Matrix

Symbolica documentation for getting started, symbolic expressions, numerical evaluation, pattern matching, and APIs in Python and Rust.

`Matrix`

Matrix()

A matrix with rational polynomial coefficients.

Methods

Name	Description
`__add__`	Add two matrices `self` and `rhs`, returning the result.
`__copy__`	Copy the matrix.
`__eq__`	Compare two matrices.
`__getitem__`	Get the entry at position `key` in the matrix.
`__matmul__`	Matrix multiply `self` and `rhs`, returning the result.
`__mul__`	Matrix multiply `self` and `rhs`, returning the result.
`__neg__`	Negate the matrix, returning the result.
`__neq__`	Compare two matrices.
`__new__`	Create a new zeroed matrix with `nrows` rows and `ncols` columns.
`__rmatmul__`	Matrix multiply `rhs` and `self`, returning the result.
`__rmul__`	Matrix multiply `rhs` and `self`, returning the result.
`__str__`	Print the matrix in a human-readable format.
`__sub__`	Subtract matrix `rhs` from `self`, returning the result.
`__truediv__`	Divide this matrix by scalar `rhs` and return the result.
`augment`	Augment the matrix with another matrix, e.g
`content`	Get the content, i.e., the GCD of the coefficients.
`det`	Return the determinant of the matrix.
`eye`	Create a new matrix with the scalars `diag` on the main diagonal and zeroes elsewhere.
`format`	Convert the matrix into a human-readable string, with tunable settings.
`from_linear`	Create a new matrix from a 1-dimensional vector of scalars.
`from_nested`	Create a new matrix from a 2-dimensional vector of scalars.
`identity`	Create a new square matrix with `nrows` rows and ones on the main diagonal and zeroes elsewhere.
`inv`	Return the inverse of the matrix, if it exists.
`is_diagonal`	Return true iff every non- main diagonal entry in the matrix is zero.
`is_zero`	Return true iff every entry in the matrix is zero.
`map`	Apply a function `f` to every entry of the matrix.
`ncols`	Get the number of columns in the matrix.
`nrows`	Get the number of rows in the matrix.
`primitive_part`	Construct the same matrix, but with the content removed.
`row_reduce`	Row-reduce the first `max_col` columns of the matrix in-place using Gaussian elimination and return the rank.
`solve`	Solve `A * x = b` for `x`, where `A` is the current matrix.
`solve_any`	Solve `A * x = b` for `x`, where `A` is the current matrix and return any solution if the system is underdetermined.
`split_col`	Split the matrix into two matrices at column `col`.
`swap_cols`	Swap columns `i` and `j` of the matrix in-place.
`swap_rows`	Swap rows `i` and `j` of the matrix in-place, starting from column `start`.
`to_latex`	Convert the matrix into a LaTeX string.
`transpose`	Return the transpose of the matrix.
`vec`	Create a new column vector from a list of scalars.

`add`

Matrix.__add__(rhs: Matrix) -> Matrix

Add two matrices self and rhs, returning the result.

Parameters

rhs (Matrix) The right-hand-side operand.

`copy`

Matrix.__copy__() -> Matrix

Copy the matrix.

`eq`

Matrix.__eq__(other: Matrix) -> bool

Compare two matrices.

Parameters

other (Matrix) The other operand to combine or compare with.

`getitem`

Matrix.__getitem__(key: tuple[int, int]) -> RationalPolynomial

Get the entry at position key in the matrix.

Parameters

key (tuple[int, int]) The (row, column) index of the entry to retrieve.

`matmul`

Matrix.__matmul__(rhs: Matrix | RationalPolynomial | Polynomial | Expression | int) -> Matrix

Matrix multiply self and rhs, returning the result.

Parameters

rhs (Matrix | RationalPolynomial | Polynomial | Expression | int) The right-hand-side operand.

`mul`

Matrix.__mul__(rhs: Matrix | RationalPolynomial | Polynomial | Expression | int) -> Matrix

Matrix multiply self and rhs, returning the result.

