docs: complete API list

Author: oameye

docs/src/API.md

@@ -1,19 +1,73 @@
+```@meta
+CollapsedDocStrings = true
+```
+
 # API
 
-## Symbolic Utilities
+```@contents
+Pages = ["API.md"]
+Depth = 2:3
+```
+
+## Classical harmonic systems
+
+### Classical equations of motion in lab frame
 
 ```@docs
+QuestBase.DifferentialEquation
+QuestBase.rearrange_standard!(::QuestBase.DifferentialEquation)
+QuestBase.rearrange!
+QuestBase.is_rearranged_standard
+QuestBase.get_equations
+QuestBase.get_independent_variables(::QuestBase.DifferentialEquation)
+QuestBase.get_variables(::QuestBase.DifferentialEquation)
+```
+
+### Harmonics
 
+```@docs
+QuestBase.HarmonicVariable
+QuestBase.add_harmonic!
 ```
 
-## Classical harmonic systems
+### Effective stroboscopic equations of motion in a rotating frame
+
+```@docs
+QuestBase.HarmonicEquation
+QuestBase.get_independent_variables(::QuestBase.HarmonicEquation)
+QuestBase.get_variables(::QuestBase.HarmonicEquation)
+QuestBase.rearrange_standard(::QuestBase.HarmonicEquation)
+QuestBase.rearrange_standard!(::QuestBase.HarmonicEquation)
+QuestBase.rearrange
+QuestBase.is_rearranged
+```
+
+## Steady state methods
 
 ```@docs
+QuestBase.HarmonicBalanceMethod
+```
+
+## Symbolic Utilities
 
+QuestBase contains a number of symbolic utilities to help with the symbolic manipulation of the equations of motion. These are function on the top of the Symbolics.jl package and are consired **non-public**.
+
+```@docs
+QuestBase.d
 ```
 
-## Classical harmonic systems
+### Exponentials
 
 ```@docs
+QuestBase.simplify_exp_products
+QuestBase.expand_exp_power
+```
+
+### Trigonometrics
 
+```@docs
+QuestBase.trig_reduce
+QuestBase.is_trig
+QuestBase.exp_to_trig
+QuestBase.trig_to_exp
 ```

docs/src/index.md

@@ -6,4 +6,21 @@ It is designed ensure compatiabilty between the different available packages.
 This documentation is made to pool together the docs of the various Quest libraries
 to paint the overarching picture and document the shared/common functionality.
 
-<!-- ## Packages of Quest Ecosystem -->
+## Packages of Quest Ecosystem
+
+### [HarmonicBalance.jl](https://github.com/QuantumEngineeredSystems/HarmonicBalance.jl):
+
+A package for applying the harmonic balance method to classical driven nonlinear resonators.
+It computes the stroboscopic effective equations of motion of the system at the characteristic response frequencies of the system.
+Both [Krylov-Bogoliubov](https://quantumengineeredsystems.github.io/HarmonicBalance.jl/stable/manual/extracting_harmonics#Krylov-Bogoliubov) averaging method to higher orders and the [harmonic balance method](https://quantumengineeredsystems.github.io/HarmonicBalance.jl/stable/manual/extracting_harmonics#Krylov-Bogoliubov) are implemented.
+
+### [HarmonicSteadyState.jl](https://github.com/QuantumEngineeredSystems/HarmonicSteadyState.jl)
+
+A package for computing the classical steady state of the effective stroboscopic systems driven nonlinear resonators. Given one has the autonomous equations of motion of the system in the rotating frame of the characteristic response frequencies, it collect steady states methods to find and describe the stationary responses of the system. It supports the following methods:
+
+- fixed point steady states with Homotopy Continuation
+- Finding Limit-cycle  with Homotopy Continuation
+- Stability analysis
+- Linear response of the steady state in the (non-)rotating frame
+- Parameter sweeps
+- Plotting utilities

src/HarmonicEquation.jl

@@ -149,6 +149,7 @@ function rearrange!(eom::HarmonicEquation, new_rhs::Vector{Num})
     return nothing
 end
 
+"Rearrange an equation system such that the field equations is equal to the vector specified in new_lhs"
 function rearrange(eom::HarmonicEquation, new_rhs::Vector{Num})
     new_eom = deepcopy(eom)
     rearrange!(new_eom, new_rhs)

src/Symbolics/fourier.jl

@@ -1,5 +1,26 @@
+"""
+    trig_reduce(x)
+
+Simplify trigonometric expressions by converting between exponential and trigonometric forms.
+This function performs the following steps:
+1. Combines fractions with common denominators
+2. Expands all brackets
+3. Converts trigonometric functions to exponentials
+4. Expands products of exponentials
+5. Simplifies exponential products
+6. Converts back to trigonometric form
+7. Simplifies complex expressions
+
+Returns the simplified expression as a `Num` type.
+"""
 
