[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

['Mark Bell' via sage-devel]

Ah, I see. Is it possible that by doing "sage -i latte_int" I have 
installed a different version of 4ti2 than the one that CoCalc uses? I'm 
still not sure why (without this option) I see different behaviours on my 
machine and on CoCalc. If it matters I have Sage 8.0 running on Mac OS 
Sierra 10.12.6.

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Dima Pasechnik]

lattE needs to compute a triangulation of the polytope; by default it uses 
4ti2, but can instead use cddlib. Hence this option. See 
https://www.math.ucdavis.edu/~latte/software/packages/latte_current/manual_v1.7.2.pdf

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

['Mark Bell' via sage-devel]

Excellent! Adding the option prevents the crash. So on CoCalc (and locally) 
I can do:
   print(P.integral_points_count(preprocess=False, triangulation='cddlib'))
And it prints out 19958.

Without this extra option this example crashes on CoCalc but runs fine 
locally. What is this this option doing?

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Matthias Koeppe]

I can't reproduce this locally, but you could see if passing  

--triangulation=cddlib

to LattE helps. 

On Sunday, November 5, 2017 at 1:46:30 AM UTC-8, Mark Bell wrote:
>
> Here is the full CoCalc output when I run "sage error.py" in a terminal, 
> either via the web interface or via sshing into the machine:
>
> Traceback (most recent call last):
>   File "error.py", line 42, in 
> print(P.integral_points_count(preprocess=False))
>   File 
> "/ext/sage/sage-8.0/local/lib/python2.7/site-packages/sage/geometry/polyhedron/base_QQ.py",
>  
> line 218, in integral_points_count
> **kwds)
>   File 
> "/ext/sage/sage-8.0/local/lib/python2.7/site-packages/sage/interfaces/latte.py",
>  
> line 159, in count
> raise RuntimeError("LattE integrale program failed (exit code 
> {})".format(ret_code) + err.strip())
> RuntimeError: LattE integrale program failed (exit code -6):
> This is LattE integrale 1.7.3
> Available from http://www.math.ucdavis.edu/~latte/
>  
> Invocation: count '--redundancy-check=none' --cdd /dev/stdin
> Warning: Not performing check for empty polytope, because it is 
> unimplemented for the CDD-style input format.
> size = 22 x 19
> Number Type = rational
> Ax <= b, given as (b|-A):
> =
> [-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
> [-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
> [-1 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
> [-1 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
> [-1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
> [-1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
> [97 -2 -8 -1 -7 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
> [-1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
> [97 -2 -5 -1 -4 0 -3 0 0 0 0 0 0 0 0 0 0 0 0]
>
> Ax = b, given as (b|-A):
> 
> [0 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1]
> [0 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0]
> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
> [0 0 1 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 0]
> [0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
> [0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0]
> [-100 2 8 1 7 0 0 0 0 0 0 0 3 0 0 0 0 0 0]
> [0 0 1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0]
> [0 0 1 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0]
> [0 0 1 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0]
> [-100 2 5 1 4 0 3 0 3 0 0 0 0 0 0 0 0 0 0]
> [-100 2 5 1 4 0 3 3 0 0 0 0 0 0 0 0 0 0 0]
> [0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]
>
> Computing hermitean normal form.
> sol:
> [0 0 0 0 0 0 -100 0 0 -100 0 0 0 0 0 0 0 0]
> Particular solution:
> Basis:
> New inequalities:
> [99 -3 -3 -5 -5 -1 0]
> [-101 3 3 5 6 2 0]
> [-1 0 0 0 0 1 0]
> [-1 0 0 0 1 0 0]
> [-1 0 0 1 0 0 0]
> [-1 1 0 0 0 0 0]
> [-3 3 3 -3 -3 0 0]
> [99 -3 -3 -4 -5 -2 0]
> [-3 0 3 0 0 0 0]
> Time for reading and preprocessing: 0 sec
> The polytope has 12 vertices.
> Time for computing vertices and supporting cones: 0 sec
> Time for dualizing general cones: 0 sec
> Dualizing all cones...All cones are now dualized.
> Time for dualizing general cones: 0 sec
> decomposeCones_Single: Decomposing all cones. (Memory Save on)
> 12 cones total to be done!decomposeCones_Single: degree = 1
> Number of cones: 12
> Triangulating cone... done.
> count: barvinok/barvinok.cpp:572: int 
> barvinokDecomposition_Single(listCone*, Single_Cone_Parameters*): Assertion 
> `num_rays == Parameters->Number_of_Variables'
> failed.
>

