diff options
| author | dos-reis <gdr@axiomatics.org> | 2008-04-03 04:23:42 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2008-04-03 04:23:42 +0000 |
| commit | 001e19b08ba7fb1b9e6f6bdb44a82ba3db3fc532 (patch) | |
| tree | da9e2fe5d81ff4cd7709d12e44b8c3e348b8a8e3 /src/algebra | |
| parent | a7bab9a6c2070d05e2dbd256ce455079c8ced385 (diff) | |
| download | open-axiom-001e19b08ba7fb1b9e6f6bdb44a82ba3db3fc532.tar.gz | |
Replace `^=' with `~='.
Diffstat (limited to 'src/algebra')
177 files changed, 932 insertions, 932 deletions
diff --git a/src/algebra/acplot.spad.pamphlet b/src/algebra/acplot.spad.pamphlet index fa57e414..383f7e9c 100644 --- a/src/algebra/acplot.spad.pamphlet +++ b/src/algebra/acplot.spad.pamphlet @@ -405,7 +405,7 @@ PlaneAlgebraicCurvePlot():Exports == Implementation where [p,x,y,xMin,xMax,yMin,yMax,[lf,rt,bt,tp],htans,vtans,bran] makeLineSketch(p,x,y,xMin,xMax,yMin,yMax) == - -- the case where p(x,y) = a x + b y + c with a ^= 0, b ^= 0 + -- the case where p(x,y) = a x + b y + c with a ~= 0, b ~= 0 -- this is a line which is neither vertical nor horizontal xMinSF := RNtoSF xMin; xMaxSF := RNtoSF xMax yMinSF := RNtoSF yMin; yMaxSF := RNtoSF yMax diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet index 86f3ca7e..e36fc72f 100644 --- a/src/algebra/aggcat.spad.pamphlet +++ b/src/algebra/aggcat.spad.pamphlet @@ -625,7 +625,7 @@ Collection(S:Type): Category == HomogeneousAggregate(S) with remove: (S,%) -> % ++ remove(x,u) returns a copy of u with all ++ elements \axiom{y = x} removed. - ++ Note: \axiom{remove(y,c) == [x for x in c | x ^= y]}. + ++ Note: \axiom{remove(y,c) == [x for x in c | x ~= y]}. removeDuplicates: % -> % ++ removeDuplicates(u) returns a copy of u with all duplicates removed. if S has ConvertibleTo InputForm then ConvertibleTo InputForm @@ -1268,7 +1268,7 @@ Dictionary(S:SetCategory): Category == s = t == eq?(s,t) => true - #s ^= #t => false + #s ~= #t => false _and/[member?(x, t) for x in parts s] remove_!(f:S->Boolean, t:%) == @@ -1925,9 +1925,9 @@ TableAggregate(Key:SetCategory, Entry:SetCategory): Category == s:% = t:% == eq?(s,t) => true - #s ^= #t => false + #s ~= #t => false for k in keys s repeat - (e := search(k, t)) case "failed" or (e::Entry) ^= s.k => false + (e := search(k, t)) case "failed" or (e::Entry) ~= s.k => false true map(f: Record(key:Key,entry:Entry)->Record(key:Key,entry:Entry), t: %): % == @@ -2570,7 +2570,7 @@ UnaryRecursiveAggregate(S:Type): Category == RecursiveAggregate S with eq?(x, y) => true for k in 0.. while not empty? x and not empty? y repeat k = cycleMax and cyclic? x => error "cyclic list" - first x ^= first y => return false + first x ~= first y => return false x := rest x y := rest y empty? x and empty? y @@ -4245,7 +4245,7 @@ OneDimensionalArrayAggregate(S:Type): Category == if S has SetCategory then reduce(f, a, identity,absorber) == - for k in minIndex a .. maxIndex a while identity ^= absorber + for k in minIndex a .. maxIndex a while identity ~= absorber repeat identity := f(identity, qelt(a, k)) identity @@ -4391,7 +4391,7 @@ OneDimensionalArrayAggregate(S:Type): Category == if S has SetCategory then x = y == - #x ^= #y => false + #x ~= #y => false for i in minIndex x .. maxIndex x repeat not(qelt(x, i) = qelt(y, i)) => return false true @@ -4407,7 +4407,7 @@ OneDimensionalArrayAggregate(S:Type): Category == a < b == for i in minIndex a .. maxIndex a for j in minIndex b .. maxIndex b repeat - qelt(a, i) ^= qelt(b, j) => return a.i < b.j + qelt(a, i) ~= qelt(b, j) => return a.i < b.j #a < #b @@ -4616,7 +4616,7 @@ ListAggregate(S:Type): Category == Join(StreamAggregate S, if S has SetCategory then reduce(f, x, i,a) == r := i - while not empty? x and r ^= a repeat + while not empty? x and r ~= a repeat r := f(r, first x) x := rest x r @@ -4679,7 +4679,7 @@ ListAggregate(S:Type): Category == Join(StreamAggregate S, position(w, x, s) == s < (m := minIndex x) => error "index out of range" x := rest(x, (s - m)::NonNegativeInteger) - for k in s.. while not empty? x and w ^= first x repeat + for k in s.. while not empty? x and w ~= first x repeat x := rest x empty? x => minIndex x - 1 k @@ -4693,7 +4693,7 @@ ListAggregate(S:Type): Category == Join(StreamAggregate S, if S has OrderedSet then x < y == while not empty? x and not empty? y repeat - first x ^= first y => return(first x < first y) + first x ~= first y => return(first x < first y) x := rest x y := rest y empty? x => not empty? y diff --git a/src/algebra/algcat.spad.pamphlet b/src/algebra/algcat.spad.pamphlet index 5c028319..f2131d58 100644 --- a/src/algebra/algcat.spad.pamphlet +++ b/src/algebra/algcat.spad.pamphlet @@ -135,7 +135,7 @@ FramedAlgebra(R:CommutativeRing, UP:UnivariatePolynomialCategory R): ++ map defined by left multiplication by \spad{a} with respect ++ to the fixed basis. --attributes - --separable <=> discriminant() ^= 0 + --separable <=> discriminant() ~= 0 add convert(x:%):Vector(R) == coordinates(x) convert(v:Vector R):% == represents(v) diff --git a/src/algebra/algext.spad.pamphlet b/src/algebra/algext.spad.pamphlet index 30e51529..7bc5057b 100644 --- a/src/algebra/algext.spad.pamphlet +++ b/src/algebra/algext.spad.pamphlet @@ -147,7 +147,7 @@ SimpleAlgebraicExtension(R:CommutativeRing, for j in 0.. while i > 0 repeat h := i rem p -- index(p) = 0$R - if h ^= 0 then + if h ~= 0 then -- here was a bug: "index" instead of -- "coerce", otherwise it wouldn't work for -- Rings R where "coerce: I-> R" is not surjective @@ -179,7 +179,7 @@ SimpleAlgebraicExtension(R:CommutativeRing, -- xi:=L.1; setelt(mat,1,1,K.1); setelt(mat,1,(deg+1),K.1) -- for i in 1..mdeg repeat -- xi:= x * xi; xp:= lift(xi) --- while xp ^= KA.0 repeat +-- while xp ~= KA.0 repeat -- setelt(mat,(mdeg+1),(degree(xp)+1),LeadingCoef(xp)) -- xp:=reductum(xp) -- setelt(mat,(mdeg+1),(deg+i+1),K.1) diff --git a/src/algebra/algfunc.spad.pamphlet b/src/algebra/algfunc.spad.pamphlet index 163734e3..3bd69cdc 100644 --- a/src/algebra/algfunc.spad.pamphlet +++ b/src/algebra/algfunc.spad.pamphlet @@ -264,7 +264,7 @@ This used to read: \begin{verbatim} hackroot(x, n) == (n = 1) or (x = 1) => x - (x ^= -1) and (((num := numer x) = 1) or (num = -1)) => + (x ~= -1) and (((num := numer x) = 1) or (num = -1)) => inv hackroot((num * denom x)::F, n) (x = -1) and n = 4 => ((-1::F) ** (1::Q / 2::Q) + 1) / ((2::F) ** (1::Q / 2::Q)) @@ -278,7 +278,7 @@ test and give $$1/(-2)^(1/n) \ne (-1/2)^(1/n)$$ <<hackroot(x, n)>>= hackroot(x, n) == (n = 1) or (x = 1) => x - (((dx := denom x) ^= 1) and + (((dx := denom x) ~= 1) and ((rx := retractIfCan(dx)@Union(Integer,"failed")) case Integer) and positive?(rx)) => hackroot((numer x)::F, n)/hackroot(rx::Integer::F, n) @@ -392,7 +392,7 @@ AlgebraicFunction(R, F): Exports == Implementation where UP2R p == ans:UPR := 0 - while p ^= 0 repeat + while p ~= 0 repeat (r := retractIfCan(leadingCoefficient p)@Union(R, "failed")) case "failed" => return "failed" ans := ans + monomial(r::R, degree p) diff --git a/src/algebra/allfact.spad.pamphlet b/src/algebra/allfact.spad.pamphlet index ccc9497d..3289cbc6 100644 --- a/src/algebra/allfact.spad.pamphlet +++ b/src/algebra/allfact.spad.pamphlet @@ -171,7 +171,7 @@ MPolyCatRationalFunctionFactorizer(E,OV,R,PRF) : C == T ground? g => g rf:PRF:=0$PRF ug:=univariate(g,x) - while ug^=0 repeat + while ug~=0 repeat rf:=rf+pushdterm(ug,x) ug := reductum ug rf diff --git a/src/algebra/array1.spad.pamphlet b/src/algebra/array1.spad.pamphlet index 9b05dab0..a304c91a 100644 --- a/src/algebra/array1.spad.pamphlet +++ b/src/algebra/array1.spad.pamphlet @@ -362,12 +362,12 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where nlim0 := nlim while i < nlim repeat j := i+1 - for k in j..nlim-1 | a.k ^= a.i repeat + for k in j..nlim-1 | a.k ~= a.i repeat a.j := a.k j := j+1 nlim := j i := i+1 - nlim ^= nlim0 => delete_!(a, i..) + nlim ~= nlim0 => delete_!(a, i..) a @ diff --git a/src/algebra/array2.spad.pamphlet b/src/algebra/array2.spad.pamphlet index ef540c42..f6a89047 100644 --- a/src/algebra/array2.spad.pamphlet +++ b/src/algebra/array2.spad.pamphlet @@ -192,7 +192,7 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where m map(f,m,n) == - (nrows(m) ^= nrows(n)) or (ncols(m) ^= ncols(n)) => + (nrows(m) ~= nrows(n)) or (ncols(m) ~= ncols(n)) => error "map: arguments must have same dimensions" ans := new(nrows m,ncols m,NIL$Lisp) for i in minRowIndex(m)..maxRowIndex(m) repeat @@ -229,7 +229,7 @@ TwoDimensionalArrayCategory(R,Row,Col): Category == Definition where m = n == eq?(m,n) => true - (nrows(m) ^= nrows(n)) or (ncols(m) ^= ncols(n)) => false + (nrows(m) ~= nrows(n)) or (ncols(m) ~= ncols(n)) => false for i in minRowIndex(m)..maxRowIndex(m) repeat for j in minColIndex(m)..maxColIndex(m) repeat not (qelt(m,i,j) = qelt(n,i,j)) => return false diff --git a/src/algebra/asp.spad.pamphlet b/src/algebra/asp.spad.pamphlet index 7899fb39..7eb29854 100644 --- a/src/algebra/asp.spad.pamphlet +++ b/src/algebra/asp.spad.pamphlet @@ -3279,7 +3279,7 @@ Asp73(name): Exports == Implementation where assign(u,(v::EXPR MachineFloat)$FEXPR)$FortranCode coerce(u:VEC FEXPR):$ == - maxIndex(u) ^= 7 => error "Vector is not of dimension 7" + maxIndex(u) ~= 7 => error "Vector is not of dimension 7" [localAssign(ALPHA@Symbol,elt(u,1)),_ localAssign(BETA@Symbol,elt(u,2)),_ localAssign(GAMMA@Symbol,elt(u,3)),_ @@ -3447,7 +3447,7 @@ Asp74(name): Exports == Implementation where localAssign(u:Symbol,v:FEXPR):FC == assign(u,(v::EXPR MFLOAT)$FEXPR)$FC coerce(u:MAT FEXPR):$ == - (nrows(u) ^= 4 or ncols(u) ^= 3) => error "Not a 4X3 matrix" + (nrows(u) ~= 4 or ncols(u) ~= 3) => error "Not a 4X3 matrix" flag:U := [IBND@Symbol::EXPR INT]$U pt0:U := [0::EXPR INT]$U pt1:U := [1::EXPR INT]$U diff --git a/src/algebra/card.spad.pamphlet b/src/algebra/card.spad.pamphlet index a1585083..ce908e9c 100644 --- a/src/algebra/card.spad.pamphlet +++ b/src/algebra/card.spad.pamphlet @@ -109,7 +109,7 @@ CardinalNumber: Join(OrderedSet, AbelianMonoid, Monoid, -- Manipulation x = y == - x.order ^= y.order => false + x.order ~= y.order => false finite? x => x.ival = y.ival true -- equal transfinites x < y == @@ -135,7 +135,7 @@ CardinalNumber: Join(OrderedSet, AbelianMonoid, Monoid, x x**y == y = 0 => - x ^= 0 => 1 + x ~= 0 => 1 error "0**0 not defined for cardinal numbers." finite? y => not finite? x => x 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)) diff --git a/src/algebra/clifford.spad.pamphlet b/src/algebra/clifford.spad.pamphlet index eeec3b36..ecedf9ac 100644 --- a/src/algebra/clifford.spad.pamphlet +++ b/src/algebra/clifford.spad.pamphlet @@ -297,7 +297,7 @@ CliffordAlgebra(n, K, Q): T == Impl where x = y == for i in 0..dim-1 repeat - if x.i ^= y.i then return false + if x.i ~= y.i then return false true x + y == (z := New; for i in 0..dim-1 repeat z.i := x.i + y.i; z) @@ -322,7 +322,7 @@ CliffordAlgebra(n, K, Q): T == Impl where c := c1 * c2 bz := b2 for i in 0..n-1 | bit?(b1,i) repeat - -- Apply rule ei*ej = -ej*ei for i^=j + -- Apply rule ei*ej = -ej*ei for i~=j k := 0 for j in i+1..n-1 | bit?(b1, j) repeat k := k+1 for j in 0..i-1 | bit?(bz, j) repeat k := k+1 @@ -339,15 +339,15 @@ CliffordAlgebra(n, K, Q): T == Impl where x * y == z := New for ix in 0..dim-1 repeat - if x.ix ^= 0 then for iy in 0..dim-1 repeat - if y.iy ^= 0 then addMonomProd(x.ix,ix,y.iy,iy,z) + if x.ix ~= 0 then for iy in 0..dim-1 repeat + if y.iy ~= 0 then addMonomProd(x.ix,ix,y.iy,iy,z) z canonMonom(c: K, lb: List PI): Record(coef: K, basel: NNI) == -- 0. Check input for b in lb repeat b > n => error "No such basis element" - -- 1. Apply identity ei*ej = -ej*ei, i^=j. + -- 1. Apply identity ei*ej = -ej*ei, i~=j. -- The Rep assumes n is small so bubble sort is ok. -- Using bubble sort keeps the exchange info obvious. wasordered := false @@ -392,7 +392,7 @@ CliffordAlgebra(n, K, Q): T == Impl where c = 1 => be c::Ex * be coerce(x): Ex == - tl := [coerceMonom(x.i,i) for i in 0..dim-1 | x.i^=0] + tl := [coerceMonom(x.i,i) for i in 0..dim-1 | x.i~=0] null tl => "0"::Ex reduce("+", tl) diff --git a/src/algebra/combinat.spad.pamphlet b/src/algebra/combinat.spad.pamphlet index 55765dc4..a70619fa 100644 --- a/src/algebra/combinat.spad.pamphlet +++ b/src/algebra/combinat.spad.pamphlet @@ -66,7 +66,7 @@ IntegerCombinatoricFunctions(I:IntegerNumberSystem): with -- since 5 = 1+1+1+1+1 = 1+1+1+2 = 1+2+2 = 1+1+3 = 1+4 = 2+3 = 5 . -- Uses O(sqrt n) term recurrence from Abramowitz & Stegun pp. 825 -- p(n) = sum (-1)**k p(n-j) where 0 < j := (3*k**2+-k) quo 2 <= n - minIndex(P) ^= 0 => error "Partition: must have minIndex of 0" + minIndex(P) ~= 0 => error "Partition: must have minIndex of 0" m := #P n < 0 => error "partition is not defined for negative integers" n < m::I => P(convert(n)@Z) diff --git a/src/algebra/contfrac.spad.pamphlet b/src/algebra/contfrac.spad.pamphlet index 2261d76c..e24d5825 100644 --- a/src/algebra/contfrac.spad.pamphlet +++ b/src/algebra/contfrac.spad.pamphlet @@ -169,12 +169,12 @@ ContinuedFraction(R): Exports == Implementation where x := reducedForm x y := reducedForm y - x.value.whole ^= y.value.whole => false + x.value.whole ~= y.value.whole => false xl := x.value.fract; yl := y.value.fract while not empty? xl and not empty? yl repeat - frst.xl.den ^= frst.yl.den => return false + frst.xl.den ~= frst.yl.den => return false xl := rst xl; yl := rst yl empty? xl and empty? yl @@ -226,7 +226,7 @@ ContinuedFraction(R): Exports == Implementation where genFromSequence apps == lo := first apps; apps := rst apps hi := first apps; apps := rst apps - while eucWhole0 lo ^= eucWhole0 hi repeat + while eucWhole0 lo ~= eucWhole0 hi repeat lo := first apps; apps := rst apps hi := first apps; apps := rst apps wh := eucWhole0 lo @@ -239,7 +239,7 @@ ContinuedFraction(R): Exports == Implementation where mt := recip mt wlo := eucWhole eval(mt, lo) whi := eucWhole eval(mt, hi) - while wlo ^= whi repeat + while wlo ~= whi repeat wlo := eucWhole eval(mt, first apps - wh0); apps := rst apps whi := eucWhole eval(mt, first apps - wh0); apps := rst apps concat([1,wlo], delay genReducedForm(wh0, apps, shift(mt, -wlo::Q))) diff --git a/src/algebra/cra.spad.pamphlet b/src/algebra/cra.spad.pamphlet index 640170d9..b5bb6378 100644 --- a/src/algebra/cra.spad.pamphlet +++ b/src/algebra/cra.spad.pamphlet @@ -42,7 +42,7 @@ CRApackage(R:EuclideanDomain): Exports == Implementation where leaves mapDown_!(t, a, "rem") chineseRemainder(lv:List(R), lm:List(R)):R == - #lm ^= #lv => error "lists of moduli and values not of same length" + #lm ~= #lv => error "lists of moduli and values not of same length" x := balancedBinaryTree(#lm, 0$R) x := setleaves_!(x, lm) mapUp_!(x,"*") diff --git a/src/algebra/crfp.spad.pamphlet b/src/algebra/crfp.spad.pamphlet index d3bb5b83..b2291289 100644 --- a/src/algebra/crfp.spad.pamphlet +++ b/src/algebra/crfp.spad.pamphlet @@ -406,7 +406,7 @@ ComplexRootFindingPackage(R, UP): public == private where zero? (d := degree p) => error _ "schwerpunkt: non-zero const. polynomial has no roots and no schwerpunkt" -- coeffient of x**d and x**(d-1) - lC : C := coefficient(p,d) -- ^= 0 + lC : C := coefficient(p,d) -- ~= 0 nC : C := coefficient(p,(d-1) pretend NNI) (denom := recip ((d::I::C)*lC)) case "failed" => error "schwerpunkt: _ degree * leadingCoefficient not invertible in ring of coefficients" @@ -561,7 +561,7 @@ ComplexRootFindingPackage(R, UP): public == private where eq : Equation UP := equation(monomial(1,1), monomial(-1$C,1)) pp : UP := p*eval(p,eq) gp : UP := 0$UP - while pp ^= 0 repeat + while pp ~= 0 repeat i:NNI := (degree pp) quo (2::NNI) coef:C:= even? i => leadingCoefficient pp diff --git a/src/algebra/curve.spad.pamphlet b/src/algebra/curve.spad.pamphlet index 5ca9495b..d216b16d 100644 --- a/src/algebra/curve.spad.pamphlet +++ b/src/algebra/curve.spad.pamphlet @@ -168,13 +168,13 @@ FunctionFieldCategory(F, UP, UPUP): Category == Definition where Q2RF q == numer(q)::UP / denom(q)::UP infOrder f == (degree denom f)::Z - (degree numer f)::Z integral? f == ground?(integralCoordinates(f).den) - integral?(f:$, a:F) == (integralCoordinates(f).den)(a) ^= 0 + integral?(f:$, a:F) == (integralCoordinates(f).den)(a) ~= 0 -- absolutelyIrreducible? == one? numberOfComponents() absolutelyIrreducible? == numberOfComponents() = 1 yCoordinates f == splitDenominator coordinates f hyperelliptic() == - degree(f := definingPolynomial()) ^= 2 => "failed" + degree(f := definingPolynomial()) ~= 2 => "failed" (u:=retractIfCan(reductum f)@Union(RF,"failed")) case "failed" => "failed" (v := retractIfCan(-(u::RF) / leadingCoefficient f)@Union(UP, "failed")) case "failed" => "failed" @@ -299,7 +299,7 @@ FunctionFieldCategory(F, UP, UPUP): Category == Definition where nostart:Boolean := true ans:Z := 0 r := row(m, i) - for j in minIndex r .. maxIndex r | qelt(r, j) ^= 0 repeat + for j in minIndex r .. maxIndex r | qelt(r, j) ~= 0 repeat ans := nostart => (nostart := false; infOrder qelt(r, j)) min(ans, infOrder qelt(r,j)) @@ -321,7 +321,7 @@ FunctionFieldCategory(F, UP, UPUP): Category == Definition where nostart:Boolean := true k:Z := 0 ii := minRowIndex m - (i0 := minIndex v) - for i in minIndex v .. maxIndex v | qelt(v, i) ^= 0 repeat + for i in minIndex v .. maxIndex v | qelt(v, i) ~= 0 repeat nk := repOrder(m, i + ii) if nostart then (nostart := false; k := nk; i0 := i) else @@ -476,7 +476,7 @@ ChangeOfVariable(F, UP, UPUP): Exports == Implementation where infIntegral?: (UPUP, UPUP) -> Boolean eval(p, x, y) == map(#1 x, p) monomial(y, 1) - good?(a, p, q) == p(a) ^= 0 and q(a) ^= 0 + good?(a, p, q) == p(a) ~= 0 and q(a) ~= 0 algPoly p == ground?(a:= retract(leadingCoefficient(q:=clearDenominator p))@UP) @@ -514,7 +514,7 @@ ChangeOfVariable(F, UP, UPUP): Exports == Implementation where ninv := inv(r.deg::Q) degy:Q := degree(retract(r.radicand)@UP) * ninv degp:Q := 0 - while p ^= 0 repeat + while p ~= 0 repeat c := leadingCoefficient p degp := max(degp, (2 + degree(numer c)::Z - degree(denom c)::Z)::Q + degree(p) * degy) @@ -666,7 +666,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where -- is a local integral basis at infinity for the curve y**d = p inftyBasis(p, m) == rt := rootPoly(p(x := inv(monomial(1, 1)$UP :: RF)), m) - m ^= rt.exponent => + m ~= rt.exponent => error "Curve not irreducible after change of variable 0 -> infinity" a := (rt.coef) x b:RF := 1 @@ -678,7 +678,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where w charPintbas(p, c, v, w) == - degree(p) ^= n => error "charPintbas: should not happen" + degree(p) ~= n => error "charPintbas: should not happen" q:UP2 := map(retract(#1)@UP, p) ib := integralBasis()$FunctionFieldIntegralBasis(UP, UP2, SimpleAlgebraicExtension(UP, UP2, q)) @@ -712,7 +712,7 @@ RadicalFunctionField(F, UP, UPUP, radicnd, n): Exports == Impl where char0StartUp() == rp := rootPoly(radicnd, n) - rp.exponent ^= n => error "RadicalFunctionField: curve is not irreducible" + rp.exponent ~= n => error "RadicalFunctionField: curve is not irreducible" newrad() := rp.radicand ib := iBasis(newrad(), n) infb := inftyBasis(radicnd, n) @@ -831,7 +831,7 @@ AlgebraicFunctionField(F, UP, UPUP, modulus): Exports == Impl where x := inv(monomial(1, 1)$UP :: RF) invmod := map(#1 x, modulus) r := mkIntegral invmod - degree(r.poly) ^= n => error "Should not happen" + degree(r.poly) ~= n => error "Should not happen" ninvmod:UP2 := map(retract(#1)@UP, r.poly) alpha := [(r.coef ** i) x for i in 0..n1]$Vector(RF) invalpha := [inv qelt(alpha, i) diff --git a/src/algebra/ddfact.spad.pamphlet b/src/algebra/ddfact.spad.pamphlet index 3871a8b8..97b8f811 100644 --- a/src/algebra/ddfact.spad.pamphlet +++ b/src/algebra/ddfact.spad.pamphlet @@ -101,12 +101,12 @@ DistinctDegreeFactorize(F,FP): C == T factlist : List(ParFact) :=empty() llf : List FFE fln :List(FP) := empty() - if (lcm:=leadingCoefficient m)^=1 then m:=(inv lcm)*m + if (lcm:=leadingCoefficient m)~=1 then m:=(inv lcm)*m llf:= factorList(squareFree(m)) for lf in llf repeat d1:= lf.xpnt pol := lf.fctr - if (lcp:=leadingCoefficient pol)^=1 then pol := (inv lcp)*pol + if (lcp:=leadingCoefficient pol)~=1 then pol := (inv lcp)*pol degree pol=1 => factlist:=cons([pol,d1]$ParFact,factlist) fln := appl(pol) factlist :=append([[pf,d1]$ParFact for pf in fln],factlist) @@ -159,7 +159,7 @@ DistinctDegreeFactorize(F,FP): C == T g := gcd(v-mon,u) dg := degree g dg =0 => "next k1" - if leadingCoefficient g ^=1 then g := (inv leadingCoefficient g)*g + if leadingCoefficient g ~=1 then g := (inv leadingCoefficient g)*g ddfact := cons([k1,g]$fact,ddfact) testirr => return ddfact u := u quo g @@ -222,7 +222,7 @@ DistinctDegreeFactorize(F,FP): C == T fln : List(FP) :=empty() --make m monic - if (lcm := leadingCoefficient m) ^=1 then m := (inv lcm)*m + if (lcm := leadingCoefficient m) ~=1 then m := (inv lcm)*m --is x**d factor of m? if (d := minimumDegree m)>0 then diff --git a/src/algebra/defintef.spad.pamphlet b/src/algebra/defintef.spad.pamphlet index d76f8a01..b8f542cb 100644 --- a/src/algebra/defintef.spad.pamphlet +++ b/src/algebra/defintef.spad.pamphlet @@ -204,7 +204,7 @@ ElementaryFunctionDefiniteIntegration(R, F): Exports == Implementation where polyIfCan(p, x) == q := univariate(p, x) ans:UP := 0 - while q ^= 0 repeat + while q ~= 0 repeat member?