fix: operate node and "remembered" math ops

We reimplemented the OperateMathNode entirely, and it should now be
relatively to entirely robust. It works based on an enum, just like
`MapMathNode`, which enormously simplifies the node itself. Note that
we're not quite done with sympy+jax implementations of everything, nor
validating that all operations have an implementation valid for all the
`InfoFlow`s that prompted it, but, nonetheless, such fixes should be
easy to work out as we go.

We also finally managed to implement "remembering". In essence,
"remembering" causes `FlowPending` to not reset the dynamic enums in
math / extract nodes. The implementation is generally per-node, and a
bit of boilerplate, but it seems quite robust on the whole - allowing
one to "keep a node tree around" even after removing simulation data.

Extract of sim data is of course more leniant, as it also "remembers"
when there is `NoFlow`. Only new `Sim Data` will reset the extraction
filter enum.

Caches are kept (not memory efficient, but convenient for me), but
only `FlowPending` is actually passed along the `InfoFlow`. This is the
semantics we want - having to deal with this all is a tradeoff of
having data-driven enums, but all in all, it still feels like the right
approach.

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/flow_kinds.py

@@ -80,7 +80,6 @@ class FlowKind(enum.StrEnum):
 				unit_system,
 			)
 		if kind == FlowKind.LazyArrayRange:
-			log.debug([kind, flow_obj, unit_system])
 			return flow_obj.rescale_to_unit_system(unit_system)
 
 		if kind == FlowKind.Params:

src/blender_maxwell/node_trees/maxwell_sim_nodes/contracts/flow_kinds/info.py

@@ -74,6 +74,12 @@ class InfoFlow:
 	output_mathtype: spux.MathType = dataclasses.field()
 	output_unit: spux.Unit | None = dataclasses.field()
 
+	@property
+	def output_shape_len(self) -> int:
+		if self.output_shape is None:
+			return 0
+		return len(self.output_shape)
+
 	# Pinned Dimension Information
 	## TODO: Add PhysicalType
 	pinned_dim_names: list[str] = dataclasses.field(default_factory=list)

src/blender_maxwell/node_trees/maxwell_sim_nodes/node_tree.py

@@ -477,7 +477,7 @@ def populate_missing_persistence(_) -> None:
 # - Blender Registration
 ####################
 bpy.app.handlers.load_post.append(initialize_sim_tree_node_link_cache)
-bpy.app.handlers.load_post.append(populate_missing_persistence)
+# bpy.app.handlers.load_post.append(populate_missing_persistence)
 ## TODO: Move to top-level registration.
 
 BL_REGISTER = [

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/extract_data.py

@@ -73,9 +73,14 @@ class ExtractDataNode(base.MaxwellSimNode):
 	####################
 	# - Computed: Sim Data
 	####################
-	@events.on_value_changed(socket_name='Sim Data')
-	def on_sim_data_changed(self) -> None:  # noqa: D102
-		log.critical('On Value Changed: Sim Data')
+	@events.on_value_changed(
+		socket_name='Sim Data',
+		input_sockets={'Sim Data'},
+		input_sockets_optional={'Sim Data': True},
+	)
+	def on_sim_data_changed(self, input_sockets) -> None:  # noqa: D102
+		has_sim_data = not ct.FlowSignal.check(input_sockets['Sim Data'])
+		if has_sim_data:
 			self.sim_data = bl_cache.Signal.InvalidateCache
 
 	@bl_cache.cached_bl_property()
@@ -112,9 +117,14 @@ class ExtractDataNode(base.MaxwellSimNode):
 	####################
 	# - Computed Properties: Monitor Data
 	####################
-	@events.on_value_changed(socket_name='Monitor Data')
-	def on_monitor_data_changed(self) -> None:  # noqa: D102
-		log.critical('On Value Changed: Sim Data')
+	@events.on_value_changed(
+		socket_name='Monitor Data',
+		input_sockets={'Monitor Data'},
+		input_sockets_optional={'Monitor Data': True},
+	)
+	def on_monitor_data_changed(self, input_sockets) -> None:  # noqa: D102
+		has_monitor_data = not ct.FlowSignal.check(input_sockets['Monitor Data'])
+		if has_monitor_data:
 			self.monitor_data = bl_cache.Signal.InvalidateCache
 
