parent of argument lost with Functions

[rws]

Some Python objects as function arguments lose their parent, i.e. the code in the specific function can no longer access it because the object was coerced into SR. This can result in violation of the rule that function input and output should be of the same type.

sage: S.<y> = PolynomialRing(RR)
sage: ex = sin(asin(y)); ex
y
sage: type(ex)
<type 'sage.symbolic.expression.Expression'>
sage: ex.is_symbol()
True

The specific function (here sin) code cannot remedy this because there the damage is already done. The problem is in symbolic/function.pyx:BuiltinFunction.__call__ where the parent of function arguments is lost.

See also #18832 and maybe #17790.

[rws]

@Jeroen: I really would appreciate any input you can give me here. If it is not possible to decide which argument of the function determines the return type, a small database of functions with more than one argument could be used that contains that information.

[rws]

It looks like the first version here can handle the binomial example of #20060 as well as the symbolic poly functions. It works by adding a field _preserved_arg to every BuiltinFunction that is set on function creation and says which of the function arguments is the one where we try to preserve the arg's parent. Then Expression.polynomial() is used to convert back in case of polynomial rings. Also, by not setting a default preserved_arg the functionality is limited to the cases where the developer has given this parameter in the function init call.

This does not work however with the title example because there the functions are nested. Since it seems we cannot decide where in a nested expression the specific element is whose parent we want to preserve I tend to exclude the nested case.

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New commits:

​eb5bf93

20312: preserving function arg parent, first version

[rws]

Tests pass.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​5c377cc

20312: fix for constant results

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​58f3d00

Merge branch 'develop' into t/20312/parent_of_argument_lost_with_functions