sqrt(abs(1+I)^2 + 14) evaluates to sqrt(16) instead of 4

[rburing]

There is some weird undesirable "holding" going on:

sage: sqrt(abs(1+I)^2 + 14)
sqrt(16)

Found in Ask SageMath question #46698: Sagemath not evaluating complicated expression.

Component: symbolics

Keywords: sqrt, abs, complex, hold, holding

Author: Dave Morris

Branch/Commit: public/27897 @ a330310

Issue created by migration from https://trac.sagemath.org/ticket/27897

[nbruin]

comment:1

It looks like there is some double wrapping happening here:

sage: (1+I).pyobject().parent()
Number Field in I with defining polynomial x^2 + 1
sage: abs(1+I).pyobject().parent()
Symbolic Ring
sage: (abs(1+I)^2).pyobject().parent()
Symbolic Ring

here things seem to be still reasonable. However, this last result is "double wrapped":

sage: (abs(1+I)^2).pyobject().pyobject().parent()
Rational Field

and it looks like that's too deep for sqrt to see through. It doesn't happen for this case:

sage: (abs(sqrt(2))^2).pyobject().parent()
Integer Ring

---

that could be a red herring, though:

sage: b=(1+I)*(1-I)+14
sage: b.pyobject().parent() #this is appropriate
Number Field in I with defining polynomial x^2 + 1
sage: sqrt(b)
sqrt(16)
sage: sqrt(b.pyobject())
4

It means that

sage: a=sqrt(abs((1+I))^2+14)
sage: b=sqrt(norm(1+I)+14)

both lead to unexpectedly "held" expressions, but with different structures:

sage: a.operands()[0].pyobject().parent()
Symbolic Ring
sage: a.operands()[0].pyobject().pyobject().parent()
Rational Field
sage: b.operands()[0].pyobject().parent()
Number Field in I with defining polynomial x^2 + 1

where

sage: b.operands()[0].pyobject().sqrt()
4

so perhaps both problems are solved if sqrt on an SR element would look a little deeper.

[embray]

comment:2

As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).

[DaveWitteMorris]

Branch: public/27897

[DaveWitteMorris]

comment:4

I think the problem is gone:

sage: sqrt(abs(1+I)^2 + 14)                                                  
4

This is with 9.3b6 on MacOS 10.15.7, but I get sqrt(16) with 9.2 on CoCalc, so something seems to have changed since then.

The PR adds a doctest. If the patchbots turn green, then I think we can close this ticket.

---

New commits:

357ba2f

doctest trac 27897 sqrt(16)

[DaveWitteMorris]

Commit: 357ba2f

[DaveWitteMorris]

Author: Dave Morris

[rburing]

comment:5

I don't have 9.3beta6 here, but I think the definition/parent of I has changed, which may well have hidden this bug instead of fixing it. Could you please check sqrt(abs(1+SR(I))^2 + 14)? The doctest would have to take this form (or similar) as well.

[sagetrac-git]

Changed commit from 357ba2f to a330310

[sagetrac-git]

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

a330310

review correction

[DaveWitteMorris]

comment:7

You're right -- thanks for catching this! With 9.3b6, we still have:

sage: sqrt(abs(1 + SR.I())^2 + 14)
sqrt(16)

Ticket #18036 changed the parent of I to be a number field.