transition from @syms to @variables

Author: shahriariravanian

Project.toml

@@ -1,7 +1,7 @@
 name = "SymbolicNumericIntegration"
 uuid = "78aadeae-fbc0-11eb-17b6-c7ec0477ba9e"
 authors = ["Shahriar Iravanian <[email protected]>"]
-version = "0.8.0"
+version = "0.8.1"
 
 [deps]
 DataDrivenDiffEq = "2445eb08-9709-466a-b3fc-47e12bd697a2"

README.md

@@ -11,7 +11,7 @@ Function `integrate` returns the integral of a univariate expression with *const
 using SymbolicUtils
 using SymbolicNumericIntegration
 
-@syms x
+@variables x
 
 julia> integrate(3x^3 + 2x - 5)
 (x^2 + (3//4)*(x^4) - (5x), 0, 0)
@@ -104,3 +104,18 @@ The test suites description based on the header of the files in the Rubi directo
 |:Timofeev    | 10 | A. F. Timofeev - Integration of Functions (1948) |
 |:Welz        | 11 | Martin Welz - posts on Sci.Math.Symbolic |
 |:Webster     | 12 | Michael Wester |
+
+## Citation
+
+If you use **SymbolicNumericIntegration.jl**, please cite [Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression](https://arxiv.org/abs/2201.12468):
+
+```
+@article{Iravanian2022,   
+   author = {Shahriar Iravanian and Carl Julius Martensen and Alessandro Cheli and Shashi Gowda and Anand Jain and Julia Computing and Yingbo Ma and Chris Rackauckas},
+   doi = {10.48550/arxiv.2201.12468},
+   month = {1},
+   title = {Symbolic-Numeric Integration of Univariate Expressions based on Sparse Regression},
+   url = {https://arxiv.org/abs/2201.12468v2},
+   year = {2022},
+}
+```

src/integral.jl

@@ -44,6 +44,8 @@ function integrate(eq, x=nothing; abstol=1e-6, num_steps=2, num_trials=5, radius
             @syms 𝑥
             x = 𝑥
         end
+    else
+        x = value(x)    # needed for the transition from @syms to @variables
     end
 
     l = Logger(verbose)

src/symbolic.jl

@@ -1,8 +1,10 @@
 function try_symbolic(T, eq, x, basis, Δbasis; kwargs...)
+    eq isa Num || return 0, 0    
     n = length(basis)
-    @syms θ[1:n]
+    # @syms θ[1:n]
+    @variables θ[1:n]
 
-    Δeq = sum(θ[j]*Δbasis[j] for j=1:n) - eq    
+    Δeq = sum(θ[j]*Δbasis[j] for j=1:n) - eq
     Δeq = expand(Δeq)
 
     terms = collect_terms(Δeq, x)
@@ -85,6 +87,7 @@ function solve_symbolic(eqs)
 end
 
 function collect_terms(eq::SymbolicUtils.Add, x)
+    println(eq)
     d = Dict{Any,Any}(1 => 0)
     for t in arguments(eq)
         if isdependent(t, x)

test/axiom.jl

@@ -6,7 +6,8 @@ using Symbolics
 using PyCall
 sympy = pyimport("sympy")
 
-@syms x 𝐞 a b c d e p t m n z
+# @syms x 𝐞 a b c d e p t m n z
+@variables x 𝐞 a b c d e p t m n z
 
 axion_rules = [
     @rule ^(𝐞, ~k) => exp(~k)
@@ -122,7 +123,7 @@ function test_axiom(L, try_sympy=true; kwargs...)
     n_catch = 0
 
     for (i,p) in enumerate(L)
-        try
+        # try
             printstyled(i, ": "; color=:yellow)
             eq = p[1]
             x = p[2]
@@ -131,6 +132,8 @@ function test_axiom(L, try_sympy=true; kwargs...)
             printstyled(eq, '\n'; color=:green)
             sol = integrate(eq, x; kwargs...)[1]
 
+            println(">>>>", sol)
+
             if isequal(sol, 0)
                 printstyled("\tFailure\n"; color=:red)
                 n_fail += 1
@@ -149,10 +152,10 @@ function test_axiom(L, try_sympy=true; kwargs...)
             end
 
             printstyled("\tAnswer: \t", ans, '\n'; color=:blue)
-        catch e
-            printstyled(i, ": ", e, '\n'; color=:red)
-            n_catch += 1
-        end
+        # catch e
+        #    printstyled(i, ": ", e, '\n'; color=:red)
+        #    n_catch += 1
+        #end
     end
 
     println()

test/runtests.jl

@@ -6,7 +6,8 @@ include("axiom.jl")
 
 ##############################################################################
 
-@syms x β
+# @syms x β
+@variables x β
 
 """
     a list of basic standard integral tests