 	@bl_cache.cached_bl_property()
@@ -319,6 +329,7 @@ class ExtractDataNode(base.MaxwellSimNode):
 		# Loaded
 		props={'extract_filter'},
 		input_sockets={'Sim Data'},
+		input_sockets_optional={'Sim Data': True},
 	)
 	def compute_monitor_data(
 		self, props: dict, input_sockets: dict
@@ -347,6 +358,7 @@ class ExtractDataNode(base.MaxwellSimNode):
 		props={'extract_filter'},
 		input_sockets={'Monitor Data'},
 		input_socket_kinds={'Monitor Data': ct.FlowKind.Value},
+		input_sockets_optional={'Monitor Data': True},
 	)
 	def compute_expr(
 		self, props: dict, input_sockets: dict
@@ -376,6 +388,7 @@ class ExtractDataNode(base.MaxwellSimNode):
 		# Loaded
 		output_sockets={'Expr'},
 		output_socket_kinds={'Expr': ct.FlowKind.Array},
+		output_sockets_optional={'Expr': True},
 	)
 	def compute_extracted_data_lazy(
 		self, output_sockets: dict
@@ -436,9 +449,18 @@ class ExtractDataNode(base.MaxwellSimNode):
 
 		has_monitor_data = not ct.FlowSignal.check(monitor_data)
 
+		# Edge Case: Dangling 'flux' Access on 'FieldMonitor'
+		## -> Sometimes works - UNLESS the FieldMonitor doesn't have all fields.
+		## -> We don't allow 'flux' attribute access, but it can dangle.
+		## -> (The method is called when updating each depschain component.)
+		if monitor_data_type == 'Field' and extract_filter == 'flux':
+			return ct.FlowSignal.FlowPending
+
 		# Retrieve XArray
 		if has_monitor_data and extract_filter is not None:
-			xarr = getattr(monitor_data, extract_filter)
+			xarr = getattr(monitor_data, extract_filter, None)
+			if xarr is None:
+				return ct.FlowSignal.FlowPending
 		else:
 			return ct.FlowSignal.FlowPending
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/map_math.py

@@ -99,6 +99,9 @@ class MapOperation(enum.StrEnum):
 	Chol = enum.auto()
 	Svd = enum.auto()
 
+	####################
+	# - UI
+	####################
 	@staticmethod
 	def to_name(value: typ.Self) -> str:
 		MO = MapOperation
@@ -150,6 +153,9 @@ class MapOperation(enum.StrEnum):
 			i,
 		)
 
+	####################
+	# - Ops from Shape
+	####################
 	@staticmethod
 	def by_element_shape(shape: tuple[int, ...] | None) -> list[typ.Self]:
 		MO = MapOperation
@@ -198,10 +204,21 @@ class MapOperation(enum.StrEnum):
 
 		return []
 
-	def jax_func(self, user_expr_func: ct.LazyValueFuncFlow | None = None):
+	def jax_func_expr(self, user_expr_func: ct.LazyValueFuncFlow):
 		MO = MapOperation
-		if self == MO.UserExpr and user_expr_func is not None:
+		if self == MO.UserExpr:
 			return lambda data: user_expr_func.func(data)
+
+		msg = "Can't generate JAX function for user-provided expression when MapOperation is not `UserExpr`"
+		raise ValueError(msg)
+
+	@property
+	def jax_func(self):
+		MO = MapOperation
+		if self == MO.UserExpr:
+			msg = "Can't generate JAX function without user-provided expression when MapOperation is `UserExpr`"
+			raise ValueError(msg)
+
 		return {
 			# By Number
 			MO.Real: lambda data: jnp.real(data),
@@ -386,8 +403,6 @@ class MapMathNode(base.MaxwellSimNode):
 
 		return 'noshape'
 
-	output_shape: tuple[int, ...] | None = bl_cache.BLField(None)
-
 	def search_operations(self) -> list[ct.BLEnumElement]:
 		if self.expr_output_shape != 'noshape':
 			return [
@@ -472,12 +487,12 @@ class MapMathNode(base.MaxwellSimNode):
 		if has_expr and operation is not None:
 			if not has_mapper:
 				return expr.compose_within(
-					operation.jax_func(),
+					operation.jax_func,
 					supports_jax=True,
 				)
 			if operation == MapOperation.UserExpr and has_mapper:
 				return expr.compose_within(
-					operation.jax_func(user_expr_func=mapper),
+					operation.jax_func_expr(user_expr_func=mapper),
 					supports_jax=True,
 				)
 		return ct.FlowSignal.FlowPending

src/blender_maxwell/node_trees/maxwell_sim_nodes/nodes/analysis/math/operate_math.py