(x, tower(c := leadingCoefficient(q)::F)) => return "failed" ans := ans + monomial(c, degree q) q := reductum q diff --git a/src/algebra/defintrf.spad.pamphlet b/src/algebra/defintrf.spad.pamphlet index 097192a5..fc89b11f 100644 --- a/src/algebra/defintrf.spad.pamphlet +++ b/src/algebra/defintrf.spad.pamphlet @@ -148,7 +148,7 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where maprat p == ans:UPQ := 0 - while p ^= 0 repeat + while p ~= 0 repeat (r := retractIfCan(c := leadingCoefficient p)@Union(Q,"failed")) case "failed" => return "failed" ans := ans + monomial(r::Q, degree p) @@ -157,14 +157,14 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where )$SparseUnivariatePolynomialFunctions2(Q, Z) intrat(a, b) == - (n := whatInfinity a) ^= 0 => + (n := whatInfinity a) ~= 0 => (r := retractIfCan(b)@Union(F,"failed")) case "failed" => ["all"] (q := retractIfCan(r::F)@Union(Q, "failed")) case "failed" => ["failed"] [[q::Q, n]] (q := retractIfCan(retract(a)@F)@Union(Q,"failed")) case "failed" => ["failed"] - (n := whatInfinity b) ^= 0 => [[q::Q, n]] + (n := whatInfinity b) ~= 0 => [[q::Q, n]] (t := retractIfCan(retract(b)@F)@Union(Q,"failed")) case "failed" => ["failed"] [[q::Q, t::Q]] @@ -187,11 +187,11 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where checkBudan(p, a, b, incl?) == r := retractIfCan(b)@Union(F, "failed") - (n := whatInfinity a) ^= 0 => + (n := whatInfinity a) ~= 0 => r case "failed" => realRoot p checkHalfAx(p, r::F, n, incl?) (za? := zero? p(aa := retract(a)@F)) and incl? => true - (n := whatInfinity b) ^= 0 => checkHalfAx(p, aa, n, incl?) + (n := whatInfinity b) ~= 0 => checkHalfAx(p, aa, n, incl?) (zb? := zero? p(bb := r::F)) and incl? => true (va := variation(p, aa)) case "failed" or (vb := variation(p, bb)) case "failed" => "failed" @@ -250,7 +250,7 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where i:Z := 0 (lastCoef := negative leadingCoefficient q) case "failed" => "failed" - while ((q := reductum q) ^= 0) repeat + while ((q := reductum q) ~= 0) repeat (next := negative leadingCoefficient q) case "failed" => return "failed" if ((not(lastCoef::B)) and next::B) or diff --git a/src/algebra/degred.spad.pamphlet b/src/algebra/degred.spad.pamphlet index dd903291..59a6f220 100644 --- a/src/algebra/degred.spad.pamphlet +++ b/src/algebra/degred.spad.pamphlet @@ -33,7 +33,7 @@ DegreeReductionPackage(R1, R2): Cat == Capsule where degrees(u: UP R1): List Integer == l: List Integer := [] - while u ^= 0 repeat + while u ~= 0 repeat l := concat(degree u,l) u := reductum u l diff --git a/src/algebra/derham.spad.pamphlet b/src/algebra/derham.spad.pamphlet index eb06ae86..06bb096c 100644 --- a/src/algebra/derham.spad.pamphlet +++ b/src/algebra/derham.spad.pamphlet @@ -87,7 +87,7 @@ ExtAlgBasis(): Export == Implement where coerce(li:(L I)) == for x in li repeat - if x ^= 1 and x ^= 0 then error "coerce: values can only be 0 and 1" + if x ~= 1 and x ~= 0 then error "coerce: values can only be 0 and 1" li degree x == (_+/x)::NNI @@ -209,7 +209,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where null a => true siz := _+/exponents(a.first.base) for ta in reductum a repeat - _+/exponents(ta.base) ^= siz => return false + _+/exponents(ta.base) ~= siz => return false true degree a == @@ -255,7 +255,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where for ta in a repeat stuff:=Nalpha(ta.base,tb.base) r:=first(stuff)*ta.coef*tb.coef - if r ^= 0 then z := z + [[rest(stuff)::EAB, r]] + if r ~= 0 then z := z + [[rest(stuff)::EAB, r]] z coerce(r):% == @@ -289,7 +289,7 @@ AntiSymm(R:Ring, lVar:List Symbol): Export == Implement where makeTerm:(R,EAB) -> O makeTerm(r,x) == - -- we know that r ^= 0 + -- we know that r ~= 0 x = Nul(dim)$EAB => r::O -- one? r => displayList(x) (r = 1) => displayList(x) @@ -400,7 +400,7 @@ DeRhamComplex(CoefRing,listIndVar:List Symbol): Export == Implement where makeTerm:(R,EAB) -> O makeTerm(r,x) == - -- we know that r ^= 0 + -- we know that r ~= 0 x = Nul(dim)$EAB => r::O -- one? r => displayList(x) (r = 1) => displayList(x) diff --git a/src/algebra/divisor.spad.pamphlet b/src/algebra/divisor.spad.pamphlet index 1d402c7b..05a201cc 100644 --- a/src/algebra/divisor.spad.pamphlet +++ b/src/algebra/divisor.spad.pamphlet @@ -121,7 +121,7 @@ FractionalIdeal(R, F, UP, A): Exports == Implementation where g := agcd nr a := (r quo (b := gcd(gcd(d, r), g)))::F::A d := d quo b - r ^= 0 and ((g exquo r) case R) => mkIdeal([a], d) + r ~= 0 and ((g exquo r) case R) => mkIdeal([a], d) invb := inv(b::F) va:VA := [invb * m for m in nr] zero? a => mkIdeal(va, d) @@ -268,7 +268,7 @@ ModularHermitianRowReduction(R): Exports == Implementation where determinantOfMinor: M -> R enumerateBinomial: (List Z, Z, Z) -> List Z - nonzero? v == any?(#1 ^= 0, v) + nonzero? v == any?(#1 ~= 0, v) -- returns [a, i, rown] if v = [0,...,0,a,0,...,0] -- where a <> 0 and i is the index of a, "failed" otherwise. @@ -276,7 +276,7 @@ ModularHermitianRowReduction(R): Exports == Implementation where ans:REC allZero:Boolean := true for i in minIndex v .. maxIndex v repeat - if qelt(v, i) ^= 0 then + if qelt(v, i) ~= 0 then if allZero then allZero := false ans := [qelt(v, i), i, rown] @@ -314,7 +314,7 @@ ModularHermitianRowReduction(R): Exports == Implementation where lc := [i for i in minColIndex x .. maxColIndex x]$List(Integer) lr := [i for i in minRowIndex x .. maxRowIndex x]$List(Integer) for i in 1..(n := binomial(nr, nc)) repeat - (d := determinant x(enumerateBinomial(lr, nc, i), lc)) ^= 0 => + (d := determinant x(enumerateBinomial(lr, nc, i), lc)) ~= 0 => j := i + 1 + (random()$Z rem (n - i)) return gcd(d, determinant x(enumerateBinomial(lr, nc, j), lc)) 0 @@ -423,7 +423,7 @@ ModularHermitianRowReduction(R): Exports == Implementation where if i > nrows then leave rown := minr - 1 for k in i .. nrows repeat - if (qelt(x,k,j) ^= 0) and ((rown = minr - 1) or + if (qelt(x,k,j) ~= 0) and ((rown = minr - 1) or sizeLess?(qelt(x,k,j), qelt(x,rown,j))) then rown := k rown = minr - 1 => "next j" x := swapRows_!(x, i, rown) @@ -442,7 +442,7 @@ ModularHermitianRowReduction(R): Exports == Implementation where qsetelt_!(x, k, j, 0) un := unitNormal qelt(x,i,j) qsetelt_!(x,i,j,un.canonical) - if un.associate ^= 1 then for jj in (j+1)..ncols repeat + if un.associate ~= 1 then for jj in (j+1)..ncols repeat qsetelt_!(x,i,jj,un.associate * qelt(x,i,jj)) xij := qelt(x,i,j) @@ -549,14 +549,14 @@ FramedModule(R, F, UP, A, ibasis): Exports == Implementation where v pretend VA norm m == - #(basis m) ^= #ibasis => error "Module not of rank n" + #(basis m) ~= #ibasis => error "Module not of rank n" determinant(coordinates(basis m) * invintmat()) m1 * m2 == m := rowEch((cd := splitDenominator wmatrix( vectProd(basis m1, basis m2))).num) module [u for i in minRowIndex m .. maxRowIndex m | - (u := W2A rowdiv(row(m, i), cd.den)) ^= 0]$VA + (u := W2A rowdiv(row(m, i), cd.den)) ~= 0]$VA if A has RetractableTo F then module(i:FractionalIdeal(R, F, UP, A)) == @@ -707,7 +707,7 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where divisor(i:ID) == -- one?(n := #(v := basis minimize i)) => divisor v minIndex v (n := #(v := basis minimize i)) = 1 => divisor v minIndex v - n ^= 2 => ERR + n ~= 2 => ERR a := v minIndex v h := v maxIndex v (u := polyIfCan a) case UP => @@ -724,7 +724,7 @@ HyperellipticFiniteDivisor(F, UP, UPUP, R): Exports == Implementation where v::UP redpolyIfCan(h, a) == - degree(p := lift h) ^= 1 => "failed" + degree(p := lift h) ~= 1 => "failed" q := - coefficient(p, 0) / coefficient(p, 1) rec := extendedEuclidean(denom q, a) not ground?(rec.generator) => "failed" @@ -886,7 +886,7 @@ FiniteDivisor(F, UP, UPUP, R): Exports == Implementation where reduce d == (i := minimize(j := ideal d)) = j => d - #(n := numer i) ^= 2 => divisor i + #(n := numer i) ~= 2 => divisor i cd := splitDenominator lift n(1 + minIndex n) b := gcd(cd.den * retract(retract(n minIndex n)@RF)@UP, retract(norm reduce(cd.num))@UP) diff --git a/src/algebra/efstruc.spad.pamphlet b/src/algebra/efstruc.spad.pamphlet index 6ac57be1..9a015122 100644 --- a/src/algebra/efstruc.spad.pamphlet +++ b/src/algebra/efstruc.spad.pamphlet @@ -205,10 +205,10 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where realElem(f, l) == smpElem(numer f, l) / smpElem(denom f, l) realElementary(f, x) == realElem(f, [x]) realElementary f == realElem(f, variables f) - toY ker == [func for k in ker | (func := ktoY k) ^= 0] - toZ ker == [func for k in ker | (func := ktoZ k) ^= 0] - toU ker == [func for k in ker | (func := ktoU k) ^= 0] - toV ker == [func for k in ker | (func := ktoV k) ^= 0] + toY ker == [func for k in ker | (func := ktoY k) ~= 0] + toZ ker == [func for k in ker | (func := ktoZ k) ~= 0] + toU ker == [func for k in ker | (func := ktoU k) ~= 0] + toV ker == [func for k in ker | (func := ktoV k) ~= 0] rtNormalize f == rootNormalize0(f).func toR(ker, x) == select(is?(#1, NTHR) and first argument(#1) = x, ker) @@ -250,7 +250,7 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where differentiate(ktoU k, x)) is?(k, NTHR) => rootDep(ker, k) comb? and is?(k, "factorial"::SY) => - factdeprel([x for x in ker | is?(x,"factorial"::SY) and x^=k],k) + factdeprel([x for x in ker | is?(x,"factorial"::SY) and x~=k],k) [true] ktoY k == @@ -325,7 +325,7 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where rooteval(f, lk, k, n) == nv := nthRoot(x := first argument k, m := retract(n)@Z) l := [r for r in concat(k, toR(lk, x)) | - retract(second argument r)@Z ^= m] + retract(second argument r)@Z ~= m] lv := [nv ** (n / (retract(second argument r)@Z::Q)) for r in l] [eval(f, l, lv), l, lv] @@ -362,8 +362,8 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where tannosimp(f, lk, k, v, fns, c) v0 := retract(inv qelt(v, rec.index))@Z lv := [qelt(v, i) for i in minIndex v .. maxIndex v | - i ^= rec.index]$List(Q) - l := [kk for kk in lk | kk ^= rec.ker] + i ~= rec.index]$List(Q) + l := [kk for kk in lk | kk ~= rec.ker] g := tanSum(-v0 * c, concat(tanNa(k::F, v0), [tanNa(x, - retract(a * v0)@Z) for a in lv for x in toV l])) [eval(f, [rec.ker], [g]), [rec.ker], [g]] @@ -407,7 +407,7 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where rischNormalize(f, v) == empty?(ker := varselect(tower f, v)) => [f, empty(), empty()] - first(ker) ^= kernel(v)@K => error "Cannot happen" + first(ker) ~= kernel(v)@K => error "Cannot happen" ker := rest ker (n := (#ker)::Z - 1) < 1 => [f, empty(), empty()] for i in 1..n for kk in rest ker repeat @@ -466,8 +466,8 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where expnosimp(f, lk, k, v, fns, exp g) v0 := retract(inv qelt(v, rec.index))@Z lv := [qelt(v, i) for i in minIndex v .. maxIndex v | - i ^= rec.index]$List(Q) - l := [kk for kk in lk | kk ^= rec.ker] + i ~= rec.index]$List(Q) + l := [kk for kk in lk | kk ~= rec.ker] h :F := */[exp(z) ** (- retract(a * v0)@Z) for a in lv for z in toY l] h := h * exp(-v0 * g) * (k::F) ** v0 [eval(f, [rec.ker], [h]), [rec.ker], [h]] @@ -641,7 +641,7 @@ InnerTrigonometricManipulations(R,F,FG): Exports == Implementation where supexp(p, f1, f2, bse) == ans:GF := 0 - while p ^= 0 repeat + while p ~= 0 repeat g := explogs2trigs(leadingCoefficient(p)::FG) if ((d := degree(p)::Z - bse) >= 0) then ans := ans + g * f1 ** d diff --git a/src/algebra/eigen.spad.pamphlet b/src/algebra/eigen.spad.pamphlet index 193b58f9..e9ab3b7a 100644 --- a/src/algebra/eigen.spad.pamphlet +++ b/src/algebra/eigen.spad.pamphlet @@ -137,7 +137,7 @@ EigenPackage(R) : C == T tff(p:SUF,x:SE) : F == degree p=0 => leadingCoefficient p r:F:=0$F - while p^=0 repeat + while p~=0 repeat r:=r+fft(p,x) p := reductum p r @@ -153,7 +153,7 @@ EigenPackage(R) : C == T ---- characteristic polynomial ---- charpol(A:M,x:SE) : F == dimA :PI := (nrows A):PI - dimA ^= ncols A => error " The matrix is not square" + dimA ~= ncols A => error " The matrix is not square" B:M:=zero(dimA,dimA) for i in 1..dimA repeat for j in 1..dimA repeat B(i,j):=A(i,j) @@ -286,7 +286,7 @@ CharacteristicPolynomialPackage(R:CommutativeRing):C == T where ---- characteristic polynomial ---- characteristicPolynomial(A:M,v:R) : R == dimA :PI := (nrows A):PI - dimA ^= ncols A => error " The matrix is not square" + dimA ~= ncols A => error " The matrix is not square" B:M:=zero(dimA,dimA) for i in 1..dimA repeat for j in 1..dimA repeat B(i,j):=A(i,j) diff --git a/src/algebra/elemntry.spad.pamphlet b/src/algebra/elemntry.spad.pamphlet index 8ddc8e52..52da98a3 100644 --- a/src/algebra/elemntry.spad.pamphlet +++ b/src/algebra/elemntry.spad.pamphlet @@ -660,8 +660,8 @@ ElementaryFunction(R, F): Exports == Implementation where ilog x ilog x == --- ((num1 := one?(num := numer x)) or num = -1) and (den := denom x) ^= 1 - ((num1 := ((num := numer x) = 1)) or num = -1) and (den := denom x) ^= 1 +-- ((num1 := one?(num := numer x)) or num = -1) and (den := denom x) ~= 1 + ((num1 := ((num := numer x) = 1)) or num = -1) and (den := denom x) ~= 1 and empty? variables x => - kernel(oplog, (num1 => den; -den)::F) kernel(oplog, x) diff --git a/src/algebra/expr.spad.pamphlet b/src/algebra/expr.spad.pamphlet index 93324931..b781f423 100644 --- a/src/algebra/expr.spad.pamphlet +++ b/src/algebra/expr.spad.pamphlet @@ -257,7 +257,7 @@ Expression(R:OrderedSet): Exports == Implementation where noalg?: SUP % -> Boolean noalg? p == - while p ^= 0 repeat + while p ~= 0 repeat not empty? algkernels kernels leadingCoefficient p => return false p := reductum p true @@ -810,7 +810,7 @@ Pi(): Exports == Implementation where p2p p == ans:PZ := 0 - while p ^= 0 repeat + while p ~= 0 repeat ans := ans + monomial(leadingCoefficient(p)::PZ, sympi, degree p) p := reductum p ans diff --git a/src/algebra/ffcat.spad.pamphlet b/src/algebra/ffcat.spad.pamphlet index f8047d80..3821e9a5 100644 --- a/src/algebra/ffcat.spad.pamphlet +++ b/src/algebra/ffcat.spad.pamphlet @@ -344,7 +344,7 @@ FiniteAlgebraicExtensionField(F : Field) : Category == _ -- norm(e) == norm(e,1) pretend F -- trace(e) == trace(e,1) pretend F minimalPolynomial(a,n) == - extensionDegree()@PI rem n ^= 0 => + extensionDegree()@PI rem n ~= 0 => error "minimalPolynomial: 2. argument must divide extension degree" f:SUP $:=monomial(1,1)$(SUP $) - monomial(a,0)$(SUP $) u:$:=Frobenius(a,n) @@ -387,7 +387,7 @@ FiniteAlgebraicExtensionField(F : Field) : Category == _ degree a == y:$:=Frobenius a deg:PI:=1 - while y^=a repeat + while y~=a repeat y := Frobenius(y) deg:=deg+1 deg @@ -1409,7 +1409,7 @@ FiniteFieldSolveLinearPolynomialEquation(F:FiniteFieldCategory, p: FPP import DistinctDegreeFactorize(F,FP) solveLinearPolynomialEquation(lp,p) == - if (oldlp ^= lp) then + if (oldlp ~= lp) then -- we have to generate a new table deg:= +/[degree u for u in lp] ans:Union(Vector List FPP,"failed"):="failed" diff --git a/src/algebra/ffcg.spad.pamphlet b/src/algebra/ffcg.spad.pamphlet index a2667c0f..212bc91b 100644 --- a/src/algebra/ffcg.spad.pamphlet +++ b/src/algebra/ffcg.spad.pamphlet @@ -185,7 +185,7 @@ FiniteFieldCyclicGroupExtensionByPolynomial(GF,defpol):_ void()$Void basis(n:PI) == - extensionDegree() rem n ^= 0 => + extensionDegree() rem n ~= 0 => error("argument must divide extension degree") m:=sizeCG quo (size()$GF**n-1) [index((1+i*m) ::PI) for i in 0..(n-1)]::Vector $ diff --git a/src/algebra/fff.spad.pamphlet b/src/algebra/fff.spad.pamphlet index 858b9505..0cfca8d4 100644 --- a/src/algebra/fff.spad.pamphlet +++ b/src/algebra/fff.spad.pamphlet @@ -145,18 +145,18 @@ FiniteFieldFunctions(GF): Exports == Implementation where lvj:M I:=zero(k::NNI,n) for v in 1..k repeat for j in 1..n repeat - if (j^=jt) or (v^=vt) then + if (j~=jt) or (v~=vt) then help:PF(p1):=t**(v-1)*pkn**(j-1)+1@PF(p1) setelt(lvj,v,j,vec.(help pretend I +1)) for j in 1..n repeat - if j^=jt then + if j~=jt then for v in 1..k repeat lvjh:=elt(lvj,v,j) setelt(multmat,j,lvjh,elt(multmat,j,lvjh)+1) for i in 1..n repeat setelt(multmat,jt,i,positiveRemainder(-k,p)::PF(p)) for v in 1..k repeat - if v^=vt then + if v~=vt then lvjh:=elt(lvj,v,jt) setelt(multmat,jt,lvjh,elt(multmat,jt,lvjh)+1) -- multmat @@ -166,7 +166,7 @@ FiniteFieldFunctions(GF): Exports == Implementation where l:L TERM:=nil()$(L TERM) v:V PF(p):=row(multmat,i) for j in (1::I)..(m::I) repeat - if (v.j ^= 0) then + if (v.j ~= 0) then -- take -v.j to get trace 1 instead of -1 term:TERM:=[(convert(-v.j)@I)::GF,(j-2) pretend SI]$TERM l:=cons(term,l)$(L TERM) @@ -203,7 +203,7 @@ FiniteFieldFunctions(GF): Exports == Implementation where setColumn_!(mat,2,Vectorise(h)$MM)$(M GF) for i in 2..m1 repeat g:=0$MM - while h ^= 0 repeat + while h ~= 0 repeat g:=g + leadingCoefficient(h) * qpow.degree(h)$MM h:=reductum(h)$MM qexp.i:=g @@ -219,7 +219,7 @@ FiniteFieldFunctions(GF): Exports == Implementation where l:L TERM:=nil()$(L TERM) v:V GF:=mat *$(M GF) Vectorise(qexp.(i-1) *$MM qexp.0)$MM for j in (1::SI)..(m::SI) repeat - if (v.j ^= 0$GF) then + if (v.j ~= 0$GF) then term:TERM:=[(v.j),j-(2::SI)]$TERM l:=cons(term,l)$(L TERM) qsetelt_!(multtable,i,copy l)$(V L TERM) diff --git a/src/algebra/ffhom.spad.pamphlet b/src/algebra/ffhom.spad.pamphlet index 50bf7ef1..6195d5b6 100644 --- a/src/algebra/ffhom.spad.pamphlet +++ b/src/algebra/ffhom.spad.pamphlet @@ -98,7 +98,7 @@ FiniteFieldHomomorphisms(F1,GF,F2): Exports == Implementation where -- a necessary condition for the one field being an subfield of -- the other one is, that the respective extension degrees are -- multiples - if max(degree1,degree2) rem min(degree1,degree2) ^= 0 then + if max(degree1,degree2) rem min(degree1,degree2) ~= 0 then error "FFHOM: one extension degree must divide the other one" conMat1to2:M:= zero(degree2,degree1)$M @@ -349,7 +349,7 @@ FiniteFieldHomomorphisms(F1,GF,F2): Exports == Implementation where -- whether the element is in the subfield of the 'bigger' field, which -- corresponds to the 'smaller' field if degree1 > degree2 then - if positiveRemainder(degree2,degree(x)$F1)^= 0 then + if positiveRemainder(degree2,degree(x)$F1)~= 0 then error "coerce: element doesn't belong to smaller field" represents(conMat1to2 *$(Matrix GF) coordinates(x)$F1)$F2 @@ -381,7 +381,7 @@ FiniteFieldHomomorphisms(F1,GF,F2): Exports == Implementation where convertWRTdifferentDefPol21(x:F2) == if init? then initialize() if degree2 > degree1 then - if positiveRemainder(degree1,degree(x)$F2)^= 0 then + if positiveRemainder(degree1,degree(x)$F2)~= 0 then error "coerce: element doesn't belong to smaller field" represents(conMat2to1 *$(Matrix GF) coordinates(x)$F2)$F1 diff --git a/src/algebra/ffnb.spad.pamphlet b/src/algebra/ffnb.spad.pamphlet index 032c3501..b342f19e 100644 --- a/src/algebra/ffnb.spad.pamphlet +++ b/src/algebra/ffnb.spad.pamphlet @@ -238,7 +238,7 @@ InnerNormalBasisFieldFunctions(GF): Exports == Implementation where else erg:VGF:=plist.