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Re: [sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

['Mark Bell' via sage-devel]

Thanks for the suggestion. That might be the case but if I run 
"/usr/bin/time -v sage error.py" then I get 

Command exited with non-zero status 1
Command being timed: "sage error.py"
User time (seconds): 2.22
System time (seconds): 0.67
Percent of CPU this job got: 86%
Elapsed (wall clock) time (h:mm:ss or m:ss): 0:03.35
Average shared text size (kbytes): 0
Average unshared data size (kbytes): 0
Average stack size (kbytes): 0
Average total size (kbytes): 0
Maximum resident set size (kbytes): 200116
Average resident set size (kbytes): 0
Major (requiring I/O) page faults: 0
Minor (reclaiming a frame) page faults: 81745
Voluntary context switches: 7875
Involuntary context switches: 191
Swaps: 0
File system inputs: 22
File system outputs: 4
Socket messages sent: 0
Socket messages received: 0
Signals delivered: 0
Page size (bytes): 4096
Exit status: 1

So it appears to be using ~200 MB of the 1000 MB shared RAM memory limit. 
Is there a better way to determine the resources being used / if I am 
hitting this limit?

On Sunday, November 5, 2017 at 2:05:31 AM UTC, William wrote:
>
> On Sat, Nov 4, 2017 at 6:27 PM, Matthias Koeppe 
>  wrote: 
> > Can you show the output of the crash on CoCalc? 
>
> Also, the crash could just be running out of memory... 
>
> > 
> > 
> > On Saturday, November 4, 2017 at 3:46:01 PM UTC-7, Mark Bell wrote: 
> >> 
> >> Thanks! 
> >> 
> >> I'm not sure if this is the right place to add this but the attached 
> >> example also causes LattE to crash, but I only see this behaviour when 
> I run 
> >> this code on CoCalc. When I run the script on my local machine with 
> >> latte_int installed it completes and prints out 19958. Surely this 
> isn't 
> >> being caused by the same bug. 
> > 
> > -- 
> > You received this message because you are subscribed to the Google 
> Groups 
> > "sage-devel" group. 
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> an 
> > email to sage-devel+...@googlegroups.com . 
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>
>
>
> -- 
> William (http://wstein.org) 
>

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

['Mark Bell' via sage-devel]

Here is the full CoCalc output when I run "sage error.py" in a terminal, 
either via the web interface or via sshing into the machine:

Traceback (most recent call last):
  File "error.py", line 42, in 
print(P.integral_points_count(preprocess=False))
  File 
"/ext/sage/sage-8.0/local/lib/python2.7/site-packages/sage/geometry/polyhedron/base_QQ.py",
 
line 218, in integral_points_count
**kwds)
  File 
"/ext/sage/sage-8.0/local/lib/python2.7/site-packages/sage/interfaces/latte.py",
 
line 159, in count
raise RuntimeError("LattE integrale program failed (exit code 
{})".format(ret_code) + err.strip())
RuntimeError: LattE integrale program failed (exit code -6):
This is LattE integrale 1.7.3
Available from http://www.math.ucdavis.edu/~latte/
 
