sage_eval evaluates a string using the globals of sage.all.

It is used in some constructors and other functions - but in most uses, likely just a few bindings, namely those emitted by the preparser, are needed. We create a module sage.repl.preparse_bindings for these bindings (Ellipsis, ellipsis_range, ellipsis_iter, Integer, RealNumber, ComplexNumber, var, symbolic_expression, ...)

It is also used by sage_input to verify inputs. We run the verification with a smaller module first before falling back to sage.all

Tickets:

• get rid of one sage_eval in complex numbers #38391
• get rid of sage_eval in grobner_fan #38392
• get rid of one sage_eval in modular #38394
• get rid of some sage-eval in gap3-related code #38395
• get rid of sage_eval in cfinite_sequence #38462
• simplify conversion code in cubic Hecke #38458

See also:

• conversion of string to complex number with sage_eval should be avoided #30977, sage_input is unreliable for elements of ComplexField #32129, conversion of string 'r' in fraction field #26155 - issues with sage_eval, sage_input
• Stop using old_style_globals #18083 Stop using old_style_globals

CC: @kwankyu @kliem @jhpalmieri @spaghettisalat @jcamp0x2a

Component: refactoring

Branch/Commit: u/mkoeppe/remove_runtime_dependency_on_everything_via_sage_eval @ 3552523

Issue created by migration from https://trac.sagemath.org/ticket/33802