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 that create mutable matrices (mutableMatrix, mutableIdentity). Certain operations over RR or CC are performed using the lapack library and require dense encoding of matrices: LUdecomposition, SVD, solve, eigenvalues, eigenvectors.

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
columnAdd -- add a multiple of one column to another
columnSwap -- interchange columns
columnPermute -- permute some columns
columnMult -- multiply a column by a ring element

matrix arithmetic

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

Functions and methods returning a mutable matrix :

mutableIdentity -- see mutableIdentity(Ring,ZZ) -- make a mutable identity matrix
mutableMatrix -- make a mutable matrix
MutableMatrix ^ ZZ (missing documentation)
randomMutableMatrix -- see randomMutableMatrix(ZZ,ZZ,RR,ZZ) -- a random mutable matrix of integers
RingMap MutableMatrix (missing documentation)

Methods that use a mutable matrix :

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
MutableMatrix == ZZ -- see == -- equality
ZZ == MutableMatrix -- see == -- equality
clean(RR,MutableMatrix) -- see clean -- Set to zero elements that are approximately zero
columnAdd(MutableMatrix,ZZ,Number,ZZ) -- see columnAdd -- add a multiple of one column to another
columnAdd(MutableMatrix,ZZ,RingElement,ZZ) -- see columnAdd -- add a multiple of one column to another
columnMult(MutableMatrix,ZZ,Number) -- see columnMult -- multiply a column by a ring element
columnMult(MutableMatrix,ZZ,RingElement) -- see columnMult -- multiply a column by a ring element
columnPermute(MutableMatrix,ZZ,List) -- see columnPermute -- permute some columns
columnRankProfile(MutableMatrix) -- see columnRankProfile -- find the column rank profile of a mutable matrix
columnSwap(MutableMatrix,ZZ,ZZ) -- see columnSwap -- interchange columns
determinant(MutableMatrix) -- see determinant -- determinant of a matrix
eigenvalues(MutableMatrix) -- see eigenvalues -- find eigenvalues of a matrix
eigenvectors(MutableMatrix) -- see eigenvectors -- find eigenvectors of a matrix over RR or CC
entries(MutableMatrix) -- see entries -- lists the entries of a matrix
fillMatrix(MutableMatrix) -- see fillMatrix -- fill a mutable matrix with random numbers
fillMatrix(MutableMatrix,ZZ) -- see fillMatrix -- fill a mutable matrix with random numbers
inverse(MutableMatrix) -- see inverse(Matrix) -- compute the inverse
lift(MutableMatrix,type of InexactNumber') (missing documentation)
lift(MutableMatrix,type of InexactNumber) (missing documentation)
lift(MutableMatrix,type of Number) (missing documentation)
lift(MutableMatrix,type of RingElement) (missing documentation)
LLL(MutableMatrix) -- see LLL -- compute an LLL basis
LUdecomposition(MutableMatrix) -- see LUdecomposition -- LU decomposition
MutableMatrix _ Sequence -- see Matrix _ Sequence -- get entry of matrix
matrix(MutableMatrix) -- make a matrix from a mutable one
mutableMatrix(MutableMatrix) -- see mutableMatrix -- make a mutable matrix
MutableMatrix * RingElement (missing documentation)
MutableMatrix * RR (missing documentation)
MutableMatrix * ZZ (missing documentation)
MutableMatrix ^ List (missing documentation)
MutableMatrix _ List (missing documentation)
MutableMatrix _ Sequence = Thing -- assignment to an element of a mutable matrix
norm(InexactField,MutableMatrix) -- see norm
norm(MutableMatrix) -- see norm
norm(RR,MutableMatrix) -- see norm
nullSpace(MutableMatrix) -- see nullSpace -- find the null space of a mutable matrix
numColumns(MutableMatrix) -- see numColumns(Matrix) -- number of columns in a matrix or mutable matrix
numRows(MutableMatrix) -- see numRows(Matrix) -- number of rows in a matrix or mutable matrix
precision(MutableMatrix) -- see precision
QRDecomposition(MutableMatrix) -- see QRDecomposition -- compute a QR decomposition of a real matrix
rank(MutableMatrix) -- see rank -- compute the rank
reducedRowEchelonForm(MutableMatrix) -- see reducedRowEchelonForm -- compute the reduced row echelon form of a matrix or mutable matrix over a field
ring(MutableMatrix) -- see ring -- get the associated ring of an object
rowAdd(MutableMatrix,ZZ,Number,ZZ) -- see rowAdd -- add a multiple of one row to another
rowAdd(MutableMatrix,ZZ,RingElement,ZZ) -- see rowAdd -- add a multiple of one row to another
rowMult(MutableMatrix,ZZ,Number) -- see rowMult -- multiply a row by a ring element
rowMult(MutableMatrix,ZZ,RingElement) -- see rowMult -- multiply a row by a ring element
rowPermute(MutableMatrix,ZZ,List) -- see rowPermute -- permute some rows
rowRankProfile(MutableMatrix) -- see rowRankProfile -- find the row rank profile of a mutable matrix
rowSwap(MutableMatrix,ZZ,ZZ) -- see rowSwap -- interchange rows
RR * MutableMatrix (missing documentation)
solve(MutableMatrix,MutableMatrix) -- see solve -- solve linear equation(s)
submatrix(MutableMatrix,VisibleList) -- see submatrix(Matrix,VisibleList) -- select columns
submatrix(MutableMatrix,VisibleList,VisibleList) -- see submatrix(Matrix,VisibleList,VisibleList) -- select part of a matrix
SVD(MutableMatrix) -- see SVD -- singular value decomposition of a matrix
transpose(MutableMatrix) -- see transpose(Matrix) -- transpose a matrix
ZZ * MutableMatrix (missing documentation)

For the programmer

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