MutableMatrix -- the class of all mutable matrices

Description

A mutable matrix in Macaulay2 is a rectangular array of elements of a specific ring, whose entries can be modified.

A mutable matrix is different from a Matrix in that a matrix contains degree information for the target and source of the matrix, while a mutable matrix has no such information. Also, more operations are provided for matrices.

For an overview of mutable matrices, see mutable matrices.

Mutable matrices can either be encoded in a sparse manner (the matrix only encodes the non-zero elements), or in a dense manner (all elements are stored -- even zeros). The distinction is an option to several of the routines which create mutable matrices (mutableMatrix, mutableZero, mutableIdentity). Certain operations on (dense) matrices over RR or CC (e.g., eigenvalues, eigenvectors, LU decomposition, SVD decomposition, and solving) are performed using the lapack library.

row and column operations

rowAdd -- add a multiple of one row to another
rowSwap -- interchange rows
rowPermute -- permute some rows
rowMult -- multiply a row by a ring element
rowDivide -- missing documentation
columnAdd -- add a multiple of one column to another
columnSwap -- interchange columns
columnPermute -- permute some columns
columnMult -- multiply a column by a ring element
columnDivide -- missing documentation

matrix arithmetic

Many matrix arithmetic routines are only available for immutabie matrices, not mutable matrices. It is necessary to use matrix to make an immutable matrix first.

Methods that use an object of class MutableMatrix :

MutableMatrix * MutableMatrix, see * -- a binary operator, usually used for multiplication
RingElement * MutableMatrix, see * -- a binary operator, usually used for multiplication
MutableMatrix + MutableMatrix, see + -- a unary or binary operator, usually used for addition
- MutableMatrix, see - -- a unary or binary operator, usually used for negation or subtraction
MutableMatrix - MutableMatrix, see - -- a unary or binary operator, usually used for negation or subtraction
MutableMatrix == MutableMatrix, see == -- equality
columnAdd(MutableMatrix,ZZ,RingElement,ZZ), see columnAdd -- add a multiple of one column to another
columnMult(MutableMatrix,ZZ,RingElement), see columnMult -- multiply a column by a ring element
columnPermute(MutableMatrix,ZZ,List), see columnPermute -- permute some columns
columnSwap(MutableMatrix,ZZ,ZZ), see columnSwap -- interchange columns
eigenvalues(MutableMatrix), see eigenvalues -- find eigenvalues of a matrix over RR or CC
eigenvectors(MutableMatrix), see eigenvectors -- find eigenvectors of a matrix over RR or CC
entries(MutableMatrix), see entries -- lists the entries of a matrix
LLL(MutableMatrix), see LLL -- compute an LLL basis
LU(MutableMatrix), see LU -- LU decomposition
matrix(MutableMatrix) -- make a matrix from a mutable one
mutableMatrix(MutableMatrix), see mutableMatrix -- make a mutable matrix
MutableMatrix _ Sequence -- missing documentation
MutableMatrix _ Sequence = Thing -- assignment to an element of a mutable matrix
new Matrix from MutableMatrix -- missing documentation
new MutableMatrix from Matrix -- missing documentation
numColumns(MutableMatrix) -- number of columns in a mutable matrix
numRows(MutableMatrix) -- number of rows in a mutable matrix
ring(MutableMatrix), see ring -- Get the associated ring of an object
rowAdd(MutableMatrix,ZZ,RingElement,ZZ), see rowAdd -- add a multiple of one row to another
rowMult(MutableMatrix,ZZ,RingElement), see rowMult -- multiply a row by a ring element
rowPermute(MutableMatrix,ZZ,List), see rowPermute -- permute some rows
rowSwap(MutableMatrix,ZZ,ZZ), see rowSwap -- interchange rows
solve(MutableMatrix,MutableMatrix), see solve -- solve a linear equation
SVD(MutableMatrix), see SVD -- singular value decomposition of a rectangular matrix over RR or CC

For the programmer

The object MutableMatrix is a type, with ancestor classes HashTable < Thing.