Examples
========

These examples are complete Python scripts that can be run on their own. The
documentation workflow runs all of them before building the HTML pages,
ensuring that their imports and demonstrated APIs remain current.

Variational forms
-----------------

This example constructs a scalar Poisson problem and a Nitsche-type form on a
two-patch domain.

.. literalinclude:: variational_forms.py
   :language: python
   :linenos:

Differential calculus
---------------------

This example demonstrates the currently supported symbolic vector-calculus
identities.

.. literalinclude:: differential_calculus.py
   :language: python
   :linenos:

Analytical mappings
-------------------

This example evaluates a built-in analytical mapping and defines a custom
mapping from coordinate expressions.

.. literalinclude:: analytical_mappings.py
   :language: python
   :linenos:

Exterior calculus
-----------------

This example demonstrates differential forms, exterior derivatives, adjoint
operators, products, contractions, and Lie derivatives.

.. literalinclude:: exterior_calculus.py
   :language: python
   :linenos:

Expression trees
----------------

This example writes the expression trees of a differential operator and of an
expanded derivative in the DOT language of Graphviz. The quickstart guide draws
both trees.

.. literalinclude:: expression_trees.py
   :language: python
   :linenos:

Linearization of nonlinear problems
-----------------------------------

This example constructs a nonlinear Poisson residual and derives its Jacobian
form symbolically.

.. literalinclude:: nonlinear_poisson.py
   :language: python
   :linenos: