Re: [Maxima-discuss] Errors in atan and atan2 limits

[Barton W. <wi...@un...>]

Hi Francisco,

Thanks for the bug report. I made a ticket for this bug; see https://sourceforge.net/p/maxima/bugs/4559/

--Barton
________________________________
From: Francisco Carbajo <fra...@up...>
Sent: Friday, May 16, 2025 11:34 AM
To: max...@li... <max...@li...>
Subject: [Maxima-discuss] Errors in atan and atan2 limits

Caution: Non-NU Email


Hi all.

Some simple limits of the functions atan and atan2 are not calculated
correctly (checked in Maxima 5.47.0 https://urldefense.com/v3/__https://maxima.sourceforge.io__;!!PvXuogZ4sRB2p-tU!H3rBpqWu89AdVKCnh3h0gMCL0X34bkdOtxOA9h4YkzyHvdUd4YEuRH7qezexOZfLpRDWnTpXDz_Ar_5qf2KAZyyU1A$
using Lisp SBCL 2.2.9.debian).

For example

(%i1) limit(atan(p/e),e,0,plus);
                                       %pi
(%o1)                             ---
                                        2
(%i2) limit(atan2(p,e),e,0,plus);
                                       %pi
(%o2)                             ---
                                        2
ignoring the sign of p. If p is declared as a negative number the answer
is correct

(%i5) assume(p<0);
(%o5)                               [p < 0]
(%i6)  limit(atan(p/e),e,0,plus);
                                        %pi
(%o6)                            - ---
                                         2
(%i7)
limit(atan2(p,e),e,0,plus);
                                        %pi
(%o7)                           - ---
                                         2
(%i8)

To avoid this error just change p to a sum of two variables  p+q

(%i2) limit(atan((p+q)/e),e,0,plus);
(%o2)                           atan2(q + p, 0)
(%i3) limit(atan2((p+q),e),e,0,plus);
(%o3)                           atan2(q + p, 0)
(%i4)

which is correct, shouldn't the answer be
limit(atan(p/e),e,0,plus)=atan2(p,0)?

Thank you very much




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