Invocation: count '--redundancy-check=none' --cdd /dev/stdin
Warning: Not performing check for empty polytope, because it is 
unimplemented for the CDD-style input format.
size = 22 x 19
Number Type = rational
Ax <= b, given as (b|-A):
=
[-1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-1 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-1 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
[97 -2 -8 -1 -7 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[-1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0]
[97 -2 -5 -1 -4 0 -3 0 0 0 0 0 0 0 0 0 0 0 0]

Ax = b, given as (b|-A):

[0 1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -1]
[0 0 1 -1 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
[0 0 1 -1 2 0 0 0 0 0 0 0 0 0 0 -1 0 0 0]
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0]
[0 0 0 0 0 0 1 0 0 0 0 0 0 -1 0 0 0 0 0]
[-100 2 8 1 7 0 0 0 0 0 0 0 3 0 0 0 0 0 0]
[0 0 1 0 1 0 0 0 0 0 0 -1 0 0 0 0 0 0 0]
[0 0 1 0 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0]
[0 0 1 1 0 0 0 0 0 -1 0 0 0 0 0 0 0 0 0]
[-100 2 5 1 4 0 3 0 3 0 0 0 0 0 0 0 0 0 0]
[-100 2 5 1 4 0 3 3 0 0 0 0 0 0 0 0 0 0 0]
[0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0]

Computing hermitean normal form.
sol:
[0 0 0 0 0 0 -100 0 0 -100 0 0 0 0 0 0 0 0]
Particular solution:
Basis:
New inequalities:
[99 -3 -3 -5 -5 -1 0]
[-101 3 3 5 6 2 0]
[-1 0 0 0 0 1 0]
[-1 0 0 0 1 0 0]
[-1 0 0 1 0 0 0]
[-1 1 0 0 0 0 0]
[-3 3 3 -3 -3 0 0]
[99 -3 -3 -4 -5 -2 0]
[-3 0 3 0 0 0 0]
Time for reading and preprocessing: 0 sec
The polytope has 12 vertices.
Time for computing vertices and supporting cones: 0 sec
Time for dualizing general cones: 0 sec
Dualizing all cones...All cones are now dualized.
Time for dualizing general cones: 0 sec
decomposeCones_Single: Decomposing all cones. (Memory Save on)
12 cones total to be done!decomposeCones_Single: degree = 1
Number of cones: 12
Triangulating cone... done.
count: barvinok/barvinok.cpp:572: int 
barvinokDecomposition_Single(listCone*, Single_Cone_Parameters*): Assertion 
`num_rays == Parameters->Number_of_Variables'
failed.

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Re: [sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[William Stein]

On Sat, Nov 4, 2017 at 6:27 PM, Matthias Koeppe
 wrote:
> Can you show the output of the crash on CoCalc?

Also, the crash could just be running out of memory...

>
>
> On Saturday, November 4, 2017 at 3:46:01 PM UTC-7, Mark Bell wrote:
>>
>> Thanks!
>>
>> I'm not sure if this is the right place to add this but the attached
>> example also causes LattE to crash, but I only see this behaviour when I run
>> this code on CoCalc. When I run the script on my local machine with
>> latte_int installed it completes and prints out 19958. Surely this isn't
>> being caused by the same bug.
>
> --
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-- 
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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Matthias Koeppe]

Can you show the output of the crash on CoCalc?

On Saturday, November 4, 2017 at 3:46:01 PM UTC-7, Mark Bell wrote:
>
> Thanks! 
>
> I'm not sure if this is the right place to add this but the attached 
> example also causes LattE to crash, but I only see this behaviour when I 
> run this code on CoCalc. When I run the script on my local machine with 
> latte_int installed it completes and prints out 19958. Surely this isn't 
> being caused by the same bug.
>

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

['Mark Bell' via sage-devel]

Thanks! 

I'm not sure if this is the right place to add this but the attached 
example also causes LattE to crash, but I only see this behaviour when I 
run this code on CoCalc. When I run the script on my local machine with 
latte_int installed it completes and prints out 19958. Surely this isn't 
being caused by the same bug.