(first(l)) i:SI:=k for j in rest(l) repeat - if j^=0 then erg:=erg *$$ qPot(plist.j,i)$$ + if j~=0 then erg:=erg *$$ qPot(plist.j,i)$$ i:=i+k erg @@ -517,7 +517,7 @@ FiniteFieldNormalBasisExtensionByPolynomial(GF,uni): Exports == _ degree(a) == d:PI:=1 b:= qPot(a::Rep,1)$INBFF - while (b^=a) repeat + while (b~=a) repeat b:= qPot(b::Rep,1)$INBFF d:=d+1 d @@ -552,7 +552,7 @@ FiniteFieldNormalBasisExtensionByPolynomial(GF,uni): Exports == _ norm(a:$) == retract norm(a,1) generator() == normalElement(extdeg)$INBFF basis(n:PI) == - (extdeg rem n) ^= 0 => error "argument must divide extension degree" + (extdeg rem n) ~= 0 => error "argument must divide extension degree" [Frobenius(trace(normalElement,n),i) for i in 0..(n-1)]::(Vector $) a:GF * x:$ == a *$Rep x diff --git a/src/algebra/ffp.spad.pamphlet b/src/algebra/ffp.spad.pamphlet index 2d97d795..9b38f959 100644 --- a/src/algebra/ffp.spad.pamphlet +++ b/src/algebra/ffp.spad.pamphlet @@ -126,7 +126,7 @@ FiniteFieldExtensionByPolynomial(GF:FiniteFieldCategory,_ initializeElt: () -> Void initializeLog: () -> Void basis(n:PI) == - (extdeg rem n) ^= 0 => error "argument must divide extension degree" + (extdeg rem n) ~= 0 => error "argument must divide extension degree" a:$:=norm(primitiveElement(),n) vector [a**i for i in 0..n-1] diff --git a/src/algebra/ffpoly.spad.pamphlet b/src/algebra/ffpoly.spad.pamphlet index eba95386..acebb710 100644 --- a/src/algebra/ffpoly.spad.pamphlet +++ b/src/algebra/ffpoly.spad.pamphlet @@ -240,7 +240,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where qexp.1:=h for i in 2..m1 repeat g:=0$SUP - while h ^= 0 repeat + while h ~= 0 repeat g:=g + leadingCoefficient(h) * qpow.degree(h) h:=reductum(h) qexp.i:=(h:=g) @@ -282,7 +282,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- -- determine the multiplicative order of q modulo n -- e : PI := 1 -- qe : PI := q --- while (qe rem n) ^= 1 repeat +-- while (qe rem n) ~= 1 repeat -- e := e + 1 -- qe := qe * q -- ((qe - 1) ** ((eulerPhi(n) quo e) pretend PI) ) pretend PI @@ -345,7 +345,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- determine the multiplicative order of q modulo d e : PI := 1 qe : PI := q - while (qe rem d) ^= 1 repeat + while (qe rem d) ~= 1 repeat e := e + 1 qe := qe * q prod := prod * _ @@ -361,7 +361,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- (cf. [LN] p.89, Th. 3.16, and p.87, following Th. 3.11) n : NNI := degree f n = 0 => false - leadingCoefficient f ^= 1 => false + leadingCoefficient f ~= 1 => false coefficient(f, 0) = 0 => false q : PI := sizeGF qn1: PI := (q**n - 1) :: NNI :: PI @@ -371,7 +371,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- may be improved by tabulating the residues x**(i*q) -- for i = 0,...,n-1 : -- - lift(x ** qn1)$MM ^= 1 => false -- X**(q**n - 1) rem f in GF[X] + lift(x ** qn1)$MM ~= 1 => false -- X**(q**n - 1) rem f in GF[X] lrec : L Record(factor:I, exponent:I) := factors(factor qn1) lfact : L PI := [] -- collect the prime factors for rec in lrec repeat -- of q**n - 1 @@ -387,7 +387,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- x, x**q, ... , x**(q**(n-1)) are linearly independent over GF n : NNI := degree f n = 0 => false - leadingCoefficient f ^= 1 => false + leadingCoefficient f ~= 1 => false coefficient(f, 0) = 0 => false n = 1 => true not irreducible? f => false @@ -428,7 +428,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ^= 1 then f := (inv lcf) * f + if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -438,7 +438,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- a new value to one of its records for term in fRepr repeat fcopy := cons(copy term, fcopy) - if term.expnt ^= 0 then + if term.expnt ~= 0 then fcopy := cons([0,0]$Rec, fcopy) tailpol : Repr := [] headpol : Repr := fcopy -- [[0,f0], ... , [n,fn]] where @@ -505,7 +505,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ^= 1 then f := (inv lcf) * f + if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -515,7 +515,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- a new value to one of its records for term in fRepr repeat fcopy := cons(copy term, fcopy) - if term.expnt ^= 0 then + if term.expnt ~= 0 then term := [0,0]$Rec fcopy := cons(term, fcopy) fcopy := reverse fcopy @@ -624,7 +624,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ^= 1 then f := (inv lcf) * f + if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -634,7 +634,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- a new value to one of its records for term in fRepr repeat fcopy := cons(copy term, fcopy) - if term.expnt ^= 0 then + if term.expnt ~= 0 then term := [0,0]$Rec fcopy := cons(term, fcopy) fcopy := reverse fcopy -- [[n,1], [r,fr], ... , [0,f0]] @@ -737,7 +737,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where n : NNI := degree f n = 0 => error "polynomial must have positive degree" -- make f monic - if (lcf := leadingCoefficient f) ^= 1 then f := (inv lcf) * f + if (lcf := leadingCoefficient f) ~= 1 then f := (inv lcf) * f -- if f = fn*X**n + ... + f{i0}*X**{i0} with the fi non-zero -- then fRepr := [[n,fn], ... , [i0,f{i0}]] fRepr : Repr := f pretend Repr @@ -747,7 +747,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- a new value to one of its records for term in fRepr repeat fcopy := cons(copy term, fcopy) - if term.expnt ^= 0 then + if term.expnt ~= 0 then term := [0,0]$Rec fcopy := cons(term, fcopy) fcopy := reverse fcopy -- [[n,1], [r,fr], ... , [0,f0]] @@ -958,7 +958,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- expt : NNI := #ragits -- for i in ragits repeat -- expt := (expt - 1) :: NNI --- if i ^= 0 then pol := pol + monomial(index(i::PI)$GF, expt) +-- if i ~= 0 then pol := pol + monomial(index(i::PI)$GF, expt) -- pol -- random == qAdicExpansion(random()$I) @@ -967,7 +967,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where -- pol := monomial(1,n)$SUP -- n1 : NNI := (n - 1) :: NNI -- for i in 0..n1 repeat --- if (c := random()$GF) ^= 0 then +-- if (c := random()$GF) ~= 0 then -- pol := pol + monomial(c, i)$SUP -- pol @@ -975,7 +975,7 @@ FiniteFieldPolynomialPackage GF : Exports == Implementation where polRepr : Repr := [] n1 : NNI := (n - 1) :: NNI for i in 0..n1 repeat - if (c := random()$GF) ^= 0 then + if (c := random()$GF) ~= 0 then polRepr := cons([i, c]$Rec, polRepr) cons([n, 1$GF]$Rec, polRepr) pretend SUP diff --git a/src/algebra/ffpoly2.spad.pamphlet b/src/algebra/ffpoly2.spad.pamphlet index 1271362a..0c76a98c 100644 --- a/src/algebra/ffpoly2.spad.pamphlet +++ b/src/algebra/ffpoly2.spad.pamphlet @@ -108,7 +108,7 @@ FiniteFieldPolynomialPackage2(F,GF):Exports == Implementation where h:=gcd(stillToFactor,trModp +$(SUP F) _ (index(j pretend PI)$GF::F::(SUP F)))$(SUP F) -- make the gcd polynomial monic - if leadingCoefficient(h)$(SUP F) ^= 1$F then + if leadingCoefficient(h)$(SUP F) ~= 1$F then h:= (inv leadingCoefficient(h)) * h degh:=degree(h)$(SUP F) degSTF:=degree(stillToFactor)$(SUP F) diff --git a/src/algebra/files.spad.pamphlet b/src/algebra/files.spad.pamphlet index 591bb1a0..f331e958 100644 --- a/src/algebra/files.spad.pamphlet +++ b/src/algebra/files.spad.pamphlet @@ -130,20 +130,20 @@ File(S:SetCategory): FileCategory(FileName, S) with iomode f == f.fileIOmode read_! f == - f.fileIOmode ^= "input" => + f.fileIOmode ~= "input" => error "File not in read state" x := VMREAD(f.fileState)$Lisp PLACEP(x)$Lisp => error "End of file" x readIfCan_! f == - f.fileIOmode ^= "input" => + f.fileIOmode ~= "input" => error "File not in read state" x: S := VMREAD(f.fileState)$Lisp PLACEP(x)$Lisp => "failed" x write_!(f, x) == - f.fileIOmode ^= "output" => + f.fileIOmode ~= "output" => error "File not in write state" z := PRINT_-FULL(x, f.fileState)$Lisp TERPRI(f.fileState)$Lisp @@ -210,25 +210,25 @@ TextFile: Cat == Def where readIfCan_! f == readLineIfCan_! f readLine_! f == - f.fileIOmode ^= "input" => error "File not in read state" + f.fileIOmode ~= "input" => error "File not in read state" s: String := read_-line(f.fileState)$Lisp PLACEP(s)$Lisp => error "End of file" s readLineIfCan_! f == - f.fileIOmode ^= "input" => error "File not in read state" + f.fileIOmode ~= "input" => error "File not in read state" s: String := read_-line(f.fileState)$Lisp PLACEP(s)$Lisp => "failed" s write_!(f, x) == - f.fileIOmode ^= "output" => error "File not in write state" + f.fileIOmode ~= "output" => error "File not in write state" PRINTEXP(x, f.fileState)$Lisp x writeLine_! f == - f.fileIOmode ^= "output" => error "File not in write state" + f.fileIOmode ~= "output" => error "File not in write state" TERPRI(f.fileState)$Lisp "" writeLine_!(f, x) == - f.fileIOmode ^= "output" => error "File not in write state" + f.fileIOmode ~= "output" => error "File not in write state" PRINTEXP(x, f.fileState)$Lisp TERPRI(f.fileState)$Lisp x @@ -316,12 +316,12 @@ BinaryFile: Cat == Def where error "file must be in read or write state" read! f == - f.fileIOmode ^= "input" => error "File not in read state" + f.fileIOmode ~= "input" => error "File not in read state" BINARY__SELECT__INPUT(f.fileState)$Lisp BINARY__READBYTE()$Lisp -- READ_-BYTE(f.fileState)$Lisp readIfCan_! f == - f.fileIOmode ^= "input" => error "File not in read state" + f.fileIOmode ~= "input" => error "File not in read state" BINARY__SELECT__INPUT(f.fileState)$Lisp n:SingleInteger:=BINARY__READBYTE()$Lisp n = -1 => "failed" @@ -329,7 +329,7 @@ BinaryFile: Cat == Def where -- READ_-BYTE(f.fileState,NIL$Lisp, -- "failed"::Union(SingleInteger,"failed"))$Lisp write_!(f, x) == - f.fileIOmode ^= "output" => error "File not in write state" + f.fileIOmode ~= "output" => error "File not in write state" x < 0 or x>255 => error "integer cannot be represented as a byte" BINARY__PRINBYTE(x)$Lisp -- WRITE_-BYTE(x, f.fileState)$Lisp @@ -337,10 +337,10 @@ BinaryFile: Cat == Def where -- # f == FILE_-LENGTH(f.fileState)$Lisp position f == - f.fileIOmode ^= "input" => error "file must be in read state" + f.fileIOmode ~= "input" => error "file must be in read state" FILE_-POSITION(f.fileState)$Lisp position_!(f,i) == - f.fileIOmode ^= "input" => error "file must be in read state" + f.fileIOmode ~= "input" => error "file must be in read state" (FILE_-POSITION(f.fileState,i)$Lisp ; i) @ @@ -415,24 +415,24 @@ KeyedAccessFile(Entry): KAFcategory == KAFcapsule where [fname, defstream(fname, mode), mode] reopen_!(f, mode) == close_! f - if mode ^= "closed" then + if mode ~= "closed" then f.fileState := defstream(f.fileName, mode) f.fileIOmode := mode f close_! f == - if f.fileIOmode ^= "closed" then + if f.fileIOmode ~= "closed" then RSHUT(f.fileState)$Lisp f.fileIOmode := "closed" f read_! f == - f.fileIOmode ^= "input" => error ["File not in read state",f] + f.fileIOmode ~= "input" => error ["File not in read state",f] ks: List Symbol := RKEYIDS(f.fileName)$Lisp null ks => error ["Attempt to read empty file", f] ix := random()$Integer rem #ks k: String := PNAME(ks.ix)$Lisp [k, SPADRREAD(k, f.fileState)$Lisp] write_!(f, pr) == - f.fileIOmode ^= "output" => error ["File not in write state",f] + f.fileIOmode ~= "output" => error ["File not in write state",f] SPADRWRITE(pr.key, pr.entry, f.fileState)$Lisp pr name f == diff --git a/src/algebra/float.spad.pamphlet b/src/algebra/float.spad.pamphlet index 3f5753f7..58606834 100644 --- a/src/algebra/float.spad.pamphlet +++ b/src/algebra/float.spad.pamphlet @@ -129,7 +129,7 @@ Float(): ++ normalize(x) normalizes x at current precision. relerror : (%, %) -> I ++ relerror(x,y) computes the absolute value of \spad{x - y} divided by - ++ y, when \spad{y \^= 0}. + ++ y, when \spad{y \~= 0}. shift: (%, I) -> % ++ shift(x,n) adds n to the exponent of float x. rationalApproximation: (%, N) -> RN @@ -313,7 +313,7 @@ Float(): s:I := d:I := shift(1,p) y := times(x,x) t := m := - shift2(y.mantissa,y.exponent+p) - for i in 3.. by 2 while t ^= 0 repeat + for i in 3.. by 2 while t ~= 0 repeat s := s + t quo i t := (m * t) quo d x * [s,-p] @@ -326,7 +326,7 @@ Float(): e:I := bits() + LENGTH bits() + LENGTH n + 1 s:I := shift(1,e) quo n t:I := s quo n2 - for k in 3.. by 2 while t ^= 0 repeat + for k in 3.. by 2 while t ~= 0 repeat s := s + t quo k t := t quo n2 normalize [s,-e] @@ -354,7 +354,7 @@ Float(): s:I := d:I := shift(1,p) m:I := - shift2(y.mantissa,y.exponent+p) t:I := m quo 6 - for i in 4.. by 2 while t ^= 0 repeat + for i in 4.. by 2 while t ~= 0 repeat s := s + t t := (m * t) quo (i*(i+1)) t := t quo d @@ -391,7 +391,7 @@ Float(): s:I := d:I := shift(1,p) m:I := - shift2(y.mantissa,y.exponent+p) t:I := m quo 2 - for i in 3.. by 2 while t ^= 0 repeat + for i in 3.. by 2 while t ~= 0 repeat s := s + t t := (m * t) quo (i*(i+1)) t := t quo d @@ -423,7 +423,7 @@ Float(): t:I := shift(1,n) quo 882 d:I := 4*882**2 s:I := 0 - for i in 2.. by 2 for j in 1123.. by 21460 while t ^= 0 repeat + for i in 2.. by 2 for j in 1123.. by 21460 while t ~= 0 repeat s := s + j*t m := -(i-1)*(2*i-1)*(2*i-3) t := (m*t) quo (d*i**3) @@ -495,7 +495,7 @@ Float(): s:I := d:I := shift(1,p) z := times(y,y) t := m := shift2(z.mantissa,z.exponent+p) - for i in 3.. by 2 while t ^= 0 repeat + for i in 3.. by 2 while t ~= 0 repeat s := s + t quo i t := m * t quo d y * [s,1-p] @@ -509,7 +509,7 @@ Float(): n := n + LENGTH n + 3 -- guard bits s:I := shift(1,n+1) quo 3 t:I := s quo 9 - for k in 3.. by 2 while t ^= 0 repeat + for k in 3.. by 2 while t ~= 0 repeat s := s + t quo k t := t quo 9 L2 := [bits(),[s,-n]] @@ -524,7 +524,7 @@ Float(): n := n + LENGTH n + 5 -- guard bits s:I := shift(1,n+1) quo 9 t:I := s quo 81 - for k in 3.. by 2 while t ^= 0 repeat + for k in 3.. by 2 while t ~= 0 repeat s := s + t quo k t := t quo 81 -- We have log 10 = log 5 + log 2 and log 5/4 = log 5 - 2 log 2 @@ -537,7 +537,7 @@ Float(): exp(x) == -- exp(n+x) = exp(1)**n exp(x) for n such that |x| < 1 p := bits(); inc 5; e1:% := 1 - if (n := wholePart x) ^= 0 then + if (n := wholePart x) ~= 0 then inc LENGTH n; e1 := exp1 ** n; dec LENGTH n x := fractionPart x if zero? x then (bits p; return normalize e1) @@ -557,7 +557,7 @@ Float(): p := bits() + LENGTH bits() + 1 s:I := d:I := shift(1,p) t:I := n:I := shift2(x.mantissa,x.exponent+p) - for i in 2.. while t ^= 0 repeat + for i in 2.. while t ~= 0 repeat s := s + t t := (n * t) quo i t := t quo d @@ -871,7 +871,7 @@ Float(): d := if OUTPREC() = -1 then digits::I else OUTPREC() -- g := convert10(abs f,digits); m := g.mantissa; e := g.exponent g := convert10(abs f,d); m := g.mantissa; e := g.exponent - if OUTPREC() ^= -1 then + if OUTPREC() ~= -1 then -- round g to OUTPREC digits after the decimal point l := length10 m if -e > OUTPREC() and -e < 2*digits::I then @@ -919,7 +919,7 @@ Float(): zero? exponent f => d := d + 1 s := convert(mantissa f)@S - OUTPREC() ^= -1 and (e := #s) > d => + OUTPREC() ~= -1 and (e := #s) > d => t:S := if zero? SPACING() then "E" else " E " concat ["0.", padFromLeft s, t, convert(e)@S] padFromRight concat(s, ".0") diff --git a/src/algebra/formula.spad.pamphlet b/src/algebra/formula.spad.pamphlet index b5668638..51506fc6 100644 --- a/src/algebra/formula.spad.pamphlet +++ b/src/algebra/formula.spad.pamphlet @@ -289,22 +289,22 @@ ScriptFormulaFormat(): public == private where args := rest args null args => concat form tmp : S := formatFormula(first args, minPrec) - if tmp ^= "" then form := append(form,[" sub ",tmp])$(List S) + if tmp ~= "" then form := append(form,[" sub ",tmp])$(List S) -- superscripts args := rest args null args => group concat form tmp : S := formatFormula(first args, minPrec) - if tmp ^= "" then form := append(form,[" sup ",tmp])$(List S) + if tmp ~= "" then form := append(form,[" sup ",tmp])$(List S) -- presuperscripts args := rest args null args => group concat form tmp : S := formatFormula(first args, minPrec) - if tmp ^= "" then form := append(form,[" presup ",tmp])$(List S) + if tmp ~= "" then form := append(form,[" presup ",tmp])$(List S) -- presubscripts args := rest args null args => group concat form tmp : S := formatFormula(first args, minPrec) - if tmp ^= "" then form := append(form,[" presub ",tmp])$(List S) + if tmp ~= "" then form := append(form,[" presub ",tmp])$(List S) group concat form op = "MATRIX" => formatMatrix rest args -- op = "ZAG" => @@ -318,7 +318,7 @@ ScriptFormulaFormat(): public == private where p < 1 => error "unknown Script Formula Formatter unary op" opPrec := plexPrecs.p n : I := #args - (n ^= 2) and (n ^= 3) => error "wrong number of arguments for plex" + (n ~= 2) and (n ~= 3) => error "wrong number of arguments for plex" s : S := op = "SIGMA" => "sum" op = "PI" => "product" @@ -327,12 +327,12 @@ ScriptFormulaFormat(): public == private where "????" hold := formatFormula(first args,minPrec) args := rest args - if op ^= "INDEFINTEGRAL" then - if hold ^= "" then + if op ~= "INDEFINTEGRAL" then + if hold ~= "" then s := concat [s," from",group concat ["\displaystyle ",hold]] if not null rest args then hold := formatFormula(first args,minPrec) - if hold ^= "" then + if hold ~= "" then s := concat [s," to",group concat ["\displaystyle ",hold]] args := rest args s := concat [s," ",formatFormula(first args,minPrec)] diff --git a/src/algebra/fortran.spad.pamphlet b/src/algebra/fortran.spad.pamphlet index c8d73e94..cf46d763 100644 --- a/src/algebra/fortran.spad.pamphlet +++ b/src/algebra/fortran.spad.pamphlet @@ -773,7 +773,7 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where checkVariables(user:List Symbol,target:List Symbol):Void == -- We don't worry about whether the user has subscripted the -- variables or not. - setDifference(map(name$Symbol,user),target) ^= empty()$List(Symbol) => + setDifference(map(name$Symbol,user),target) ~= empty()$List(Symbol) => s1 : String := mkString(user) s2 : String := mkString(target) error ["Incompatible variable lists:", s1, s2] @@ -788,7 +788,7 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where retractIfCan(lhs u)@Union(Kernel(EXPR MINT),"failed") case "failed" => error "left hand side is not a kernel" vList : List Symbol := variables lhs u - #vList ^= #arguments => + #vList ~= #arguments => error "Incorrect number of arguments" veList : List EXPR MINT := [w::EXPR(MINT) for w in vList] aeList : List EXPR MINT := [w::EXPR(MINT) for w in arguments] @@ -805,7 +805,7 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where retractIfCan(lhs u)@Union(Kernel(EXPR MFLOAT),"failed") case "failed" => error "left hand side is not a kernel" vList : List Symbol := variables lhs u - #vList ^= #arguments => + #vList ~= #arguments => error "Incorrect number of arguments" veList : List EXPR MFLOAT := [w::EXPR(MFLOAT) for w in vList] aeList : List EXPR MFLOAT := [w::EXPR(MFLOAT) for w in arguments] @@ -822,7 +822,7 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where retractIfCan(lhs u)@Union(Kernel EXPR MCMPLX,"failed") case "failed"=> error "left hand side is not a kernel" vList : List Symbol := variables lhs u - #vList ^= #arguments => + #vList ~= #arguments => error "Incorrect number of arguments" veList : List EXPR MCMPLX := [w::EXPR(MCMPLX) for w in vList] aeList : List EXPR MCMPLX := [w::EXPR(MCMPLX) for w in arguments] @@ -852,7 +852,7 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where retractIfCan(lhs u)@Union(Kernel(EXPR INT),"failed") case "failed" => error "left hand side is not a kernel" vList : List Symbol := variables lhs u - #vList ^= #arguments => + #vList ~= #arguments => error "Incorrect number of arguments" veList : List EXPR INT := [w::EXPR(INT) for w in vList] aeList : List EXPR INT := [w::EXPR(INT) for w in arguments] @@ -869,7 +869,7 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where retractIfCan(lhs u)@Union(Kernel(EXPR Float),"failed") case "failed" => error "left hand side is not a kernel" vList : List Symbol := variables lhs u - #vList ^= #arguments => + #vList ~= #arguments => error "Incorrect number of arguments" veList : List EXPR Float := [w::EXPR(Float) for w in vList] aeList : List EXPR Float := [w::EXPR(Float) for w in arguments] @@ -886,7 +886,7 @@ FortranProgram(name,returnType,arguments,symbols): Exports == Implement where retractIfCan(lhs u)@Union(Kernel EXPR CMPX Float,"failed") case "failed"=> error "left hand side is not a kernel" vList : List Symbol := variables lhs u - #vList ^= #arguments => + #vList ~= #arguments => error "Incorrect number of arguments" veList : List EXPR CMPX Float := [w::EXPR(CMPX Float) for w in vList] aeList : List EXPR CMPX Float := [w::EXPR(CMPX Float) for w in arguments] diff --git a/src/algebra/fr.spad.pamphlet b/src/algebra/fr.spad.pamphlet index fc180573..4e5df0b9 100644 --- a/src/algebra/fr.spad.pamphlet +++ b/src/algebra/fr.spad.pamphlet @@ -187,7 +187,7 @@ Factored(R: IntegralDomain): Exports == Implementation where -- l := concat(convert(rec.fctr)@InputForm, l) -- l := concat(convert(rec.fctr)@InputForm ** rec.xpnt, l) empty? l => convert(unit x)@InputForm - if unit x ^= 1 then l := concat(convert(unit x)@InputForm,l) + if unit x ~= 1 then l := concat(convert(unit x)@InputForm,l) empty? rest l => first l binary(convert(_*::Symbol)@InputForm, l)@InputForm diff --git a/src/algebra/free.spad.pamphlet b/src/algebra/free.spad.pamphlet index 95e17711..9dbf0ea5 100644 --- a/src/algebra/free.spad.pamphlet +++ b/src/algebra/free.spad.pamphlet @@ -108,7 +108,7 @@ ListMonoidOps(S, E, un): Exports == Implementation where mapExpon(f, l) == ans:List(REC) := empty() for x in l repeat - if (a := f(x.exp)) ^= 0 then ans := concat([x.gen, a], ans) + if (a := f(x.exp)) ~= 0 then ans := concat([x.gen, a], ans) reverse_! ans outputForm(l, op, opexp, id) == @@ -132,7 +132,7 @@ ListMonoidOps(S, E, un): Exports == Implementation where concat([s, un], f) commutativeEquality(s1:$, s2:$):Boolean == - #s1 ^= #s2 => false + #s1 ~= #s2 => false for t1 in s1 repeat if not member?