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Frame Theory

FrameTheory.jl is a collection of tools for working with Frames in Julia. A large portion of this package uses the Julia Package Oscar.jl.

This package was originally developed as companion software for the paper [5] to compute frames over finite field, which represent a large majority of the package. Later the packages was expanded to work with frames over real and complex numbers, both using exact arithmetic, and numerical arithmetic.

Current FrameTheory.jl Functionality

Getting Started

Please refer to the Oscar.jl installation instructions here.

Activate and load this package: In the FrameTheory directory

pkg> activate .
pkg> instantiate  # Press ']' to enter the Pkg REPL mode.

Or by running using Pkg; Pkg.activate("."); Pkg.instantiate();.

Then 

julia> using FrameTheory; using Oscar;

File Utilities

Currently, this package only supports file utilities for numerically defined frames.

FrameTheory.load_matrix_from_file — Function
load_matrix_from_file(file_loc, d, n[, format]) -> Matrix{Number}

Arguments

  • file_loc::String:
  • d::Int:
  • n::Int:
  • format::Symbol: file format

Returns

  • loaded_matrix::Matrix{Number}: either a matrix of BigFloat or Complex{BigFloat} read in from file.

Reads in a text file in the format from Game of Sloanes. Currently format=:gos is the only accepted format.

source

Referneces

[OSCAR] OSCAR – Open Source Computer Algebra Research system, Version 1.7.2, The OSCAR Team, 2026. (https://www.oscar-system.org)

[OSCAR-book] Wolfram Decker, Christian Eder, Claus Fieker, Max Horn, Michael Joswig, eds. The Computer Algebra System OSCAR: Algorithms and Examples, Algorithms and Computation in Mathematics, Springer, 2025. (https://link.springer.com/book/9783031621260)

[1] Greaves, G., Iverson, J., Jasper, J., & Mixon, D. (2022). Frames over finite fields: basic theory and equiangular lines in unitary geometry. Finite Fields Appl., 77, Paper No. 101954, 41.

[2] Greaves, G., Iverson, J., Jasper, J., & Mixon, D. (2022). Frames over finite fields: equiangular lines in orthogonal geometry. Linear Algebra Appl., 639, 50–80.

[3] Iverson, J., King, E., & Mixon, D. (2021). A note on tight projective 2-designs. J. Combin. Des., 29(12), 809–832.

[4] Joseph W. Iverson, & Dustin G. Mixon. (2025). Asymmetric SICs over finite fields.

[5] Ian Jorquera, & Emily J. King. (2025). On the Structure of Frames and Equiangular Lines over Finite Fields and their Connections to Design Theory.

[6] Fickus, M., Jasper, J., King, E., & Mixon, D. (2018). Equiangular tight frames that contain regular simplices. Linear Algebra Appl., 555, 98–138.

[7] Chien, T.-Y., & Waldron, S. (2018). The Projective Symmetry Group of a Finite Frame. New Zealand Journal of Mathematics, 48, 55–81. https://doi.org/10.53733/35