Cannot plot Cone that is a halfplane in 2d

[yuan-zhou]

sage: halfplane = Cone([(1,0), (0,1), (-1,0)])
sage: halfplane.plot() 

raises UnboundLocalError: local variable 'r1' referenced before assignment.

CC: @novoselt @jplab @mkoeppe @orlitzky

Component: geometry

Keywords: Cone, plot, IMA-PolyGeom

Branch/Commit: u/yzh/cannot_plot_cone_that_is_a_halfplane_in_2d @ 57f5898

Issue created by migration from https://trac.sagemath.org/ticket/25114

[yuan-zhou]

Branch: u/yzh/cannot_plot_cone_that_is_a_halfplane_in_2d

[yuan-zhou]

New commits:

959187f

represent the rays of wall by a matrix. add doctest

[yuan-zhou]

Commit: 959187f

[yuan-zhou]

Changed keywords from Cone, plot to Cone, plot, IMA-PolyGeom

[novoselt]

comment:3

While this may fix the plotting issue, it hides the real problem:

sage: N = ToricLattice(2); N
2-d lattice N
sage: NQ = N.base_extend(QQ); NQ
Vector space of dimension 2 over Rational Field
sage: r = N.gen(0); r
N(1, 0)
sage: S = N.submodule([r]); S
Sublattice <N(1, 0)>
sage: SQ = S.base_extend(QQ); SQ
 
Vector space of degree 2 and dimension 1 over Rational Field
Basis matrix:
[1 0]
sage: r in N, r in NQ
(True, True)
sage: r in S, r in SQ
(True, False)

Why is there this difference in behaviour of vector spaces and subspaces? The original code likely worked for halfplanes when it was written and there is no reason for it to stop.

[jplab]

comment:4

Replying to @novoselt:

While this may fix the plotting issue, it hides the real problem:

sage: N = ToricLattice(2); N
2-d lattice N
sage: NQ = N.base_extend(QQ); NQ
Vector space of dimension 2 over Rational Field
sage: r = N.gen(0); r
N(1, 0)
sage: S = N.submodule([r]); S
Sublattice <N(1, 0)>
sage: SQ = S.base_extend(QQ); SQ
 
Vector space of degree 2 and dimension 1 over Rational Field
Basis matrix:
[1 0]
sage: r in N, r in NQ
(True, True)
sage: r in S, r in SQ
(True, False)

Why is there this difference in behaviour of vector spaces and subspaces? The original code likely worked for halfplanes when it was written and there is no reason for it to stop.

Looking at the file src/sage/structure/parent.pyx in the __contains__ function, it returns False because:

sage: type(r)
<class 'sage.geometry.toric_lattice_element.ToricLatticeElement'>
sage: r2 = SQ(r); r2
(1, 0)
sage: type(r2)
<class 'sage.modules.vector_rational_dense.Vector_rational_dense'>

and

sage: r2 == r
False

Now, should this return True? I am not sure how to fix this...

[mkoeppe]

comment:5

pushing these forward to 9.2

[mkoeppe]

comment:8

Setting new milestone based on a cursory review of ticket status, priority, and last modification date.

[yuan-zhou]

comment:9

Is it possible to make the plotting work at least? It's a bit annoying to have encountered this same error after each reinstallation of Sage.

[sagetrac-git]

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

57f5898

Merge branch 'develop' of git://trac.sagemath.org/sage into HEAD

[sagetrac-git]

Changed commit from 959187f to 57f5898

[orlitzky]

comment:11

Replying to @yuan-zhou:

Is it possible to make the plotting work at least? It's a bit annoying to have encountered this same error after each reinstallation of Sage.

I was juuuust about to agree with you. But the underlying problem here is serious. Equality is not transitive:

sage: N = ToricLattice(2)                                                       
sage: NQ = N.base_extend(QQ)                                                    
sage: r = N.gen(0)                                                              
sage: S = N.submodule([r])                                                      
sage: SQ = S.base_extend(QQ)                                                    
sage: r == S(r)                                                                 
True
sage: S(r) == SQ(r)                                                             
True
sage: r == SQ(r)                                                                
False

[mkoeppe]

comment:12

Setting a new milestone for this ticket based on a cursory review.