allow preventing automatic evaluation of symbolic expressions (hold)

[burcin]

Symbolic expressions automatically evaluate themselves to simplify the data structures, representation, etc. For example,

sage: x+x
2*x
sage: x*x
x^2

The ability to disable this evaluation is a feature requested very often.

Component: symbolics

Keywords: pynac

Author: Burcin Erocal, Karl-Dieter Crisman

Reviewer: Karl-Dieter Crisman, Jean-Pierre Flori

Merged: sage-4.6.alpha3

Issue created by migration from https://trac.sagemath.org/ticket/9879

[burcin]

Author: Burcin Erocal

[burcin]

comment:1

Attachment: trac_9879-hold.patch.gz

With attachment: trac_9879-hold.patch and the new pynac package at #9201, one can do:

sage: x.add(x,(x+1), hold=True)
x + x + (x + 1)
sage: sin(pi, hold=True)
sin(pi)

The pynac package includes patches for #9394, #9834, #9878, #9881, #9900 as well as this ticket. See the ticket description of #9901 for the list (and order) of patches associated to the new version.

[burcin]

comment:2

Replying to @burcin:

With attachment: trac_9879-hold.patch and the new pynac package at #9201

at #9901. Sorry for the noise.

[kcrisman]

comment:3

A question arises in reviewing:

>> Do all the holds in the Pynac code (such as ``return
>> conjugate_function(asin(x)).hold();``) prevent someone from ever
>> evaluating these?  I just don't know how it works.
>
> The hold() function sets the evaluated flag of a basic object in
> GiNaC. The automatic evaluation is skipped if this flag is set. Perhaps
> the duplicate() method ignores this, I'm not sure.
>
> In any case, we should provide a method to force this evaluation, but
> this should be on a separate ticket. Also see my comments below about
> this.

This is now #10034.

[kcrisman]

comment:4

Making a context for holding is now #10035.

[kcrisman]

Attachment: trac_9879-hold-review.patch.gz

Apply after initial patch

[kcrisman]

comment:5

This still needs review, just because the review patch itself is so long. I've added myself as author, but obviously I didn't do much Pynac - just trying to document thoroughly - so if someone disagrees they can change that.

Burcin, can you review this? With this I pass all doctests.

Also, here are some issues which I believe should NOT be addressed here, but need to be on followup tickets. My philosophy here is that mathematically correct brand-new functionality can be merged even if there are enhancements to it needed. This ticket shouldn't be closed until new tickets are opened for these issues.

• Typesetting issues. There is nothing mathematically wrong with these (you can try it), but they are obviously confusing to users.

sage: i.mul(2)
2*I
sage: i.mul(2,hold=True)
2*I*
sage: i.mul(2,hold=True).simplify()
2*I
sage: i.mul(i)
-1
sage: i.mul(i,hold=True)
-
sage: i.mul(i,hold=True).simplify()
-1

• heaviside(0) != SR(0).step() This is already true in Sage, so we don't need to address in this ticket, but it becomes obvious when trying to simplify a 'held' expression with step().

• There is no way to get Order(hold=True) to evaluate! Same problem with csgn and step (the latter could be fixed via the above). This is annoying but probably they are still useful.

• Big problem, which is why I didn't make log_gamma symbolic:

sage: log_gamma(i).n()
-0.0219785471672303 - 0.168184318273662*I
sage: log_gamma(pari(i))
-0.650923199301856 - 1.87243664726243*I
(%i3) ev(log_gamma(%i),numer);
(%o3)             - 1.872436647262428 %i - .6509231993018556

So no new error has been introduced with this patch, but it exposed this Pynac difference/bug.

• Enhancement - coth, sech, csch and their arc-guys basically already are purely symbolic and hold doesn't do much for them. For instance:

sage: cosh(0)
1
sage: sech(0)
sech(0)

So we should do something about that. But Maxima knows:

sage: sech(0).simplify()
1

• Here is something where I was able to make it work in the doctests, but honestly don't know what is going on.

sage: I.log(hold=True).simplify()
1/2*I*pi
sage: var('I')
I
sage: I.log(hold=True).simplify()
log(I)
sage: restore('I')
sage: I.log(hold=True).simplify()
log(I)

This turns out to cause trouble in doctests. I don't know why this happens.

[kcrisman]

Changed author from Burcin Erocal to Burcin Erocal, Karl-Dieter Crisman

[kcrisman]

Reviewer: Karl-Dieter Crisman