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author | dos-reis <gdr@axiomatics.org> | 2009-06-11 21:51:23 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2009-06-11 21:51:23 +0000 |
commit | 7bd82b57975bbc1ff5b87fed0739815c620ecdcc (patch) | |
tree | 4cf4d2b4af144e87a86cc1ac2f85a5f4148cb8fb /src/algebra/matcat.spad.pamphlet | |
parent | fb75980589a0611aee3b8e5e25408725a5c5a531 (diff) | |
download | open-axiom-7bd82b57975bbc1ff5b87fed0739815c620ecdcc.tar.gz |
* algebra/: Remove quotes from operator namaes in signatures.
Diffstat (limited to 'src/algebra/matcat.spad.pamphlet')
-rw-r--r-- | src/algebra/matcat.spad.pamphlet | 36 |
1 files changed, 18 insertions, 18 deletions
diff --git a/src/algebra/matcat.spad.pamphlet b/src/algebra/matcat.spad.pamphlet index 97af1385..0be83d9a 100644 --- a/src/algebra/matcat.spad.pamphlet +++ b/src/algebra/matcat.spad.pamphlet @@ -143,40 +143,40 @@ MatrixCategory(R,Row,Col): Category == Definition where --% Arithmetic - "+": (%,%) -> % + +: (%,%) -> % ++ \spad{x + y} is the sum of the matrices x and y. ++ Error: if the dimensions are incompatible. - "-": (%,%) -> % + -: (%,%) -> % ++ \spad{x - y} is the difference of the matrices x and y. ++ Error: if the dimensions are incompatible. - "-": % -> % + -: % -> % ++ \spad{-x} returns the negative of the matrix x. - "*": (%,%) -> % + *: (%,%) -> % ++ \spad{x * y} is the product of the matrices x and y. ++ Error: if the dimensions are incompatible. - "*": (R,%) -> % + *: (R,%) -> % ++ \spad{r*x} is the left scalar multiple of the scalar r and the ++ matrix x. - "*": (%,R) -> % + *: (%,R) -> % ++ \spad{x * r} is the right scalar multiple of the scalar r and the ++ matrix x. - "*": (Integer,%) -> % + *: (Integer,%) -> % ++ \spad{n * x} is an integer multiple. - "*": (%,Col) -> Col + *: (%,Col) -> Col ++ \spad{x * c} is the product of the matrix x and the column vector c. ++ Error: if the dimensions are incompatible. - "*": (Row,%) -> Row + *: (Row,%) -> Row ++ \spad{r * x} is the product of the row vector r and the matrix x. ++ Error: if the dimensions are incompatible. - "**": (%,NonNegativeInteger) -> % + **: (%,NonNegativeInteger) -> % ++ \spad{x ** n} computes a non-negative integral power of the matrix x. ++ Error: if the matrix is not square. if R has IntegralDomain then - "exquo": (%,R) -> Union(%,"failed") + exquo: (%,R) -> Union(%,"failed") ++ \spad{exquo(m,r)} computes the exact quotient of the elements ++ of m by r, returning \axiom{"failed"} if this is not possible. if R has Field then - "/": (%,R) -> % + /: (%,R) -> % ++ \spad{m/r} divides the elements of m by r. Error: if \spad{r = 0}. --% Linear algebra @@ -205,7 +205,7 @@ MatrixCategory(R,Row,Col): Category == Definition where ++ \spad{inverse(m)} returns the inverse of the matrix m. ++ If the matrix is not invertible, "failed" is returned. ++ Error: if the matrix is not square. - "**": (%,Integer) -> % + **: (%,Integer) -> % ++ \spad{m**n} computes an integral power of the matrix m. ++ Error: if matrix is not square or if the matrix ++ is square but not invertible. @@ -651,11 +651,11 @@ RectangularMatrixCategory(m,n,R,Row,Col): Category == Definition where --% Arithmetic if R has IntegralDomain then - "exquo": (%,R) -> Union(%,"failed") + exquo: (%,R) -> Union(%,"failed") ++ \spad{exquo(m,r)} computes the exact quotient of the elements ++ of m by r, returning \axiom{"failed"} if this is not possible. if R has Field then - "/": (%,R) -> % + /: (%,R) -> % ++ \spad{m/r} divides the elements of m by r. Error: if \spad{r = 0}. --% Linear algebra @@ -748,10 +748,10 @@ SquareMatrixCategory(ndim,R,Row,Col): Category == Definition where diagonalProduct: % -> R ++ \spad{diagonalProduct(m)} returns the product of the elements on the ++ diagonal of the matrix m. - "*": (%,Col) -> Col + *: (%,Col) -> Col ++ \spad{x * c} is the product of the matrix x and the column vector c. ++ Error: if the dimensions are incompatible. - "*": (Row,%) -> Row + *: (Row,%) -> Row ++ \spad{r * x} is the product of the row vector r and the matrix x. ++ Error: if the dimensions are incompatible. @@ -768,7 +768,7 @@ SquareMatrixCategory(ndim,R,Row,Col): Category == Definition where inverse: % -> Union(%,"failed") ++ \spad{inverse(m)} returns the inverse of the matrix m, if that ++ matrix is invertible and returns "failed" otherwise. - "**": (%,Integer) -> % + **: (%,Integer) -> % ++ \spad{m**n} computes an integral power of the matrix m. ++ Error: if the matrix is not invertible. |