Change default domain of SR.var()

[RuchitJagodara]

This patch fixes #36833 by changing the default domain of SR.var()
function to complex. By this way, every variable whose domain is not defined will be considered
in complex plane, by default.

The issue was with the default value only because whenever we were defining a variable without specifying any domain it was calling symbol() function with domain=None; Subsequently, it calls new_Expression_symbol() function with domain=None. In this code, I found that it was not giving any specific domain to the variable and so when we define a new variable using SR.var() function, it is passing the is_real() (Because it does not have any specific domain) test but giving the wrong answer on factor() function, if we assume that the variable is in complex plane by default which is correct according to the documentation.

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[dimpase]

Could you point out where in documentation you see this " considered in complex plane" ?

[RuchitJagodara]

[dimpase]

thanks!

[dimpase]

we might see lots of doctest errors now, not sure.

[RuchitJagodara]

Then, I think it would be good if we change the factor function instead of doing this. I'll change it and will update.

[RuchitJagodara]

@dimpase Do you know any function that can return the domain of a symbolic variable?

[dimpase]

@dimpase Do you know any function that can return the domain of a symbolic variable?

no, I don't.

By the way, I just saw the place where it's claimed that var by default returns
complex variable - it's in the output sage: var? - so you can find it in the code by
e.g. looking at the bottom of sage: var??

[RuchitJagodara]

Can't we implement a new class for variables of symbolic ring? By this method, we will be able to track domain of the variable and once we are able to access the domain of variable, I think it will be easier to handle these type of issues.

[dimpase]

I don't think it's a good idea to make domain="complex" the default. It seems that most everything in Sage assumes it to be real. E.g. if you make this change then differentiating with default variables will become complex differentiation, which is a rather different story, mathematically - and Sage does not do it.
E.g.

sage: y = SR.var("y",domain="complex")
sage: f(y) = y * conjugate(y)
sage: f.diff(y)
y |--> y*diff(conjugate(y), y) + conjugate(y)

doesn't make much sense, as in fact $\frac{d\overline{y}}{dy}$ does not exist (e.g. as Cauchy equations don't hold).

[RuchitJagodara]

Hmm, got it. But when we declare a variable without declaring any domain, it is clear that it is not real from the following,

sage: n = SR.var("n"); n
n
sage: n.is_real()
False

So it simply implies that it is complex. So I am not getting the point that what is wrong here, if the variable is not real then it should not be simplified to y^2, anyhow. But factor function is doing so. I think the error is occurring with the maxima. Actually maxima is simplifying many functions which should not be simplified like 0^n is being converted to 0 (this is referenced from the issue #36838 ) , here y * conjugate(y) is being converted to y^2.

[dimpase]

On 12 December 2023 15:48:25 GMT, Ruchit Jagodara ***@***.***> wrote: Hmm, got it. But when we declare a variable without declaring any domain, it is clear that it is not real from the following, ```python sage: n = SR.var("n"); n n sage: n.is_real() False ``` So it simply implies that it is complex.

it'd imply this if our docs were correct:-) By default `domain=None`, and it could be that `is_real()` just checked that.

So I am not getting the point that what is wrong here, if the variable is not real then it should not be simplified to y^2, anyhow. But factor function is doing so. I think the error is occurring with the maxima. Actually maxima is simplifying many functions which should not be simplified like 0^n is being converted to 0 (this is referenced from the issue #36838 ) , here y * conjugate(y) is being converted to y^2.

maxima has no concept of a domain for a variable, it seems to me.

[RuchitJagodara]

maxima has no concept of a domain for a variable, it seems to me.

But it has to be, because when we do operation like below

sage: n = var('n',domain="complex"); n
n
sage: f1 = n * conjugate(n); f1
n*conjugate(n)
sage: f1.factor()
n*conjugate(n)

Here, we can clearly see that it is giving correct answer if we declare domain="complex", but it is not giving the same answer when we do it as below, which means it has something to do with the domain.

sage: b = var("b")
sage: f2 = b * conjugate(b); f2
b*conjugate(b)
sage: f2.factor()
b^2

[dimpase]

maxima has no concept of a domain for a variable, it seems to me.

But it has to be, because when we do operation like below

sage: n = var('n',domain="complex"); n
n
sage: f1 = n * conjugate(n); f1
n*conjugate(n)
sage: f1.factor()
n*conjugate(n)

Here, we can clearly see that it is giving correct answer if we declare domain="complex", but it is not giving the same answer when we do it as below, which means it has something to do with the domain.

sage: b = var("b")
sage: f2 = b * conjugate(b); f2
b*conjugate(b)
sage: f2.factor()
b^2

Sorry, indeed, you are right. Maxima has domain, which is a domain for computation to be done (although it's not to declare that a variable is real or complex) , and a similar thing called assume (which allows things like assume(x>0), or indeed x to be real).

Better, it has declare - which seems to be exactly what is needed here. So one can do

$ maxima 
Maxima 5.47.0 https://maxima.sourceforge.io
using Lisp SBCL 2.3.9
Distributed under the GNU Public License. See the file COPYING.
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i4) declare(x, complex);
(%o4)                                done
(%i5) x*conjugate(x);
(%o5)                           x conjugate(x)
(%i6) declare(y, real);
(%o6)                                done
(%i7) y*conjugate(y);
                                       2
(%o7)                                 y
(%i8) 

[RuchitJagodara]

Hmm... But in sage when we are doing this

sage: y = SR.var("y","real"); y
y
sage: f = y * conjugate(y); f
y*conjugate(y)
sage: f
y*conjugate(y)
sage: f.simplify_full()
y^2

Here, you can see that for variable whose domain is real, it is not simplifying conjugate(y) and for that I have to use simplify_full() function but I think this should be done when we were multiplying y with conjuage(y) so the value of f should be y^2 not y*conjugate(y).

[RuchitJagodara]

I found an issue where one had similar problem with maxima, discussion link

[RuchitJagodara]

Should I change the documentation instead, which may specify that the default domain of var is None? This means that the variable will not have any specific domain. Or should I just leave it as it is?

[dimpase]

Yes, please, we are not going to make the default domain complex. Please fix the documentation instead, to specify that the default domain is None.

[RuchitJagodara]

Sorry for the delay! Actually, I was checking if there is any other fix that can be applied, but I think we cannot do anything as the problem is with maxima only. So, I have changed the documentation.

Can you please review my changes now ?

[github-actions]

Documentation preview for this PR (built with commit 053d50c; changes) is ready! 🎉

[dimpase]

OK