diff options
| -rw-r--r-- | src/algebra/vector.spad.pamphlet | 38 |
1 files changed, 18 insertions, 20 deletions
diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet index e11e41e9..8555d05d 100644 --- a/src/algebra/vector.spad.pamphlet +++ b/src/algebra/vector.spad.pamphlet @@ -330,16 +330,13 @@ DirectProductCategory(dim:NonNegativeInteger, R:Type): Category == DirectProduct(dim:NonNegativeInteger, R:Type): DirectProductCategory(dim, R) == Vector R add - - Rep := Vector R - - coerce(z:%):Vector(R) == copy(z)$Rep pretend Vector(R) - coerce(r:R):% == new(dim, r)$Rep + coerce(z:%):Vector(R) == copy rep z + coerce(r:R):% == per new(dim, r)$Vector(R) parts x == VEC2LIST(x)$Lisp directProduct z == - size?(z, dim) => copy(z)$Rep + size?(z, dim) => per copy z error "Not of the correct length" @@ -347,7 +344,7 @@ DirectProduct(dim:NonNegativeInteger, R:Type): same?: % -> Boolean same? z == every?(#1 = z(minIndex z), z) - x = y == and/[qelt(x,i)$Rep = qelt(y,i)$Rep for i in 1..dim] + x = y == and/[qelt(rep x,i) = qelt(rep y,i) for i in 1..dim] retract(z:%):R == same? z => z(minIndex z) @@ -359,42 +356,42 @@ DirectProduct(dim:NonNegativeInteger, R:Type): if R has AbelianSemiGroup then - u:% + v:% == map(_+ , u, v)$Rep + u:% + v:% == per map(_+ , rep u, rep v) if R has AbelianMonoid then - 0 == zero(dim)$Vector(R) pretend % + 0 == per zero(dim)$Vector(R) if R has Monoid then - 1 == new(dim, 1)$Vector(R) pretend % - u:% * r:R == map(#1 * r, u) - r:R * u:% == map(r * #1, u) - x:% * y:% == [x.i * y.i for i in 1..dim]$Vector(R) pretend % + 1 == per new(dim, 1)$Vector(R) + u:% * r:R == per map(#1 * r, rep u) + r:R * u:% == per map(r * #1, rep u) + x:% * y:% == per [x.i * y.i for i in 1..dim]$Vector(R) if R has CancellationAbelianMonoid then subtractIfCan(u:%, v:%):Union(%,"failed") == w := new(dim,0)$Vector(R) for i in 1..dim repeat - (c := subtractIfCan(qelt(u, i)$Rep, qelt(v,i)$Rep)) case "failed" => + (c := subtractIfCan(qelt(rep u, i), qelt(rep v,i))) case "failed" => return "failed" - qsetelt!(w, i, c::R)$Rep - w pretend % + qsetelt!(w, i, c::R) + per w if R has Ring then - u:% * v:% == map(_* , u, v)$Rep + u:% * v:% == per map(_* ,rep u,rep v) recip z == w := new(dim,0)$Vector(R) for i in minIndex w .. maxIndex w repeat (u := recip qelt(z, i)) case "failed" => return "failed" qsetelt!(w, i, u::R) - w pretend % + per w unitVector i == v:= new(dim,0)$Vector(R) v.i := 1 - v pretend % + per v if R has OrderedSet then x < y == @@ -403,7 +400,8 @@ DirectProduct(dim:NonNegativeInteger, R:Type): qelt(x,i) > qelt(y,i) => return false false - if R has OrderedAbelianMonoidSup then sup(x, y) == map(sup, x, y) + if R has OrderedAbelianMonoidSup then + sup(x,y) == per map(sup, rep x, rep y) @ \section{package DIRPROD2 DirectProductFunctions2} |