@@ -29,37 +29,226 @@ from ... import base, events
 
 log = logger.get(__name__)
 
-FUNCS = {
+
+####################
+# - Operation Enum
+####################
+class BinaryOperation(enum.StrEnum):
+	"""Valid operations for the `OperateMathNode`.
+
+	Attributes:
+		Add: Addition w/broadcasting.
+		Sub: Subtraction w/broadcasting.
+		Mul: Hadamard-product multiplication.
+		Div: Hadamard-product based division.
+		Pow: Elementwise expontiation.
+		Atan2: Quadrant-respecting arctangent variant.
+		VecVecDot: Dot product for vectors.
+		Cross: Cross product.
+		MatVecDot: Matrix-Vector dot product.
+		LinSolve: Solve a linear system.
+		LsqSolve: Minimize error of an underdetermined linear system.
+		MatMatDot: Matrix-Matrix dot product.
+	"""
+
 	# Number | Number
-	'ADD': lambda exprs: exprs[0] + exprs[1],
-	'SUB': lambda exprs: exprs[0] - exprs[1],
-	'MUL': lambda exprs: exprs[0] * exprs[1],
-	'DIV': lambda exprs: exprs[0] / exprs[1],
-	'POW': lambda exprs: exprs[0] ** exprs[1],
-	'ATAN2': lambda exprs: sp.atan2(exprs[1], exprs[0]),
-	# Vector | Vector
-	'VEC_VEC_DOT': lambda exprs: exprs[0].dot(exprs[1]),
-	'CROSS': lambda exprs: exprs[0].cross(exprs[1]),
-}
+	Add = enum.auto()
+	Sub = enum.auto()
+	Mul = enum.auto()
+	Div = enum.auto()
+	Pow = enum.auto()
+	Atan2 = enum.auto()
 