Parameters

rhs (Matrix | RationalPolynomial | Polynomial | Expression | int) The right-hand-side operand.

`neg`

Matrix.__neg__() -> Matrix

Negate the matrix, returning the result.

`neq`

Matrix.__neq__(other: Matrix) -> bool

Compare two matrices.

Parameters

other (Matrix) The other operand to combine or compare with.

`new`

Matrix.__new__(nrows: int, ncols: int) -> Matrix

Create a new zeroed matrix with nrows rows and ncols columns.

Parameters

nrows (int) The number of rows.
ncols (int) The number of columns.

`rmatmul`

Matrix.__rmatmul__(rhs: RationalPolynomial | Polynomial | Expression | int) -> Matrix

Matrix multiply rhs and self, returning the result.

Parameters

rhs (RationalPolynomial | Polynomial | Expression | int) The right-hand-side operand.

`rmul`

Matrix.__rmul__(rhs: RationalPolynomial | Polynomial | Expression | int) -> Matrix

Matrix multiply rhs and self, returning the result.

Parameters

rhs (RationalPolynomial | Polynomial | Expression | int) The right-hand-side operand.

`str`

Matrix.__str__() -> str

Print the matrix in a human-readable format.

`sub`

Matrix.__sub__(rhs: Matrix) -> Matrix

Subtract matrix rhs from self, returning the result.

Parameters

rhs (Matrix) The right-hand-side operand.

`truediv`

Matrix.__truediv__(rhs: RationalPolynomial | Polynomial | Expression | int) -> Matrix

Divide this matrix by scalar rhs and return the result.

Parameters

rhs (RationalPolynomial | Polynomial | Expression | int) The right-hand-side operand.

`augment`

Matrix.augment(b: Matrix) -> Matrix

Augment the matrix with another matrix, e.g. create [A B] from matrix A and B.

Returns an error when the matrices do not have the same number of rows.

Parameters

b (Matrix) The matrix to append as additional columns.

`content`

Matrix.content() -> RationalPolynomial

Get the content, i.e., the GCD of the coefficients.

`det`

Matrix.det() -> RationalPolynomial

Return the determinant of the matrix.

`eye`

Matrix.eye(diag: Sequence[RationalPolynomial | Polynomial | Expression | int]) -> Matrix

Create a new matrix with the scalars diag on the main diagonal and zeroes elsewhere.

Parameters

diag (Sequence[RationalPolynomial | Polynomial | Expression | int]) The entries to place on the diagonal.

`format`

Matrix.format(
    mode: PrintMode = PrintMode.Symbolica,
    max_line_length: int | None = 80,
    indentation: int = 4,
    fill_indented_lines: bool = True,
    pretty_matrix = True,
    number_thousands_separator: str | None = None,
    multiplication_operator: str = '*',
    double_star_for_exponentiation: bool = False,
    square_brackets_for_function: bool = False,
    function_brackets: tuple[str, str] = ('(', ')'),
    num_exp_as_superscript: bool = True,
    precision: int | None = None,
    show_namespaces: bool = False,
    hide_namespace: str | None = None,
    include_attributes: bool = False,
    max_terms: int | None = None,
    custom_print_mode: int | None = None,
) -> str

Convert the matrix into a human-readable string, with tunable settings.

Parameters

mode (PrintMode) The mode that controls how the input is interpreted or formatted.
max_line_length (int | None) The preferred maximum line length before wrapping.
indentation (int) The number of spaces used for wrapped lines.
fill_indented_lines (bool) Whether wrapped lines should be padded to the configured indentation.
pretty_matrix (Any) Whether matrices should be printed in the pretty multi-line layout.
number_thousands_separator (str | None) The separator inserted between groups of digits in printed integers.
multiplication_operator (str) The string used to print multiplication.
double_star_for_exponentiation (bool) Whether exponentiation should be printed as ** instead of ^.
square_brackets_for_function (bool) Whether function calls should be printed with square brackets.
function_brackets (tuple[str, str]) The opening and closing brackets used when printing function arguments.
num_exp_as_superscript (bool) Whether small integer exponents should be printed as superscripts.
precision (int | None) The decimal precision used when printing numeric coefficients.
show_namespaces (bool) Whether namespaces should be included in the formatted output.
hide_namespace (str | None) A namespace prefix to omit from printed symbol names.
include_attributes (bool) Whether symbol attributes should be included in the printed output.
max_terms (int | None) The maximum number of terms to print before truncating the output.
custom_print_mode (int | None) A custom print-mode identifier passed through to custom print callbacks.

