sage: ZZI.<I> = GaussianIntegers()
sage: ZZI.category()
Category of principal ideal domains
"""
from sage.rings.complex_double import CDF
from sage.rings.number_field.number_field import NumberField
from sage.categories.principal_ideal_domains import PrincipalIdealDomains
f = ZZ['x']([1, 0, 1])
nf = NumberField(f, names, embedding=CDF(0, 1), latex_name=latex_name)
return nf.ring_of_integers()
order = nf.ring_of_integers()
order._refine_category_(PrincipalIdealDomains())
return order


def EisensteinIntegers(names='omega'):
Expand All @@ -2973,9 +2982,18 @@ def EisensteinIntegers(names='omega'):
x^2 + x + 1
sage: EisensteinIntegers().basis()
[1, omega]

TESTS::

sage: R.<omega> = EisensteinIntegers()
sage: R.category()
Category of principal ideal domains
"""
from sage.rings.complex_double import CDF
from sage.rings.number_field.number_field import NumberField
from sage.categories.principal_ideal_domains import PrincipalIdealDomains
f = ZZ['x']([1, 1, 1])
nf = NumberField(f, names, embedding=CDF(-0.5, 0.8660254037844386))
return nf.ring_of_integers()
order = nf.ring_of_integers()
order._refine_category_(PrincipalIdealDomains())
return order
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