(t1,s2) then return false true @@ -301,15 +301,15 @@ FreeMonoid(S: SetCategory): FMcategory == FMdefinition where hclf(f, g) == h:List(REC) := empty() for f0 in listOfMonoms f for g0 in listOfMonoms g repeat - f0.gen ^= g0.gen => return makeMulti h + f0.gen ~= g0.gen => return makeMulti h h := concat_!(h, [f0.gen, min(f0.exp, g0.exp)]) - f0.exp ^= g0.exp => return makeMulti h + f0.exp ~= g0.exp => return makeMulti h makeMulti h lquo(aq, a) == size a > #(laq := copy listOfMonoms aq) => "failed" for a0 in listOfMonoms a repeat - a0.gen ^= laq.first.gen or a0.exp > laq.first.exp => + a0.gen ~= laq.first.gen or a0.exp > laq.first.exp => return "failed" if a0.exp = laq.first.exp then laq := rest laq else setfirst_!(laq, [laq.first.gen, diff --git a/src/algebra/fspace.spad.pamphlet b/src/algebra/fspace.spad.pamphlet index 902aa197..d044d256 100644 --- a/src/algebra/fspace.spad.pamphlet +++ b/src/algebra/fspace.spad.pamphlet @@ -256,19 +256,19 @@ ExpressionSpace(): Category == Defn where elt(op:OP, args:List %) == not belong? op => error "Unknown operator" - ((u := arity op) case N) and (#args ^= u::N) + ((u := arity op) case N) and (#args ~= u::N) => error "Wrong number of arguments" (v := evaluate(op,args)$BasicOperatorFunctions1(%)) case % => v::% okkernel(op, args) retract f == (k := mainKernel f) case "failed" => error "not a kernel" - k::K::% ^= f => error "not a kernel" + k::K::% ~= f => error "not a kernel" k::K retractIfCan f == (k := mainKernel f) case "failed" => "failed" - k::K::% ^= f => "failed" + k::K::% ~= f => "failed" k is?(f:%, s:SY) == @@ -1572,7 +1572,7 @@ FunctionSpace(R:OrderedSet): Category == Definition where a:% := 0 f := eval((lfunc.n) arg, lop, lexp, lfunc) e := lexp.n - while q ^= 0 repeat + while q ~= 0 repeat m := degree q qr := divide(m, e) t1 := f ** (qr.quotient)::N @@ -1621,14 +1621,14 @@ FunctionSpace(R:OrderedSet): Category == Definition where u := third l arg := argument k ans:% := 0 - if (not member?(u,done)) and (ans := differentiate(u,x))^=0 then + if (not member?(u,done)) and (ans := differentiate(u,x))~=0 then ans := ans * kernel(opdiff, [subst(expr, [kd], [kernel(opdiff, [first l, gg, gg])]), gg, u]) done := concat(gg, done) is?(k, opdiff) => ans + diffdiff0(arg, x, expr, k, done) for i in minIndex arg .. maxIndex arg for b in arg repeat - if (not member?(b,done)) and (bp:=differentiate(b,x))^=0 then + if (not member?(b,done)) and (bp:=differentiate(b,x))~=0 then g := symsub(gendiff, i)::% ans := ans + bp * kernel(opdiff, [subst(expr, [kd], [kernel(opdiff, [substArg(op, arg, i, g), gg, u])]), g, b]) @@ -1676,7 +1676,7 @@ FunctionSpace(R:OrderedSet): Category == Definition where grad := (u := derivative op) case "failed" => opderiv(op, n) u::List(List % -> %) - if #grad ^= n then grad := opderiv(op, n) + if #grad ~= n then grad := opderiv(op, n) [g args for g in grad] -- SPECIALDIFF contains a map (List %, Symbol) -> % diff --git a/src/algebra/funcpkgs.spad.pamphlet b/src/algebra/funcpkgs.spad.pamphlet index 41f979ef..eae260a6 100644 --- a/src/algebra/funcpkgs.spad.pamphlet +++ b/src/algebra/funcpkgs.spad.pamphlet @@ -82,7 +82,7 @@ FunctionSpaceUnivariatePolynomialFactor(R, F, UP): UP2ifCan p == ansq := 0$UPQ ; ansa := 0$UPA goforq? := true - while p ^= 0 repeat + while p ~= 0 repeat if goforq? then rq := retractIfCan(leadingCoefficient p)@Union(Q, "failed") if rq case Q then @@ -114,7 +114,7 @@ FunctionSpaceUnivariatePolynomialFactor(R, F, UP): UP2ifCan p == ansq := 0$UPQ - while p ^= 0 repeat + while p ~= 0 repeat rq := retractIfCan(leadingCoefficient p)@Union(Q, "failed") if rq case Q then ansq := ansq + monomial(rq::Q, degree p) else return [true] diff --git a/src/algebra/gaussfac.spad.pamphlet b/src/algebra/gaussfac.spad.pamphlet index 1b1e3197..660d9f4c 100644 --- a/src/algebra/gaussfac.spad.pamphlet +++ b/src/algebra/gaussfac.spad.pamphlet @@ -80,7 +80,7 @@ GaussianFactorizationPackage() : C == T for i in 2.. while (s=1 or s=qq1) repeat s:=reduce(i,q)**(r::NNI) t:=s - while t^=qq1 repeat + while t~=qq1 repeat s:=t t:=t**2 s::Z @@ -132,7 +132,7 @@ GaussianFactorizationPackage() : C == T result : List FFE :=[] unity:ZI:=1$ZI - if d^=1 then + if d~=1 then a:=(a exquo d)::Z b:=(b exquo d)::Z r:= intfactor(d) @@ -163,13 +163,13 @@ GaussianFactorizationPackage() : C == T m:=m quo z result:=concat(part,result) - if m^=1 then unity:=unity * m + if m~=1 then unity:=unity * m makeFR(unity,result) ---- write p prime like sum of two squares ---- sumSquares(p:Z) : List Z == p=2 => [1,1] - p rem 4 ^= 1 => error "no solutions" + p rem 4 ~= 1 => error "no solutions" sumsq1(p) @@ -180,9 +180,9 @@ GaussianFactorizationPackage() : C == T prime?(n)$IntegerPrimesPackage(Z) => true re : Z := real a im : Z := imag a - re^=0 and im^=0 => false + re~=0 and im~=0 => false p : Z := abs(re+im) -- a is of the form p, -p, %i*p or -%i*p - p rem 4 ^= 3 => false + p rem 4 ~= 3 => false -- return-value true, if p is a rational prime, -- and false, otherwise prime?(p)$IntegerPrimesPackage(Z) diff --git a/src/algebra/gaussian.spad.pamphlet b/src/algebra/gaussian.spad.pamphlet index ccbd0728..b45a902e 100644 --- a/src/algebra/gaussian.spad.pamphlet +++ b/src/algebra/gaussian.spad.pamphlet @@ -157,7 +157,7 @@ ComplexCategory(R:CommutativeRing): Category == coordinates(x:%, v:Vector %):Vector(R) == ra := real(a := v(minIndex v)) rb := real(b := v(maxIndex v)) - (#v ^= 2) or + (#v ~= 2) or ((d := recip(ra * (ib := imag b) - (ia := imag a) * rb)) case "failed") =>error "coordinates: vector is not a basis" rx := real x @@ -332,12 +332,12 @@ ComplexCategory(R:CommutativeRing): Category == xx := x * y1 x1 := real(xx) rem r a := x1 - if x1^=0 and sizeLess?(r, 2 * x1) then + if x1~=0 and sizeLess?(r, 2 * x1) then a := x1 - r if sizeLess?(x1, a) then a := x1 + r x2 := imag(xx) rem r b := x2 - if x2^=0 and sizeLess?(r, 2 * x2) then + if x2~=0 and sizeLess?(r, 2 * x2) then b := x2 - r if sizeLess?(x2, b) then b := x2 + r y1 := (complex(a, b) exquo y1)::% @@ -759,7 +759,7 @@ ComplexIntegerSolveLinearPolynomialEquation(R,CR): C == T slpePrime:R:=(2::R) oldtable:Vector List CP := empty() solveLinearPolynomialEquation(lp,p) == - if (oldlp ^= lp) then + if (oldlp ~= lp) then -- we have to generate a new table deg:= _+/[degree u for u in lp] ans:Union(Vector List CP,"failed"):="failed" diff --git a/src/algebra/gb.spad.pamphlet b/src/algebra/gb.spad.pamphlet index e62ca71f..4cff4aac 100644 --- a/src/algebra/gb.spad.pamphlet +++ b/src/algebra/gb.spad.pamphlet @@ -128,13 +128,13 @@ GroebnerPackage(Dom, Expon, VarSet, Dpol): T == C where groebner( Pol: List(Dpol) ) == Pol=[] => Pol - Pol:=[x for x in Pol | x ^= 0] + Pol:=[x for x in Pol | x ~= 0] Pol=[] => [0] minGbasis(sort( degree #1 > degree #2, gbasis(Pol,0,0))) groebner( Pol: List(Dpol), xx1: String) == Pol=[] => Pol - Pol:=[x for x in Pol | x ^= 0] + Pol:=[x for x in Pol | x ~= 0] Pol=[] => [0] xx1 = "redcrit" => minGbasis(sort( degree #1 > degree #2, gbasis(Pol,1,0))) @@ -149,7 +149,7 @@ GroebnerPackage(Dom, Expon, VarSet, Dpol): T == C where groebner( Pol: List(Dpol), xx1: String, xx2: String) == Pol=[] => Pol - Pol:=[x for x in Pol | x ^= 0] + Pol:=[x for x in Pol | x ~= 0] Pol=[] => [0] (xx1 = "redcrit" and xx2 = "info") or (xx1 = "info" and xx2 = "redcrit") => diff --git a/src/algebra/gbeuclid.spad.pamphlet b/src/algebra/gbeuclid.spad.pamphlet index 0ff28e44..660e9230 100644 --- a/src/algebra/gbeuclid.spad.pamphlet +++ b/src/algebra/gbeuclid.spad.pamphlet @@ -252,7 +252,7 @@ EuclideanGroebnerBasisPackage(Dom, Expon, VarSet, Dpol): T == C where if xx2 = 1 then prinpolINFO(Pol) print(" THE GROEBNER BASIS over EUCLIDEAN DOMAIN"::Ex) - if xx1 = 1 and xx2 ^= 1 then + if xx1 = 1 and xx2 ~= 1 then print(" THE GROEBNER BASIS over EUCLIDEAN DOMAIN"::Ex) H @@ -272,7 +272,7 @@ EuclideanGroebnerBasisPackage(Dom, Expon, VarSet, Dpol): T == C where ecredPol(h: Dpol, F: List(Dpol) ) == h0:Dpol:= 0 null F => h - while h ^= 0 repeat + while h ~= 0 repeat h0:= h0 + monomial(leadingCoefficient(h),degree(h)) h:= eRed(red(h), F, F) h0 @@ -464,7 +464,7 @@ EuclideanGroebnerBasisPackage(Dom, Expon, VarSet, Dpol): T == C where lepol(p1:Dpol)== n: Integer n:= 0 - while p1 ^= 0 repeat + while p1 ~= 0 repeat n:= n + 1 p1:= red(p1) n diff --git a/src/algebra/gbintern.spad.pamphlet b/src/algebra/gbintern.spad.pamphlet index 1ba941b2..2c3d430f 100644 --- a/src/algebra/gbintern.spad.pamphlet +++ b/src/algebra/gbintern.spad.pamphlet @@ -168,7 +168,7 @@ GroebnerInternalPackage(Dom, Expon, VarSet, Dpol): T == C where if xx2 = 1 then prinpolINFO(Pol) messagePrint(" THE GROEBNER BASIS POLYNOMIALS") - if xx1 = 1 and xx2 ^= 1 then + if xx1 = 1 and xx2 ~= 1 then messagePrint(" THE GROEBNER BASIS POLYNOMIALS") Pol @@ -295,7 +295,7 @@ GroebnerInternalPackage(Dom, Expon, VarSet, Dpol): T == C where --- lcm(eh,ei) and eik ^equal lcm(eh,ek) critB(eh:Expon, eik:Expon, ei:Expon, ek:Expon) == - critM(eh, eik) and (eik ^= sup(eh, ei)) and (eik ^= sup(eh, ek)) + critM(eh, eik) and (eik ~= sup(eh, ei)) and (eik ~= sup(eh, ek)) ---------------------------- @@ -313,7 +313,7 @@ GroebnerInternalPackage(Dom, Expon, VarSet, Dpol): T == C where credPol(h: Dpol, F: List(Dpol) ) == null F => h h0:Dpol:= monomial(leadingCoefficient h, degree h) - while (h:=reductum h) ^= 0 repeat + while (h:=reductum h) ~= 0 repeat hred:= redPo(h, F) h := hred.poly h0:=(hred.mult)*h0 + monomial(leadingCoefficient(h),degree h) @@ -335,7 +335,7 @@ GroebnerInternalPackage(Dom, Expon, VarSet, Dpol): T == C where lepol(p1:Dpol)== n: Integer n:= 0 - while p1 ^= 0 repeat + while p1 ~= 0 repeat n:= n + 1 p1:= reductum(p1) n diff --git a/src/algebra/gdirprod.spad.pamphlet b/src/algebra/gdirprod.spad.pamphlet index c12b2fd4..622e8726 100644 --- a/src/algebra/gdirprod.spad.pamphlet +++ b/src/algebra/gdirprod.spad.pamphlet @@ -202,7 +202,7 @@ SplitHomogeneousDirectProduct(dimtot,dim1,S) : T == C where (v1:% < v2:%):Boolean == lessThanRlex(v1,v2,1,dim1) => true for i in 1..dim1 repeat - if qelt(v1,i) ^= qelt(v2,i) then return false + if qelt(v1,i) ~= qelt(v2,i) then return false lessThanRlex(v1,v2,dim1+1,dimtot) @ diff --git a/src/algebra/gdpoly.spad.pamphlet b/src/algebra/gdpoly.spad.pamphlet index 6c3ae4fd..49a77794 100644 --- a/src/algebra/gdpoly.spad.pamphlet +++ b/src/algebra/gdpoly.spad.pamphlet @@ -148,10 +148,10 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where p := reductum p for i in 1..n repeat maxdeg.i := max(maxdeg.i, tdeg.i) - [index(i:PositiveInteger) for i in 1..n | maxdeg.i^=0] + [index(i:PositiveInteger) for i in 1..n | maxdeg.i~=0] reorder(p: %,perm: List Integer):% == - #perm ^= n => error "must be a complete permutation of all vars" + #perm ~= n => error "must be a complete permutation of all vars" q := [[directProduct [term.k.j for j in perm]$Vec,term.c]$Term for term in p] sort(#1.k > #2.k,q) @@ -209,7 +209,7 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where monomial(leadingCoefficient p,0) q := univariate(p,v:: OV) ans:SUP(R) := 0 - while q ^= 0 repeat + while q ~= 0 repeat ans := ans + monomial(ground leadingCoefficient q,degree q) q := reductum q ans @@ -254,7 +254,7 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where t.k.i = 1 => l := cons(vl1.i,l) l := cons(vl1.i ** t.k.i ::OutputForm,l) l := reverse l - if (t.c ^= 1) or (null l) then l := cons(t.c :: OutputForm,l) + if (t.c ~= 1) or (null l) then l := cons(t.c :: OutputForm,l) 1 = #l => lt := cons(first l,lt) lt := cons(reduce("*",l),lt) 1 = #lt => first lt diff --git a/src/algebra/geneez.spad.pamphlet b/src/algebra/geneez.spad.pamphlet index 74076d65..5568763b 100644 --- a/src/algebra/geneez.spad.pamphlet +++ b/src/algebra/geneez.spad.pamphlet @@ -96,7 +96,7 @@ GenExEuclid(R,BP) : C == T exactquo(u:BP,v:BP,p:R):Union(BP,"failed") == invlcv:=modInverse(leadingCoefficient v,p) r:=monicDivide(u,reduction(invlcv*v,p)) - reduction(r.remainder,p) ^=0 => "failed" + reduction(r.remainder,p) ~=0 => "failed" reduction(invlcv*r.quotient,p) FP:=EuclideanModularRing(R,BP,R,reduction,merge,exactquo) @@ -120,7 +120,7 @@ GenExEuclid(R,BP) : C == T ftab:Vector L FP := map(reduceList(#1,lmod),table)$VectorFunctions2(List BP,List FP) sln:L FP:=[0$FP for xx in ftab.1 ] - for i in 0 .. d |(cc:=coefficient(err,i)) ^=0 repeat + for i in 0 .. d |(cc:=coefficient(err,i)) ~=0 repeat sln:=[slp+reduce(cc::BP,lmod)*pp for pp in ftab.(i+1) for slp in sln] nsol:=[f-lmodk*reduction(g::BP,lmod) for f in oldsol for g in sln] @@ -141,12 +141,12 @@ GenExEuclid(R,BP) : C == T testModulus(pmod, listPol) == redListPol := reduceList(listPol, pmod) for pol in listPol for rpol in redListPol repeat - degree(pol) ^= degree(rpol::BP) => return false + degree(pol) ~= degree(rpol::BP) => return false while not empty? redListPol repeat rpol := first redListPol redListPol := rest redListPol for rpol2 in redListPol repeat - gcd(rpol, rpol2) ^= 1 => return false + gcd(rpol, rpol2) ~= 1 => return false true if R has Field then @@ -165,7 +165,7 @@ GenExEuclid(R,BP) : C == T -- Actually, there's no possibility of failure d:=degree m sln:L BP:=[0$BP for xx in table.1] - for i in 0 .. d | coefficient(m,i)^=0 repeat + for i in 0 .. d | coefficient(m,i)~=0 repeat sln:=[slp+coefficient(m,i)*pp for pp in table.(i+1) for slp in sln] sln @@ -192,7 +192,7 @@ GenExEuclid(R,BP) : C == T map(reduceList(#1,pmod),table)$VectorFunctions2(List BP,List FP) lpolys:L BP:=table.(#table) sln:L FP:=[0$FP for xx in ftab.1] - for i in 0 .. d | coefficient(m,i)^=0 repeat + for i in 0 .. d | coefficient(m,i)~=0 repeat sln:=[slp+reduce(coefficient(m,i)::BP,pmod)*pp for pp in ftab.(i+1) for slp in sln] soln:=[slp::BP for slp in sln] diff --git a/src/algebra/ghensel.spad.pamphlet b/src/algebra/ghensel.spad.pamphlet index 79d49c13..5643e7e2 100644 --- a/src/algebra/ghensel.spad.pamphlet +++ b/src/algebra/ghensel.spad.pamphlet @@ -63,7 +63,7 @@ GeneralHenselPackage(RP,TP):C == T where exactquo(u:TP,v:TP,p:RP):Union(TP,"failed") == invlcv:=modInverse(leadingCoefficient v,p) r:=monicDivide(u,reduction(invlcv*v,p)) - reduction(r.remainder,p) ^=0 => "failed" + reduction(r.remainder,p) ~=0 => "failed" reduction(invlcv*r.quotient,p) FP:=EuclideanModularRing(RP,TP,RP,reduction,merge,exactquo) @@ -78,7 +78,7 @@ GeneralHenselPackage(RP,TP):C == T where factlist=[] => [[pol] for pol in fln] maxd := +/[degree f for f in fln] quo 2 auxfl:List List TP := [] - for poly in fln while factlist^=[] repeat + for poly in fln while factlist~=[] repeat factlist := [term for term in factlist | ^member?(poly,term)] dp := degree poly for term in factlist repeat @@ -112,7 +112,7 @@ GeneralHenselPackage(RP,TP):C == T where fln = nfln and zero?(err:=poly-*/fln) => leave "finished" fln := nfln Modulus := prime*Modulus - if constp^=0 then fln:=cons(constp,fln) + if constp~=0 then fln:=cons(constp,fln) [fln,Modulus] completeHensel(m:TP,tl1:List TP,prime:RP,bound:PI) == @@ -127,9 +127,9 @@ GeneralHenselPackage(RP,TP):C == T where dfn :NonNegativeInteger := nm lcm1 := leadingCoefficient m mm := lcm1*m - while dfn>0 and (factlist := genFact(fln,factlist))^=[] repeat + while dfn>0 and (factlist := genFact(fln,factlist))~=[] repeat auxfl := [] - while factlist^=[] repeat + while factlist~=[] repeat auxl := factlist.first factlist := factlist.rest tc := reduceCoef((lcm1 * */[coefficient(poly,0) diff --git a/src/algebra/gpgcd.spad.pamphlet b/src/algebra/gpgcd.spad.pamphlet index bf758915..85f20722 100644 --- a/src/algebra/gpgcd.spad.pamphlet +++ b/src/algebra/gpgcd.spad.pamphlet @@ -139,7 +139,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where => g*gcd(c1,c2)::SUPP -- divdes them both, so is the gcd v:=variables g -- there can be at most these variables in answer v1:=setDifference(vp1,v) - if #v1 ^= 0 then + if #v1 ~= 0 then g:=recursivelyGCDCoefficients(g,v,p1,v1) -- one? g => return gcd(c1,c2)::SUPP (g = 1) => return gcd(c1,c2)::SUPP @@ -222,7 +222,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where g:=monomial(lcp,degree gR)+map(#1::P,reductum gR) cf:=monomial(lcp,degree cfR)+map(#1::P,reductum cfR) p:=lcp*p -- impose leaidng coefficient of p on each factor - while lv ^= [] repeat + while lv ~= [] repeat v:=first lv r:=first lr lv:=rest lv @@ -243,7 +243,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where g:=g+pn*first step cf:=cf+pn*second step pn:=pn*prime - thisp ^= g*cf => return "failed" + thisp ~= g*cf => return "failed" g recursivelyGCDCoefficients(g:SUPP,v:List OV,p:SUPP,pv:List OV) == mv:=first pv -- take each coefficient w.r.t. mv @@ -256,7 +256,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where else g:=recursivelyGCDCoefficients(p,v,p1,pv) -- one? g => return 1 (g = 1) => return 1 - g^=oldg => + g~=oldg => oldv:=v v:=variables g pv:=setUnion(pv,setDifference(v,oldv)) @@ -265,7 +265,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where #lv = 0 => p1 lr:=[ randomR() for vv in lv] dg:=degree p1 - while dg ^= degree (ans:= map(eval(#1,lv,lr),p1)) repeat + while dg ~= degree (ans:= map(eval(#1,lv,lr),p1)) repeat lr:=[ randomR() for vv in lv] ans -- eval(p1:SUPP,lv:List OV,lr:List R) == map(eval(#1,lv,lr),p1) @@ -305,9 +305,9 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD range:=2*range --JHD lval:=[(random()$I rem (2*range) - range)::R for i in 1..nvr] --JHD uf1:SUPR:=univariate eval(p1,lvr,lval) ---JHD degree uf1 ^= d1 => "new point" +--JHD degree uf1 ~= d1 => "new point" --JHD uf2:SUPR:=univariate eval(p2,lvr,lval) ---JHD degree uf2 ^= d2 => "new point" +--JHD degree uf2 ~= d2 => "new point" --JHD u:=gcd(uf1,uf2) --JHD du:=degree u --JHD --the univariate gcd is 1 @@ -324,7 +324,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD dd=d1 => --JHD if ^((f:=p2 exquo p1) case "failed") then --JHD return [[u],lval,p1]$UTerm ---JHD if dd^=d2 then dd:=(dd-1)::NNI +--JHD if dd~=d2 then dd:=(dd-1)::NNI --JHD --JHD dd=d2 => --JHD if ^((f:=p1 exquo p2) case "failed") then @@ -369,7 +369,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD (gd1,gd2):=(l,l) --JHD ul:=univariate(eval(l,lvar1,lval)) --JHD dl:=degree ul ---JHD if degree gcd(ul,differentiate ul) ^=0 then +--JHD if degree gcd(ul,differentiate ul) ~=0 then --JHD newchoice:=good(l,lvar.rest) --JHD ul:=newchoice.upol --JHD lval:=newchoice.inval @@ -381,7 +381,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD