NONLINEAR requires sympy --analytic.

src/language/nmodl.yaml

@@ -1140,15 +1140,15 @@
                             type: Expression
 
                   - NonLinEquation:
-                      brief: "TODO"
+                      brief: "One equation in a system of equations that collectively make a NONLINEAR block."
                       nmodl: "~ "
                       members:
                         - lhs:
-                            brief: "TODO"
+                            brief: "Left-hand-side of the equation."
                             type: Expression
                             suffix: {value: " = "}
                         - rhs:
-                            brief: "TODO"
+                            brief: "Right-hand-side of the equation."
                             type: Expression
 
                   - LinEquation:

src/main.cpp

@@ -516,6 +516,8 @@ int run_nmodl(int argc, const char* argv[]) {
 
             enable_sympy(solver_exists(*ast, "derivimplicit"), "'SOLVE ... METHOD derivimplicit'");
             enable_sympy(node_exists(*ast, ast::AstNodeType::LINEAR_BLOCK), "'LINEAR' block");
+            enable_sympy(node_exists(*ast, ast::AstNodeType::NON_LINEAR_BLOCK),
+                         "'NONLINEAR' block");
             enable_sympy(solver_exists(*ast, "sparse"), "'SOLVE ... METHOD sparse'");
         }
 

test/usecases/nonlinear/nonlin.mod

@@ -0,0 +1,21 @@
+NEURON {
+    SUFFIX nonlin
+}
+
+STATE { x }
+
+FUNCTION solve() {
+    : Iterative solvers need a starting guess.
+    x = 1.0
+    SOLVE eq
+
+    solve = x
+}
+
+NONLINEAR eq {
+    ~ x*x = 4.0
+}
+
+FUNCTION residual(x) {
+    residual = x - 2.0
+}

test/usecases/nonlinear/test_nonlin.py

@@ -0,0 +1,15 @@
+from neuron import h, gui
+
+
+def test_nonlin():
+    s = h.Section()
+    s.insert("nonlin")
+    inst = s(0.5).nonlin
+
+    x = inst.solve()
+    error = inst.residual(x)
+    assert abs(error) < 1e-9, f"{x = }, {error = }"
+
+
+if __name__ == "__main__":
+    test_nonlin()