Merge branch 'RootFinding' of https://github.com/n0rbed/Symbolics.jl …

…into RootFinding

Project.toml

@@ -1,7 +1,7 @@
 name = "Symbolics"
 uuid = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 authors = ["Shashi Gowda <[email protected]>"]
-version = "6.1.0"
+version = "6.2.0"
 
 [deps]
 ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
@@ -53,7 +53,7 @@ SymbolicsForwardDiffExt = "ForwardDiff"
 SymbolicsGroebnerExt = "Groebner"
 SymbolicsLuxCoreExt = "LuxCore"
 SymbolicsNemoExt = "Nemo"
-SymbolicsPreallocationToolsExt = "PreallocationTools"
+SymbolicsPreallocationToolsExt = ["PreallocationTools", "ForwardDiff"]
 SymbolicsSymPyExt = "SymPy"
 
 [compat]
@@ -78,6 +78,7 @@ LogExpFunctions = "0.3"
 LuxCore = "0.1.11"
 MacroTools = "0.5"
 NaNMath = "1"
+Nemo = "0.45, 0.46"
 PreallocationTools = "0.4"
 PrecompileTools = "1"
 RecipesBase = "1.1"

docs/Project.toml

@@ -1,19 +1,21 @@
 [deps]
 BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
+Groebner = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
 Latexify = "23fbe1c1-3f47-55db-b15f-69d7ec21a316"
+Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
 OrdinaryDiffEq = "1dea7af3-3e70-54e6-95c3-0bf5283fa5ed"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
 SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
-Groebner = "0b43b601-686d-58a3-8a1c-6623616c7cd4"
-Nemo = "2edaba10-b0f1-5616-af89-8c11ac63239a"
 
 [compat]
 BenchmarkTools = "1.3"
 Documenter = "1"
+Groebner = "0.7"
 Latexify = "0.15, 0.16"
+Nemo = "0.45, 0.46"
 OrdinaryDiffEq = "6.31"
 Plots = "1.36"
 StaticArrays = "1.5"

docs/src/manual/solver.md

@@ -1,7 +1,8 @@
 # Solver
-The main `symbolic` solver for Symbolics.jl is `symbolic_solve`. Symbolic solving
-means that it only uses analytical methods and manually solves equations for input variables.
-It uses no numerical methods and only outputs exact solutions.
+
+The main symbolic solver for Symbolics.jl is `symbolic_solve`. Symbolic solving
+means that it only uses symbolic (algebraic) methods and outputs exact solutions.
+
 ```@docs
 Symbolics.symbolic_solve
 ```
@@ -19,17 +20,20 @@ that this functionality is only used with floating point values if necessary. In
 directly handles floating point values using standard factorizations.
 
 ### More technical details and examples
+
 #### Technical details
+
 The `symbolic_solve` function uses 4 hidden solvers in order to solve the user's input. Its base,
 `solve_univar`, uses analytic solutions up to polynomials of degree 4 and factoring as its method
 for solving univariate polynomials. The function's `solve_multipoly` uses GCD on the input polynomials then throws passes the result
 to `solve_univar`. The function's `solve_multivar` uses Groebner basis and a separating form in order to create linear equations in the
-input variables and a single high degree equation in the separating variable. Each equation resulting from the basis is then passed
-to `solve_univar`. We can see that essentially, `solve_univar` is the building block of `symbolic_solve`.if the input is not a valid polynomial and can not be solved by the algorithm above, `symbolic_solve` passes
-it to `ia_solve`, which attempts solving by attraction and isolation [^1]. This only works when the input is a single expression
+input variables and a single high degree equation in the separating variable [^1]. Each equation resulting from the basis is then passed
+to `solve_univar`. We can see that essentially, `solve_univar` is the building block of `symbolic_solve`. If the input is not a valid polynomial and can not be solved by the algorithm above, `symbolic_solve` passes
+it to `ia_solve`, which attempts solving by attraction and isolation [^2]. This only works when the input is a single expression
 and the user wants the answer in terms of a single variable. Say `log(x) - a == 0` gives us `[e^a]`.
 
