[sage-devel] Re: imaginary unit I is smaller than 1

[Simon King]

Hi,

On 2017-02-20, Daniel Krenn  wrote:
> On 2017-02-19 17:57, rjf wrote:
>> It might be comparing the real parts.  What did you expect?  Perhaps
>> Error "<" requires that both operands be members of the same ordered
>> field  ??
>> Or perhaps just
>> False
>
> I, for sure, did not expect "True".

It is clear that there is no mathematical meaning associated with the
comparison "I<1" --- so, I wouldn't have any expectation of mathematical
meaning here. "bool(I<1)" is a different story: It *has* to return
True/False for political reasons (Python decided against using "Unknown"
or "Alternative" as truth values). Or it could raise an error.
Indeed it would be a good idea to have a switch as in Maxima.

I believe it would be good to have an "Ordered" axiom for fields, so that
one can easily check "CC in Fields.Ordered()" respectively
"QQ in Fields.Ordered()".

Also, for an *ordered* field K, it might be a good idea to have a method
K.cmp (implemented via Fields.Ordered.ParentMethods) so that K.cmp(x,y)
returns -1,0,+1, according to how the elements x,y of K compare (and
raises an error if x,y do not coerce into K): Explicit is better than
implicit.

Best regards,
Simon


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Re: [sage-devel] Re: imaginary unit I is smaller than 1

[Daniel Krenn]

On 2017-02-19 17:57, rjf wrote:
> It might be comparing the real parts.  What did you expect?  Perhaps
> Error "<" requires that both operands be members of the same ordered
> field  ??
> Or perhaps just
> False

I, for sure, did not expect "True".


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[sage-devel] Re: imaginary unit I is smaller than 1

[Ralf Stephan]

Certainly the design of bool(rel) (where rel compares symbolics) can
be improved, including the interface to Maxima with all its switches,
but this specific case is better solved by moving I out of SR:

https://trac.sagemath.org/ticket/18036

Regards,

On Sunday, February 19, 2017 at 12:56:49 PM UTC+1, Daniel Krenn wrote:
>
> Dear all, 
>
> I am surprised by 
>   sage: bool(I < 1) 
>   True 
>
> Best Daniel 
>

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[sage-devel] Re: imaginary unit I is smaller than 1

[rjf]

There are a whole bunch of issues raised in the context of   bool(x>0) and 
some mention of what
Maxima does, in that thread from 4 years ago.

But the description of what Maxima* actually does* was essentially missing 
from the discussion.

As is often the case when several different conflicting opinions emerged in 
the design community
for Macsyma/ Maxima , a flag is available to choose a design

Thus
is (a>0)returns unknown.

prederror:true;
is(a>0)   produces an error  "unable to evaluate predicate a>0"


There are  probably other options that have to do with domain:real or 
domain:complex,
and assumptions on individual names.  It is also possible for the system to
return an unevaluated conditional as

if (a>=0 then 1 else 2
  returns unevaluated.   (though  is (a>0)   returns unknown  )

[note difference between is()   and if. ]

I suppose (but have not observed this) that the unevaluated 'if' could be 
simplified. e.g.

if (a^2=a) then 1 else 2 might be simplified to

if  (a=1)or(a=0) then 1 else 2

Now if you wanted to have a program that evaluated a boolean expression 
where
each value was a canonical True or False, and objected somehow otherwise,
that might be a different functionality, and certainly WAY simpler than 
what 
people seem to expect in a computer algebra system.

You could also have a 3 way branching if:   yes/no/unknown.  if a then be 
else c otherwise d.

Perhaps related,

Note also that for IEEE standard floats with  NaNs  (Not a numbers), of 
which there
are a huge number ..all comparisons return false.  That
is for N a NaN and X a float,  all these are false:
N>x
N
> In my opinion not this only particular case but the current bool() design 
> in sage is a tremendous failure.
> This was already discussed on sage-devel several times. 
>
> Here is one of that threads:
> https://groups.google.com/d/msg/sage-devel/vNxnHSeRBW4/UkaBOPGYT0QJ
>
> Jakob
>
> Am Sonntag, 19. Februar 2017 12:56:49 UTC+1 schrieb Daniel Krenn:
>>
>> Dear all, 
>>
>> I am surprised by 
>>   sage: bool(I < 1) 
>>   True 
>>
>> Best Daniel 
>>
>

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[sage-devel] Re: imaginary unit I is smaller than 1

[Jakob Kroeker]

In my opinion not this only particular case but the current bool() design 
in sage is a tremendous failure.
This was already discussed on sage-devel several times. 

Here is one of that threads:
https://groups.google.com/d/msg/sage-devel/vNxnHSeRBW4/UkaBOPGYT0QJ

Jakob

Am Sonntag, 19. Februar 2017 12:56:49 UTC+1 schrieb Daniel Krenn:
>
> Dear all, 
>
> I am surprised by 
>   sage: bool(I < 1) 
>   True 
>
> Best Daniel 
>

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[sage-devel] Re: imaginary unit I is smaller than 1

[rjf]

It might be comparing the real parts.  What did you expect?  Perhaps
Error "<" requires that both operands be members of the same ordered field 
 ??
Or perhaps just
False


On Sunday, February 19, 2017 at 3:56:49 AM UTC-8, Daniel Krenn wrote:
>
> Dear all, 
>
> I am surprised by 
>   sage: bool(I < 1) 
>   True 
>
> Best Daniel 
>

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