d:SUPR:=gcd(cons(ul,ulist)) --JHD if degree d =0 then return gd1 --JHD lquo:=(ul exquo d)::SUPR ---JHD if degree lquo ^=0 then +--JHD if degree lquo ~=0 then --JHD lgcd:=gcd(cons(leadingCoefficient univariate(l,x),lcpol)) --JHD gd2:=lift(l,d,lquo,lgcd,lvar,ldeg,lval) --JHD l:=gd2 @@ -546,7 +546,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD df:=degree(f,x) --JHD leadlist:List(P):=[] --JHD ---JHD if lgcd^=1$P then +--JHD if lgcd~=1$P then --JHD leadpol:=true --JHD f:=lgcd*f --JHD ldeg:=[n0+n1 for n0 in ldeg for n1 in degree(lgcd,lvar)] @@ -558,7 +558,7 @@ GeneralPolynomialGcdPackage(E,OV,R,P):C == T where --JHD lg:=imposelc([d,uf],lvar,lval,leadlist) --JHD plist:=lifting(univariate(f,x),lvar,lg,lval,leadlist,ldeg)::List P --JHD (p0:P,p1:P):=(plist.first,plist.2) ---JHD if univariate eval(p0,rest lvar,lval) ^= lg.first then +--JHD if univariate eval(p0,rest lvar,lval) ~= lg.first then --JHD (p0,p1):=(p1,p0) --JHD ^leadpol => p0 --JHD cprim:=contprim([p0]) diff --git a/src/algebra/gpol.spad.pamphlet b/src/algebra/gpol.spad.pamphlet index a4563b03..3d09fc08 100644 --- a/src/algebra/gpol.spad.pamphlet +++ b/src/algebra/gpol.spad.pamphlet @@ -87,7 +87,7 @@ LaurentPolynomial(R, UP): Exports == Implementation where zero? p => 0::Z::O l := nil()$List(O) v := monomial(1, 1)$UP :: O - while p ^= 0 repeat + while p ~= 0 repeat l := concat(l, toutput(leadingCoefficient p, degree p, v)) p := reductum p reduce("+", l) @@ -140,7 +140,7 @@ LaurentPolynomial(R, UP): Exports == Implementation where poly(p) * monomial(1, order(p)::N)$UP retractIfCan(p:%):Union(R, "failed") == - order(p) ^= 0 => "failed" + order(p) ~= 0 => "failed" retractIfCan poly p if R has Field then diff --git a/src/algebra/groebf.spad.pamphlet b/src/algebra/groebf.spad.pamphlet index 68cc216c..47225404 100644 --- a/src/algebra/groebf.spad.pamphlet +++ b/src/algebra/groebf.spad.pamphlet @@ -200,8 +200,8 @@ GroebnerFactorizationPackage(Dom, Expon, VarSet, Dpol): T == C where basis := [[0,1$Dpol]$sugarPol] terminateWithBasis := true - -- if "nP" ^= 0, then we continue, otherwise we determine next "nP" - nP ^= 0$Dpol => + -- if "nP" ~= 0, then we continue, otherwise we determine next "nP" + nP ~= 0$Dpol => -- now we divide "nP", if possible, by the polynomials -- from "nonZeroRestrictions" for q in nonZeroRestrictions repeat @@ -224,8 +224,8 @@ GroebnerFactorizationPackage(Dom, Expon, VarSet, Dpol): T == C where basis := [[0,1$Dpol]$sugarPol] terminateWithBasis := true -- doSplitting? is still false - -- if "nP" ^= 0, then we continue, otherwise we determine next "nP" - nP ^= 0$Dpol => + -- if "nP" ~= 0, then we continue, otherwise we determine next "nP" + nP ~= 0$Dpol => -- now we factorize "nP", which is not constant irreducibleFactors : L Dpol := createAllFactors(nP) -- if there are more than 1 factors we reduce them and split @@ -254,7 +254,7 @@ GroebnerFactorizationPackage(Dom, Expon, VarSet, Dpol): T == C where doSplitting? => for fnP in allReducedFactors repeat - if fnP ^= 1$Dpol + if fnP ~= 1$Dpol then newInputPolys : L Dpol := _ sort( degree #1 > degree #2 ,cons(fnP,inputPolys)) diff --git a/src/algebra/groebsol.spad.pamphlet b/src/algebra/groebsol.spad.pamphlet index b2e4ab76..482c960f 100644 --- a/src/algebra/groebsol.spad.pamphlet +++ b/src/algebra/groebsol.spad.pamphlet @@ -77,7 +77,7 @@ GroebnerSolve(lv,F,R) : C == T lc := (lc exquo gg)::DPoly linp:SUP:=monomial(lc,1$NNI)$SUP + monomial(trailp,0$NNI)$SUP g:DPoly:=multivariate(uf-linp**df,x) - redPol(g,lpol) ^= 0 => "failed" + redPol(g,lpol) ~= 0 => "failed" multivariate(linp,x) -- is the 0-dimensional ideal I in general position ? -- @@ -96,7 +96,7 @@ GroebnerSolve(lv,F,R) : C == T then return "failed" newlpol :=concat(redPol(g::DPoly,newlpol),newlpol) rlvar:=rest rlvar - else if redPol(f,newlpol)^=0 then return"failed" + else if redPol(f,newlpol)~=0 then return"failed" newlpol @@ -152,7 +152,7 @@ GroebnerSolve(lv,F,R) : C == T val:=(x::HDPoly)-val ans:=[totolex groebner [elt(univariate(p,x),val) for p in lp] for lp in result] - [ll for ll in ans | ll^=[1]] + [ll for ll in ans | ll~=[1]] zeroDim?(lp: List HDPoly,lvar:L OV) : Boolean == empty? lp => false diff --git a/src/algebra/ideal.spad.pamphlet b/src/algebra/ideal.spad.pamphlet index f1ba1d61..980cba38 100644 --- a/src/algebra/ideal.spad.pamphlet +++ b/src/algebra/ideal.spad.pamphlet @@ -174,7 +174,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T q=0$newPoly => 0$DPoly dq:newExpon:=degree q n:NNI:=selectfirst (dq) - n^=0 => "failed" + n~=0 => "failed" ((g:=oldpoly reductum q) case "failed") => "failed" monomial(leadingCoefficient q,selectsecond dq)$DPoly + (g::DPoly) @@ -218,7 +218,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T lsubset : List List VarSet := sort(#(#1)>#(#2),subset(lv)) for subs in lsubset repeat ldif:List VarSet:= lv - for mvset in monvar while ldif ^=[] repeat + for mvset in monvar while ldif ~=[] repeat ldif:=setDifference(mvset,subs) if ^(empty? ldif) then return #subs 0 @@ -378,7 +378,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T vec2.i:=1 g:nPoly:=0$nPoly pol:=0$P - while f^=0 repeat + while f~=0 repeat df:=degree(f-reductum f,lvint) lcf:=leadingCoefficient f pol:=pol+monompol(df,lcf,lvint) @@ -390,7 +390,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T leq : List Equation P := [p = pol for p in npol for pol in reverse lp ] lf:=(groebner lf)$gp - while lf^=[] repeat + while lf~=[] repeat q:=lf.first dq:nExponent:=degree q n:=selectfirst (dq) @@ -399,7 +399,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T solsn:List P:=[] for q in lf repeat g:Polynomial F :=0 - while q^=0 repeat + while q~=0 repeat dq:=degree q lcq:=leadingCoefficient q q:=reductum q @@ -416,7 +416,7 @@ PolynomialIdeals(F,Expon,VarSet,DPoly) : C == T empty? Idl => [0$DPoly] :: OutputForm Idl :: OutputForm - ideal(Id:List DPoly) :Ideal == [[f for f in Id|f^=0],false] + ideal(Id:List DPoly) :Ideal == [[f for f in Id|f~=0],false] groebnerIdeal(Id:List DPoly) : Ideal == [Id,true] diff --git a/src/algebra/idecomp.spad.pamphlet b/src/algebra/idecomp.spad.pamphlet index 9ba4d219..740d60de 100644 --- a/src/algebra/idecomp.spad.pamphlet +++ b/src/algebra/idecomp.spad.pamphlet @@ -145,7 +145,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't lf:=Id.first pv:DPoly:=0 pw:DPoly:=0 - while degree(lf,y)^=1 repeat + while degree(lf,y)~=1 repeat val:=random()$Z rem 23 pv:=px+val*py pw:=px-val*py @@ -153,7 +153,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't lf:=Id.first ris:= generators(zeroRadComp(groebnerIdeal(Id.rest),truelist.rest)) ris:=cons(lf,ris) - if pv^=0 then + if pv~=0 then ris:=[(univariate(h,x)).pw for h in ris] groebnerIdeal(groebner ris) @@ -172,12 +172,12 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't truelist=[] => true n:=#truelist Jd:=groebner generators J - for x in truelist while Jd^=[] repeat + for x in truelist while Jd~=[] repeat f := Jd.first Jd:=Jd.rest - if ((y:=mainVariable f) case "failed") or (y::OV ^=x ) + if ((y:=mainVariable f) case "failed") or (y::OV ~=x ) or _^ (ismonic (f,x)) then return false - while Jd^=[] and (mainVariable Jd.first)::OV=x repeat Jd:=Jd.rest + while Jd~=[] and (mainVariable Jd.first)::OV=x repeat Jd:=Jd.rest if Jd=[] and position(x,truelist)<n then return false true @@ -246,7 +246,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't pushdown(g:DPoly,x:OV) : DPoly == rf:DPoly:=0$DPoly i:=position(x,lvint) - while g^=0 repeat + while g~=0 repeat g1:=reductum g rf:=rf+pushdterm(g-g1,x,i) g := g1 @@ -266,11 +266,11 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't rf:DPoly:=0$DPoly g := f xp := convert(x)@SE - while g^=0 repeat + while g~=0 repeat h:=lcm(trueden(denom leadingCoefficient g,xp),h) g:=reductum g f:=(h::F)*f - while f^=0 repeat + while f~=0 repeat g:=reductum f rf:=rf+pushuterm(f-g,xp,x) f:=g @@ -296,7 +296,7 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't is0dimprimary(J:FIdeal,truelist:List OV) : Boolean == element?(1,J) => true Jd:=generators(groebner J) - #(factors factor Jd.last)^=1 => return false + #(factors factor Jd.last)~=1 => return false i:=subtractIfCan(#truelist,1) (i case "failed") => return true JR:=(reverse Jd);JM:=groebnerIdeal([JR.first]);JP:List(DPoly):=[] @@ -353,10 +353,10 @@ IdealDecompositionPackage(vl,nv) : C == T -- take away nv, now doesn't element?(1,J) => true n:NNI:=#vl;i:NNI:=1 Jd:=generators J - #Jd^=n => false + #Jd~=n => false for f in Jd repeat if _^ ismonic(f,lvint.i) then return false - if i<n and (degree univariate(f,lvint.i))^=1 then return false + if i<n and (degree univariate(f,lvint.i))~=1 then return false i:=i+1 g:=Jd.n #(lfact:=factors(factor g)) >1 => false diff --git a/src/algebra/indexedp.spad.pamphlet b/src/algebra/indexedp.spad.pamphlet index 41f9bc89..34d62e96 100644 --- a/src/algebra/indexedp.spad.pamphlet +++ b/src/algebra/indexedp.spad.pamphlet @@ -65,8 +65,8 @@ IndexedDirectProductObject(A:SetCategory,S:OrderedSet): IndexedDirectProductCate --define x = y == while not null x and _^ null y repeat - x.first.k ^= y.first.k => return false - x.first.c ^= y.first.c => return false + x.first.k ~= y.first.k => return false + x.first.c ~= y.first.c => return false x:=x.rest y:=y.rest null x and null y @@ -159,10 +159,10 @@ IndexedDirectProductAbelianMonoid(A:AbelianMonoid,S:OrderedSet): n * x == n = 0 => 0 n = 1 => x - [[u.k,a] for u in x | (a:=n*u.c) ^= 0$A] + [[u.k,a] for u in x | (a:=n*u.c) ~= 0$A] monomial(r,s) == (r = 0 => 0; [[s,r]]) - map(f,x) == [[tm.k,a] for tm in x | (a:=f(tm.c)) ^= 0$A] + map(f,x) == [[tm.k,a] for tm in x | (a:=f(tm.c)) ~= 0$A] reductum x == (null x => 0; rest x) leadingCoefficient x == (null x => 0; x.first.c) @@ -253,7 +253,7 @@ IndexedDirectProductAbelianGroup(A:AbelianGroup,S:OrderedSet): n * x == n = 0 => 0 n = 1 => x - [[u.k,a] for u in x | (a:=n*u.c) ^= 0$A] + [[u.k,a] for u in x | (a:=n*u.c) ~= 0$A] qsetrest!: (Rep, Rep) -> Rep qsetrest!(l: Rep, e: Rep): Rep == RPLACD(l, e)$Lisp diff --git a/src/algebra/intaf.spad.pamphlet b/src/algebra/intaf.spad.pamphlet index 23f73b17..8a4e2b94 100644 --- a/src/algebra/intaf.spad.pamphlet +++ b/src/algebra/intaf.spad.pamphlet @@ -389,7 +389,7 @@ PureAlgebraicIntegration(R, F, L): Exports == Implementation where linearInXIfCan(x, y) == a := b := 0$UP p := clearDenominator lift(minPoly y, x) - while p ^= 0 repeat + while p ~= 0 repeat degree(q := numer leadingCoefficient p) > 1 => return "failed" a := a + monomial(coefficient(q, 1), d := degree p) b := b - monomial(coefficient(q, 0), d) @@ -401,7 +401,7 @@ PureAlgebraicIntegration(R, F, L): Exports == Implementation where prootintegrate(f, x, y) == modulus := lift(p := minPoly y, x) rf := reductum(ff := univariate(f, x, y, p)) - ((r := retractIfCan(rf)@Union(RF,"failed")) case RF) and rf ^= 0 => + ((r := retractIfCan(rf)@Union(RF,"failed")) case RF) and rf ~= 0 => -- in this case, ff := lc(ff) y^i + r so we integrate both terms -- separately to gain time map(#1(x::F), integrate(r::RF)) + @@ -481,7 +481,7 @@ PureAlgebraicIntegration(R, F, L): Exports == Implementation where -- returns either "failed" or r(u, z) chvarIfCan(p, d, u, u1) == ans:UPUP := 0 - while p ^= 0 repeat + while p ~= 0 repeat (v := composite(u1 * leadingCoefficient(p) / d ** degree(p), u)) case "failed" => return "failed" ans := ans + monomial(v::RF, degree p) diff --git a/src/algebra/intalg.spad.pamphlet b/src/algebra/intalg.spad.pamphlet index a08b41fa..c9002c53 100644 --- a/src/algebra/intalg.spad.pamphlet +++ b/src/algebra/intalg.spad.pamphlet @@ -292,11 +292,11 @@ AlgebraicIntegrate(R0, F, UP, UPUP, R): Exports == Implementation where varRoot?(p, derivation) == for c in coefficients primitivePart p repeat - derivation(c) ^= 0 => return true + derivation(c) ~= 0 => return true false pLogDeriv(log, derivation) == - map(derivation, log.coeff) ^= 0 => + map(derivation, log.coeff) ~= 0 => error "can only handle logs with constant coefficients" -- one?(n := degree(log.coeff)) => ((n := degree(log.coeff)) = 1) => diff --git a/src/algebra/intaux.spad.pamphlet b/src/algebra/intaux.spad.pamphlet index d8d3493f..d2452f79 100644 --- a/src/algebra/intaux.spad.pamphlet +++ b/src/algebra/intaux.spad.pamphlet @@ -106,13 +106,13 @@ IntegrationResult(F:Field): Exports == Implementation where coeffp:O := (outputForm(rec.coeff, alpha) = 0::Z::O)@O logandp := alpha * prefix("log"::Symbol::O, [outputForm(rec.logand, alpha)]) - if (cc := Q2F(rec.scalar)) ^= 1 then + if (cc := Q2F(rec.scalar)) ~= 1 then logandp := cc::O * logandp sum(logandp, coeffp) nesimp l == [[u,x] for x in removeDuplicates_!([ne.intvar for ne in l]$List(F)) - | (u := neselect(l, x)) ^= 0] + | (u := neselect(l, x)) ~= 0] if (F has LiouvillianFunctionCategory) and (F has RetractableTo Symbol) then retractIfCan u == @@ -152,7 +152,7 @@ IntegrationResult(F:Field): Exports == Implementation where error "pNeDeriv: cannot differentiate not elementary part into F" pLogDeriv(log, derivation) == - map(derivation, log.coeff) ^= 0 => + map(derivation, log.coeff) ~= 0 => error "pLogDeriv: can only handle logs with constant coefficients" -- one?(n := degree(log.coeff)) => ((n := degree(log.coeff)) = 1) => @@ -173,7 +173,7 @@ IntegrationResult(F:Field): Exports == Implementation where coerce(u:%):O == (r := retractIfCan u) case F => r::F::O l := reverse_! [LOG2O f for f in logpart u]$List(O) - if ratpart u ^= 0 then l := concat(ratpart(u)::O, l) + if ratpart u ~= 0 then l := concat(ratpart(u)::O, l) if not elem? u then l := concat([NE2O f for f in notelem u], l) null l => 0::O reduce("+", l) diff --git a/src/algebra/intclos.spad.pamphlet b/src/algebra/intclos.spad.pamphlet index 4470fc41..802f079d 100644 --- a/src/algebra/intclos.spad.pamphlet +++ b/src/algebra/intclos.spad.pamphlet @@ -206,8 +206,8 @@ IntegralBasisTools(R,UP,F): Exports == Implementation where (not square? rb1) or (not square? rbinv1) or (not square? rb2) _ or (not square? rbinv2) => error "moduleSum: matrices must be square" - ((n := nrows rb1) ^= (nrows rbinv1)) or (n ^= (nrows rb2)) _ - or (n ^= (nrows rbinv2)) => + ((n := nrows rb1) ~= (nrows rbinv1)) or (n ~= (nrows rb2)) _ + or (n ~= (nrows rbinv2)) => error "moduleSum: matrices of imcompatible dimensions" (zero? rbden1) or (zero? rbden2) => error "moduleSum: denominator must be non-zero" @@ -755,8 +755,8 @@ NumberFieldIntegralBasis(UP,F): Exports == Implementation where rbinv := UpTriBddDenomInv(rb, rbden) indexChange := index quo oldIndex; oldIndex := index disc := disc quo (indexChange * indexChange) --- one? indexChange or gcd(p2,disc) ^= p2 => - (indexChange = 1) or gcd(p2,disc) ^= p2 => +-- one? indexChange or gcd(p2,disc) ~= p2 => + (indexChange = 1) or gcd(p2,disc) ~= p2 => return [rb, rbden, rbinv, disc] discriminant() == diff --git a/src/algebra/intef.spad.pamphlet b/src/algebra/intef.spad.pamphlet index 4dbbc26f..0ba69df7 100644 --- a/src/algebra/intef.spad.pamphlet +++ b/src/algebra/intef.spad.pamphlet @@ -117,7 +117,7 @@ ElementaryIntegration(R, F): Exports == Implementation where and ((z := retractIfCan(zz := third l)@Union(SE, "failed")) case SE) and (z::SE = x) and ((u := droponex(first l, a, ka, zz)) case F) => u::F::IR - (da := differentiate(a := denom(f)::F, x)) ^= 0 and + (da := differentiate(a := denom(f)::F, x)) ~= 0 and zero? differentiate(c := numer(f)::F / da, x) => (c * log a)::IR mkAnswer(0, empty(), [[f, x::F]]) @@ -130,7 +130,7 @@ ElementaryIntegration(R, F): Exports == Implementation where eval(f, [ka], [x]) unklimint(f, x, lu) == - for u in lu | u ^= 0 repeat + for u in lu | u ~= 0 repeat zero? differentiate(c := f * u / differentiate(u, x), x) => [0,[[c,u]]] "failed" @@ -254,7 +254,7 @@ ElementaryIntegration(R, F): Exports == Implementation where primextint(f, x, k, g) == lk := varselect([a for a in tower f - | k ^= a and is?(a, "log"::SE)], x) + | k ~= a and is?(a, "log"::SE)], x) (u1 := primextendedint(univariate(f, k), differentiate(#1, differentiate(#1, x), differentiate(k::F, x)::UP), lfextlimint(#1, x, k, lk), univariate(g, k))) case "failed" @@ -278,7 +278,7 @@ ElementaryIntegration(R, F): Exports == Implementation where primint(f, x, k) == lk := varselect([a for a in tower f - | k ^= a and is?(a, "log"::SE)], x) + | k ~= a and is?(a, "log"::SE)], x) r1 := primintegrate(univariate(f, k), differentiate(#1, differentiate(#1, x), differentiate(k::F, x)::UP), lfextlimint(#1, x, k, lk)) @@ -313,7 +313,7 @@ ElementaryIntegration(R, F): Exports == Implementation where primlimint(f, x, k, lu) == lk := varselect([a for a in tower f - | k ^= a and is?(a, "log"::SE)], x) + | k ~= a and is?(a, "log"::SE)], x) (u1 := primlimitedint(univariate(f, k), differentiate(#1, differentiate(#1, x), differentiate(k::F, x)::UP), lfextlimint(#1, x, k, lk), [univariate(u, k) for u in lu])) diff --git a/src/algebra/integer.spad.pamphlet b/src/algebra/integer.spad.pamphlet index 3aa12fa9..787b3b74 100644 --- a/src/algebra/integer.spad.pamphlet +++ b/src/algebra/integer.spad.pamphlet @@ -41,7 +41,7 @@ IntegerSolveLinearPolynomialEquation(): C ==T slpePrime:Integer:=(2::Integer) oldtable:Vector List ZP := empty() solveLinearPolynomialEquation(lp,p) == - if (oldlp ^= lp) then + if (oldlp ~= lp) then -- we have to generate a new table deg:= _+/[degree u for u in lp] ans:Union(Vector List ZP,"failed"):="failed" diff --git a/src/algebra/intfact.spad.pamphlet b/src/algebra/intfact.spad.pamphlet index 996b9232..316da86a 100644 --- a/src/algebra/intfact.spad.pamphlet +++ b/src/algebra/intfact.spad.pamphlet @@ -330,7 +330,7 @@ IntegerRoots(I:IntegerNumberSystem): Exports == Implementation where return ((1 + s + a quo s) quo two) -- initial approximation for the root is within a factor of 2 (new, old) := (shift(1, n quo two), 1) - while new ^= old repeat + while new ~= old repeat (new, old) := ((1 + new + a quo new) quo two, new) new diff --git a/src/algebra/intpm.spad.pamphlet b/src/algebra/intpm.spad.pamphlet index 49f03dbe..dad6bfa9 100644 --- a/src/algebra/intpm.spad.pamphlet +++ b/src/algebra/intpm.spad.pamphlet @@ -117,7 +117,7 @@ PatternMatchIntegration(R, F): Exports == Implementation where [cc, nc] if (v := isPower f) case Record(val:F, exponent:Z) then vv := v::Record(val:F, exponent:Z) - (vv.exponent ^= 1) => + (vv.exponent ~= 1) => rec := splitConstant(vv.val, x) return [rec.const ** vv.exponent, rec.nconst ** vv.exponent] error "splitConstant: should not happen" @@ -233,7 +233,7 @@ PatternMatchIntegration(R, F): Exports == Implementation where and failed?(res := patternMatch(f,convert(patci0)@PAT,res0)) => [NONE, 0, 0] l := mkalist res - (b := l.pmb) ^= 2 * (a := l.pma) => [NONE, 0, 0] + (b := l.pmb) ~= 2 * (a := l.pma) => [NONE, 0, 0] db := differentiate(b, x) d := (cc := l.pmc) / db zero? differentiate(d, x) => @@ -248,11 +248,11 @@ PatternMatchIntegration(R, F): Exports == Implementation where rec := froot(y, 2)$PolynomialRoots(IndexedExponents K, K, R, P, F) -- one?(rec.exponent) => rec.coef * rec.radicand ((rec.exponent) = 1) => rec.coef * rec.radicand - rec.exponent ^=2 => error "insqrt: hould not happen" + rec.exponent ~=2 => error "insqrt: hould not happen" rec.coef * sqrt(rec.radicand) pmintegrate(f, x) == - (rc := splitConstant(f, x)).const ^= 1 => + (rc := splitConstant(f, x)).const ~= 1 => (u := pmintegrate(rc.nconst, x)) case "failed" => "failed" rec := u::ANS [rc.const * rec.special, rc.const * rec.integrand] @@ -270,7 +270,7 @@ PatternMatchIntegration(R, F): Exports == Implementation where "failed" pmComplexintegrate(f, x) == - (rc := splitConstant(f, x)).const ^= 1 => + (rc := splitConstant(f, x)).const ~= 1 => (u := pmintegrate(rc.nconst, x)) case "failed" => "failed" rec := u::ANS [rc.const * rec.special, rc.const * rec.integrand] diff --git a/src/algebra/intrf.spad.pamphlet b/src/algebra/intrf.spad.pamphlet index 17f21167..73a73040 100644 --- a/src/algebra/intrf.spad.pamphlet +++ b/src/algebra/intrf.spad.pamphlet @@ -97,7 +97,7 @@ SubResultantPackage(R, UP): Exports == Implementation where F := Sn null l => error "SUBRESP: strange Subresultant chain from PRS" zero? Sn => error "SUBRESP: strange Subresultant chain from PRS" - while (l ^= []) repeat + while (l ~= []) repeat res.