`from_linear`

Matrix.from_linear(
    nrows: int,
    ncols: int,
    entries: Sequence[RationalPolynomial | Polynomial | Expression | int],
) -> Matrix

Create a new matrix from a 1-dimensional vector of scalars.

Parameters

nrows (int) The number of rows.
ncols (int) The number of columns.
entries (Sequence[RationalPolynomial | Polynomial | Expression | int]) The matrix entries in row-major order.

`from_nested`

Matrix.from_nested(entries: Sequence[Sequence[RationalPolynomial | Polynomial | Expression | int]]) -> Matrix

Create a new matrix from a 2-dimensional vector of scalars.

Parameters

entries (Sequence[Sequence[RationalPolynomial | Polynomial | Expression | int]]) The nested row entries of the matrix.

`identity`

Matrix.identity(nrows: int) -> Matrix

Create a new square matrix with nrows rows and ones on the main diagonal and zeroes elsewhere.

Parameters

nrows (int) The number of rows.

`inv`

Matrix.inv() -> Matrix

Return the inverse of the matrix, if it exists.

`is_diagonal`

Matrix.is_diagonal() -> bool

Return true iff every non- main diagonal entry in the matrix is zero.

`is_zero`

Matrix.is_zero() -> bool

Return true iff every entry in the matrix is zero.

`map`

Matrix.map(f: Callable[[RationalPolynomial], RationalPolynomial]) -> Matrix

Apply a function f to every entry of the matrix.

Parameters

f (Callable[[RationalPolynomial], RationalPolynomial]) The callback or function to apply.

`ncols`

Matrix.ncols() -> int

Get the number of columns in the matrix.

`nrows`

Matrix.nrows() -> int

Get the number of rows in the matrix.

`primitive_part`

Matrix.primitive_part() -> Matrix

Construct the same matrix, but with the content removed.

`row_reduce`

Matrix.row_reduce(max_col: int) -> int

Row-reduce the first max_col columns of the matrix in-place using Gaussian elimination and return the rank.

Parameters

max_col (int) The highest column index included in row reduction.

`solve`

Matrix.solve(b: Matrix) -> Matrix

Solve A * x = b for x, where A is the current matrix.

Parameters

b (Matrix) The right-hand-side matrix b in A * x = b.

`solve_any`

Matrix.solve_any(b: Matrix) -> Matrix

Solve A * x = b for x, where A is the current matrix and return any solution if the system is underdetermined.

Parameters

b (Matrix) The right-hand-side matrix b in A * x = b.

`split_col`

Matrix.split_col(col: int) -> tuple[Matrix, Matrix]

Split the matrix into two matrices at column col.

Parameters

col (int) The column index at which to split the matrix.

`swap_cols`

Matrix.swap_cols(i: int, j: int) -> None

Swap columns i and j of the matrix in-place.

Parameters

i (int) The first index.
j (int) The second index.

`swap_rows`

Matrix.swap_rows(i: int, j: int, start: int = 0) -> None

Swap rows i and j of the matrix in-place, starting from column start.

Parameters

i (int) The first index.
j (int) The second index.
start (int) The starting index or value.

`to_latex`

Matrix.to_latex() -> str

Convert the matrix into a LaTeX string.

`transpose`

Matrix.transpose() -> Matrix

Return the transpose of the matrix.

`vec`

Matrix.vec(entries: Sequence[RationalPolynomial | Polynomial | Expression | int]) -> Matrix

Create a new column vector from a list of scalars.

Parameters

entries (Sequence[RationalPolynomial | Polynomial | Expression | int]) The entries of the column vector, from top to bottom.