Replay gfan interface history

[antonleykin]

Summary

This PR brings the Tropical branch's work on gfanInterface.m2 (developed
during the 2026 Warwick workshop, building on 2023 workshop code) into
development. The full per-commit history is preserved: the changes are
replayed as 37 linear commits on top of development, with no unrelated-history
merge or disconnected root.

Changes to gfanInterface

• gfanTropicalPrevariety — reworked method with two new options:
  • "matrixoutput" => Boolean — exposes gfan's --matrixoutput flag; each
    half-open cone is returned as an ambient dimension plus three matrices
    (nonstrict inequalities, equations, strict inequalities).
  • "halfopenrestrictions" — passes gfan's --halfopenrestrictions, letting
    the computation be restricted to a supplied list of half-open cones.
  • Fixes to max cones and to gfanParsePolyhedralFan.
• p-adic support — adds gfanPadicInitialIdeal and wires up the
  gfan _padic command (code originally written in the 2023 workshop
  development branch).
• Mixed volume — corrected gfan _mixedvolume handling.
• MarkedPolynomialList — implemented == for marked polynomial lists.
• Documentation & tests — new/updated docs for gfanTropicalPrevariety
  (including "matrixoutput" and "halfopenrestrictions" examples), plus
  numerous test fixes (homogeneity space, fan product, mixed volume).

Net change: +514 / −239 in M2/Macaulay2/packages/gfanInterface.m2.

Checklist (per the M2 PR guide)

• Targets the development branch (not stable).
• Keywords => {"Interfaces"} present in the package header.
• DebuggingMode not enabled in newPackage (defaults to false).
• Existing distributed package — no =distributed-packages change needed.

Contributors

@antonleykin
Diane Maclagan (github id info lost in commits) @dmaclagan ?
@GabrielRiffoJ
@VictoriaSchleis

[d-torrance]

As I recall, gfanTropicalPrevariety requires gfan 0.8, right?

This is an issue on legacy systems since gfan doesn't compile unless you have a relatively modern gcc (or even on modern systems with clang).

What's the preferred path forward?

• Check for the gfan version and do something sensible (either raise an error and skip the tests/used cached documentation or maybe just implement the algorithm in M2). Also remove the version check in the autotools build or change it from an error to a warning.
• Work on getting gfan to compile on these legacy systems before the November release