From ca1a14b276f37026842c5c891dec1bdc401ad1e8 Mon Sep 17 00:00:00 2001
From: Greg Vernon <greg.j.vernon@gmail.com>
Date: Mon, 7 Aug 2023 21:35:04 -0600
Subject: [PATCH 1/2] add support for definite integration

---
 src/integral.jl | 7 ++++++-
 1 file changed, 6 insertions(+), 1 deletion(-)

diff --git a/src/integral.jl b/src/integral.jl
index 93eaf21..4f8c467 100644
--- a/src/integral.jl
+++ b/src/integral.jl
@@ -1,5 +1,6 @@
 using LinearAlgebra
 using Statistics: mean, std
+using Symbolics
 
 Base.signbit(z::Complex{T}) where {T <: Number} = signbit(real(z))
 Base.signbit(x::SymbolicUtils.Sym{Number}) = false
@@ -21,6 +22,7 @@ Arguments:
 ----------
 - `eq`: a univariate expression
 - `x`: the independent variable (optional)
+- `domain`: the domain upon which to evaluate a definite integral (optional)
 
 Keyword Arguments:
 ------------------
@@ -44,7 +46,7 @@ Output:
 - `unsolved`: the residual unsolved portion of the input
 - `err`: the numerical error in reaching the solution
 """
-function integrate(eq, x = nothing; abstol = 1e-6, num_steps = 2, num_trials = 10,
+function integrate(eq, x = nothing, domain::Vector{<:Number} = nothing; abstol = 1e-6, num_steps = 2, num_trials = 10,
                    radius = 1.0,
                    show_basis = false, opt = STLSQ(exp.(-10:1:0)), bypass = false,
                    symbolic = true, max_basis = 100, verbose = false, complex_plane = true,
@@ -71,6 +73,9 @@ function integrate(eq, x = nothing; abstol = 1e-6, num_steps = 2, num_trials = 1
     s, u, ϵ = integrate_sum(eq, x, l; bypass, abstol, num_trials, num_steps,
                             radius, show_basis, opt, symbolic,
                             max_basis, verbose, complex_plane, use_optim)
+    if domain != nothing
+        s = substitute( s, Dict( [ x=>domain[1] ] ) ) - substitute( s, Dict( [ x=>domain[2] ] ) )
+    end
     # return simplify(s), u, ϵ
     return s, u, ϵ
 end

From 9aaa42e1781358b04b634f93c22001c476580e4f Mon Sep 17 00:00:00 2001
From: Greg Vernon <greg.j.vernon@gmail.com>
Date: Tue, 8 Aug 2023 21:50:33 -0600
Subject: [PATCH 2/2] add simple tests for definite integration

---
 src/integral.jl  |  4 ++--
 test/runtests.jl | 19 +++++++++++++++++++
 2 files changed, 21 insertions(+), 2 deletions(-)

diff --git a/src/integral.jl b/src/integral.jl
index 4f8c467..8470738 100644
--- a/src/integral.jl
+++ b/src/integral.jl
@@ -46,7 +46,7 @@ Output:
 - `unsolved`: the residual unsolved portion of the input
 - `err`: the numerical error in reaching the solution
 """
-function integrate(eq, x = nothing, domain::Vector{<:Number} = nothing; abstol = 1e-6, num_steps = 2, num_trials = 10,
+function integrate(eq, x = nothing, domain::Vector{<:Number} = [NaN]; abstol = 1e-6, num_steps = 2, num_trials = 10,
                    radius = 1.0,
                    show_basis = false, opt = STLSQ(exp.(-10:1:0)), bypass = false,
                    symbolic = true, max_basis = 100, verbose = false, complex_plane = true,
@@ -73,7 +73,7 @@ function integrate(eq, x = nothing, domain::Vector{<:Number} = nothing; abstol =
     s, u, ϵ = integrate_sum(eq, x, l; bypass, abstol, num_trials, num_steps,
                             radius, show_basis, opt, symbolic,
                             max_basis, verbose, complex_plane, use_optim)
-    if domain != nothing
+    if !all( domain .=== NaN )
         s = substitute( s, Dict( [ x=>domain[1] ] ) ) - substitute( s, Dict( [ x=>domain[2] ] ) )
     end
     # return simplify(s), u, ϵ
diff --git a/test/runtests.jl b/test/runtests.jl
index 9c94f76..aae091f 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -240,8 +240,27 @@ function test_integrals(; kw...)
     return n
 end
 
+function test_definite_integrals()
+    miss_count = 0
+    eqn = x
+    val = SymbolicNumericIntegration.integrate( eqn, x, [ 0, 1 ] )[1]
+    miss_count += ( isapprox( val, 0.5 ) ) && ( typeof( val ) == typeof( 1 ) )
+    val = SymbolicNumericIntegration.integrate( eqn, x, [ 0.0, 1.0 ] )[1]
+    miss_count += ( isapprox( val, 0.5 ) ) && ( typeof( val ) == typeof( 1.0 ) )
+    val = SymbolicNumericIntegration.integrate( eqn, x, [ 0//1, 1//1 ] )[1]
+    miss_count += ( isapprox( val, 0.5 ) ) && ( typeof( val ) == typeof( 1//1 ) )
+    val = SymbolicNumericIntegration.integrate( eqn, x, [ Num(π), Num(2π) ] )[1]
+    miss_count += ( isequal( val, 3*Num(π)^2/2 ) ) && ( typeof( val ) == typeof( Num(π) ) )
+    return miss_count
+end
+
 @testset "integral" begin
     n = test_integrals(; symbolic = false, verbose = false, homotopy = true, num_steps = 2,
                        num_trials = 10)
     @test n > 0
 end
+
+@testset "definite_integral" begin
+    n = test_definite_integrals()
+    @test n == 0
+end