MORI.X(1)

📦
version 2.21 · 3 versions
, in debian bookworm, debian trixie, ubuntu jammy, ubuntu noble, ubuntu questing, ubuntu resolute, ubuntu stonking

💖 MORI.X 💖

okay bestie, welcome to mori.x (and its whole little friend group mori-<num>d.x) — we're doing star triangulations of a polytope P* in N today and honestly? it's giving geometry main character energy. 🌟

✨ SYNOPSIS ✨

mori.x [-<Option-string>] [in-file [out-file]]

🌸 DESCRIPTION 🌸

So like. Mori cone of the corresponding toric ambient spaces intersection rings of embedded (CY) hypersurfaces. Yes that's a lot of nouns in a row and yes it slays. 💅

The mori-<num>d.x variant programs, where <num> is one of 4, 5, 6 and 11, work in different dimensions 🦋 — like, they each live in their own dimension, no cap. And mori.x itself defaults to dimension 6, because six is the moment.

🎀 Options 🎀

(concatenate any number of them into <Option-string> — yes literally just squish them together, it's a whole vibe check) 💖

  • -h — print this information. the "help me bestie" button 🫶
  • -f — use as filter. it's giving sieve 🧚
  • -g — general output: triangulation and Stanley-Reisner ideal. the classic combo meal ✨
  • -I — incidence information of the facets (ignoring IPs of facets). facets only, no IPs, we said what we said 🙈
  • -m — Mori generators of the ambient space. the Mori-est of them all 👑
  • -P — IP-simplices among points of P* (ignoring IPs of facets). again, IPs of facets are simply not invited to this party 💀
  • -K — points of P* in Kreuzer polynomial form. fancy polynomial outfit 🌈
  • -b — arithmetic genera and Euler number. numbers but make it aesthetic ⭐
  • -i — intersection ring. ring ring, it's the intersection calling 📞
  • -c — Chern classes of the (CY) hypersurface. Chern classes periodt. 🔥
  • -t — triple intersection numbers. three. times. the intersections. 🍓
  • -d — topological information on toric divisors & del Pezzo conditions. del Pezzo stans rise 💜
  • -a — all of the above except h, f, I and K. so close to everything, but not h, f, I, K. read the list bestie, I'm not gonna say it twice 😭
  • -D — lattice polytope points of P* as input (default CWS). switching up the input format, highkey iconic 💫
  • -H — arbitrary (also non-CY) hypersurface `H = c1*D1 + c2*D2 + ...' input: coefficients `c1 c2 ...'. you hand it the coefficients, it handles the chaos 🎀
  • -M — manual input of triangulation. you're driving this one yourself, main character style 👑

🌈 Input 🌈

  1. standard: degrees and weights
`d1 w11 w12 ... d2 w21 w22 ...'
  1. alternative (use -D): d np or np d (d=Dimension, np=#[points]) and (after newline) np*d coordinates
note the little newline moment in option 2 — the coordinates come after it, not squished on the same line 🫶

💜 Output 💜

as specified by options. yeah. that's the whole spec. you picked the options, you get the output, that's the deal ✨

🦋 SEE ALSO 🦋

A complete manual is available here : http://arxiv.org/abs/1205.4147

go read it, it's the extended cut 💖

okay that's the whole page, you ate that. this was mori.x version 2.1, from May 2012 — yes she's an elder but she's still THAT girl, and we love her for it. bye bestie, go triangulate something 🎀💅✨

📦 where this page comes from