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Diffstat (limited to 'src/algebra/matrix.spad.pamphlet')
| -rw-r--r-- | src/algebra/matrix.spad.pamphlet | 74 |
1 files changed, 3 insertions, 71 deletions
diff --git a/src/algebra/matrix.spad.pamphlet b/src/algebra/matrix.spad.pamphlet index 04bbb1fe..8d9242e5 100644 --- a/src/algebra/matrix.spad.pamphlet +++ b/src/algebra/matrix.spad.pamphlet @@ -9,74 +9,7 @@ \eject \tableofcontents \eject -\section{domain IMATRIX IndexedMatrix} -<<domain IMATRIX IndexedMatrix>>= -)abbrev domain IMATRIX IndexedMatrix -++ Author: Grabmeier, Gschnitzer, Williamson -++ Date Created: 1987 -++ Date Last Updated: July 1990 -++ Basic Operations: -++ Related Domains: Matrix, RectangularMatrix, SquareMatrix, -++ StorageEfficientMatrixOperations -++ Also See: -++ AMS Classifications: -++ Keywords: matrix, linear algebra -++ Examples: -++ References: -++ Description: -++ An \spad{IndexedMatrix} is a matrix where the minimal row and column -++ indices are parameters of the type. The domains Row and Col -++ are both IndexedVectors. -++ The index of the 'first' row may be obtained by calling the -++ function \spadfun{minRowIndex}. The index of the 'first' column may -++ be obtained by calling the function \spadfun{minColIndex}. The index of -++ the first element of a 'Row' is the same as the index of the -++ first column in a matrix and vice versa. -IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where - R : Ring - mnRow, mnCol : Integer - Row ==> IndexedVector(R,mnCol) - Col ==> IndexedVector(R,mnRow) - MATLIN ==> MatrixLinearAlgebraFunctions(R,Row,Col,$) - - Exports ==> MatrixCategory(R,Row,Col) - - Implementation ==> - InnerIndexedTwoDimensionalArray(R,mnRow,mnCol,Row,Col) add - - swapRows!(x,i1,i2) == - (i1 < minRowIndex(x)) or (i1 > maxRowIndex(x)) or _ - (i2 < minRowIndex(x)) or (i2 > maxRowIndex(x)) => - error "swapRows!: index out of range" - i1 = i2 => x - minRow := minRowIndex x - xx := x pretend PrimitiveArray(PrimitiveArray(R)) - n1 := i1 - minRow; n2 := i2 - minRow - row1 := qelt(xx,n1) - qsetelt!(xx,n1,qelt(xx,n2)) - qsetelt!(xx,n2,row1) - xx pretend $ - - if R has commutative("*") then - - determinant x == determinant(x)$MATLIN - minordet x == minordet(x)$MATLIN - - if R has EuclideanDomain then - - rowEchelon x == rowEchelon(x)$MATLIN - - if R has IntegralDomain then - - rank x == rank(x)$MATLIN - nullity x == nullity(x)$MATLIN - nullSpace x == nullSpace(x)$MATLIN - - if R has Field then - - inverse x == inverse(x)$MATLIN -@ \section{domain MATRIX Matrix} <<domain MATRIX Matrix>>= )abbrev domain MATRIX Matrix @@ -84,7 +17,7 @@ IndexedMatrix(R,mnRow,mnCol): Exports == Implementation where ++ Date Created: 1987 ++ Date Last Updated: July 1990 ++ Basic Operations: -++ Related Domains: IndexedMatrix, RectangularMatrix, SquareMatrix +++ Related Domains: RectangularMatrix, SquareMatrix ++ Also See: ++ AMS Classifications: ++ Keywords: matrix, linear algebra @@ -259,7 +192,7 @@ Matrix(R): Exports == Implementation where ++ Date Created: 1987 ++ Date Last Updated: July 1990 ++ Basic Operations: -++ Related Domains: IndexedMatrix, Matrix, SquareMatrix +++ Related Domains: Matrix, SquareMatrix ++ Also See: ++ AMS Classifications: ++ Keywords: matrix, linear algebra @@ -346,7 +279,7 @@ RectangularMatrix(m,n,R): Exports == Implementation where ++ Date Created: 1987 ++ Date Last Updated: July 1990 ++ Basic Operations: -++ Related Domains: IndexedMatrix, Matrix, RectangularMatrix +++ Related Domains: Matrix, RectangularMatrix ++ Also See: ++ AMS Classifications: ++ Keywords: matrix, linear algebra @@ -520,7 +453,6 @@ SquareMatrix(ndim,R): Exports == Implementation where <<*>>= <<license>> -<<domain IMATRIX IndexedMatrix>> <<domain MATRIX Matrix>> <<domain RMATRIX RectangularMatrix>> <<domain SQMATRIX SquareMatrix>> |