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from sage.all import Polyhedron

eqns = [
[0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, -1, 0, 0, 0], 
[0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 1, 1, -1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, -1, -1, 0, 0, 1, 0 , 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, -1, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, -1, 0],
[0, 0, -1, -1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1],
[0, -1, 0, -1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[-100, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0]
]
ieqs = [
[-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
[-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[50, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
]

P = Polyhedron(eqns=eqns, ieqs=ieqs)
print(P.integral_points_count(preprocess=False))

[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Matthias Koeppe]

On Friday, November 3, 2017 at 5:44:43 PM UTC-7, Matthias Koeppe wrote:
>
> On Friday, November 3, 2017 at 5:22:16 PM UTC-7, Matthias Koeppe wrote:
>>
>> On Friday, November 3, 2017 at 5:06:13 PM UTC-7, Matthias Koeppe wrote:
>>>
>>> On Friday, November 3, 2017 at 1:41:33 PM UTC-7, Mark Bell wrote:

 So when k = 19, sage.interfaces.latte.count 
 
  
 and P.integral_points_count() give different answers. This seems to be the 
 cause of the difference. Here is some more code showing the difference.

>>>
>>> The bug appears to be in the preprocessing code of 
>>> integral_points_count().
>>> If you use preprocess=False, the number of lattice points is correct 
>>> (19).
>>>
>>> Looks like to_linear_program() handles equations wrong!
>>
>
> Ticket at https://trac.sagemath.org/ticket/24154 
>

Ticket needs review. 

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Matthias Koeppe]

On Friday, November 3, 2017 at 5:22:16 PM UTC-7, Matthias Koeppe wrote:
>
> On Friday, November 3, 2017 at 5:06:13 PM UTC-7, Matthias Koeppe wrote:
>>
>> On Friday, November 3, 2017 at 1:41:33 PM UTC-7, Mark Bell wrote:
>>>
>>> So when k = 19, sage.interfaces.latte.count 
>>> 
>>>  
>>> and P.integral_points_count() give different answers. This seems to be the 
>>> cause of the difference. Here is some more code showing the difference.
>>>
>>
>> The bug appears to be in the preprocessing code of 
>> integral_points_count().
>> If you use preprocess=False, the number of lattice points is correct (19).
>>
>> Looks like to_linear_program() handles equations wrong!
>

Ticket at https://trac.sagemath.org/ticket/24154 

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Matthias Koeppe]

On Friday, November 3, 2017 at 5:06:13 PM UTC-7, Matthias Koeppe wrote:
>
> On Friday, November 3, 2017 at 1:41:33 PM UTC-7, Mark Bell wrote:
>>
>> So when k = 19, sage.interfaces.latte.count 
>> 
>>  
>> and P.integral_points_count() give different answers. This seems to be the 
>> cause of the difference. Here is some more code showing the difference.
>>
>
> The bug appears to be in the preprocessing code of integral_points_count().
> If you use preprocess=False, the number of lattice points is correct (19).
>
> Looks like to_linear_program() handles equations wrong!
 

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Matthias Koeppe]

On Friday, November 3, 2017 at 1:41:33 PM UTC-7, Mark Bell wrote:
>
> So when k = 19, sage.interfaces.latte.count 
> 
>  
> and P.integral_points_count() give different answers. This seems to be the 
> cause of the difference. Here is some more code showing the difference.
>

The bug appears to be in the preprocessing code of integral_points_count().
If you use preprocess=False, the number of lattice points is correct (19).

 

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

['Mark Bell' via sage-devel]

So when k = 19, sage.interfaces.latte.count 

 
and P.integral_points_count() give different answers. This seems to be the 
cause of the difference. Here is some more code showing the difference.

