Opened 3 years ago

Last modified 3 years ago

#21758 needs_work enhancement

Hold symbolic powers unevaluated if evaluation fails

Reported by: rws Owned by:
Priority: major Milestone: sage-7.5
Component: symbolics Keywords:
Cc: vdelecroix Merged in:
Authors: Ralf Stephan Reviewers:
Report Upstream: N/A Work issues:
Branch: u/rws/hold_symbolic_powers_unevaluated_if_evaluation_fails (Commits) Commit: 49ab13301f5b44f946701f3fdcaff6c4613c0de7
Dependencies: Stopgaps:

Description

Automatic evaluation of symbolic expressions of "numerics" prevents construction of such expressions despite them being perfectly numerically approximatable (or otherwise useful) if exact evaluation in the algebraic sense fails. This is usually not a problem with function expressions (because of the easily added hold=True), and sums and products (?), but powers have to be constructed awkwardly: 

            sage: SR(2) ^ SR(QQbar(sqrt(2)))
            Traceback (most recent call last):
            ...
            TypeError: no canonical coercion ...
            sage: SR(2).power(SR(QQbar(sqrt(2))), hold=True)
            2^1.414213562373095?

The ticket catches TypeErrors in the first case and automatically uses the second form, to allow: 

            sage: SR(2) ^ SR(QQbar(sqrt(2)))
            2^1.414213562373095?

Change History (6)

comment:1 Changed 3 years ago by rws

  • Branch set to u/rws/hold_symbolic_powers_unevaluated_if_evaluation_fails

comment:2 Changed 3 years ago by rws

  • Authors set to Ralf Stephan
  • Cc vdelecroix added
  • Commit set to 49ab13301f5b44f946701f3fdcaff6c4613c0de7
  • Status changed from new to needs_review

New commits:

​49ab13321758: Hold symbolic powers unevaluated if evaluation fails

comment:3 follow-up: Changed 3 years ago by vdelecroix

  • Status changed from needs_review to needs_work 
sage: a = SR(2) ^ QQbar(3).sqrt()
sage: a
2^1.732050807568878?
sage: b = a + 1
sage: b
<repr(<sage.symbolic.expression.Expression at ...>) failed: TypeError: no canonical coercion from Algebraic Field to Rational Field>
Last edited 3 years ago by vdelecroix (previous) (diff)

comment:4 follow-up: Changed 3 years ago by vdelecroix

Why algebraic numbers behave differently from pi? 

sage: a = 2 ^ pi.sqrt() + 1
sage: a
2^sqrt(pi) + 1
sage: a.n()
4.41634542118404

And why is pi not numeric? 

sage: pi.is_numeric()
False

comment:5 in reply to: ↑ 4 Changed 3 years ago by rws

Replying to vdelecroix:

Why algebraic numbers behave differently from pi? 

sage: a = 2 ^ pi.sqrt() + 1
sage: a
2^sqrt(pi) + 1
sage: a.n()
4.41634542118404

Because traditionally in Pynac all Python objects that can't be converted to Pynac objects are wrapped inside a numeric object. Constants can be converted and are handled correctly. That's why pi is non-numeric.

comment:6 in reply to: ↑ 3 Changed 3 years ago by rws

Replying to vdelecroix: 

sage: a = SR(2) ^ QQbar(3).sqrt()
sage: a
2^1.732050807568878?
sage: b = a + 1
sage: b
<repr(<sage.symbolic.expression.Expression at ...>) failed: TypeError: no canonical coercion from Algebraic Field to Rational Field>

I have opened a Pynac issue although atm I have no idea where exactly to fix. ​https://github.com/pynac/pynac/issues/208

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