(n) := Sn F := first(l) l := rest(l) @@ -422,7 +422,7 @@ TranscendentalIntegration(F, UP): Exports == Implementation where -- in k[z] of the restriction of D to k. kappa(p, derivation) == ans:UP := 0 - while p ^= 0 repeat + while p ~= 0 repeat ans := ans + derivation(leadingCoefficient(p)::UP)*monomial(1,degree p) p := reductum p ans @@ -469,7 +469,7 @@ TranscendentalIntegration(F, UP): Exports == Implementation where expintegratepoly(p, FRDE) == coef0:F := 0 notelm := answr := 0$GP - while p ^= 0 repeat + while p ~= 0 repeat ans1 := FRDE(n := degree p, a := leadingCoefficient p) answr := answr + monomial(ans1.ans, n) if ~ans1.sol? then -- Risch d.e. has no complete solution @@ -487,7 +487,7 @@ TranscendentalIntegration(F, UP): Exports == Implementation where tanintegratespecial(f, derivation, FRDE) == ans:RF := 0 p := monomial(1, 2)$UP + 1 - while (n := degree(denom f) quo 2) ^= 0 repeat + while (n := degree(denom f) quo 2) ~= 0 repeat r := numer(f) rem p a := coefficient(r, 1) b := coefficient(r, 0) @@ -507,21 +507,21 @@ TranscendentalIntegration(F, UP): Exports == Implementation where expextintfrac(f, derivation, g) == zero? f => [0, 0] degree numer f >= degree denom f => error "Not a proper fraction" - order(denom f,monomial(1,1)) ^= 0 => error "Not integral at t = 0" + order(denom f,monomial(1,1)) ~= 0 => error "Not integral at t = 0" r := HermiteIntegrate(f, derivation) zero? g => - r.logpart ^= 0 => "failed" + r.logpart ~= 0 => "failed" [r.answer, 0] degree numer g >= degree denom g => error "Not a proper fraction" - order(denom g,monomial(1,1)) ^= 0 => error "Not integral at t = 0" - differentiate(c := r.logpart / g, derivation) ^= 0 => "failed" + order(denom g,monomial(1,1)) ~= 0 => error "Not integral at t = 0" + differentiate(c := r.logpart / g, derivation) ~= 0 => "failed" [r.answer, c] limitedLogs(f, logderiv, lu) == zero? f => empty() empty? lu => "failed" empty? rest lu => - logderiv(c0 := f / logderiv(u0 := first lu)) ^= 0 => "failed" + logderiv(c0 := f / logderiv(u0 := first lu)) ~= 0 => "failed" [[c0, u0]] num := numer f den := denom f @@ -538,14 +538,14 @@ TranscendentalIntegration(F, UP): Exports == Implementation where m := rowEchelon m ans := empty()$LLG for i in minRowIndex m .. maxRowIndex m | - qelt(m, i, maxColIndex m) ^= 0 repeat + qelt(m, i, maxColIndex m) ~= 0 repeat OK := false for pp in l1 for j in minColIndex m .. maxColIndex m - 1 while not OK repeat - if qelt(m, i, j) ^= 0 then + if qelt(m, i, j) ~= 0 then OK := true c := qelt(m, i, maxColIndex m) / qelt(m, i, j) - logderiv(c0 := c::UP::RF) ^= 0 => return "failed" + logderiv(c0 := c::UP::RF) ~= 0 => return "failed" ans := concat([c0, pp.logand2], ans) not OK => return "failed" ans @@ -553,13 +553,13 @@ TranscendentalIntegration(F, UP): Exports == Implementation where -- returns q in UP s.t. p = q', or "failed" primintfldpoly(p, extendedint, t') == (u := primintegratepoly(p, extendedint, t')) case UPUP => "failed" - u.a0 ^= 0 => "failed" + u.a0 ~= 0 => "failed" u.answer -- returns q in GP st p = q', or "failed" expintfldpoly(p, FRDE) == (u := expintegratepoly(p, FRDE)) case GPGP => "failed" - u.a0 ^= 0 => "failed" + u.a0 ~= 0 => "failed" u.answer -- returns (v in RF, c1...cn in RF, a in F) s.t. ci' = 0, @@ -649,7 +649,7 @@ TranscendentalIntegration(F, UP): Exports == Implementation where r := monomialIntPoly(rec.polypart, derivation) t := monomial(1, 1)$UP c := coefficient(r.polypart, 1) / leadingCoefficient(derivation t) - derivation(c::UP) ^= 0 => + derivation(c::UP) ~= 0 => [i1 + mkAnswer(r.answer::RF, empty(), [[r.polypart::RF + rec.specpart, dummy]$NE]), 0] logs:List(LOG) := @@ -721,10 +721,10 @@ TranscendentalIntegration(F, UP): Exports == Implementation where degree numer f >= degree denom f => error "Not a proper fraction" r := HermiteIntegrate(f, derivation) zero? g => - r.logpart ^= 0 => "failed" + r.logpart ~= 0 => "failed" [r.answer, 0] degree numer g >= degree denom g => error "Not a proper fraction" - differentiate(c := r.logpart / g, derivation) ^= 0 => "failed" + differentiate(c := r.logpart / g, derivation) ~= 0 => "failed" [r.answer, c] @ diff --git a/src/algebra/irexpand.spad.pamphlet b/src/algebra/irexpand.spad.pamphlet index 2a39f76b..e725ca76 100644 --- a/src/algebra/irexpand.spad.pamphlet +++ b/src/algebra/irexpand.spad.pamphlet @@ -215,7 +215,7 @@ IntegrationResultToFunction(R, F): Exports == Implementation where rec := froot(y, 2)$PolynomialRoots(IndexedExponents K, K, R, P, F) -- one?(rec.exponent) => [[rec.coef * rec.radicand, 1], 1] ((rec.exponent) = 1) => [[rec.coef * rec.radicand, 1], 1] - rec.exponent ^=2 => error "Should not happen" + rec.exponent ~=2 => error "Should not happen" [[rec.coef, rec.radicand], ((s := sign(rec.radicand)) case "failed" => 0; s::Z)] diff --git a/src/algebra/kl.spad.pamphlet b/src/algebra/kl.spad.pamphlet index 0ebb9578..26a8b374 100644 --- a/src/algebra/kl.spad.pamphlet +++ b/src/algebra/kl.spad.pamphlet @@ -233,7 +233,7 @@ Kernel(S:OrderedSet): Exports == Implementation where k1.posit < k2.posit kernel(fn, x, n) == - ((u := arity fn) case N) and (#x ^= u::N) + ((u := arity fn) case N) and (#x ~= u::N) => error "Wrong number of arguments" enterInCache([fn, x, n, 0]$Rep, triage) @@ -249,13 +249,13 @@ Kernel(S:OrderedSet): Exports == Implementation where (u::(List OutputForm -> OutputForm)) l triage(k1, k2) == - k1.nest ^= k2.nest => B2Z(k1.nest < k2.nest) - k1.op ^= k2.op => B2Z(k1.op < k2.op) - (n1 := #(argument k1)) ^= (n2 := #(argument k2)) => B2Z(n1 < n2) + k1.nest ~= k2.nest => B2Z(k1.nest < k2.nest) + k1.op ~= k2.op => B2Z(k1.op < k2.op) + (n1 := #(argument k1)) ~= (n2 := #(argument k2)) => B2Z(n1 < n2) ((func := property(operator k1, SPECIALEQUAL)) case None) and (((func::None) pretend ((%, %) -> Boolean)) (k1, k2)) => 0 for x1 in argument(k1) for x2 in argument(k2) repeat - x1 ^= x2 => return B2Z(x1 < x2) + x1 ~= x2 => return B2Z(x1 < x2) 0 if S has ConvertibleTo InputForm then diff --git a/src/algebra/laplace.spad.pamphlet b/src/algebra/laplace.spad.pamphlet index 6f81b2ee..b3a6767c 100644 --- a/src/algebra/laplace.spad.pamphlet +++ b/src/algebra/laplace.spad.pamphlet @@ -134,7 +134,7 @@ LaplaceTransform(R, F): Exports == Implementation where [c, c1, c0] if (v := isPower f) case Record(val:F, exponent:Integer) then w := v::Record(val:F, exponent:Integer) - (w.exponent ^= 1) and + (w.exponent ~= 1) and ((r := aexp(w.val, t)) case Record(coef:F,coef1:F,coef0:F)) => rec := r::Record(coef:F, coef1:F, coef0:F) return [rec.coef ** w.exponent, w.exponent * rec.coef1, @@ -178,7 +178,7 @@ LaplaceTransform(R, F): Exports == Implementation where oplap(f, tt, ss) (u := mkPlus f) case List(F) => +/[locallaplace(g, t, tt, s, ss) for g in u::List(F)] - (rec := splitConstant(f, t)).const ^= 1 => + (rec := splitConstant(f, t)).const ~= 1 => rec.const * locallaplace(rec.nconst, t, tt, s, ss) (v := atn(f, t)) case Record(coef:F, deg:PI) => vv := v::Record(coef:F, deg:PI) diff --git a/src/algebra/laurent.spad.pamphlet b/src/algebra/laurent.spad.pamphlet index ab0417c1..1a162ede 100644 --- a/src/algebra/laurent.spad.pamphlet +++ b/src/algebra/laurent.spad.pamphlet @@ -506,13 +506,13 @@ UnivariateLaurentSeriesConstructor(Coef,UTS):_ empty? uu => (0$Coef) :: OUT n : NNI ; count : NNI := _$streamCount$Lisp for n in 0..count while not empty? uu repeat - if frst(uu) ^= 0 then + if frst(uu) ~= 0 then l := concat(termOutput((n :: I) + m,frst(uu),xxx),l) uu := rst uu if showAll?() then for n in (count + 1).. while explicitEntries? uu and _ not eq?(uu,rst uu) repeat - if frst(uu) ^= 0 then + if frst(uu) ~= 0 then l := concat(termOutput((n::I) + m,frst(uu),xxx),l) uu := rst uu l := diff --git a/src/algebra/leadcdet.spad.pamphlet b/src/algebra/leadcdet.spad.pamphlet index 73635266..21a1048f 100644 --- a/src/algebra/leadcdet.spad.pamphlet +++ b/src/algebra/leadcdet.spad.pamphlet @@ -62,7 +62,7 @@ LeadingCoefDetermination(OV,E,Z,P) : C == T q := unitNormal(lval.i).canonical for j in 0..(i-1)::NNI repeat y := distlist.((i-j)::NNI) - while y^=1 repeat + while y~=1 repeat y := gcd(y,q) q := q quo y if q=1 then return false @@ -87,7 +87,7 @@ LeadingCoefDetermination(OV,E,Z,P) : C == T d := vl.i quo d unilist.i := d*unilist.i contm := contm quo d - if contm ^=1 then for i in 1..nf repeat pl.i := contm*pl.i + if contm ~=1 then for i in 1..nf repeat pl.i := contm*pl.i [pl,contm,unilist]$LeadFact distFact(contm:Z,unilist:List(BP),plead:FinalFact, @@ -109,7 +109,7 @@ LeadingCoefDetermination(OV,E,Z,P) : C == T for k in 1..(# lpol) repeat lexp.k=0 => "next factor" h:= checkpow(vl.k,c) - if h ^=0 then + if h ~=0 then if h>lexp.k then return "failed" lexp.k:=lexp.k-h aux.i := aux.i*(lpol.k ** h) @@ -117,7 +117,7 @@ LeadingCoefDetermination(OV,E,Z,P) : C == T vlp.i:= vlp.i*d c:= c quo d if contm=1 then vlp.i:=c - for k in 1..(# lpol) repeat if lexp.k ^= 0 then return "failed" + for k in 1..(# lpol) repeat if lexp.k ~= 0 then return "failed" contm =1 => [[vlp.i*aux.i for i in 1..nf],1,unilist]$LeadFact distribute(contm,unilist,aux,vlp,lvar,lval) diff --git a/src/algebra/limitps.spad.pamphlet b/src/algebra/limitps.spad.pamphlet index a388417e..9e8b3b53 100644 --- a/src/algebra/limitps.spad.pamphlet +++ b/src/algebra/limitps.spad.pamphlet @@ -151,7 +151,7 @@ PowerSeriesLimitPackage(R,FE): Exports == Implementation where for k in xkers repeat (fval := limitPlus(k::FE,x)) case "failed" => return specialLimitNormalize(fcn,x) - whatInfinity(val := fval::OFE) ^= 0 => + whatInfinity(val := fval::OFE) ~= 0 => return specialLimitNormalize(fcn,x) (valu := retractIfCan(val)@Union(FE,"failed")) case "failed" => return specialLimitNormalize(fcn,x) @@ -163,11 +163,11 @@ PowerSeriesLimitPackage(R,FE): Exports == Implementation where specialLimitNormalize(fcn,x) == -- tries to normalize result first nfcn := normalize(fcn) - fcn ^= nfcn => limitPlus(nfcn,x) + fcn ~= nfcn => limitPlus(nfcn,x) xkers := [k for k in tower fcn | member?(x,variables(k::FE))] - # xkers ^= 2 => "failed" + # xkers ~= 2 => "failed" expKers := [k for k in xkers | is?(k, "exp" :: Symbol)] - # expKers ^= 1 => "failed" + # expKers ~= 1 => "failed" -- fcn is a rational function of x and exp(g(x)) for some rational function g expKer := first expKers (fval := limitPlus(expKer::FE,x)) case "failed" => "failed" @@ -188,7 +188,7 @@ PowerSeriesLimitPackage(R,FE): Exports == Implementation where specialLimit1(fcn,x) == -- find the first interesting kernel in tower(fcn) xkers := [k for k in kernels fcn | member?(x,variables(k::FE))] - #xkers ^= 1 => "failed" + #xkers ~= 1 => "failed" ker := first xkers vv := new()$SY; eq : EQ FE := equation(ker :: FE,vv :: FE) cc := eval(fcn,eq) @@ -631,7 +631,7 @@ ElementaryFunctionSign(R,F): Exports == Implementation where n * plusInfinity()$ORF ofesign a == - (n := whatInfinity a) ^= 0 => convert(n)@Z + (n := whatInfinity a) ~= 0 => convert(n)@Z sign(retract(a)@F) insign(f, x, a, m) == @@ -641,7 +641,7 @@ ElementaryFunctionSign(R,F): Exports == Implementation where eq : Equation OFE := equation(x :: F :: OFE,a) (u := limit(f,eq)) case "failed" => "failed" u case OFE => - (n := whatInfinity(u::OFE)) ^= 0 => convert(n)@Z + (n := whatInfinity(u::OFE)) ~= 0 => convert(n)@Z (v := retract(u::OFE)@F) = 0 => (s := insign(differentiate(f, x), x, a, m + 1)) case "failed" => "failed" @@ -663,7 +663,7 @@ ElementaryFunctionSign(R,F): Exports == Implementation where eq : Equation F := equation(x :: F,a) (u := limit(f,eq,st)) case "failed" => "failed" u case OFE => - (n := whatInfinity(u::OFE)) ^= 0 => convert(n)@Z + (n := whatInfinity(u::OFE)) ~= 0 => convert(n)@Z (v := retract(u::OFE)@F) = 0 => (s := psign(differentiate(f,x),x,a,st,m + 1)) case "failed"=> "failed" diff --git a/src/algebra/lingrob.spad.pamphlet b/src/algebra/lingrob.spad.pamphlet index 29e2b34f..290c39e6 100644 --- a/src/algebra/lingrob.spad.pamphlet +++ b/src/algebra/lingrob.spad.pamphlet @@ -115,7 +115,7 @@ LinGroebnerPackage(lv,F) : C == T ofirstmon:DPoly:=1$DPoly orecfmon:Record(poly:HDPoly, mult:F) := [1,1] i:NNI:=2 - while (firstmon:=choosemon(firstmon,ltresult))^=1 repeat + while (firstmon:=choosemon(firstmon,ltresult))~=1 repeat if (v:=firstmon exquo ofirstmon) case "failed" then recfmon:=rRedPol(transform firstmon,B) else @@ -213,7 +213,7 @@ LinGroebnerPackage(lv,F) : C == T part:List HDPoly :=[] for f in lr repeat g:=x::HDPoly * f - if redPo(g,mB).poly^=0 then part:=concat(g,part) + if redPo(g,mB).poly~=0 then part:=concat(g,part) concat(part,intcompBasis(x,part,mB)) ----- coordinate of f with respect to the basis B ----- @@ -221,7 +221,7 @@ LinGroebnerPackage(lv,F) : C == T coord(f:HDPoly,B:List HDPoly) : VF == ndim := #B vv:VF:=new(ndim,0$F)$VF - while f^=0 repeat + while f~=0 repeat rf := reductum f lf := f-rf lcf := leadingCoefficient f @@ -241,7 +241,7 @@ LinGroebnerPackage(lv,F) : C == T for x in reverse lvar repeat xx:=x ::DPoly mf:=xx*mf - if redPo(mf,nB).poly ^= 0 then return mf + if redPo(mf,nB).poly ~= 0 then return mf dx := degree(mf,x) mf := (mf exquo (xx ** dx))::DPoly mf @@ -272,7 +272,7 @@ LinGroebnerPackage(lv,F) : C == T ofirstmon:DPoly:=1$DPoly orecfmon:Record(poly:HDPoly, mult:F) := [1,1] lx:= lvar.last - while (firstmon:=choosemon(firstmon,ltresult))^=1 repeat + while (firstmon:=choosemon(firstmon,ltresult))~=1 repeat if (v:=firstmon exquo ofirstmon) case "failed" then recfmon:=rRedPol(transform(eval(firstmon,lx,nval)),B) else diff --git a/src/algebra/list.spad.pamphlet b/src/algebra/list.spad.pamphlet index 93c7b627..e702f8f1 100644 --- a/src/algebra/list.spad.pamphlet +++ b/src/algebra/list.spad.pamphlet @@ -118,7 +118,7 @@ IndexedList(S:Type, mn:Integer): Exports == Implementation where x = y == Qeq(x,y) => true while not Qnull x and not Qnull y repeat - Qfirst x ^=$S Qfirst y => return false + Qfirst x ~=$S Qfirst y => return false x := Qrest x y := Qrest y Qnull x and Qnull y @@ -1533,7 +1533,7 @@ AssociationList(Key:SetCategory, Entry:SetCategory): first(l).entry prev := l curr := rest l - while not empty? curr and first(curr).key ^= k repeat + while not empty? curr and first(curr).key ~= k repeat prev := curr curr := rest curr empty? curr => "failed" diff --git a/src/algebra/listgcd.spad.pamphlet b/src/algebra/listgcd.spad.pamphlet index f626adbd..2f4ccde4 100644 --- a/src/algebra/listgcd.spad.pamphlet +++ b/src/algebra/listgcd.spad.pamphlet @@ -78,7 +78,7 @@ HeuGcd (BP):C == T --compute the height of a polynomial height(f:BP):PI == k:PI:=1 - while f^=0 repeat + while f~=0 repeat k:=max(k,abs(leadingCoefficient(f)@Z)::PI) f:=reductum f k @@ -88,7 +88,7 @@ HeuGcd (BP):C == T genpoly(dval:Z,value:PI):BP == d:=0$BP val:=dval - for i in 0.. while (val^=0) repeat + for i in 0.. while (val~=0) repeat val1:=negShiftz(val rem value,value) d:= d+monomial(val1,i) val:=(val-val1) quo value diff --git a/src/algebra/lmdict.spad.pamphlet b/src/algebra/lmdict.spad.pamphlet index cba196e2..f7b820f5 100644 --- a/src/algebra/lmdict.spad.pamphlet +++ b/src/algebra/lmdict.spad.pamphlet @@ -140,7 +140,7 @@ ListMultiDictionary(S:SetCategory): MultiDictionary(S) with a := copy s while not empty? a repeat x := inspect a - count(x, s) ^= count(x, t) => return false + count(x, s) ~= count(x, t) => return false remove_!(x, a) true diff --git a/src/algebra/lodo.spad.pamphlet b/src/algebra/lodo.spad.pamphlet index c25901eb..dbf0cdbc 100644 --- a/src/algebra/lodo.spad.pamphlet +++ b/src/algebra/lodo.spad.pamphlet @@ -59,7 +59,7 @@ LinearOrdinaryDifferentialOperatorCategory(A:Ring): Category == adjoint a == ans:% := 0 - while a ^= 0 repeat + while a ~= 0 repeat ans := ans + m1monom(degree a) * leadingCoefficient(a)::% a := reductum a ans @@ -118,7 +118,7 @@ LinearOrdinaryDifferentialOperatorsOps(A, L): Exports == Implementation where killer : (P, N, List V, List P, A -> A) -> L vec2LODO : Vector A -> L - nonTrivial? v == any?(#1 ^= 0, v)$Vector(A) + nonTrivial? v == any?(#1 ~= 0, v)$Vector(A) vec2LODO v == +/[monomial(v.i, (i-1)::N) for i in 1..#v] symmetricPower(l, m, diff) == @@ -164,7 +164,7 @@ LinearOrdinaryDifferentialOperatorsOps(A, L): Exports == Implementation where applyLODO(l, v) == p:P := 0 - while l ^= 0 repeat + while l ~= 0 repeat p := p + monomial(leadingCoefficient(l)::P, differentiate(v, degree l), 1) l := reductum l diff --git a/src/algebra/lodof.spad.pamphlet b/src/algebra/lodof.spad.pamphlet index fd72c15a..3a35261a 100644 --- a/src/algebra/lodof.spad.pamphlet +++ b/src/algebra/lodof.spad.pamphlet @@ -149,7 +149,7 @@ SetOfMIntegersInOneToN(m, n): Exports == Implementation where while found < k repeat if b.i then found := found + 1 if found < k then i := i + 1 - b.p and i ^= p => "failed" + b.p and i ~= p => "failed" newb := copy b newb.p := true newb.i := false @@ -309,7 +309,7 @@ AssociatedEquations(R, L):Exports == Implementation where u := incrementKthElement(wi, k::PI)$S if u case S then eq(lookup(u::S)) := 1 if member?(n, wi) then - for j in 1..n | a.j ^= 0 repeat + for j in 1..n | a.j ~= 0 repeat u := replaceKthElement(wi, m, j::PI) if u case S then eq(lookup(u::S)) := (odd? delta(wi, m, j::PI) => -a.j; a.j) @@ -334,8 +334,8 @@ AssociatedEquations(R, L):Exports == Implementation where computeIt: (L, PI, N) -> REC makeeq(v, m, i, n) == - [v.i, makeop row(m, i) - 1, [v.j for j in 1..n | j ^= i], - [makeop row(m, j) for j in 1..n | j ^= i]] + [v.i, makeop row(m, i) - 1, [v.j for j in 1..n | j ~= i], + [makeop row(m, j) for j in 1..n | j ~= i]] associatedEquations(op, m) == (u := firstUncouplingMatrix(op, m)) case "failed" => computeIt(op,m,1) @@ -414,7 +414,7 @@ LinearOrdinaryDifferentialOperatorFactorizer(F, UP): Exports == Impl where first sol expsols(l, zeros, ezfactor, all?) == - sol := [differentiate(f)/f for f in ratDsolve(l, 0).basis | f ^= 0] + sol := [differentiate(f)/f for f in ratDsolve(l, 0).basis | f ~= 0] not(all? or empty? sol) => sol concat(sol, ricDsolve(l, zeros, ezfactor)) diff --git a/src/algebra/lodop.spad.pamphlet b/src/algebra/lodop.spad.pamphlet index f1e5eebb..680ed017 100644 --- a/src/algebra/lodop.spad.pamphlet +++ b/src/algebra/lodop.spad.pamphlet @@ -34,7 +34,7 @@ ++ ++ Note that multiplication is not necessarily commutative. ++ In fact, if \spad{a} is in \spad{R}, it is quite normal -++ to have \spad{a*G \^= G*a}. +++ to have \spad{a*G \~= G*a}. MonogenicLinearOperator(R): Category == Defn where E ==> NonNegativeInteger @@ -46,7 +46,7 @@ MonogenicLinearOperator(R): Category == Defn where ++ \spad{l = sum(monomial(a(i),i), i = 0..n)}. minimumDegree: $ -> E ++ minimumDegree(l) is the smallest \spad{k} such that - ++ \spad{a(k) \^= 0} if + ++ \spad{a(k) \~= 0} if ++ \spad{l = sum(monomial(a(i),i), i = 0..n)}. leadingCoefficient: $ -> R ++ leadingCoefficient(l) is \spad{a(n)} if @@ -163,7 +163,7 @@ NonCommutativeOperatorDivision(P, F): PDcat == PDdef where q: P := 0 r: P := a iv:F := inv leadingCoefficient b - while degree r >= degree b and r ^= 0 repeat + while degree r >= degree b and r ~= 0 repeat h := monomial(iv*leadingCoefficient r, (degree r - degree b)::NonNegativeInteger)$P r := r - b*h @@ -189,7 +189,7 @@ NonCommutativeOperatorDivision(P, F): PDcat == PDdef where b0 := b u := monomial(1,0)$P v := 0 - while leadingCoefficient b ^= 0 repeat + while leadingCoefficient b ~= 0 repeat qr := leftDivide(a,b) (a, b) := (b, qr.remainder) (u, v) := (u*qr.quotient+v, u) diff --git a/src/algebra/manip.spad.pamphlet b/src/algebra/manip.spad.pamphlet index 2322ac7c..5cad4e61 100644 --- a/src/algebra/manip.spad.pamphlet +++ b/src/algebra/manip.spad.pamphlet @@ -368,8 +368,8 @@ AlgebraicManipulations(R, F): Exports == Implementation where inroot(op, x, n) == -- one? x => x (x = 1) => x --- (x ^= -1) and (one?(num := numer x) or (num = -1)) => - (x ^= -1) and (((num := numer x) = 1) or (num = -1)) => +-- (x ~= -1) and (one?