-SP_FUNCS = FUNCS
-JAX_FUNCS = FUNCS | {
-	# Number | *
-	'ATAN2': lambda exprs: jnp.atan2(exprs[1], exprs[0]),
 	# Vector | Vector
-	'VEC_VEC_DOT': lambda exprs: jnp.matmul(exprs[0], exprs[1]),
-	'CROSS': lambda exprs: jnp.cross(exprs[0], exprs[1]),
+	VecVecDot = enum.auto()
+	Cross = enum.auto()
+
 	# Matrix | Vector
-	'MAT_VEC_DOT': lambda exprs: jnp.matmul(exprs[0], exprs[1]),
-	'LIN_SOLVE': lambda exprs: jnp.linalg.solve(exprs[0], exprs[1]),
-	'LSQ_SOLVE': lambda exprs: jnp.linalg.lstsq(exprs[0], exprs[1]),
+	MatVecDot = enum.auto()
+	LinSolve = enum.auto()
+	LsqSolve = enum.auto()
+
 	# Matrix | Matrix
-	'MAT_MAT_DOT': lambda exprs: jnp.matmul(exprs[0], exprs[1]),
-}
+	MatMatDot = enum.auto()
+
+	####################
+	# - UI
+	####################
+	@staticmethod
+	def to_name(value: typ.Self) -> str:
+		BO = BinaryOperation
+		return {
+			# Number | Number
+			BO.Add: 'ℓ + r',
+			BO.Sub: 'ℓ - r',
+			BO.Mul: 'ℓ ⊙ r',  ## Notation for Hadamard Product
+			BO.Div: 'ℓ / r',
+			BO.Pow: 'ℓʳ',
+			BO.Atan2: 'atan2(ℓ,r)',
+			# Vector | Vector
+			BO.VecVecDot: '𝐥 · 𝐫',
+			BO.Cross: 'cross(L,R)',
+			# Matrix | Vector
+			BO.MatVecDot: '𝐋 · 𝐫',
+			BO.LinSolve: '𝐋 ∖ 𝐫',
+			BO.LsqSolve: 'argminₓ∥𝐋𝐱−𝐫∥₂',
+			# Matrix | Matrix
+			BO.MatMatDot: '𝐋 · 𝐑',
+		}[value]
+
+	@staticmethod
+	def to_icon(value: typ.Self) -> str:
+		return ''
+
+	def bl_enum_element(self, i: int) -> ct.BLEnumElement:
+		BO = BinaryOperation
+		return (
+			str(self),
+			BO.to_name(self),
+			BO.to_name(self),
+			BO.to_icon(self),
+			i,
+		)
+
+	####################
+	# - Ops from Shape
+	####################
+	@staticmethod
+	def by_infos(info_l: int, info_r: int) -> list[typ.Self]:
+		"""Deduce valid binary operations from the shapes of the inputs."""
+		BO = BinaryOperation
+
+		ops_number_number = [
+			BO.Add,
+			BO.Sub,
+			BO.Mul,
+			BO.Div,
+			BO.Pow,
+			BO.Atan2,
+		]
+
+		match (info_l.output_shape_len, info_r.output_shape_len):
+			# Number | *
+			## Number | Number
+			case (0, 0):
+				return ops_number_number
+
+			## Number | Vector
+			## -> Broadcasting allows Number|Number ops to work as-is.
+			case (0, 1):
+				return ops_number_number
+
+			## Number | Matrix
+			## -> Broadcasting allows Number|Number ops to work as-is.
+			case (0, 2):
+				return ops_number_number
+
+			# Vector | *
+			## Vector | Number
+			case (1, 0):
+				return ops_number_number
+
+			## Vector | Number
+			case (1, 1):
+				return [*ops_number_number, BO.VecVecDot, BO.Cross]
+
+			## Vector | Matrix
+			case (1, 2):
+				return []
+
+			# Matrix | *
+			## Matrix | Number
+			case (2, 0):
+				return [*ops_number_number, BO.MatMatDot]
+
+			## Matrix | Vector
+			case (2, 1):
+				return [BO.MatVecDot, BO.LinSolve, BO.LsqSolve]
+
+			## Matrix | Matrix
+			case (2, 2):
+				return [*ops_number_number, BO.MatMatDot]
+
+		return []
+
+	####################
+	# - Function Properties
+	####################
+	@property
+	def sp_func(self):
+		"""Deduce an appropriate sympy-based function that implements the binary operation for symbolic inputs."""
+		BO = BinaryOperation
+
+		## TODO: Make this compatible with sp.Matrix inputs
+		return {
+			# Number | Number
+			BO.Add: lambda exprs: exprs[0] + exprs[1],
+			BO.Sub: lambda exprs: exprs[0] - exprs[1],
+			BO.Mul: lambda exprs: exprs[0] * exprs[1],
+			BO.Div: lambda exprs: exprs[0] / exprs[1],
+			BO.Pow: lambda exprs: exprs[0] ** exprs[1],
+			BO.Atan2: lambda exprs: sp.atan2(exprs[1], exprs[0]),
+		}[self]
+
+	@property
+	def jax_func(self):
+		"""Deduce an appropriate jax-based function that implements the binary operation for array inputs."""
+		BO = BinaryOperation
+
+		return {
+			# Number | Number
+			BO.Add: lambda exprs: exprs[0] + exprs[1],
+			BO.Sub: lambda exprs: exprs[0] - exprs[1],
+			BO.Mul: lambda exprs: exprs[0] * exprs[1],
+			BO.Div: lambda exprs: exprs[0] / exprs[1],
+			BO.Pow: lambda exprs: exprs[0] ** exprs[1],
+			BO.Atan2: lambda exprs: sp.atan2(exprs[1], exprs[0]),
+			# Vector | Vector
+			BO.VecVecDot: lambda exprs: jnp.dot(exprs[0], exprs[1]),
+			BO.Cross: lambda exprs: jnp.cross(exprs[0], exprs[1]),
+			# Matrix | Vector
+			BO.MatVecDot: lambda exprs: jnp.matmul(exprs[0], exprs[1]),
+			BO.LinSolve: lambda exprs: jnp.linalg.solve(exprs[0], exprs[1]),
+			BO.LsqSolve: lambda exprs: jnp.linalg.lstsq(exprs[0], exprs[1]),
+			# Matrix | Matrix
+			BO.MatMatDot: lambda exprs: jnp.matmul(exprs[0], exprs[1]),
+		}[self]
+
+	####################
+	# - InfoFlow Transform
+	####################
+	def transform_infos(self, info_l: ct.InfoFlow, info_r: ct.InfoFlow):
+		BO = BinaryOperation
+
+		info_largest = (
+			info_l if info_l.output_shape_len > info_l.output_shape_len else info_l
+		)
+		info_any = info_largest
+		return {
+			# Number | * or * | Number
+			BO.Add: info_largest,
+			BO.Sub: info_largest,
+			BO.Mul: info_largest,
+			BO.Div: info_largest,
+			BO.Pow: info_largest,
+			BO.Atan2: info_largest,
+			# Vector | Vector
+			BO.VecVecDot: info_any,
+			BO.Cross: info_any,
+			# Matrix | Vector
+			BO.MatVecDot: info_r,
+			BO.LinSolve: info_r,
+			BO.LsqSolve: info_r,
+			# Matrix | Matrix
+			BO.MatMatDot: info_any,
+		}[self]
 
