Fix Polyhedron.volume() in 0-dimensional space

[gh-kliem]

In dimension 0, we now use the counting measure for volume:

sage: Polyhedron(vertices=[[]]).volume()
1
sage: Polyhedron(vertices=[]).volume()
0

Originally there was an attribute error:

sage: Polyhedron(vertices=[[]]).volume()
Traceback (most recent call last)
...
AttributeError: 'int' object has no attribute 'set_immutable'

[gh-kliem]

New commits:

​3bd7a03

fixed AttributeError of Polyhedron.volume()

[gh-kliem]

When thinking about it again, I'm not sure anymore that this is the correct output.

However, an AttributeError? is strange and the dostring does not indicate, what should happen.

Also it's confusing that the empty Polyhedron gives an output.

[jipilab]

This might be related to #17339. If you want to have fun in the maze of defaulting behaviour, I challenge you to come up with a full-proof default behavior that will please everyone.

One thing that you should be aware of, is the current handling of things via different H and V inputs.

sage: P = Polyhedron(vertices=[])
sage: Q = Polyhedron(vertices=[[]])
sage: P
The empty polyhedron in ZZ^0
sage: Q
A 0-dimensional polyhedron in ZZ^0 defined as the convex hull of 1 vertex

The first one is the empty polyhedron. The second one is just one point, i.e. the full space. They are not the same.

[gh-kliem]

Well, I can live with a meaningful 'NotImplementedError?'.

Either there is a measure with ambient dimension zero or not. So the empty and the one point polyhedron in zero dimensional space should either have a well-defined behaiviour or not.

The reason I looked into it is that the original error is hard to trace back. It took me a bit to figure out, what went wrong there.

Replying to jipilab:

This might be related to #17339. If you want to have fun in the maze of defaulting behaviour, I challenge you to come up with a full-proof default behavior that will please everyone.

One thing that you should be aware of, is the current handling of things via different H and V inputs.

sage: P = Polyhedron(vertices=[])
sage: Q = Polyhedron(vertices=[[]])
sage: P
The empty polyhedron in ZZ^0
sage: Q
A 0-dimensional polyhedron in ZZ^0 defined as the convex hull of 1 vertex

The first one is the empty polyhedron. The second one is just one point, i.e. the full space. They are not the same.

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​cfa12c7

volume in dimension 0 is counting measure

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​7995b24

a bit nicer documentation

[jipilab]

You should change the title and description of the ticket to reflect faithfully the changes inside the ticket.

[jipilab]

Failed doctest:

sage -t --long src/sage/geometry/polyhedron/base.py
**********************************************************************
File "src/sage/geometry/polyhedron/base.py", line 5251, in sage.geometry.polyhedron.base.Polyhedron_base.volume
Failed example:
    P = Polyhedron(vertices=[]); P
Expected:
    The empty polyhedron in ZZ^0
    0
Got:
    The empty polyhedron in ZZ^0
**********************************************************************

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​dd6f981	Merge branch 'develop' of git://trac.sagemath.org/sage into public/27673
​98e05b5	fixed doctest mistake

[jipilab]

Looks good to me now.

[vbraun]

Merge conflict, but isn't it also also mathematically wrong:

• In the "ambient" measure, if ambient dim > 0, the volume of a point is 0
• In the "ambient" measure, if ambient dim == 0, the volume of a point is 1
• In the induced measures, the volume of a point is 1
• The volume of the empty polyhedron is always 0

[gh-kliem]

Replying to vbraun:

Merge conflict, but isn't it also also mathematically wrong:

• In the "ambient" measure, if ambient dim > 0, the volume of a point is 0

See line above. Which returns 0 in that case.

• In the "ambient" measure, if ambient dim == 0, the volume of a point is 1
• In the induced measures, the volume of a point is 1

A point is projected to 0-dimensional space an then 1 is returned.

• The volume of the empty polyhedron is always 0

It has dimension -1 but ambient dimension at least 0, so zero will be returned.

I don't see which criteria is not met.

[vbraun]

Oh ok, I misread the docstring.

Still a merge conflict though.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. Last 10 new commits:

​b543c6d	remove an obsolete note in schemes, pep cleanup of zariski_vankampen
​12373c6	Change format of a 'not tested' doc test annotation
​8783bec	leave GMP's spkg-configure.m4 as it was
​64f4b4d	update docs, as discussed on #24905
​2fa1373	Mention libterm-readkey-perl
​406ece2	Mention libterm-readline-gnu-perl
​a031f09	polymake: Mention MOngoDB for polydb
​473178e	polymake: Update info on macOS
​9a4bac1	polymake: update MongoDB information for linux distros
​343130c	Updated SageMath version to 8.8.beta5

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​33b1ff9

fixed 0-dimensional volume

[gh-kliem]

Why does the merge fail again?

Last time I fixed it, was appearently a waste of time. I guess I could start a new branch again, but only if someone sets it to positive review before the merge fails again.

[jipilab]

Replying to gh-kliem:

Why does the merge fail again?

Last time I fixed it, was appearently a waste of time. I guess I could start a new branch again, but only if someone sets it to positive review before the merge fails again.

#25091 Modified the volume function and got merged in 8.8.beta6 that's most likely the conflict.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​7a7e57d

volume in dimension 0 is counting measure

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​df1f549

should be back to the original

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​a7bf147

fixed 0-dimensional volume

[gh-kliem]

I have no idea, how one is supposed to get rebase to work.

This is basically just writing the old text in the newest develop again.

[jipilab]

Looks good to me now.