diff options
Diffstat (limited to 'src/algebra/vector.spad.pamphlet')
| -rw-r--r-- | src/algebra/vector.spad.pamphlet | 20 |
1 files changed, 10 insertions, 10 deletions
diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet index 7342a113..2d52b422 100644 --- a/src/algebra/vector.spad.pamphlet +++ b/src/algebra/vector.spad.pamphlet @@ -31,24 +31,24 @@ VectorCategory(R:Type): Category == OneDimensionalArrayAggregate R with if R has AbelianSemiGroup then - _+ : (%, %) -> % + + : (%, %) -> % ++ x + y returns the component-wise sum of the vectors x and y. ++ Error: if x and y are not of the same length. if R has AbelianMonoid then zero: NonNegativeInteger -> % ++ zero(n) creates a zero vector of length n. if R has AbelianGroup then - _- : % -> % + - : % -> % ++ -x negates all components of the vector x. - _- : (%, %) -> % + - : (%, %) -> % ++ x - y returns the component-wise difference of the vectors x and y. ++ Error: if x and y are not of the same length. - _* : (Integer, %) -> % + * : (Integer, %) -> % ++ n * y multiplies each component of the vector y by the integer n. if R has Monoid then - _* : (R, %) -> % + * : (R, %) -> % ++ r * y multiplies the element r times each component of the vector y. - _* : (%, R) -> % + * : (%, R) -> % ++ y * r multiplies each component of the vector y by the element r. if R has Ring then dot: (%, %) -> R @@ -86,7 +86,7 @@ VectorCategory(R:Type): Category == OneDimensionalArrayAggregate R with if R has Ring then dot(u, v) == #u ~= #v => error "Vectors must be of the same length" - _+/[qelt(u, i) * qelt(v, i) for i in minIndex u .. maxIndex u] + +/[qelt(u, i) * qelt(v, i) for i in minIndex u .. maxIndex u] outerProduct(u, v) == matrix [[qelt(u, i) * qelt(v,j) for i in minIndex u .. maxIndex u] _ for j in minIndex v .. maxIndex v] @@ -256,10 +256,10 @@ DirectProductCategory(dim:NonNegativeInteger, R:Type): Category == if R has CancellationAbelianMonoid then CancellationAbelianMonoid if R has Monoid then Monoid - _* : (R, %) -> % + * : (R, %) -> % ++ r * y multiplies the element r times each component of the ++ vector y. - _* : (%, R) -> % + * : (%, R) -> % ++ y * r multiplies each component of the vector y by the element r. if R has Finite then Finite if R has CommutativeRing then @@ -346,7 +346,7 @@ DirectProduct(dim:NonNegativeInteger, R:Type): same?: % -> Boolean same? z == every?(#1 = z(minIndex z), z) - x = y == _and/[qelt(x,i)$Rep = qelt(y,i)$Rep for i in 1..dim] + x = y == and/[qelt(x,i)$Rep = qelt(y,i)$Rep for i in 1..dim] retract(z:%):R == same? z => z(minIndex z) |