 
+####################
+# - Node
+####################
 class OperateMathNode(base.MaxwellSimNode):
-	r"""Applies a function that depends on two inputs.
+	r"""Applies a binary function between two expressions.
 
 	Attributes:
 		category: The category of operations to apply to the inputs.
@@ -76,196 +265,86 @@ class OperateMathNode(base.MaxwellSimNode):
 		'Expr R': sockets.ExprSocketDef(active_kind=ct.FlowKind.LazyValueFunc),
 	}
 	output_sockets: typ.ClassVar = {
-		'Expr': sockets.ExprSocketDef(active_kind=ct.FlowKind.LazyValueFunc),
+		'Expr': sockets.ExprSocketDef(
+			active_kind=ct.FlowKind.LazyValueFunc, show_info_columns=True
+		),
 	}
 
 	####################
 	# - Properties
 	####################
-	category: enum.StrEnum = bl_cache.BLField(
-		enum_cb=lambda self, _: self.search_categories()
+	@events.on_value_changed(
+		socket_name={'Expr L', 'Expr R'},
+		input_sockets={'Expr L', 'Expr R'},
+		input_socket_kinds={'Expr L': ct.FlowKind.Info, 'Expr R': ct.FlowKind.Info},
+		input_sockets_optional={'Expr L': True, 'Expr R': True},
+	)
+	def on_input_exprs_changed(self, input_sockets) -> None:  # noqa: D102
+		has_info_l = not ct.FlowSignal.check(input_sockets['Expr L'])
+		has_info_r = not ct.FlowSignal.check(input_sockets['Expr R'])
+
+		info_l_pending = ct.FlowSignal.check_single(
+			input_sockets['Expr L'], ct.FlowSignal.FlowPending
+		)
+		info_r_pending = ct.FlowSignal.check_single(
+			input_sockets['Expr R'], ct.FlowSignal.FlowPending
 		)
 
-	operation: enum.StrEnum = bl_cache.BLField(
-		enum_cb=lambda self, _: self.search_operations()
+		if has_info_l and has_info_r and not info_l_pending and not info_r_pending:
+			self.expr_infos = bl_cache.Signal.InvalidateCache
+
+	@bl_cache.cached_bl_property()
+	def expr_infos(self) -> tuple[ct.InfoFlow, ct.InfoFlow] | None:
+		info_l = self._compute_input('Expr L', kind=ct.FlowKind.Info)
+		info_r = self._compute_input('Expr R', kind=ct.FlowKind.Info)
+
+		has_info_l = not ct.FlowSignal.check(info_l)
+		has_info_r = not ct.FlowSignal.check(info_r)
+
+		if has_info_l and has_info_r:
+			return (info_l, info_r)
+
+		return None
+
+	operation: BinaryOperation = bl_cache.BLField(
+		enum_cb=lambda self, _: self.search_operations(),
+		cb_depends_on={'expr_infos'},
 	)
 