 #### Nice examples
+
 ```@example solver
 using Symbolics, Nemo;
 @variables x;
@@ -49,6 +53,16 @@ eqs = [x^2 + y + z - 1, x + y^2 + z - 1, x + y + z^2 - 1]
 Symbolics.symbolic_solve(eqs, [x,y,z])
 ```
 
+### Feature completeness
+
+- [x] Linear and polynomial equations
+- [x] Systems of linear and polynomial equations
+- [x] Some transcendental functions
+- [x] Systems of linear equations with parameters (via `symbolic_linear_solve`)
+- [ ] Systems of polynomial equations with parameters
+- [ ] Inequalities
+
 # References
-[^1]: [R. W. Hamming, Coding and Information Theory, ScienceDirect, 1980](https://www.sciencedirect.com/science/article/pii/S0747717189800070).
 
+[^1] [Rouillier, F. Solving Zero-Dimensional Systems Through the Rational Univariate Representation. AAECC 9, 433–461 (1999).](https://doi.org/10.1007/s002000050114)
+[^2]: [R. W. Hamming, Coding and Information Theory, ScienceDirect, 1980](https://www.sciencedirect.com/science/article/pii/S0747717189800070).

ext/SymbolicsPreallocationToolsExt.jl

@@ -2,7 +2,7 @@ module SymbolicsPreallocationToolsExt
 
 using PreallocationTools
 import PreallocationTools: _restructure, get_tmp
-using Symbolics, PreallocationTools.ForwardDiff
+using Symbolics, ForwardDiff
 
 function get_tmp(dc::DiffCache, u::Type{X}) where {T,N, X<: ForwardDiff.Dual{T, Num, N}}
     if length(dc.du) > length(dc.any_du)

src/Symbolics.jl

@@ -133,6 +133,7 @@ using LogExpFunctions
 include("logexpfunctions-lib.jl")
 
 include("linear_algebra.jl")
+export symbolic_linear_solve, solve_for
 
 include("groebner_basis.jl")
 export groebner_basis, is_groebner_basis
@@ -153,7 +154,6 @@ include("plot_recipes.jl")
 
 include("semipoly.jl")
 
-export lambertw
 
 include("parsing.jl")
 export parse_expr_to_symbolic

src/solver/main.jl

@@ -30,17 +30,19 @@ Currently, `symbolic_solve` supports
 
 ### `solve_univar` (uses factoring and analytic solutions up to degree 4)
 ```jldoctest
+julia> @variables x a b;
+
 julia> expr = expand((x + b)*(x^2 + 2x + 1)*(x^2 - a))
 -a*b - a*x - 2a*b*x - 2a*(x^2) + b*(x^2) + x^3 - a*b*(x^2) - a*(x^3) + 2b*(x^3) + 2(x^4) + b*(x^4) + x^5
 
-julia> Symbolics.symbolic_solve(expr, x)
+julia> symbolic_solve(expr, x)
 4-element Vector{Any}:
  -1
    -b
    (1//2)*√(4a)
    (-1//2)*√(4a)
 
-julia> Symbolics.symbolic_solve(expr, x, dropmultiplicity=false)
+julia> symbolic_solve(expr, x, dropmultiplicity=false)
 5-element Vector{Any}:
  -1
  -1
@@ -49,7 +51,7 @@ julia> Symbolics.symbolic_solve(expr, x, dropmultiplicity=false)
    (-1//2)*√(4a)
 ```
 ```jldoctest
-julia> Symbolics.symbolic_solve(x^2 + a*x + 6, x)
+julia> symbolic_solve(x^2 + a*x + 6, x)
 2-element Vector{SymbolicUtils.BasicSymbolic{Real}}:
  (1//2)*(-a + √(-24 + a^2))
  (1//2)*(-a - √(-24 + a^2))
@@ -108,13 +110,11 @@ julia> symbolic_solve(a*x^b + c, x)
 ((-c)^(1 / b)) / (a^(1 / b))
 ```
 """
-function symbolic_solve(expr, x; dropmultiplicity=true, warns=true)
-    type_x = typeof(x)
+function symbolic_solve(expr, x::T; dropmultiplicity=true, warns=true) where {T}
     expr_univar = false
     x_univar = false
 
-
-    if (type_x == Num || type_x == SymbolicUtils.BasicSymbolic{Real})
+    if (T == Num || T == SymbolicUtils.BasicSymbolic{Real})
         x_univar = true
         @assert is_singleton(unwrap(x)) "Expected a variable, got $x"
     else