Frame Theory
FrameTheory.jl is a collection of tool for working with Frames in Julia. A large portion of this package uses the Julia Package Oscar.jl.
Current FrameTheory.jl Functionality
Algorithms
This package implements a variety of algorithms for each of the above types of frames.
Binder Finder
Projective Symmetry Groups
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;Since Oscar is used through FrameTheory.jl it is reccommended to also load it.
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