Merge pull request #1335 from n0rbed/new_feature

An attempt at #29

Author: ChrisRackauckas

src/Symbolics.jl

@@ -209,6 +209,7 @@ include("solver/polynomialization.jl")
 include("solver/attract.jl")
 include("solver/ia_main.jl")
 include("solver/main.jl")
+include("solver/ia_rules.jl")
 export symbolic_solve
 
 function symbolics_to_sympy end

src/solver/ia_rules.jl

@@ -0,0 +1,87 @@
+function cross_multiply(eq)
+    og_oper = operation(unwrap(eq))
+    done = true
+    loop_add = false
+
+    term_tm = 1
+    if og_oper === (/)
+        done = false
+        args = arguments(unwrap(eq))
+        eq = wrap(args[1])
+    end
+
+    # do this until no / are present
+    if og_oper === (+)
+        while !loop_add
+            args = arguments(unwrap(eq))
+            loop_add = true
+
+            for arg in args
+                !iscall(arg) && continue
+                oper = operation(arg)
+                if oper == (/) 
+                    done = false
+                    loop_add = false
+                    term_tm *= wrap(arguments(arg)[2])
+                end
+            end
+            args = [arg*term_tm for arg in args]
+            eq = expand(Symbolics.term((+), unwrap.(args)...))
+            term_tm = 1
+        end
+    end
+
+    if done
+        return eq
+    else
+        return cross_multiply(eq)
+    end
+end
+
+function solve_interms_ofvar(eq, s; dropmultiplicity=true, warns=true)
+    @assert iscall(unwrap(eq))
+    vars = Symbolics.get_variables(eq)
+    vars = filter(v -> !isequal(v, s), vars)
+    vars = wrap.(vars)
+
+    term_tm = 1
+        
+    eq = cross_multiply(eq)
+    coeffs, constant = polynomial_coeffs(eq, [s])
+    eqs = wrap.(collect(values(coeffs)))
+
+    solve_multivar(eqs, vars, dropmultiplicity=dropmultiplicity, warns=warns)
+end
+
+# an attempt at using ia_solve recursively.
+function find_v(eqs, v, vars)
+    vars = filter(var -> !isequal(var, v), vars)
+    n_eqs = deepcopy(eqs)
+
+    if isequal(n_eqs[1], 0)
+        n_eqs = n_eqs[2:end]
+    end
+    
+    present_vars = Symbolics.get_variables(n_eqs[1])
+    var = present_vars[1]
+    if length(present_vars) == 1 && isequal(present_vars[1], v)
+        return ia_solve(n_eqs[1], var)
+    end
+    if isequal(present_vars[1], v)
+        var = present_vars[2]
+    end
+
+    @info "" n_eqs[1]
+    @info "" var
+    sols = ia_solve(n_eqs[1], var)
+    isequal(sols, nothing) && return []
+
+    for s in sols
+        for j in 2:length(n_eqs)
+            n_eqs[j] = substitute(n_eqs[j], Dict(var => s))
+        end
+        # other solutions are cut out here
+        return find_v(n_eqs[2:end], v, vars)
+    end
+
+end