(num := numer x) or (num = -1)) => + (x ~= -1) and (((num := numer x) = 1) or (num = -1)) => inv inroot(op, (num * denom x)::F, n) (u := isExpt(x, op)) case "failed" => kernel(op, [x, n::F]) pr := u::Record(var:K, exponent:Integer) @@ -752,7 +752,7 @@ TranscendentalManipulations(R, F): Exports == Implementation where supexp(p, f1, f2, bse) == ans:F := 0 - while p ^= 0 repeat + while p ~= 0 repeat g := htrigs(leadingCoefficient(p)::F) if ((d := degree(p)::Z - bse) >= 0) then ans := ans + g * f1 ** d @@ -781,7 +781,7 @@ TranscendentalManipulations(R, F): Exports == Implementation where exlog(numer(x := expand arg)) - exlog denom x num := numer arg den := denom arg - (b := (reductum num) / den) ^= 0 => + (b := (reductum num) / den) ~= 0 => a := (leadingMonomial num) / den is?(op, "exp"::Symbol) => exp(expand a) * expand(exp b) is?(op, "sin"::Symbol) => @@ -801,7 +801,7 @@ TranscendentalManipulations(R, F): Exports == Implementation where smpexp p == ans:F := 0 - while p ^= 0 repeat + while p ~= 0 repeat ans := ans + termexp leadingMonomial p p := reductum p ans diff --git a/src/algebra/matcat.spad.pamphlet b/src/algebra/matcat.spad.pamphlet index f7bc1ef8..90b62b28 100644 --- a/src/algebra/matcat.spad.pamphlet +++ b/src/algebra/matcat.spad.pamphlet @@ -225,24 +225,24 @@ MatrixCategory(R,Row,Col): Category == Definition where diagonal? x == not square? x => false for i in minr x .. maxr x repeat - for j in minc x .. maxc x | (j - minc x) ^= (i - minr x) repeat + for j in minc x .. maxc x | (j - minc x) ~= (i - minr x) repeat not zero? qelt(x, i, j) => return false true symmetric? x == - (nRows := nrows x) ^= ncols x => false + (nRows := nrows x) ~= ncols x => false mr := minRowIndex x; mc := minColIndex x for i in 0..(nRows - 1) repeat for j in (i + 1)..(nRows - 1) repeat - qelt(x,mr + i,mc + j) ^= qelt(x,mr + j,mc + i) => return false + qelt(x,mr + i,mc + j) ~= qelt(x,mr + j,mc + i) => return false true antisymmetric? x == - (nRows := nrows x) ^= ncols x => false + (nRows := nrows x) ~= ncols x => false mr := minRowIndex x; mc := minColIndex x for i in 0..(nRows - 1) repeat for j in i..(nRows - 1) repeat - qelt(x,mr + i,mc + j) ^= -qelt(x,mr + j,mc + i) => + qelt(x,mr + i,mc + j) ~= -qelt(x,mr + j,mc + i) => return false true @@ -256,7 +256,7 @@ MatrixCategory(R,Row,Col): Category == Definition where rows : NonNegativeInteger := 1; cols := # first l cols = 0 => error "matrices with zero columns are not supported" for ll in rest l repeat - cols ^= # ll => error "matrix: rows of different lengths" + cols ~= # ll => error "matrix: rows of different lengths" rows := rows + 1 ans := new(rows,cols,0) for i in minr(ans)..maxr(ans) for ll in l repeat @@ -323,7 +323,7 @@ MatrixCategory(R,Row,Col): Category == Definition where ans horizConcat(x,y) == - (rows := nrows x) ^= nrows y => + (rows := nrows x) ~= nrows y => error "HConcat: matrices must have same number of rows" ans := new(rows,(cols := ncols x) + ncols y,0) for i in minr(x)..maxr(x) repeat @@ -335,7 +335,7 @@ MatrixCategory(R,Row,Col): Category == Definition where ans vertConcat(x,y) == - (cols := ncols x) ^= ncols y => + (cols := ncols x) ~= ncols y => error "HConcat: matrices must have same number of columns" ans := new((rows := nrows x) + nrows y,cols,0) for i in minr(x)..maxr(x) repeat @@ -397,7 +397,7 @@ MatrixCategory(R,Row,Col): Category == Definition where for ej in colList repeat (ej < minc(x)) or (ej > maxc(x)) => error "setelt: index out of range" - ((# rowList) ^= (nrows y)) or ((# colList) ^= (ncols y)) => + ((# rowList) ~= (nrows y)) or ((# colList) ~= (ncols y)) => error "setelt: matrix has bad dimensions" for ei in rowList for i in minr(y)..maxr(y) repeat for ej in colList for j in minc(y)..maxc(y) repeat @@ -434,7 +434,7 @@ MatrixCategory(R,Row,Col): Category == Definition where --% Arithmetic x + y == - ((r := nrows x) ^= nrows y) or ((c := ncols x) ^= ncols y) => + ((r := nrows x) ~= nrows y) or ((c := ncols x) ~= ncols y) => error "can't add matrices of different dimensions" ans := new(r,c,0) for i in minr(x)..maxr(x) repeat @@ -443,7 +443,7 @@ MatrixCategory(R,Row,Col): Category == Definition where ans x - y == - ((r := nrows x) ^= nrows y) or ((c := ncols x) ^= ncols y) => + ((r := nrows x) ~= nrows y) or ((c := ncols x) ~= ncols y) => error "can't subtract matrices of different dimensions" ans := new(r,c,0) for i in minr(x)..maxr(x) repeat @@ -458,7 +458,7 @@ MatrixCategory(R,Row,Col): Category == Definition where m:Integer * x:% == map(m * #1,x) x:% * y:% == - (ncols x ^= nrows y) => + (ncols x ~= nrows y) => error "can't multiply matrices of incompatible dimensions" ans := new(nrows x,ncols y,0) for i in minr(x)..maxr(x) repeat @@ -492,8 +492,8 @@ MatrixCategory(R,Row,Col): Category == Definition where if Col has shallowlyMutable then x:% * v:Col == - ncols(x) ^= #v => - error "can't multiply matrix A and vector v if #cols A ^= #v" + ncols(x) ~= #v => + error "can't multiply matrix A and vector v if #cols A ~= #v" w : Col := new(nrows x,0) for i in minr(x)..maxr(x) for k in mini(w)..maxi(w) repeat w.k := @@ -506,8 +506,8 @@ MatrixCategory(R,Row,Col): Category == Definition where if Row has shallowlyMutable then v:Row * x:% == - nrows(x) ^= #v => - error "can't multiply vector v and matrix A if #rows A ^= #v" + nrows(x) ~= #v => + error "can't multiply vector v and matrix A if #rows A ~= #v" w : Row := new(ncols x,0) for j in minc(x)..maxc(x) for k in mini(w)..maxi(w) repeat w.k := @@ -682,24 +682,24 @@ RectangularMatrixCategory(m,n,R,Row,Col): Category == Definition where not square? x => false for i in minRowIndex x .. maxRowIndex x repeat for j in minColIndex x .. maxColIndex x - | (j - minColIndex x) ^= (i - minRowIndex x) repeat + | (j - minColIndex x) ~= (i - minRowIndex x) repeat not zero? qelt(x, i, j) => return false true symmetric? x == - m ^= n => false + m ~= n => false mr := minRowIndex x; mc := minColIndex x for i in 0..(n - 1) repeat for j in (i + 1)..(n - 1) repeat - qelt(x,mr + i,mc + j) ^= qelt(x,mr + j,mc + i) => return false + qelt(x,mr + i,mc + j) ~= qelt(x,mr + j,mc + i) => return false true antisymmetric? x == - m ^= n => false + m ~= n => false mr := minRowIndex x; mc := minColIndex x for i in 0..(n - 1) repeat for j in i..(n - 1) repeat - qelt(x,mr + i,mc + j) ^= -qelt(x,mr + j,mc + i) => + qelt(x,mr + i,mc + j) ~= -qelt(x,mr + j,mc + i) => return false true diff --git a/src/algebra/matfuns.spad.pamphlet b/src/algebra/matfuns.spad.pamphlet index 59d08748..776895ee 100644 --- a/src/algebra/matfuns.spad.pamphlet +++ b/src/algebra/matfuns.spad.pamphlet @@ -66,7 +66,7 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ -- determines if the ith row of x consists only of zeroes -- internal function: no check on index i for j in minColIndex(x)..maxColIndex(x) repeat - qelt(x,i,j) ^= 0 => return false + qelt(x,i,j) ~= 0 => return false true colAllZeroes?: (M,I) -> Boolean @@ -74,7 +74,7 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ -- determines if the ith column of x consists only of zeroes -- internal function: no check on index j for i in minRowIndex(x)..maxRowIndex(x) repeat - qelt(x,i,j) ^= 0 => return false + qelt(x,i,j) ~= 0 => return false true rowEchelon y == @@ -87,19 +87,19 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ for j in minC..maxC repeat i > maxR => return x n := minR - 1 - -- n = smallest k such that k >= i and x(k,j) ^= 0 + -- n = smallest k such that k >= i and x(k,j) ~= 0 for k in i..maxR repeat - if qelt(x,k,j) ^= 0 then leave (n := k) + if qelt(x,k,j) ~= 0 then leave (n := k) n = minR - 1 => "no non-zeroes" -- put nth row in ith position - if i ^= n then swapRows_!(x,i,n) + if i ~= n then swapRows_!(x,i,n) -- divide ith row by its first non-zero entry b := inv qelt(x,i,j) qsetelt_!(x,i,j,1) for k in (j+1)..maxC repeat qsetelt_!(x,i,k,b * qelt(x,i,k)) -- perform row operations so that jth column has only one 1 for k in minR..maxR repeat - if k ^= i and qelt(x,k,j) ^= 0 then + if k ~= i and qelt(x,k,j) ~= 0 then for k1 in (j+1)..maxC repeat qsetelt_!(x,k,k1,qelt(x,k,k1) - qelt(x,k,j) * qelt(x,i,k1)) qsetelt_!(x,k,j,0) @@ -160,7 +160,7 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ qsetelt_!(w,l,1) basis := cons(w,basis) for k in minC..(j-1) for ll in minR..(l-1) repeat - if qelt(v,k) ^= minR - 1 then + if qelt(v,k) ~= minR - 1 then qsetelt_!(w,ll,-qelt(x,qelt(v,k),j)) qsetelt_!(w,l,1) basis := cons(w,basis) @@ -168,7 +168,7 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ basis determinant y == - (ndim := nrows y) ^= (ncols y) => + (ndim := nrows y) ~= (ncols y) => error "determinant: matrix must be square" -- Gaussian Elimination ndim = 1 => qelt(y,minRowIndex y,minColIndex y) @@ -180,13 +180,13 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ if qelt(x,i,j) = 0 then rown := minR - 1 for k in (i+1)..maxR repeat - qelt(x,k,j) ^= 0 => leave (rown := k) + qelt(x,k,j) ~= 0 => leave (rown := k) if rown = minR - 1 then return 0 swapRows_!(x,i,rown); ans := -ans ans := qelt(x,i,j) * ans; b := -inv qelt(x,i,j) for l in (j+1)..maxC repeat qsetelt_!(x,i,l,b * qelt(x,i,l)) for k in (i+1)..maxR repeat - if (b := qelt(x,k,j)) ^= 0 then + if (b := qelt(x,k,j)) ~= 0 then for l in (j+1)..maxC repeat qsetelt_!(x,k,l,qelt(x,k,l) + b * qelt(x,i,l)) qelt(x,maxR,maxC) * ans @@ -208,7 +208,7 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ map(elt(#1,0),yy)$MATCAT22 inverse x == - (ndim := nrows x) ^= (ncols x) => + (ndim := nrows x) ~= (ncols x) => error "inverse: matrix must be square" ndim = 2 => ans2 : M := zero(ndim, ndim) @@ -457,10 +457,10 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where ++ of first kind elRow2! : (M,R,I,I) -> M ++ elRow2!(m,a,i,j) adds to row i a*row(m,j) : elementary operation of - ++ second kind. (i ^=j) + ++ second kind. (i ~=j) elColumn2! : (M,R,I,I) -> M ++ elColumn2!(m,a,i,j) adds to column i a*column(m,j) : elementary - ++ operation of second kind. (i ^=j) + ++ operation of second kind. (i ~=j) if R has IntegralDomain then rank: M -> NonNegativeInteger @@ -502,7 +502,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where -- determines if the ith row of x consists only of zeroes -- internal function: no check on index i for j in minColIndex(x)..maxColIndex(x) repeat - qelt(x,i,j) ^= 0 => return false + qelt(x,i,j) ~= 0 => return false true colAllZeroes?: (M,I) -> Boolean @@ -510,7 +510,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where -- determines if the ith column of x consists only of zeroes -- internal function: no check on index j for i in minRowIndex(x)..maxRowIndex(x) repeat - qelt(x,i,j) ^= 0 => return false + qelt(x,i,j) ~= 0 => return false true minorDet:(M,I,List I,I,PrimitiveArray(Union(R,"uncomputed")))-> R @@ -521,7 +521,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where j := first l; l := rest l; pos := true minR := minRowIndex x; minC := minColIndex x; repeat - if qelt(x,j + minR,i + minC) ^= 0 then + if qelt(x,j + minR,i + minC) ~= 0 then ans := md := minorDet(x,m - 2**(j :: NonNegativeInteger),_ concat_!(reverse rl,l),i + 1,v) *_ @@ -534,7 +534,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where pos := not pos; rl := cons(j,rl); j := first l; l := rest l minordet x == - (ndim := nrows x) ^= (ncols x) => + (ndim := nrows x) ~= (ncols x) => error "determinant: matrix must be square" -- minor expansion with (s---loads of) memory n1 : I := ndim - 1 @@ -553,14 +553,14 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where m -- elementary operation of second kind: add to row i-- - -- a*row j (i^=j) -- + -- a*row j (i~=j) -- elRow2!(m : M,a:R,i:I,j:I) : M == vec:= map(a*#1,row(m,j)) vec:=map("+",row(m,i),vec) setRow!(m,i,vec) m -- elementary operation of second kind: add to column i -- - -- a*column j (i^=j) -- + -- a*column j (i~=j) -- elColumn2!(m : M,a:R,i:I,j:I) : M == vec:= map(a*#1,column(m,j)) vec:=map("+",column(m,i),vec) @@ -579,7 +579,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where if qelt(x,i,j) = 0 then -- candidate for pivot = 0 rown := minR - 1 for k in (i+1)..maxR repeat - if qelt(x,k,j) ^= 0 then + if qelt(x,k,j) ~= 0 then rown := k -- found a pivot leave if rown > minR - 1 then @@ -623,14 +623,14 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where subMatrix(x,minR,maxR,maxC1,exCol) invertIfCan(y) == - (nr:=nrows y) ^= (ncols y) => + (nr:=nrows y) ~= (ncols y) => error "invertIfCan: matrix must be square" adjRec := adjoint y (den:=recip(adjRec.detMat)) case "failed" => "failed" den::R * adjRec.adjMat adjoint(y) == - (nr:=nrows y) ^= (ncols y) => error "adjoint: matrix must be square" + (nr:=nrows y) ~= (ncols y) => error "adjoint: matrix must be square" maxR := maxRowIndex y maxC := maxColIndex y x := horizConcat(copy y,scalarMatrix(nr,1$R)) @@ -668,7 +668,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where nullSpace m == nullSpace(m)$IMATQF determinant y == - (nrows y) ^= (ncols y) => error "determinant: matrix must be square" + (nrows y) ~= (ncols y) => error "determinant: matrix must be square" fm:=fractionFreeGauss!(copy y) fm(maxRowIndex fm,maxColIndex fm) @@ -736,7 +736,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where un := unitNormal qelt(x,i,j) qsetelt_!(x,i,j,un.canonical) - if un.associate ^= 1 then for jj in (j+1)..maxC repeat + if un.associate ~= 1 then for jj in (j+1)..maxC repeat qsetelt_!(x,i,jj,un.associate * qelt(x,i,jj)) xij := qelt(x,i,j) diff --git a/src/algebra/mathml.spad.pamphlet b/src/algebra/mathml.spad.pamphlet index 747dbfca..cde994f9 100644 --- a/src/algebra/mathml.spad.pamphlet +++ b/src/algebra/mathml.spad.pamphlet @@ -704,7 +704,7 @@ returning Void. I really only need the one coerce function. -- Finds the closing ">" for either a start or end tag of a mathML -- element, so the return value is the position of ">" in mathML. pI:I := pos - while (mathML.pI ^= char ">") repeat + while (mathML.pI ~= char ">") repeat pI := pI+1 u:US := segment(pos,pI)$US --sayTeX$Lisp "tagEnd: "mathML.u @@ -899,8 +899,8 @@ have to be switched by swapping names. -- {{{SUB}{y}{{CONCAT}{{CONCAT}{{CONCAT}{{CONCAT}{,}{1}}{{CONCAT}{,}{1}}}{{CONCAT}{,}{2}}}{{CONCAT}{,}{1}}}}{x}{z}} atomE : L E := atomize(expr) op : S := stringify first atomE - op ^= "SUB" => "<mtext>Mistake in formatSub: no SUB</mtext>" - stringify first rest rest atomE ^= "CONCAT" => "<mtext>Mistake in formatSub: no CONCAT</mtext>" + op ~= "SUB" => "<mtext>Mistake in formatSub: no SUB</mtext>" + stringify first rest rest atomE ~= "CONCAT" => "<mtext>Mistake in formatSub: no CONCAT</mtext>" -- expecting form for atomE like --[{SUB}{func}{CONCAT}...{CONCAT}{,}{n}{CONCAT}{,}{n}...{CONCAT}{,}{n}], --counting the first CONCATs before the comma gives the number of @@ -973,8 +973,8 @@ have to be switched by swapping names. -- args is {{x}{z}} atomE : L E := atomize(expr) op : S := stringify first atomE - op ^= "SUB" => "<mtext>Mistake in formatSub: no SUB</mtext>" - stringify first rest rest atomE ^= "CONCAT" => "<mtext>Mistake in formatSub: no CONCAT</mtext>" + op ~= "SUB" => "<mtext>Mistake in formatSub: no SUB</mtext>" + stringify first rest rest atomE ~= "CONCAT" => "<mtext>Mistake in formatSub: no CONCAT</mtext>" -- expecting form for atomE like --[{SUB}{func}{CONCAT}...{CONCAT}{,}{n}{CONCAT}{,}{n}...{CONCAT}{,}{n}], --counting the first CONCATs before the comma gives the number of @@ -1024,8 +1024,8 @@ have to be switched by swapping names. -- first have to divine the semantics, add cases as needed atomE : L E := atomize(expr) op : S := stringify first atomE - op ^= "SUPERSUB" => "<mtext>Mistake in formatSuperSub: no SUPERSUB1</mtext>" - #args ^= 1 => "<mtext>Mistake in SuperSub1: #args <> 1</mtext>" + op ~= "SUPERSUB" => "<mtext>Mistake in formatSuperSub: no SUPERSUB1</mtext>" + #args ~= 1 => "<mtext>Mistake in SuperSub1: #args <> 1</mtext>" var : E := first args -- should be looking at something like {{SUPERSUB}{var}{ }{,,...,}} for -- example here's the second derivative of y w.r.t. x @@ -1053,8 +1053,8 @@ have to be switched by swapping names. -- first have to divine the semantics, add cases as needed atomE : L E := atomize(expr) op : S := stringify first atomE - op ^= "SUPERSUB" => "<mtext>Mistake in formatSuperSub: no SUPERSUB</mtext>" - #args ^= 1 => "<mtext>Mistake in SuperSub: #args <> 1</mtext>" + op ~= "SUPERSUB" => "<mtext>Mistake in formatSuperSub: no SUPERSUB</mtext>" + #args ~= 1 => "<mtext>Mistake in SuperSub: #args <> 1</mtext>" var : E := first args -- should be looking at something like {{SUPERSUB}{var}{ }{,,...,}} for -- example here's the second derivative of y w.r.t. x @@ -1079,7 +1079,7 @@ have to be switched by swapping names. op = "INTSIGN" => formatIntSign(args,minPrec) opPrec := plexPrecs.p n : I := #args - (n ^= 2) and (n ^= 3) => error "wrong number of arguments for plex" + (n ~= 2) and (n ~= 3) => error "wrong number of arguments for plex" s : S := op = "SIGMA" => checkarg := true @@ -1104,14 +1104,14 @@ have to be switched by swapping names. "????" hold := formatMml(first args,minPrec) args := rest args - if op ^= "INDEFINTEGRAL" then - if hold ^= "" then + if op ~= "INDEFINTEGRAL" then + if hold ~= "" then s := concat ["<munderover>",s,group hold] else s := concat ["<munderover>",s,group " "] if not null rest args then hold := formatMml(first args,minPrec) - if hold ^= "" then + if hold ~= "" then s := concat [s,group hold,"</munderover>"] else s := concat [s,group " ","</munderover>"] diff --git a/src/algebra/matrix.spad.pamphlet b/src/algebra/matrix.spad.pamphlet index 3704e00e..a5c173dc 100644 --- a/src/algebra/matrix.spad.pamphlet +++ b/src/algebra/matrix.spad.pamphlet @@ -205,7 +205,7 @@ Matrix(R): Exports == Implementation where -- -- error check: this is a top level function -- cols := # v.mini(v) -- for k in (mini(v) + 1)..maxi(v) repeat --- cols ^= # v.k => error "matrix: rows of different lengths" +-- cols ~= # v.k => error "matrix: rows of different lengths" -- ans := new(rows,cols,0) -- for i in minr(ans)..maxr(ans) for k in mini(v)..maxi(v) repeat -- vv := v.k @@ -303,9 +303,9 @@ RectangularMatrix(m,n,R): Exports == Implementation where matrix(l: List List R) == -- error check: this is a top level function - #l ^= m => error "matrix: wrong number of rows" + #l ~= m => error "matrix: wrong number of rows" for ll in l repeat - #ll ^= n => error "matrix: wrong number of columns" + #ll ~= n => error "matrix: wrong number of columns" ans : Matrix R := new(m,n,0) for i in minr(ans)..maxr(ans) for ll in l repeat for j in minc(ans)..maxc(ans) for r in ll repeat @@ -318,7 +318,7 @@ RectangularMatrix(m,n,R): Exports == Implementation where coerce(x:$):Matrix(R) == copy(x pretend Matrix(R)) rectangularMatrix x == - (nrows(x) ^= m) or (ncols(x) ^= n) => + (nrows(x) ~= m) or (ncols(x) ~= n) => error "rectangularMatrix: matrix of bad dimensions" copy(x) pretend $ @@ -410,9 +410,9 @@ SquareMatrix(ndim,R): Exports == Implementation where matrix(l: List List R) == -- error check: this is a top level function - #l ^= ndim => error "matrix: wrong number of rows" + #l ~= ndim => error "matrix: wrong number of rows" for ll in l repeat - #ll ^= ndim => error "matrix: wrong number of columns" + #ll ~= ndim => error "matrix: wrong number of columns" ans : Matrix R := new(ndim,ndim,0) for i in minr(ans)..maxr(ans) for ll in l repeat for j in minc(ans)..maxc(ans) for r in ll repeat @@ -426,14 +426,14 @@ SquareMatrix(ndim,R): Exports == Implementation where scalarMatrix r == scalarMatrix(ndim,r)$Matrix(R) pretend $ diagonalMatrix l == - #l ^= ndim => + #l ~= ndim => error "diagonalMatrix: wrong number of entries in list" diagonalMatrix(l)$Matrix(R) pretend $ coerce(x:$):Matrix(R) == copy(x pretend Matrix(R)) squareMatrix x == - (nrows(x) ^= ndim) or (ncols(x) ^= ndim) => + (nrows(x) ~= ndim) or (ncols(x) ~= ndim) => error "squareMatrix: matrix of bad dimensions" copy(x) pretend $ diff --git a/src/algebra/mfinfact.spad.pamphlet b/src/algebra/mfinfact.spad.pamphlet index 685afc57..2e3a3183 100644 --- a/src/algebra/mfinfact.spad.pamphlet +++ b/src/algebra/mfinfact.spad.pamphlet @@ -213,12 +213,12 @@ MultFiniteFactorize(OV,E,F,PG) : C == T ldeg:=ldeg.rest lvar:=lvar.rest - if varch.nvar.1 ^= x then + if varch.nvar.1 ~= x then lvar:= varch.nvar