# basix.polynomials¶

Functions for working with polynomials.

Functions

 dim(ptype, celltype, degree) Dimension of a polynomial space. reshape_coefficients(poly_type, cell_type, ...) Reshape the coefficients. restriction(ptype, cell, restriction_cell) Get the polyset type that represents the restrictions of a type on a subentity. superset(cell, type1, type2) Get the polyset type that is a superset of two types on the given cell. tabulate_polynomial_set(celltype, ptype, ...) Tabulate a polynomial set. tabulate_polynomials(ptype, celltype, ...) Tabulate a set of polynomials on a reference cell.
basix.polynomials.dim(ptype: PolynomialType, celltype: CellType, degree: int) int

Dimension of a polynomial space.

Parameters:
• ptype – The polynomial type

• celltype – The cell type

• degree – The polynomial degree

Returns:

The dimension of the polynomial space

basix.polynomials.reshape_coefficients(poly_type: PolynomialType, cell_type: CellType, coefficients: ndarray[Any, dtype[float64]], value_size: int, input_degree: int, output_degree: int) ndarray[Any, dtype[float64]]

Reshape the coefficients.

Parameters:
• poly_type – The polynomial type.

• cell_type – The cell type

• coefficients – The coefficients

• value_size – The value size of the polynomials associated with the coefficients.

• input_degree – The maximum degree of polynomials associated with the input coefficients.

• output_degree – The maximum degree of polynomials associated with the output coefficients.

Returns:

Coefficients representing the same coefficients as the input in the set of polynomials of the output degree.

basix.polynomials.tabulate_polynomial_set(celltype: CellType, ptype: PolysetType, degree: int, nderiv: int, pts: ndarray[Any, dtype[_ScalarType_co]]) _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes]

Tabulate a polynomial set.

Parameters:
• celltype – The cell type

• ptype – The polyset type

• degree – The polynomial degree

• nderiv – The number of derivatives

• pts – The points to tabulat at

Returns:

Tabulated polynomial set