Merge pull request #26583 from haru-44/classify_pde

Refactoring of `classify_pde`

sympy/solvers/pde.py

@@ -300,8 +300,7 @@ def classify_pde(eq, func=None, dict=False, *, prep=True, **kwargs):
         if dict:
             matching_hints["default"] = None
             return matching_hints
-        else:
-            return ()
+        return ()
 
     eq = expand(eq)
 
@@ -313,31 +312,20 @@ def classify_pde(eq, func=None, dict=False, *, prep=True, **kwargs):
     n = Wild('n', exclude = [x, y])
     # Try removing the smallest power of f(x,y)
     # from the highest partial derivatives of f(x,y)
-    reduced_eq = None
+    reduced_eq = eq
     if eq.is_Add:
-        var = set(combinations_with_replacement((x,y), order))
-        dummyvar = var.copy()
         power = None
-        for i in var:
-            coeff = eq.coeff(f(x,y).diff(*i))
-            if coeff != 1:
-                match = coeff.match(a*f(x,y)**n)
-                if match and match[a]:
-                    power = match[n]
-                    dummyvar.remove(i)
-                    break
-            dummyvar.remove(i)
-        for i in dummyvar:
+        for i in set(combinations_with_replacement((x,y), order)):
             coeff = eq.coeff(f(x,y).diff(*i))
-            if coeff != 1:
-                match = coeff.match(a*f(x,y)**n)
-                if match and match[a] and match[n] < power:
+            if coeff == 1:
+                continue
+            match = coeff.match(a*f(x,y)**n)
+            if match and match[a]:
+                if power is None or match[n] < power:
                     power = match[n]
         if power:
             den = f(x,y)**power
             reduced_eq = Add(*[arg/den for arg in eq.args])
-    if not reduced_eq:
-        reduced_eq = eq
 
     if order == 1:
         reduced_eq = collect(reduced_eq, f(x, y))
@@ -348,14 +336,12 @@ def classify_pde(eq, func=None, dict=False, *, prep=True, **kwargs):
                 ## equation with constant coefficients
                 r.update({'b': b, 'c': c, 'd': d})
                 matching_hints["1st_linear_constant_coeff_homogeneous"] = r
-            else:
-                if r[b]**2 + r[c]**2 != 0:
-                    ## Linear first-order general partial-differential
-                    ## equation with constant coefficients
-                    r.update({'b': b, 'c': c, 'd': d, 'e': e})
-                    matching_hints["1st_linear_constant_coeff"] = r
-                    matching_hints[
-                        "1st_linear_constant_coeff_Integral"] = r
+            elif r[b]**2 + r[c]**2 != 0:
+                ## Linear first-order general partial-differential
+                ## equation with constant coefficients
+                r.update({'b': b, 'c': c, 'd': d, 'e': e})
+                matching_hints["1st_linear_constant_coeff"] = r
+                matching_hints["1st_linear_constant_coeff_Integral"] = r
 
         else:
             b = Wild('b', exclude=[f(x, y), fx, fy])
@@ -367,20 +353,19 @@ def classify_pde(eq, func=None, dict=False, *, prep=True, **kwargs):
                 matching_hints["1st_linear_variable_coeff"] = r
 
     # Order keys based on allhints.
-    retlist = [i for i in allhints if i in matching_hints]
+    rettuple = tuple(i for i in allhints if i in matching_hints)
 
     if dict:
         # Dictionaries are ordered arbitrarily, so make note of which
         # hint would come first for pdsolve().  Use an ordered dict in Py 3.
         matching_hints["default"] = None
-        matching_hints["ordered_hints"] = tuple(retlist)
+        matching_hints["ordered_hints"] = rettuple
         for i in allhints:
             if i in matching_hints:
                 matching_hints["default"] = i
                 break
         return matching_hints
-    else:
-        return tuple(retlist)
+    return rettuple
 
 
 def checkpdesol(pde, sol, func=None, solve_for_func=True):