diff options
Diffstat (limited to 'src/algebra/carten.spad.pamphlet')
| -rw-r--r-- | src/algebra/carten.spad.pamphlet | 46 |
1 files changed, 23 insertions, 23 deletions
diff --git a/src/algebra/carten.spad.pamphlet b/src/algebra/carten.spad.pamphlet index 0f1d2952..064b0865 100644 --- a/src/algebra/carten.spad.pamphlet +++ b/src/algebra/carten.spad.pamphlet @@ -219,7 +219,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where ++ kroneckerDelta() is the rank 2 tensor defined by ++ \spad{kroneckerDelta()(i,j)} ++ \spad{= 1 if i = j} - ++ \spad{= 0 if i \^= j} + ++ \spad{= 0 if i \~= j} leviCivitaSymbol: () -> % ++ leviCivitaSymbol() is the rank \spad{dim} tensor defined by @@ -269,7 +269,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where qr := divide(n, dim) n := qr.quotient indv.((rnk-i+1) pretend NNI) := qr.remainder + minix - n ^= 0 => error "Index error (too big)" + n ~= 0 => error "Index error (too big)" indv index2int(indv: INDEX): Integer == @@ -287,17 +287,17 @@ CartesianTensor(minix, dim, R): Exports == Implementation where v = dim3 => 3 v = dim4 => 4 rx := 0 - while v ^= 0 repeat + while v ~= 0 repeat qr := divide(v, dim) v := qr.quotient - if v ^= 0 then - qr.remainder ^= 0 => error "Rank is not a whole number" + if v ~= 0 then + qr.remainder ~= 0 => error "Rank is not a whole number" rx := rx + 1 rx -- l must be a list of the numbers 1..#l mkPerm(n: NNI, l: List Integer): PERM == - #l ^= n => + #l ~= n => error "The list is not a permutation." p: PERM := new(n, 0) seen: Vector Boolean := new(n, false) @@ -320,14 +320,14 @@ CartesianTensor(minix, dim, R): Exports == Implementation where -- sum minix..minix+#v-1. maxix := minix+#v-1 psum := (((maxix+1)*maxix - minix*(minix-1)) exquo 2)::Integer - -- +/v ^= psum => 0 + -- +/v ~= psum => 0 n := 0 for i in 1..#v repeat n := n + v.i - n ^= psum => 0 + n ~= psum => 0 -- Bubble sort! This is pretty grotesque. totTrans: Integer := 0 nTrans: Integer := 1 - while nTrans ^= 0 repeat + while nTrans ~= 0 repeat nTrans := 0 for i in 1..#v-1 for j in 2..#v repeat if v.i > v.j then @@ -335,7 +335,7 @@ CartesianTensor(minix, dim, R): Exports == Implementation where e := v.i; v.i := v.j; v.j := e totTrans := totTrans + nTrans for i in 1..dim repeat - if v.i ^= minix+i-1 then return 0 + if v.i ~= minix+i-1 then return 0 odd? totTrans => -1 1 @@ -373,23 +373,23 @@ CartesianTensor(minix, dim, R): Exports == Implementation where lengthRankOrElse n elt(x) == - #x ^= 1 => error "Index error (the rank is not 0)" + #x ~= 1 => error "Index error (the rank is not 0)" get(x,0) elt(x, i: I) == - #x ^= dim => error "Index error (the rank is not 1)" + #x ~= dim => error "Index error (the rank is not 1)" get(x,(i-minix)) elt(x, i: I, j: I) == - #x ^= dim2 => error "Index error (the rank is not 2)" + #x ~= dim2 => error "Index error (the rank is not 2)" get(x,(dim*(i-minix) + (j-minix))) elt(x, i: I, j: I, k: I) == - #x ^= dim3 => error "Index error (the rank is not 3)" + #x ~= dim3 => error "Index error (the rank is not 3)" get(x,(dim2*(i-minix) + dim*(j-minix) + (k-minix))) elt(x, i: I, j: I, k: I, l: I) == - #x ^= dim4 => error "Index error (the rank is not 4)" + #x ~= dim4 => error "Index error (the rank is not 4)" get(x,(dim3*(i-minix) + dim2*(j-minix) + dim*(k-minix) + (l-minix))) elt(x, i: List I) == - #i ^= rank x => error "Index error (wrong rank)" + #i ~= rank x => error "Index error (wrong rank)" n: I := 0 for ii in i repeat ix := ii - minix @@ -398,15 +398,15 @@ CartesianTensor(minix, dim, R): Exports == Implementation where get(x,n) coerce(lr: List R): % == - #lr ^= dim => error "Incorrect number of components" + #lr ~= dim => error "Incorrect number of components" z := new(dim, 0) for r in lr for i in 0..dim-1 repeat set_!(z, i, r) z coerce(lx: List %): % == - #lx ^= dim => error "Incorrect number of slices" + #lx ~= dim => error "Incorrect number of slices" rx := rank first lx for x in lx repeat - rank x ^= rx => error "Inhomogeneous slice ranks" + rank x ~= rx => error "Inhomogeneous slice ranks" nx := # first lx z := new(dim * nx, 0) for x in lx for offz in 0.. by nx repeat @@ -453,18 +453,18 @@ CartesianTensor(minix, dim, R): Exports == Implementation where z x = y == - #x ^= #y => false + #x ~= #y => false for i in 0..#x-1 repeat - if get(x,i) ^= get(y,i) then return false + if get(x,i) ~= get(y,i) then return false true x + y == - #x ^= #y => error "Rank mismatch" + #x ~= #y => error "Rank mismatch" -- z := [xi + yi for xi in x for yi in y] z := new(#x, 0) for i in 0..#x-1 repeat set_!(z, i, get(x,i) + get(y,i)) z x - y == - #x ^= #y => error "Rank mismatch" + #x ~= #y => error "Rank mismatch" -- [xi - yi for xi in x for yi in y] z := new(#x, 0) for i in 0..#x-1 repeat set_!(z, i, get(x,i) - get(y,i)) |