2020-06-09 21:34:25 +0200 | answered a question | Toric Ideal of Point Configuration Yielding Whole Ring? I believe I have some more insight as to why this issue was happening. Since I want to consider toric ideals in the context of a lattice polytope $P$, my point configuration matrix should have had a row of $1$'s appended to the bottom since I'm really looking at the polytope embedded at height $1$ in the cone over $P$ (${\rm cone}(P)$). I was operating in the wrong dimension! Generating the whole ring makes sense with the setup in my original problem statement since two of the lattice points are the standard basis vectors. I made this realization because the ideal should be homogenenous as the polytope given as the convex hull of those $7$ points is IDP but several of the generators contained a constant term. So, I should have had something more along the lines of |

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2020-06-09 17:52:17 +0200 | commented answer | Toric Ideal of Point Configuration Yielding Whole Ring? Not sure if this is useful for anyone, but I wrote another implementation that obtains the appropriate naive ideal using the basis for kernel of the point configuration matrix. The answer is the same as |

2020-06-09 17:15:15 +0200 | commented answer | Toric Ideal of Point Configuration Yielding Whole Ring? Awesome, thank you so much! I think this will work well for my purposes. Greatly appreciate it! |

2020-06-09 17:13:11 +0200 | commented question | Toric Ideal of Point Configuration Yielding Whole Ring? Thank you so much! |

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2020-06-09 07:03:49 +0200 | asked a question | Toric Ideal of Point Configuration Yielding Whole Ring? So I am trying to find the toric ideal of a point configuration given by the lattice points contained within a family of polytopes I am studying to assess regularity/unimodularity of triangulations of the point configuration (I'm attempting to follow the guidelines specified in Bernd Sturmfels' text Grobner Bases and Convex Polytopes). I know that toric ideals are supposed to be prime and their reduced Grobner bases are generated by binomials, but for whatever reason, the For example, say that we're looking at the point configuration given by the lattice points (1,0), (0,1), (0,0), (0,-1), (-1,-1), (-1,-2), (-2,-3). Inputting these points as columns in a matrix and computing the toric ideal as indicated in the sage documentation should be as simple as: However, when I run this I get the following output: I cannot determine why this is the case. For some context, I asked a colleague to compute the toric ideal using |

2020-04-27 17:58:07 +0200 | commented answer | Attribute error: "'Graphics' object has no attribute 'get_pos'" with plotting Hasse diagram of poset You are my hero! Worked like a charm. Thank you so much. I greatly appreciate it. |

2020-04-27 16:27:26 +0200 | commented answer | Attribute error: "'Graphics' object has no attribute 'get_pos'" with plotting Hasse diagram of poset Thank you for your comment! So this makes sense if I want to obtain the positions of |

2020-04-26 01:21:18 +0200 | commented question | Attribute error: "'Graphics' object has no attribute 'get_pos'" with plotting Hasse diagram of poset If you were to insert |

2020-04-26 01:16:07 +0200 | commented answer | Attribute error: "'Graphics' object has no attribute 'get_pos'" with plotting Hasse diagram of poset I see. Thank you. So there is no way to obtain the positions used for displaying the Hasse diagram of the poset? |

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2020-04-25 02:03:07 +0200 | asked a question | Attribute error: "'Graphics' object has no attribute 'get_pos'" with plotting Hasse diagram of poset So I am trying to obtain the position dictionary used for displaying a poset P that can be used in the plotting of the Hasse diagram of P through the hasse_diagram() function. To clarify, if I run the following code: The locations of the vertices of G do not line up with where the corresponding elements of the poset were. I know that we can save the position dictionary for graphs, but for whatever reason, I'm struggling with obtaining the position dictionary of elements in a poset. (With the specific posets I am working with, maintaining the position when obtaining the undirected Hasse diagram is important because I need a particular planar embedding which is not being preserved if I simply use the hasse_diagram() function in its canned form). In the finite posets SageMath documentation, the I get an attribute error: Is there any way to extract a position dictionary of a graphics object corresponding to the Hasse diagram of a poset? |

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