implement maximum_degree (#244)

symfem/basis_functions.py

@@ -7,6 +7,8 @@
 
 import sympy
 
+import symfem
+
 from .functions import AnyFunction, FunctionInput, ScalarFunction, SympyFormat, ValuesToSubstitute
 from .geometry import PointType
 from .references import Reference
@@ -355,6 +357,20 @@ def __iter__(self) -> typing.Iterator[AnyFunction]:
         f = self.get_function()
         return f.__iter__()
 
+    def maximum_degree(self, cell: symfem.references.Reference) -> int:
+        """Return the maximum degree of the function on a reference cell.
+
+        This function returns the order of the lowerst order Lagrange space on the input cell
+        that includes this function.
+
+        Args:
+            cell: The cell
+
+        Returns:
+            A version the function with floats as coefficients
+        """
+        return self.get_function().maximum_degree(cell)
+
 
 class SubbedBasisFunction(BasisFunction):
     """A basis function following a substitution."""
@@ -404,3 +420,17 @@ def plot_values(
             n: The number of plotting points
         """
         self.get_function().plot_values(reference, img, value_scale, n)
+
+    def maximum_degree(self, cell: symfem.references.Reference) -> int:
+        """Return the maximum degree of the function on a reference cell.
+
+        This function returns the order of the lowerst order Lagrange space on the input cell
+        that includes this function.
+
+        Args:
+            cell: The cell
+
+        Returns:
+            A version the function with floats as coefficients
+        """
+        raise ValueError("Cannot infer degree of a substituted basis function.")

symfem/elements/dual.py

@@ -62,6 +62,11 @@ def get_polynomial_basis(
         """
         raise ValueError("Polynomial basis not supported for barycentric dual elements.")
 
+    @property
+    def maximum_degree(self) -> int:
+        """Get the maximum degree of this polynomial set for the element."""
+        raise NotImplementedError()
+
     def get_dual_matrix(self) -> sympy.matrices.dense.MutableDenseMatrix:
         """Get the dual matrix.
 

symfem/finite_element.py

@@ -4,7 +4,7 @@
 
 import math
 import typing
-from abc import ABC, abstractmethod
+from abc import ABC, abstractmethod, abstractproperty
 from itertools import product
 
 import sympy
@@ -75,7 +75,6 @@ def dof_plot_positions(self) -> typing.List[PointType]:
         Returns:
             The DOF positions
         """
-        pass
 
     @abstractmethod
     def dof_directions(self) -> typing.List[typing.Union[PointType, None]]:
@@ -84,7 +83,6 @@ def dof_directions(self) -> typing.List[typing.Union[PointType, None]]:
         Returns:
             The DOF directions
         """
-        pass
 
     @abstractmethod
     def dof_entities(self) -> typing.List[typing.Tuple[int, int]]:
@@ -93,7 +91,6 @@ def dof_entities(self) -> typing.List[typing.Tuple[int, int]]:
         Returns:
             The entities
         """
-        pass
 
     def plot_dof_diagram(
         self, filename: typing.Union[str, typing.List[str]],
@@ -154,7 +151,6 @@ def entity_dofs(self, entity_dim: int, entity_number: int) -> typing.List[int]:
         Returns:
             The numbers of the DOFs associated with the entity
         """
-        pass
 
     @abstractmethod
     def get_basis_functions(
@@ -168,7 +164,6 @@ def get_basis_functions(
         Returns:
             The basis functions
         """
-        pass
 
     def get_basis_function(self, n: int) -> BasisFunction:
         """Get a single basis function of the element.
@@ -283,7 +278,6 @@ def map_to_cell(
         Returns:
             The basis functions mapped to the cell
         """
-        pass
 
     @abstractmethod
     def get_polynomial_basis(self) -> typing.List[AnyFunction]:
@@ -292,7 +286,10 @@ def get_polynomial_basis(self) -> typing.List[AnyFunction]:
         Returns:
             The polynomial basis
         """
-        pass
+
+    @abstractproperty
+    def maximum_degree(self) -> int:
+        """Get the maximum degree of this polynomial set for the element."""
 
     def test(self):
         """Run tests for this element."""
@@ -510,6 +507,9 @@ def __init__(
             assert isinstance(b, AnyFunction)
         self.dofs = dofs
         self._basis_functions: typing.Union[typing.List[AnyFunction], None] = None
+        self._maximum_degree = None
+        if reference.name == "pyramid":
+            self._maximum_degree = order
 
     def entity_dofs(self, entity_dim: int, entity_number: int) -> typing.List[int]:
         """Get the numbers of the DOFs associated with the given entity.
@@ -555,6 +555,13 @@ def get_polynomial_basis(self) -> typing.List[AnyFunction]:
         """
         return self._basis
 
+    @property
+    def maximum_degree(self) -> int:
+        """Get the maximum degree of this polynomial set for the element."""
+        if self._maximum_degree is None:
+            self._maximum_degree = max(p.maximum_degree(self.reference) for p in self._basis)
+        return self._maximum_degree
+
     def get_dual_matrix(
         self, inverse=False, caching=True
     ) -> sympy.matrices.dense.MutableDenseMatrix:
@@ -890,6 +897,11 @@ def get_polynomial_basis(self) -> typing.List[AnyFunction]:
         """
         raise NotImplementedError()
 
+    @property
+    def maximum_degree(self) -> int:
+        """Get the maximum degree of this polynomial set for the element."""
+        raise NotImplementedError()
+
     def test(self):
         """Run tests for this element."""
         super().test()
@@ -1066,6 +1078,11 @@ def get_polynomial_basis(self) -> typing.List[AnyFunction]:
         """
         raise NotImplementedError()
 
+    @property
+    def maximum_degree(self) -> int:
+        """Get the maximum degree of this polynomial set for the element."""
+        raise NotImplementedError()
+
     def test(self):
         """Run tests for this element."""
         super().test()