Orders in number fields certainly need work.
This Sage Trac query:
https://trac.sagemath.org/query?order=id&desc=1&summary=~orders
and similar queries with "order" or "ring of integers" reveal the following
open tickets
#28706 clarify order generation in number fields with bracket syntax
#28552 Elements in orders in number fields are considered as field
elements
#27413 Implement picard group and unit group for non-maximal orders
#25709 inject_variables is broken for orders of number fields
#24934 Orders are not unique parents
#24031 Coercion between Matrices over orders and over the number field
#23971 Euclidean division in quadratic imaginary orders
#23321 Implemented functionality for Quotient Rings of Orders
#23236 Create p-maximal orders
#18865 Can't make ring homomorphism from ring of integers to a residue
field
#16556 AbsoluteOrder.random_element and
PolynomialQuotientRing_integer.random_element
#14740 Infinite loop in creation of number field order
#13568 Quaternion Orders over Number Fields
#12242 Divisibility of number field order elements needs work
#5893 Norm Form for Number Fields and Orders
#4738 base_ring of orders in relative number fields is wrong
#1134 optimize creating elements of orders and number fields by
coercing in lists
I can also link to discussions on other channels if that seems useful.
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