symfem.polynomials.degree_computation
=====================================

.. py:module:: symfem.polynomials.degree_computation

.. autoapi-nested-parse::

   Functions to compute the degree of polynomials.



Functions
---------

.. autoapisummary::

   symfem.polynomials.degree_computation.monomial_degree
   symfem.polynomials.degree_computation.simplex_degree
   symfem.polynomials.degree_computation.tp_degree
   symfem.polynomials.degree_computation.prism_degree
   symfem.polynomials.degree_computation.pyramid_degree
   symfem.polynomials.degree_computation.degree


Module Contents
---------------

.. py:function:: monomial_degree(term: sympy.core.expr.Expr, vars: tuple[sympy.Symbol, Ellipsis] = x) -> int

   Get the degree of a sympy monomial.


.. py:function:: simplex_degree(polynomial: sympy.core.expr.Expr, vars: tuple[sympy.Symbol, Ellipsis] = x) -> int

   Get the degree of a polynomial on a simplex cell.

   :param polynomial: The polynomial

   :returns: The degree of the polynomial on a simplex cell


.. py:function:: tp_degree(polynomial: sympy.core.expr.Expr, vars: tuple[sympy.Symbol, Ellipsis] = x) -> int

   Get the degree of a polynomial on a tensor product cell.

   :param polynomial: The polynomial

   :returns: The degree of the polynomial on a tensor product cell


.. py:function:: prism_degree(polynomial: sympy.core.expr.Expr, vars: tuple[sympy.Symbol, Ellipsis] = x) -> int

   Get the degree of a polynomial on a prism.

   :param polynomial: The polynomial

   :returns: The degree of the polynomial on a prism


.. py:function:: pyramid_degree(polynomial: sympy.core.expr.Expr, vars: tuple[sympy.Symbol, Ellipsis] = x) -> int

   Get the degree of a polynomial on a pyramid.

   :param polynomial: The polynomial

   :returns: The degree of the polynomial on a pyramid


.. py:function:: degree(reference: symfem.references.Reference, polynomial: symfem.functions.Function, vars: tuple[sympy.Symbol, Ellipsis] = x) -> int

   Get the Lagrange degree of a polynomial on a reference cell.

   :param reference: The reference cell
   :param polynomial: The polynomial

   :returns: The degree of the polynomial on the reference cell