-	def search_categories(self) -> list[ct.BLEnumElement]:
-		"""Deduce and return a list of valid categories for the current socket set and input data."""
-		expr_l_info = self._compute_input(
-			'Expr L',
-			kind=ct.FlowKind.Info,
-		)
-		expr_r_info = self._compute_input(
-			'Expr R',
-			kind=ct.FlowKind.Info,
-		)
-
-		has_expr_l_info = not ct.FlowSignal.check(expr_l_info)
-		has_expr_r_info = not ct.FlowSignal.check(expr_r_info)
-
-		# Categories by Socket Set
-		NUMBER_NUMBER = (
-			'Number | Number',
-			'Number | Number',
-			'Operations between numerical elements',
-		)
-		NUMBER_VECTOR = (
-			'Number | Vector',
-			'Number | Vector',
-			'Operations between numerical and vector elements',
-		)
-		NUMBER_MATRIX = (
-			'Number | Matrix',
-			'Number | Matrix',
-			'Operations between numerical and matrix elements',
-		)
-		VECTOR_VECTOR = (
-			'Vector | Vector',
-			'Vector | Vector',
-			'Operations between vector elements',
-		)
-		MATRIX_VECTOR = (
-			'Matrix | Vector',
-			'Matrix | Vector',
-			'Operations between vector and matrix elements',
-		)
-		MATRIX_MATRIX = (
-			'Matrix | Matrix',
-			'Matrix | Matrix',
-			'Operations between matrix elements',
-		)
-		categories = []
-
-		if has_expr_l_info and has_expr_r_info:
-			# Check Valid Broadcasting
-			## Number | Number
-			if expr_l_info.output_shape is None and expr_r_info.output_shape is None:
-				categories = [NUMBER_NUMBER]
-
-			## * | Number
-			elif expr_r_info.output_shape is None:
-				categories = []
-
-			## Number | Vector
-			elif (
-				expr_l_info.output_shape is None and len(expr_r_info.output_shape) == 1
-			):
-				categories = [NUMBER_VECTOR]
-
-			## Number | Matrix
-			elif (
-				expr_l_info.output_shape is None and len(expr_r_info.output_shape) == 2
-			):
-				categories = [NUMBER_MATRIX]
-
-			## Vector | Vector
-			elif (
-				len(expr_l_info.output_shape) == 1
-				and len(expr_r_info.output_shape) == 1
-			):
-				categories = [VECTOR_VECTOR]
-
-			## Matrix | Vector
-			elif (
-				len(expr_l_info.output_shape) == 2  # noqa: PLR2004
-				and len(expr_r_info.output_shape) == 1
-			):
-				categories = [MATRIX_VECTOR]
-
-			## Matrix | Matrix
-			elif (
-				len(expr_l_info.output_shape) == 2  # noqa: PLR2004
-				and len(expr_r_info.output_shape) == 2  # noqa: PLR2004
-			):
-				categories = [MATRIX_MATRIX]
-
-		return [
-			(*category, '', i) if category is not None else None
-			for i, category in enumerate(categories)
-		]
-
 	def search_operations(self) -> list[ct.BLEnumElement]:
-		items = []
-		if self.category in ['Number | Number', 'Number | Vector', 'Number | Matrix']:
-			items += [
-				('ADD', 'L + R', 'Add'),
-				('SUB', 'L - R', 'Subtract'),
-				('MUL', 'L · R', 'Multiply'),
-				('DIV', 'L / R', 'Divide'),
-				('POW', 'L^R', 'Power'),
-				('ATAN2', 'atan2(L,R)', 'atan2(L,R)'),
-			]
-		if self.category == 'Vector | Vector':
-			if items:
-				items += [None]
-			items += [
-				('VEC_VEC_DOT', 'L · R', 'Vector-Vector Product'),
-				('CROSS', 'L x R', 'Cross Product'),
-			]
-		if self.category == 'Matrix | Vector':
-			if items:
-				items += [None]
-			items += [
-				('MAT_VEC_DOT', 'L · R', 'Matrix-Vector Product'),
-				('LIN_SOLVE', 'Lx = R -> x', 'Linear Solve'),
-				('LSQ_SOLVE', 'Lx = R ~> x', 'Least Squares Solve'),
-			]
-		if self.category == 'Matrix | Matrix':
-			if items:
-				items += [None]
-			items += [
-				('MAT_MAT_DOT', 'L · R', 'Matrix-Matrix Product'),
-			]
-
+		if self.expr_infos is not None:
 			return [
-			(*item, '', i) if item is not None else None for i, item in enumerate(items)
+				operation.bl_enum_element(i)
+				for i, operation in enumerate(
+					BinaryOperation.by_infos(*self.expr_infos)
+				)
 			]
+		return []
 
 	####################
 	# - UI
 	####################
 	def draw_label(self):
-		labels = {
-			'ADD': lambda: 'L + R',
-			'SUB': lambda: 'L - R',
-			'MUL': lambda: 'L · R',
-			'DIV': lambda: 'L / R',
-			'POW': lambda: 'L^R',
-			'ATAN2': lambda: 'atan2(L,R)',
-		}
+		"""Show the current operation (if any) in the node's header label.
 
-		if (label := labels.get(self.operation)) is not None:
-			return 'Operate: ' + label()
+		Notes:
+			Called by Blender to determine the text to place in the node's header.
+		"""
+		if self.operation is not None:
+			return 'Op: ' + BinaryOperation.to_name(self.operation)
 
 		return self.bl_label
 
 	def draw_props(self, _: bpy.types.Context, layout: bpy.types.UILayout) -> None:
-		layout.prop(self, self.blfields['category'], text='')
+		"""Draw node properties in the node.
+
+		Parameters:
+			col: UI target for drawing.
+		"""
 		layout.prop(self, self.blfields['operation'], text='')
 
 	####################
-	# - Events
-	####################
-	@events.on_value_changed(
-		# Trigger
-		socket_name={'Expr L', 'Expr R'},
-		run_on_init=True,
-	)
-	def on_socket_changed(self) -> None:
-		# Recompute Valid Categories
-		self.category = bl_cache.Signal.ResetEnumItems
-		self.operation = bl_cache.Signal.ResetEnumItems
-
-	@events.on_value_changed(
-		prop_name='category',
-		run_on_init=True,
-	)
-	def on_category_changed(self) -> None:
-		self.operation = bl_cache.Signal.ResetEnumItems
-
-	####################
-	# - Output
+	# - FlowKind.Value|LazyValueFunc
 	####################
 	@events.computes_output_socket(
 		'Expr',
@@ -285,8 +364,10 @@ class OperateMathNode(base.MaxwellSimNode):
 		has_expr_l_value = not ct.FlowSignal.check(expr_l)
 		has_expr_r_value = not ct.FlowSignal.check(expr_r)
 
+		# Compute Sympy Function
+		## -> The operation enum directly provides the appropriate function.
 		if has_expr_l_value and has_expr_r_value and operation is not None:
-			return SP_FUNCS[operation]([expr_l, expr_r])
+			operation.sp_func([expr_l, expr_r])
 
 		return ct.Flowsignal.FlowPending
 
@@ -311,43 +392,17 @@ class OperateMathNode(base.MaxwellSimNode):
 		has_expr_l = not ct.FlowSignal.check(expr_l)
 		has_expr_r = not ct.FlowSignal.check(expr_r)
 
+		# Compute Jax Function
+		## -> The operation enum directly provides the appropriate function.
 		if has_expr_l and has_expr_r:
 			return (expr_l | expr_r).compose_within(
-				JAX_FUNCS[operation],
+				operation.jax_func,
 				supports_jax=True,
 			)
 		return ct.FlowSignal.FlowPending
 
-	@events.computes_output_socket(
-		'Expr',
-		kind=ct.FlowKind.Array,
-		output_sockets={'Expr'},
-		output_socket_kinds={
-			'Expr': {ct.FlowKind.LazyValueFunc, ct.FlowKind.Params},
-		},
-		unit_systems={'BlenderUnits': ct.UNITS_BLENDER},
-	)
-	def compute_array(self, output_sockets, unit_systems) -> ct.ArrayFlow:
-		lazy_value_func = output_sockets['Expr'][ct.FlowKind.LazyValueFunc]
-		params = output_sockets['Expr'][ct.FlowKind.Params]
-
-		has_lazy_value_func = not ct.FlowSignal.check(lazy_value_func)
-		has_params = not ct.FlowSignal.check(params)
-
-		if has_lazy_value_func and has_params:
-			unit_system = unit_systems['BlenderUnits']
-			return ct.ArrayFlow(
-				values=lazy_value_func.func_jax(
-					*params.scaled_func_args(unit_system),
-					**params.scaled_func_kwargs(unit_system),
-				),
-				unit=None,
-			)
-
-		return ct.FlowSignal.FlowPending
-
 	####################
-	# - Auxiliary: Info
+	# - FlowKind.Info
 	####################
 	@events.computes_output_socket(
 		'Expr',
@@ -367,17 +422,20 @@ class OperateMathNode(base.MaxwellSimNode):
 		has_info_l = not ct.FlowSignal.check(info_l)
 		has_info_r = not ct.FlowSignal.check(info_r)
 
