FunTable

FunTable is a Wolfram Language (Mathematica) package for generating numerical tables of conformal-bootstrap functionals (1d / 2d / 3d) and assembling them into linear-programming (LP) bootstrap problems.

It evaluates the 1d crossing functionals in arbitrary precision, builds the 2d and 3d functionals from them by dimensional reduction, and exports packed HDF5 tables for downstream LP solvers.

Requirements

• Wolfram Language / Mathematica (developed with 13.x–14.x).
• A working C compiler (gcc/clang). Performance-critical kernels in src/Table.wl are compiled with CompilationTarget -> "C" and cached in lib/ on first load; the cache is platform-specific and is (re)built automatically if absent.

Loading

Load the package as a file, so $InputFileName resolves the src/ paths:

Get["/path/to/FunTable/FunTable.wl"]

FunTable.wl sets its own directory and loads src/OneDfunctional.wl, src/OneDAsymp.wl, and src/Table.wl in order.

Quick start

Generate a 3d functional table (HDF5) at external dimension Δφ:

Get["/path/to/FunTable/FunTable.wl"];   (* as a file *)
LaunchKernels[];                        (* the 1d generation step is parallel *)

dphi3d = 5181488023/10000000000;        (* exact rational; e.g. the 3d Ising point *)
dphi1d = dphi3d/2;                      (* convention: 1d dphi = 3d Δφ / 2 *)

(* 1. 1d table (.mx): orderMax = 10, ΔMax_gen = 650, exp-normalized *)
generate1ptmx["Ising.mx", dphi1d, 10, 650, True];

(* 2. 3d table: normalized, with 30 sub-bound "ghost" interpolation rows *)
lp = init3DTablePatch["Ising.mx", 10, Range[0, 100, 2], 150, 500,
                      "normed" -> True, "fill" -> 30];

(* 3. export to HDF5 *)
lpN = KeyDrop[KeyMap[# /. "Δtable" -> "dtable" &, lp], "normed"];
Export["Ising.h5", Normal[lpN], "HDF5"];

The FunTable.nb notebook is a runnable version of this (1d single-point evaluation + the full 3d-table pipeline). For the complete technical reference see H5_generation_technical_summary.md.

Repository layout

path	contents
FunTable.wl	top-level loader; defines generate1ptmx
src/OneDfunctional.wl	1d crossing functionals (arbitrary-precision, hypergeometric)
src/OneDAsymp.wl	large-Δ asymptotic expansions of the same functionals
src/asympcoeff.wl	hardcoded asymptotic-series coefficients
src/Table.wl	2d/3d construction, normalization, HDF5 tables, LP setup
FunTable.nb	usage-example notebook
H5_generation_technical_summary.md	technical reference for the generation pipeline
doc/	focused notes (exp-only normalization, init3DTablePatch)
lib/	compiled-kernel cache (generated on first load; not shipped)

Key entry points

• generate1ptmx[file, dphi1d, orderMax, ΔMax_gen, normed] — build and save the 1d table (.mx).
• init1DTable / init2DTable / init3DTable / init3DTablePatch — load a saved table or derive a higher-dimensional one; return an Association ("functablePacked", "dtable", "spinlist", "order", …).
• sectionPosList, gapcostlist, initLP — build the Δ index slabs and the LP problem.

Conventions

• 1d dphi = 3d Δφ / 2 (external dimension).
• Δ grids: 1d Range[0, ΔMax_gen, 1/202]; 2d/3d spacing 1/101 (halfstep = 101), index i ↔ Δ = (i−1)/101.
• Use exact rationals for Δφ so the high-precision generation is not limited by float rounding of the input.
• Generation configs: High (ΔMax_gen = 500, nmax = 350), VeryHigh (650, 500); orderMax is the functional truncation order (10 standard, 12 extended).

Normalization, the ghost-node fill, the packed data layout, and special-Δφ handling are documented in H5_generation_technical_summary.md.

License

(No license file yet — add one before public release.)