Concepts

The concept library captures every concept learned, implemented in every
applicable language, with tests proving equivalence.

Structure

Each concept is a directory under its domain:

concepts/
  math/
    calculus/
      notes.tex         # Standalone LaTeX document
      notes_body.tex    # Body only (for \input into collections)
      calculus.rb       # Ruby reference implementation
      test.rb           # Cross-implementation equivalence tests
    linear_algebra/
      ...
  circuits/
    rc_lowpass/
      notes.tex
      rc_lowpass.cir    # ngspice netlist
      rc_lowpass.rb     # Ruby implementation
      test.rb
  control/
    pid/
      notes.tex
      pid.rb            # Ruby
      pid.c             # C
      pid.v             # Verilog
      pid.comp          # GLSL compute shader
      test.rb

Domains

Domain	Directory	Primary Tool
Pure math	`math/`	Maxima (symbolic), Ruby (numerical)
Signals & systems	`signals/`	Maxima, Ruby, GLSL
Control theory	`control/`	Maxima, Ruby, Verilog
Circuit theory	`circuits/`	ngspice, Maxima
Digital electronics	`digital/`	Verilog, C
Electromagnetics	`electromagnetics/`	Maxima, Elmer
Physics	`physics/`	Maxima, Ruby, Elmer
Chemistry	`chemistry/`	Maxima, Ruby, Elmer
Programming	`programming/`	Ruby, C
Embedded systems	`embedded/`	C, Verilog
Computer architecture	`computer_architecture/`	Verilog, C
Numerical methods	`numerical_methods/`	Ruby, C, GLSL
Communications	`communications/`	Maxima, Ruby, GLSL

Sparse Matrix

Not every concept maps to every language. Implement where it makes sense.

See Concept Library in the long-term plan for details.