Assumptions on symbols not preserved with some unevaluated integrals

[rwst]

In a fresh Sage, assumptions on symbols within expressions are preserved when Maxima returns the same expression in an unevaluated integral. But in this case the domain/flag information of m is somehow cleared/deleted:

sage: _ = var('m')
sage: (x^m / sqrt(2+3*x)).integral(x)
integrate(x^m/sqrt(3*x + 2), x)
sage: _= var('m', domain='integer')
sage: (x^m / sqrt(2+3*x)).integral(x)
integrate(x^m/sqrt(3*x + 2), x)
sage: _.operands()[0].operands()[1]
x^m
sage: _.operands()[1].is_integer()
False

assume(m, 'integer') cannot restore the flag of m in the returned integral.

The problem does not occur without the first two lines. Maybe the first creation of m does somehow irrevocably set something in Maxima (or Sage's module for backtranslation)?

CC: @nbruin

Component: symbolics

Author: Ralf Stephan

Branch/Commit: u/rws/assumptions_on_symbols_not_preserved_with_some_unevaluated_integrals @ 39567f4

Issue created by migration from https://trac.sagemath.org/ticket/22763

[rwst]

comment:1

#22650 depends on this.

[rwst]

comment:2

It looks like sage.interfaces.maxima_lib.sr_to_max has several symbol dicts. sage_sym_dict's keys are symbols and registered constants. At the first encounter of (x^m / sqrt(2+3*x)).integral(x) m is inserted there. The hash of the second m is the same, and presumably that's why there is no change in the dictionary. As the ms are different the hash should be different too and there is the Pynac bug that if fixed should fix this ticket too. Alternatively the dicts should be updated in var when variables are created.

[rwst]

comment:3

Actually hashes have nothing to do with it. The vars are not the keys in the dictionary and, even if they were, hash makes no difference because keys are compared via bool(a==b), ie ex.__nonzero__() is used and there lhs-rhs is zero even for vars with different flags or hashes.

[rwst]

Branch: u/rws/assumptions_on_symbols_not_preserved_with_some_unevaluated_integrals

[rwst]

Author: Ralf Stephan

[rwst]

Commit: 39567f4

[rwst]

New commits:

39567f4

22763: update maxima_lib about variable changes

[fchapoton]

comment:7

red branch => needs work