Strange behaviour when multiplying imaginary inf by 1

[AlexMonk]

BPO	24438
Nosy	@mdickinson, @stevendaprano

^{Note: these values reflect the state of the issue at the time it was migrated and might not reflect the current state.}

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GitHub fields:

assignee = None
closed_at = <Date 2015-06-12.17:38:52.287>
created_at = <Date 2015-06-12.13:22:58.393>
labels = ['type-bug', 'invalid']
title = 'Strange behaviour when multiplying imaginary inf by 1'
updated_at = <Date 2015-06-12.17:38:52.286>
user = 'https://bugs.python.org/AlexMonk'

bugs.python.org fields:

activity = <Date 2015-06-12.17:38:52.286>
actor = 'mark.dickinson'
assignee = 'none'
closed = True
closed_date = <Date 2015-06-12.17:38:52.287>
closer = 'mark.dickinson'
components = []
creation = <Date 2015-06-12.13:22:58.393>
creator = 'Alex Monk'
dependencies = []
files = []
hgrepos = []
issue_num = 24438
keywords = []
message_count = 4.0
messages = ['245247', '245257', '245265', '245266']
nosy_count = 3.0
nosy_names = ['mark.dickinson', 'steven.daprano', 'Alex Monk']
pr_nums = []
priority = 'normal'
resolution = 'not a bug'
stage = 'resolved'
status = 'closed'
superseder = None
type = 'behavior'
url = 'https://bugs.python.org/issue24438'
versions = []

[AlexMonk]

alex@alex-laptop:~$ python3
Python 3.4.3 (default, Mar 26 2015, 22:03:40) 
[GCC 4.9.2] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> infj = complex(0, float("inf"))
>>> infj
infj
>>> infj*1
(nan+infj)
>>> infj*1*1
(nan+nanj)

[stevendaprano]

I've found the same behaviour going back to Python 1.5.

I think what happens here is that (0+∞j)*1 evaluates the multiplication by implicitly coercing the int to a complex:

(0+∞j)*(1+0j)
=> (0*1 + ∞j*1 + 0*0j + ∞j*0j)
=> (0-NAN + ∞j+0j)
=> (NAN + ∞j)

rather than using the "simple" way (1*0 + 1*∞j) => (0+∞j).

The problem here is that while there is no mathematical difference between multiplying by 1 or (1+0j), once you involve NANs and INFs, it does. So even though they give different answers, both methods are correct, for some value of "correct".

I don't see that this is necessarily a bug to be fixed, it might count as a change in behaviour needing to go through a deprecation period first. Perhaps it should be discussed on python-ideas first?

My personal feeling is that Python should multiply a complex by a non-complex in the "simple" way, rather than implicitly converting the int to a complex. Anyone who wants the old behaviour can easily get it by explicitly converting 1 to a complex first.

So I guess this is a +1 to "fixing" this.

(Oh, the same applies to the / operator.)

[mdickinson]

There's no bug here: as Steven explained, this is simply the result of the usual arithmetic conversions when performing a mixed-type operation.

Python should multiply a complex by a non-complex in the "simple" way

I think this would just be adding unnecessary complication. -1 from me.

[mdickinson]

Closing as not a bug; for the suggestion of changing the mixed-type arithmetic behaviour, I think that's something that should be discussed on the python-ideas mailing list.