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from sage.all import Polyhedron
from sage.interfaces.latte import count

eqns = [
[0, -1, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, -1, 0, 0, 1, 1, -1, 0, 0],
[0, 0, 0, 0, -1, 0, -1, 1, 0, 1, 0, 0, 0],
[0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 1, 1, -1],
[0, 0, -1, -1, 0, 1, 0, 0, 0, 0, 0, 1, 0],
[0, -1, 1, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1],
[-100, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[-19, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
]
ieqs = [
[-1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0],
[-1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1]
]

P = Polyhedron(eqns=eqns, ieqs=ieqs)
print(P.integral_points_count())
print(count(P.cdd_Hrepresentation(), cdd=True))

[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

['Mark Bell' via sage-devel]

Great suggestion. Could you ask polymake to compute what the number of 
lattice points in each x_0 = k (for k = 1, ..., 100) slice? Does it match:
[84, 84, 84, 81, 81, 81, 75, 75, 75, 66, 66, 66, 54, 54, 54, 39, 39, 
39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 
0, 0, 0, 0, 0, 0, 0, 0]

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Simon King]

I opened trac ticket #24152 for the bug in converting the polyhedron
into polymake.

On 2017-11-03, Simon King  wrote:
> First of all, there seems to be some bug in the polymake interface
> (that I authored, so: Sorry...):
>   sage: P = Polyhedron(eqns = eqns, ieqs=ieqs)
>   sage: PP = polymake(P)

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[sage-devel] Re: Polyhedron.integral_points_count() gives inconsistent answers on slices

[Simon King]

Hi!

On 2017-11-03, 'Mark Bell' via sage-devel  wrote:
> And so I did:
>> Polyhedron(eqns=eqns, ieqs=ieqs).integral_points_count()
> 1260
>
> However, if I look at all of the slices obtained by fixing the first 
> variable x_0 (which must be 1 <= x_0 <= 100 by the first equation and 
> inequality) then I get the following numbers of integral points in each 
> slice:
>
>> [Polyhedron(eqns=eqns+[[-k, 1, 0,0,0,0,0,0,0,0,0,0,0]], 
> ieqs=ieqs).integral_points_count() for k in range(1, 101)]
> [84, 84, 84, , 0, 0, 0]
>
> Which is fewer points in total:
>
>> sum(_)
> 1197

Sorry that I am not directly answering your question. What does polymake
have to say about that polyhedron?

First of all, there seems to be some bug in the polymake interface
(that I authored, so: Sorry...):
  sage: P = Polyhedron(eqns = eqns, ieqs=ieqs)
  sage: PP = polymake(P)

The conversion of P into a polymake polytope fails first (that's the bug),
but when one tries again, there is no complaint.

sage: PP.VERTICES
1 1 1 46/3 1 49/3 46/3 0 49/3 49/3 49/3 0 1
1 45/2 45/2 1 1 47/2 1 0 47/2 2 2 0 1
1 45/2 1 1 1 2 1 0 47/2 2 47/2 0 45/2
1 1 1 1 45/2 2 1 0 2 47/2 47/2 0 45/2
1 1 45/2 1 45/2 47/2 1 0 2 47/2 2 0 1
sage: P.vertices_list()   # Sage agrees with Polymake
[[1, 1, 46/3, 1, 49/3, 46/3, 0, 49/3, 49/3, 49/3, 0, 1],
 [45/2, 45/2, 1, 1, 47/2, 1, 0, 47/2, 2, 2, 0, 1],
 [45/2, 1, 1, 1, 2, 1, 0, 47/2, 2, 47/2, 0, 45/2],
 [1, 1, 1, 45/2, 2, 1, 0, 2, 47/2, 47/2, 0, 45/2],
 [1, 45/2, 1, 45/2, 47/2, 1, 0, 2, 47/2, 2, 0, 1]]
sage: PP.N_LATTICE_POINTS # Sage agrees with Polymake again.
1260

Best regards,
Simon

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