-"Expand all sin/cos powers in `x`."
+"""
+    is_trig(f::Num)
+
+Check if the given expression `f` is a trigonometric function (sine or cosine).
+
+Returns `true` if `f` is either `sin` or `cos`, `false` otherwise.
+"""
 function trig_reduce(x)
     x = add_div(x) # a/b + c/d = (ad + bc)/bd
     x = expand(x) # open all brackets
@@ -19,8 +40,24 @@ function is_trig(f::Num)
 end
 
 """
-$(TYPEDSIGNATURES)
-Returns the coefficient of cos(ωt) in `x`.
+    fourier_cos_term(x, ω, t)
+
+Extract the coefficient of cos(ωt) from the expression `x`.
+Used in Fourier analysis to find the cosine components of a periodic function.
+
+# Arguments
+- `x`: The expression to analyze
+- `ω`: The angular frequency
+- `t`: The time variable
+"""
+
+"""
+    add_div(x)
+
+Simplify fractions by combining terms with common denominators.
+Transforms expressions of the form a/b + c/d into (ad + bc)/bd.
+
+Returns the simplified fraction as a `Num` type.
 """
 function fourier_cos_term(x, ω, t)
     return _fourier_term(x, ω, t, cos)
@@ -30,13 +67,34 @@ end
 add_div(x) = wrap(Postwalk(add_with_div; maketerm=frac_maketerm)(unwrap(x)))
 
 """
-$(TYPEDSIGNATURES)
-Returns the coefficient of sin(ωt) in `x`.
+    fourier_sin_term(x, ω, t)
+
+Extract the coefficient of sin(ωt) from the expression `x`.
+Used in Fourier analysis to find the sine components of a periodic function.
+
+# Arguments
+- `x`: The expression to analyze
+- `ω`: The angular frequency
+- `t`: The time variable
 """
 function fourier_sin_term(x, ω, t)
     return _fourier_term(x, ω, t, sin)
 end
 
+"""
+    _fourier_term(x::Equation, ω, t, f)
+    _fourier_term(x, ω, t, f)
+
+Internal function to extract Fourier coefficients from expressions.
+Handles both equations and regular expressions, returning the coefficient
+of the specified trigonometric function f(ωt).
+
+# Arguments
+- `x`: The expression or equation to analyze
+- `ω`: The angular frequency
+- `t`: The time variable
+- `f`: The trigonometric function (sin or cos)
+"""
 function _fourier_term(x::Equation, ω, t, f)
     return Equation(_fourier_term(x.lhs, ω, t, f), _fourier_term(x.rhs, ω, t, f))
 end
@@ -51,7 +109,15 @@ function _fourier_term(x, ω, t, f)
     return Symbolics.expand(ft)
 end
 
-"Convert all sin/cos terms in `x` into exponentials."
+
+"""
+    trig_to_exp(x::Num)
+
+Convert all trigonometric terms (sin, cos) in expression `x` to their exponential form
+using Euler's formula: ``\\exp(ix) = \\cos(x) + i*\\sin(x)``.
+
+Returns the converted expression as a `Num` type.
+"""
 function trig_to_exp(x::Num)
     all_terms = get_all_terms(x)
     trigs = filter(z -> is_trig(z), all_terms)
@@ -82,6 +148,22 @@ end
 convert_to_Num(x::Complex{Num})::Num = Num(first(x.re.val.arguments))
 convert_to_Num(x::Num)::Num = x
 
+"""
+    exp_to_trig(x::BasicSymbolic)
+    exp_to_trig(x)
+    exp_to_trig(x::Num)
+    exp_to_trig(x::Complex{Num})
+
+Convert exponential expressions to their trigonometric form using
+the inverse of Euler's formula:
+``\\cos(x) = (\\exp(ix) + \\exp(-ix))/2``
+and
+``\\sin(x) = (\\exp(ix) - \\exp(-ix))/(2i)``.
+
+Handles various input types including basic symbolic expressions,
+complex numbers, and `Num` types. Standardizes the sign of
+trigonometric arguments for consistent simplification.
+"""
 function exp_to_trig(x::BasicSymbolic)
     if isadd(x) || isdiv(x) || ismul(x)
         return _apply_termwise(exp_to_trig, x)