-		# Return Info of RHS
-		## -> Fundamentall, this is why 'category' only has the given options.
-		## -> Via 'category', we enforce that the operated-on structure is always RHS.
-		## -> That makes it super duper easy to track info changes.
-		if has_info_l and has_info_r and operation is not None:
-			return info_r
+		# Compute Info
+		## -> The operation enum directly provides the appropriate transform.
+		if (
+			has_info_l
+			and has_info_r
+			and operation is not None
+			and operation in BinaryOperation.by_infos(info_l, info_r)
+		):
+			return operation.transform_infos(info_l, info_r)
 
 		return ct.FlowSignal.FlowPending
 
 	####################
-	# - Auxiliary: Params
+	# - FlowKind.Params
 	####################
 	@events.computes_output_socket(
 		'Expr',
@@ -397,8 +455,11 @@ class OperateMathNode(base.MaxwellSimNode):
 		has_params_l = not ct.FlowSignal.check(params_l)
 		has_params_r = not ct.FlowSignal.check(params_r)
 
+		# Compute Params
+		## -> Operations don't add new parameters, so just concatenate L|R.
 		if has_params_l and has_params_r and operation is not None:
 			return params_l | params_r
+
 		return ct.FlowSignal.FlowPending
 
 

src/blender_maxwell/node_trees/maxwell_sim_nodes/sockets/expr.py

@@ -186,7 +186,7 @@ class ExprBLSocket(base.MaxwellSimSocket):
 	# UI: Info
 	show_info_columns: bool = bl_cache.BLField(False)
 	info_columns: set[InfoDisplayCol] = bl_cache.BLField(
-		{InfoDisplayCol.MathType, InfoDisplayCol.Unit}
+		{InfoDisplayCol.Length, InfoDisplayCol.MathType}
 	)
 
 	####################

src/blender_maxwell/utils/bl_cache/bl_field.py

@@ -329,8 +329,8 @@ class BLField:
 				# Retrieve Old Enum Item
 				## -> This is verbatim what is being used.
 				## -> De-Coerce None -> 'NONE' to avoid special-cased search.
-				_old_item = self.bl_prop.read(bl_instance)
-				old_item = 'NONE' if _old_item is None else _old_item
+				old_item = self.bl_prop.read(bl_instance)
+				raw_old_item = 'NONE' if old_item is None else str(old_item)
 
 				# Swap Enum Items
 				## -> This is the hot stuff - the enum elements are overwritten.
@@ -343,7 +343,7 @@ class BLField:
 				## -> If so, the user will expect it to "remain".
 				## -> Thus, we set it - Blender sees a change, user doesn't.
 				## -> DO NOT trigger on_prop_changed (since "nothing changed").
-				if any(old_item == item[0] for item in current_items):
+				if any(raw_old_item == item[0] for item in current_items):
 					self.suppress_next_update(bl_instance)
 					self.bl_prop.write(bl_instance, old_item)
 					## -> TODO: Don't write if not needed.
@@ -352,10 +352,8 @@ class BLField:
 				## -> In this case, fallback to the first current item.
 				## -> DO trigger on_prop_changed (since it changed!)
 				else:
-					_first_current_item = current_items[0][0]
-					first_current_item = (
-						_first_current_item if _first_current_item != 'NONE' else None
-					)
+					raw_first_current_item = current_items[0][0]
+					first_current_item = self.bl_prop.decode(raw_first_current_item)
 
 					self.suppress_next_update(bl_instance)
 					self.bl_prop.write(bl_instance, first_current_item)

src/blender_maxwell/utils/bl_cache/bl_prop.py

@@ -198,7 +198,12 @@ class BLProp:
 		)
 
 	def read(self, bl_instance: bl_instance.BLInstance) -> typ.Any:
-		"""Read the Blender property's particular value on the given `bl_instance`."""
+		"""Read the persisted Blender property value for this property, from a particular `BLInstance`.
+
+		Parameters:
+			bl_instance: The Blender object to
+				**NOTE**: `bl_instance` must not be `None`, as neighboring methods sometimes allow.
+		"""
 		persisted_value = self.decode(
 			managed_cache.read(
 				bl_instance,

src/blender_maxwell/utils/bl_instance.py

@@ -50,6 +50,7 @@ class BLInstance:
 	# - Attributes
 	####################
 	instance_id: bpy.props.StringProperty(default='')
+	is_updating: bpy.props.BoolProperty(default=False)
 
 	blfields: typ.ClassVar[dict[str, str]] = MappingProxyType({})
 	blfield_deps: typ.ClassVar[dict[str, list[str]]] = MappingProxyType({})