Doctest fix: f.subs(I==...) does not work

[zimmermann6]

Minimal case:

sage: (I*x).subs(I==0)
I*x

Originally:

the substitute command does not work with I:

sage: f = sin(x*I)+I*x^2+cos(exp(I))
sage: f.subs(I=0)
I*x^2 + cos(e^I) + sin(I*x)

Depends on #24838

Component: calculus

Issue created by migration from https://trac.sagemath.org/ticket/23964

[rwst]

comment:1

The documentation: Substitute with keyword arguments (works only with symbols):. For you I is a symbol but for Pynac it's numeric. Just use dictionary or relational syntax:

sage: f = sin(x*I)+I*x^2+cos(exp(I))
sage: f
I*x^2 + cos(e^I) + I*sinh(x)
sage: f.subs({I:0})
I*x^2 + cos(1) + I*sinh(x)
sage: f.subs(I==0)
I*x^2 + cos(1) + I*sinh(x)

As you can see the I inside cos(e^I) is now replaced. I agree that the other Is not being replaced is a bug. The bug is independent of which numeric is to be substituted:

sage: f = sin(x*2)+2*x^2+cos(exp(2))
sage: f
2*x^2 + cos(e^2) + sin(2*x)
sage: f.subs({2:0})
cos(1) + sin(2*x) + 2

[zimmermann6]

comment:2

thank you. Should I open a new ticket for this bug? Or simply change the ticket description?

[rwst]

comment:3

Done. I think I will restrict the numerics that can be replaced (not 0 nor 1).

[zimmermann6]

comment:4

btw it is strange that you get I*sinh(x) since with Sage 8.0 I get sin(I*x), i.e., this term is unchanged.

[zimmermann6]

comment:6

sorry we edited the ticket simultaneously and I discarded your edit in the title and maybe in the description. I've put the title back to === but I'm not sure about the description.

[rwst]

comment:7

Yeah that was an enhancement in a recent Pynac (#23820).

[jdemeyer]

comment:8

Why should (I*x).subs(I=0) work? This I isn't a variable, it's a complex number. Would you expect (2*x).subs({2:3}) to give (3*x)?

[rwst]

comment:9

Well, subs was always about termwise substitution. Maxima does it too:

(%i3) subst(%i=y,%i*x);
(%o3)                                 x y
(%i4) subst(2=y,2*x);
(%o4)                                 x y

[rwst]

comment:10

This will be available with pynac-0.7.18 and should be doctested here.

[rwst]

Dependencies: #24838

[rwst]

comment:12

The original case works now, the minimal case I*x not, so there is an inconsistency to resolve.