x := lvar.1 lvar:=lvar.rest pc:= gcd coefficients um - if pc^=1 then + if pc~=1 then um:=(um exquo pc)::SUP P ffactor:=multivariate(um,x) for lcterm in mFactor(pc,dx).factors repeat @@ -228,7 +228,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T -- should be unitNormal if unified, but for now it is easier lcum:F:= leadingCoefficient leadingCoefficient leadingCoefficient um - if lcum ^=1 then + if lcum ~=1 then um:=((inv lcum)::R::P) * um flead.contp := (lcum::R) *flead.contp @@ -286,13 +286,13 @@ MultFiniteFactorize(OV,E,F,PG) : C == T lpol:= dist.polfac dd := dist.correct unifact:=dist.corrfact - if dd^=1 then + if dd~=1 then unifact := [dd*unifact.i for i in 1..nfact] um := ((dd**(nfact-1)::NNI)::P)*um (ffin:= lifting(um,lvar,unifact,lval,lpol,ldeg,pM(unifact))) case "failed" => intfact(um,lvar,ldeg,tleadpol,ltry) factfin: L SUP P:=ffin :: L SUP P - if dd^=1 then + if dd~=1 then factfin:=[primitivePart ff for ff in factfin] factfin @@ -301,7 +301,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T pushup(f:P,x:OV) :PG == ground? f => pushupconst((retract f)@R,x) rr:PG:=0 - while f^=0 repeat + while f~=0 repeat lf:=leadingMonomial f cf:=pushupconst(leadingCoefficient f,x) lvf:=variables lf @@ -314,7 +314,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T ground? g => ((retract g)@F)::R::P rf:P:=0$P ug:=univariate(g,x) - while ug^=0 repeat + while ug~=0 repeat cf:=monomial(1,degree ug)$R rf:=rf+cf*pushdcoef(leadingCoefficient ug) ug := reductum ug @@ -324,7 +324,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T pushupconst(r:R,x:OV):PG == ground? r => (retract r)@F ::PG rr:PG:=0 - while r^=0 repeat + while r~=0 repeat rr:=rr+monomial((leadingCoefficient r)::PG,x,degree r)$PG r:=reductum r rr @@ -385,19 +385,19 @@ MultFiniteFactorize(OV,E,F,PG) : C == T leadcomp1:=[retract eval(pol,lvar,lval) for pol in plist] testp and or/[unit? epl for epl in leadcomp1] => range:=range+1 newm:SUP R:=completeEval(um,lvar,lval) - degum ^= degree newm or minimumDegree newm ^=0 => range:=range+1 + degum ~= degree newm or minimumDegree newm ~=0 => range:=range+1 lffc1:=content newm newm:=(newm exquo lffc1)::SUP R testp and leadtest and ^ polCase(lffc1*clc,#plist,leadcomp1) => range:=range+1 Dnewm := differentiate newm D2newm := map(differentiate, newm) - degree(gcd [newm,Dnewm,D2newm])^=0 => range:=range+1 + degree(gcd [newm,Dnewm,D2newm])~=0 => range:=range+1 -- if R has Integer then luniv:=henselFact(newm,false)$ -- else lcnm:F:=1 -- should be unitNormal if unified, but for now it is easier - if (lcnm:=leadingCoefficient leadingCoefficient newm)^=1 then + if (lcnm:=leadingCoefficient leadingCoefficient newm)~=1 then newm:=((inv lcnm)::R)*newm dx:="max"/[degree uc for uc in coefficients newm] luniv:=generalTwoFactor(newm)$TwoFactorize(F) diff --git a/src/algebra/mlift.spad.jhd.pamphlet b/src/algebra/mlift.spad.jhd.pamphlet index 637d1b32..ea1a70ed 100644 --- a/src/algebra/mlift.spad.jhd.pamphlet +++ b/src/algebra/mlift.spad.jhd.pamphlet @@ -82,7 +82,7 @@ MultivariateLifting(E,OV,R,P) : C == T flcoef:=corrPoly(um,lvar,fval.rest,ld.rest,listpolv,table,pmod) if flcoef case "failed" then return "failed" else lcoef:=flcoef :: L SUP - listcong:=[*/[flist.i for i in 1..np | i^=l] for l in 1..np] + listcong:=[*/[flist.i for i in 1..np | i~=l] for l in 1..np] polc:SUP:= (monomial(1,y,1) - a)::SUP pol := 1$SUP diff:=m- +/[lcoef.i*listcong.i for i in 1..np] @@ -156,13 +156,13 @@ MultivariateLifting(E,OV,R,P) : C == T else lalpha:=flalpha :: L SUP plist:=[term-alpha*pol for term in plist for alpha in lalpha] for term in plist repeat degj:=degj-maxDegree(term,x) - degj ^= 0 => return "failed" + degj ~= 0 => return "failed" plist --There are not extraneous factors maxDegree(um:SUP,x:OV):NonNegativeInteger == ans:NonNegativeInteger:=0 - while um ^= 0 repeat + while um ~= 0 repeat ans:=max(ans,degree(leadingCoefficient um,x)) um:=reductum um ans @@ -220,7 +220,7 @@ MultivariateLifting(E,OV,R,P) : C == T new:=monomial(leadingCoefficient um,dm) for k in dm-1..0 by -1 repeat i:NNI:=k::NNI - empty?(lterm) or lterm.first.expt^=i => + empty?(lterm) or lterm.first.expt~=i => new:=new+monomial(coefficient(um,i),i) new:=new+monomial(lterm.first.pcoef,i) lterm:=lterm.rest diff --git a/src/algebra/mlift.spad.pamphlet b/src/algebra/mlift.spad.pamphlet index 4ec8d14c..8ccdf72a 100644 --- a/src/algebra/mlift.spad.pamphlet +++ b/src/algebra/mlift.spad.pamphlet @@ -85,7 +85,7 @@ MultivariateLifting(E,OV,R,P) : C == T flcoef:=corrPoly(um,lvar,fval.rest,ld.rest,listpolv,table,pmod) if flcoef case "failed" then return "failed" else lcoef:=flcoef :: L SUP - listcong:=[*/[flist.i for i in 1..np | i^=l] for l in 1..np] + listcong:=[*/[flist.i for i in 1..np | i~=l] for l in 1..np] polc:SUP:= (monomial(1,y,1) - a)::SUP pol := 1$SUP diff:=m- +/[lcoef.i*listcong.i for i in 1..np] @@ -167,7 +167,7 @@ MultivariateLifting(E,OV,R,P) : C == T maxDegree(um:SUP,x:OV):NonNegativeInteger == ans:NonNegativeInteger:=0 - while um ^= 0 repeat + while um ~= 0 repeat ans:=max(ans,degree(leadingCoefficient um,x)) um:=reductum um ans @@ -225,7 +225,7 @@ MultivariateLifting(E,OV,R,P) : C == T new:=monomial(leadingCoefficient um,dm) for k in dm-1..0 by -1 repeat i:NNI:=k::NNI - empty?(lterm) or lterm.first.expt^=i => + empty?(lterm) or lterm.first.expt~=i => new:=new+monomial(coefficient(um,i),i) new:=new+monomial(lterm.first.pcoef,i) lterm:=lterm.rest diff --git a/src/algebra/moddfact.spad.pamphlet b/src/algebra/moddfact.spad.pamphlet index 19692d42..7c12510c 100644 --- a/src/algebra/moddfact.spad.pamphlet +++ b/src/algebra/moddfact.spad.pamphlet @@ -79,7 +79,7 @@ ModularDistinctDegreeFactorizer(U):C == T where exactquo(u:U,v:U,p:I):Union(U,"failed") == invlcv:=modInverse(leadingCoefficient v,p) r:=monicDivide(u,reduction(invlcv*v,p)) - reduction(r.remainder,p) ^=0 => "failed" + reduction(r.remainder,p) ~=0 => "failed" reduction(invlcv*r.quotient,p) EMR := EuclideanModularRing(Integer,U,Integer, reduction,merge,exactquo) @@ -114,7 +114,7 @@ ModularDistinctDegreeFactorizer(U):C == T where ans::U ddfactor(u) == - if (c:= lc(u)) ^= 1$I then u:= makeMonic(u) + if (c:= lc(u)) ~= 1$I then u:= makeMonic(u) ans:= sepfact(ddfact(u)) cons(c::EMR,[makeMonic(f) for f in ans | degree(f) > 0]) @@ -133,7 +133,7 @@ ModularDistinctDegreeFactorizer(U):C == T where w:= reduce(monomial(1,1)$U,p) m:= w d:I:= 1 - if (c:= lc(u)) ^= 1$I then u:= makeMonic u + if (c:= lc(u)) ~= 1$I then u:= makeMonic u ans:DDList:= [] repeat w:= exptmod(w,p,u) @@ -173,7 +173,7 @@ ModularDistinctDegreeFactorizer(U):C == T where u:= f.factor p:=modulus u (d := f.degree) = 0 => [u] - if (c:= lc(u)) ^= 1$I then u:= makeMonic(u) + if (c:= lc(u)) ~= 1$I then u:= makeMonic(u) d = (du := degree(u)) => [u] ans:L EMR:= [] x:U:= monomial(1,1) diff --git a/src/algebra/modgcd.spad.pamphlet b/src/algebra/modgcd.spad.pamphlet index a2f056cf..f26ac49d 100644 --- a/src/algebra/modgcd.spad.pamphlet +++ b/src/algebra/modgcd.spad.pamphlet @@ -205,7 +205,7 @@ InnerModularGcd(R,BP,pMod,nextMod):C == T exactquo(u:BP,v:BP,p:R):Union(BP,"failed") == invlcv:=modInverse(leadingCoefficient v,p) r:=monicDivide(u,reduction(invlcv*v,p)) - reduction(r.remainder,p) ^=0 => "failed" + reduction(r.remainder,p) ~=0 => "failed" reduction(invlcv*r.quotient,p) diff --git a/src/algebra/modmon.spad.pamphlet b/src/algebra/modmon.spad.pamphlet index cc8bebec..0d4241e2 100644 --- a/src/algebra/modmon.spad.pamphlet +++ b/src/algebra/modmon.spad.pamphlet @@ -75,7 +75,7 @@ ModMonic(R,Rep): C == T setPoly (mon : Rep) == mon =$Rep m => mon oldm := m - leadingCoefficient mon ^= 1 => error "polynomial must be monic" + leadingCoefficient mon ~= 1 => error "polynomial must be monic" -- following copy code needed since FFPOLY can modify mon copymon:Rep:= 0 while not zero? mon repeat @@ -141,7 +141,7 @@ ModMonic(R,Rep): C == T frobenius(a:%):% == aq:% := 0 - while a^=0 repeat + while a~=0 repeat aq:= aq + leadingCoefficient(a)*frobeniusPower(degree a) a := reductum a aq diff --git a/src/algebra/modmonom.spad.pamphlet b/src/algebra/modmonom.spad.pamphlet index f96b812c..593d5aa8 100644 --- a/src/algebra/modmonom.spad.pamphlet +++ b/src/algebra/modmonom.spad.pamphlet @@ -96,7 +96,7 @@ GeneralModulePolynomial(vl, R, IS, E, ff, P): public == private where ----------------------------------------------------------------------------- - ---- WARNING: assumes c ^= 0 + ---- WARNING: assumes c ~= 0 multMonom(c:R, e:E, mp:$):$ == zero? mp => mp diff --git a/src/algebra/modring.spad.pamphlet b/src/algebra/modring.spad.pamphlet index 015a5c84..bfd9912a 100644 --- a/src/algebra/modring.spad.pamphlet +++ b/src/algebra/modring.spad.pamphlet @@ -85,7 +85,7 @@ ModularRing(R,Mod,reduction:(R,Mod) -> R, exQuo(x,y) == xm:=x.modulo - if xm ^=$Mod y.modulo then xm:=newmodulo(xm,y.modulo) + if xm ~=$Mod y.modulo then xm:=newmodulo(xm,y.modulo) r:=exactQuo(x.val,y.val,xm) r case "failed"=> "failed" [r::R,xm]$Rep diff --git a/src/algebra/mring.spad.pamphlet b/src/algebra/mring.spad.pamphlet index 04c50f32..3d2ca1c7 100644 --- a/src/algebra/mring.spad.pamphlet +++ b/src/algebra/mring.spad.pamphlet @@ -109,7 +109,7 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where for j in 0.. while i > 0 repeat h := i rem p -- we use index(p) = 0$R - if h ^= 0 then + if h ~= 0 then c : R := index(h :: PositiveInteger)$R m : M := index((j+n) :: PositiveInteger)$M --ans := ans + c *$% m @@ -161,7 +161,7 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where else (r:R) * (a:%) == r = 0 => 0 - [[rt, t.Mn] for t in a | (rt:=r*t.Cf) ^= 0] + [[rt, t.Mn] for t in a | (rt:=r*t.Cf) ~= 0] if R has noZeroDivisors then (n:Integer) * (a:%) == @@ -170,8 +170,8 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where else (n:Integer) * (a:%) == n = 0 => 0 - [[nt, t.Mn] for t in a | (nt:=n*t.Cf) ^= 0] - map(f, a) == [[ft, t.Mn] for t in a | (ft:=f(t.Cf)) ^= 0] + [[nt, t.Mn] for t in a | (nt:=n*t.Cf) ~= 0] + map(f, a) == [[ft, t.Mn] for t in a | (ft:=f(t.Cf)) ~= 0] numberOfMonomials a == #a retractIfCan(a:%):Union(M, "failed") == @@ -188,13 +188,13 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where if M has Group then recip a == lt := terms a - #lt ^= 1 => "failed" + #lt ~= 1 => "failed" (u := recip lt.first.Cf) case "failed" => "failed" --(u::R) * inv lt.first.Mn monomial((u::R), inv lt.first.Mn)$% else recip a == - #a ^= 1 or a.first.Mn ^= 1 => "failed" + #a ~= 1 or a.first.Mn ~= 1 => "failed" (u := recip a.first.Cf) case "failed" => "failed" u::R::% @@ -215,9 +215,9 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where reductum a == (empty? a => a; rest a) a = b == - #a ^= #b => false + #a ~= #b => false for ta in a for tb in b repeat - ta.Cf ^= tb.Cf or ta.Mn ^= tb.Mn => return false + ta.Cf ~= tb.Cf or ta.Mn ~= tb.Mn => return false true a + b == @@ -298,7 +298,7 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where else -- M hasn't OrderedSet -- Terms are stored in random order. a = b == - #a ^= #b => false + #a ~= #b => false brace(a pretend List(Term)) =$Set(Term) brace(b pretend List(Term)) coefficient(a, m) == diff --git a/src/algebra/mset.spad.pamphlet b/src/algebra/mset.spad.pamphlet index abe5d56d..678265f9 100644 --- a/src/algebra/mset.spad.pamphlet +++ b/src/algebra/mset.spad.pamphlet @@ -269,13 +269,13 @@ Multiset(S: SetCategory): MultisetAggregate S with union(difference(m1,m2), difference(m2,m1)) m1 = m2 == - m1.count ^= m2.count => false + m1.count ~= m2.count => false t1 := m1.table t2 := m2.table for e in keys t1 repeat - t1.e ^= t2.e => return false + t1.e ~= t2.e => return false for e in keys t2 repeat - t1.e ^= t2.e => return false + t1.e ~= t2.e => return false true m1 < m2 == diff --git a/src/algebra/mts.spad.pamphlet b/src/algebra/mts.spad.pamphlet index a7335877..1d26d0a1 100644 --- a/src/algebra/mts.spad.pamphlet +++ b/src/algebra/mts.spad.pamphlet @@ -142,7 +142,7 @@ SparseMultivariateTaylorSeries(Coef,Var,SMP):_ rst s eval(s:%,v:L Var,q:L %) == - #v ^= #q => + #v ~= #q => error "eval: number of variables should equal number of values" nq : L StS := [restCheck(i pretend StS) for i in q] addiag(map(csubst(v,nq),s pretend StS)$ST2(SMP,StS))$STT pretend % @@ -250,12 +250,12 @@ SparseMultivariateTaylorSeries(Coef,Var,SMP):_ n : NNI; count : NNI := _$streamCount$Lisp l : List OUT := empty() for n in 0..count while not empty? uu repeat - if frst(uu) ^= 0 then l := concat(tout frst uu,l) + if frst(uu) ~= 0 then l := concat(tout frst uu,l) uu := rst uu if showAll?() then for n in n.. while explicitEntries? uu and _ not eq?(uu,rst uu) repeat - if frst(uu) ^= 0 then l := concat(tout frst uu,l) + if frst(uu) ~= 0 then l := concat(tout frst uu,l) uu := rst uu l := explicitlyEmpty? uu => l diff --git a/src/algebra/multfact.spad.pamphlet b/src/algebra/multfact.spad.pamphlet index 6efcd462..0aa0bb59 100644 --- a/src/algebra/multfact.spad.pamphlet +++ b/src/algebra/multfact.spad.pamphlet @@ -182,7 +182,7 @@ InnerMultFact(OV,E,R,P) : C == T "max"/[numberOfMonomials ff for ff in lum] "max"/[+/[euclideanSize cc for i in 0..degree ff| - (cc:= coefficient(ff,i))^=0] for ff in lum] + (cc:= coefficient(ff,i))~=0] for ff in lum] --- Choose the integer to reduce to univariate case --- intChoose(um:USP,lvar:L OV,clc:R,plist:L P,ltry:L L R, @@ -220,12 +220,12 @@ InnerMultFact(OV,E,R,P) : C == T leadcomp1:=[retract eval(pol,lvar,lval) for pol in plist] testp and or/[unit? epl for epl in leadcomp1] => range:=2*range newm:BP:=completeEval(um,lvar,lval) - degum ^= degree newm or minimumDegree newm ^=0 => range:=2*range + degum ~= degree newm or minimumDegree newm ~=0 => range:=2*range lffc1:=content newm newm:=(newm exquo lffc1)::BP testp and leadtest and ^ polCase(lffc1*clc,#plist,leadcomp1) => range:=2*range - degree(gcd [newm,differentiate(newm)])^=0 => range:=2*range + degree(gcd [newm,differentiate(newm)])~=0 => range:=2*range luniv:=ufactor(newm) lunivf:= factors luniv lffc1:R:=retract(unit luniv)@R * lffc1 @@ -325,7 +325,7 @@ InnerMultFact(OV,E,R,P) : C == T lpol:= dist.polfac dd := dist.correct unifact:=dist.corrfact - if dd^=1 then + if dd~=1 then -- if polcase then lpol := [unitCanonical lp for lp in lpol] -- dd:=unitCanonical(dd) unifact := [dd * unif for unif in unifact] @@ -334,7 +334,7 @@ InnerMultFact(OV,E,R,P) : C == T (ffin:=lifting(umd,lvar,unifact,lval,lpol,ldeg,pmod)) case "failed" => intfact(um,lvar,ldeg,tleadpol,ltry,ufactor) factfin: L USP:=ffin :: L USP - if dd^=1 then + if dd~=1 then factfin:=[primitivePart ff for ff in factfin] factfin @@ -351,7 +351,7 @@ InnerMultFact(OV,E,R,P) : C == T ans:USP := monomial(1,n) n:=(n-1)::NonNegativeInteger prod:P:=1 - while (um:=reductum(um)) ^= 0 repeat + while (um:=reductum(um)) ~= 0 repeat i := degree um lc := leadingCoefficient um prod := prod * c ** (n-(n:=i))::NonNegativeInteger @@ -420,12 +420,12 @@ InnerMultFact(OV,E,R,P) : C == T x:=lvar.first ldeg:=ldeg.rest lvar := lvar.rest - if varch.nvar.first ^= x then + if varch.nvar.first ~= x then lvar:= varch.nvar x := lvar.first lvar := lvar.rest pc:= gcd coefficients um - if pc^=1 then + if pc~=1 then um:=(um exquo pc)::USP ffactor:=multivariate(um,x) for lcterm in mFactor(pc,ufactor).factors repeat diff --git a/src/algebra/multpoly.spad.pamphlet b/src/algebra/multpoly.spad.pamphlet index 86e5548a..99ab7833 100644 --- a/src/algebra/multpoly.spad.pamphlet +++ b/src/algebra/multpoly.spad.pamphlet @@ -180,7 +180,7 @@ SparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet): C == T where monomial? p == p case R => true sup : D := p.ts - 1 ^= numberOfMonomials(sup) => false + 1 ~= numberOfMonomials(sup) => false monomial? leadingCoefficient(sup)$D -- local @@ -487,11 +487,11 @@ SparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet): C == T where gcd(leadingCoefficient b, content a)::SUP $ conta := content a mona:SUP $ := monomial(conta, minimumDegree a) - if mona ^= 1 then + if mona ~= 1 then a := (a exquo mona)::SUP $ contb := content b monb:SUP $ := monomial(contb, minimumDegree b) - if monb ^= 1 then + if monb ~= 1 then b := (b exquo monb)::SUP $ mong:SUP $ := monomial(gcd(conta, contb), min(degree mona, degree monb)) @@ -618,7 +618,7 @@ SparseMultivariatePolynomial(R: Ring,VarSet: OrderedSet): C == T where u := univariate(p, mv := mainVariable(p)::VarSet) weight:NonNegativeInteger := (member?(mv,Lvar) => 1; 0) tdeg:NonNegativeInteger := 0 - while u ^= 0 repeat + while u ~= 0 repeat termdeg:NonNegativeInteger := weight*degree u + totalDegree(leadingCoefficient u, Lvar) tdeg := max(tdeg, termdeg) diff --git a/src/algebra/multsqfr.spad.pamphlet b/src/algebra/multsqfr.spad.pamphlet index fbc32eeb..4d71bd73 100644 --- a/src/algebra/multsqfr.spad.pamphlet +++ b/src/algebra/multsqfr.spad.pamphlet @@ -111,19 +111,19 @@ MultivariateSquareFree (E,OV,R,P) : C == T where exp0:Z:=0 unitsq:P:=1 lcf:P:=leadingCoefficient f - if ctf^=1 then + if ctf~=1 then f0:=ctf*f0 f:=(ctf::P)*f lcf:=ctf*lcf sqlead:List FFEP:= empty() sqlc:Factored P:=1 - if lcf^=1$P then + if lcf~=1$P then leadpol:=true sqlc:=squareFree lcf unitsq:=unitsq*(unit sqlc) sqlead:= factors sqlc lfact:=sort(#1.exponent > #2.exponent,lfact) - while lfact^=[] repeat + while lfact~=[] repeat pfact:=lfact.first (g0,exp0):=(pfact.factor,pfact.exponent) lfact:=lfact.rest @@ -132,7 +132,7 @@ MultivariateSquareFree (E,OV,R,P) : C == T where gg := unitNormal leadingCoefficient f sqdec:=cons([gg.associate*f,exp0],sqdec) return [gg.unit, sqdec]$squareForm - if ctf^=1 then g0:=ctf*g0 + if ctf~=1 then g0:=ctf*g0 npol:=consnewpol(f,f0,exp0) (d,d0):=(npol.pol,npol.polval) if leadpol then lcoef:=coefChoose(exp0,sqlc) @@ -147,8 +147,8 @@ MultivariateSquareFree (E,OV,R,P) : C == T where f:=h::SUP f0:=completeEval(h,lvar,lval) lcr:P:=leadingCoefficient result0 - if leadpol and lcr^=1$P then - for lpfact in sqlead while lcr^=1 repeat + if leadpol and lcr~=1$P then + for lpfact in sqlead while lcr~=1 repeat ground? lcr => unitsq:=(unitsq exquo lcr)::P lcr:=1$P @@ -195,7 +195,7 @@ MultivariateSquareFree (E,OV,R,P) : C == T where y:=lvar.im p:=p*monomial(1$P,y,n) result1:=cons(["sqfr",y::P,n],result1) - if p^=1$P then + if p~=1$P then f := (f exquo p)::P if ground? f then return makeFR(f, result1) lvar:=variables(f) @@ -206,7 +206,7 @@ MultivariateSquareFree (E,OV,R,P) : C == T where makeFR(unit result,append(result1,factorList result)) ldeg:=degree(f,lvar) --- general case --- - m:="min"/[j for j in ldeg|j^=0] + m:="min"/[j for j in ldeg|j~=0] i:Z:=1 for j in ldeg while j>m repeat i:=i+1 x:=lvar.i @@ -241,7 +241,7 @@ MultivariateSquareFree (E,OV,R,P) : C == T where member?(lval,ltry) => "new integer" ltry:=cons(lval,ltry) f0:=completeEval(f,lvar,lval) - degree f0 ^=degf => "new integer" + degree f0 ~=degf => "new integer" ctf:=content f0 lfact:List(FFE):=factors(squareFree((f0 exquo (ctf:R)::BP)::BP)) @@ -303,7 +303,7 @@ MultivariateSquareFree (E,OV,R,P) : C == T where plist:=lifting(ud,lvar,[g0,g1],lval,leadlist,ldeg,pmod) plist case "failed" => "failed" (p0:SUP,p1:SUP):=((plist::List SUP).1,(plist::List SUP).2) - if completeEval(p0,lvar,lval) ^= g0 then (p0,p1):=(p1,p0) + if completeEval(p0,lvar,lval) ~= g0 then (p0,p1):=(p1,p0) [primitivePart p0,primitivePart p1] ---- the polynomial is univariate ---- diff --git a/src/algebra/naalg.spad.pamphlet b/src/algebra/naalg.spad.pamphlet index ec93ce54..f252ef74 100644 --- a/src/algebra/naalg.spad.pamphlet +++ b/src/algebra/naalg.spad.pamphlet @@ -491,7 +491,7 @@ second argument") structuralConstants(ls:L S, mt: M POLY R) == nn := #(ls) - nrows(mt) ^= nn or ncols(mt) ^= nn => + nrows(mt) ~= nn or ncols(mt) ~= nn => error "structuralConstants: size of second argument does not _ agree with number of generators" gamma : L M POLY R := [] @@ -505,14 +505,14 @@ agree with number of generators" totalDegree(p,ls) > 1 => error "structuralConstants: entries of second argument _ must be linear polynomials in the generators" - if (c := coefficient(p, s, 1) ) ^= 0 then qsetelt_!(mat,i,j,c) + if (c := coefficient(p, s, 1) ) ~= 0 then qsetelt_!(mat,i,j,c) gamma := cons(mat, gamma) lscopy := rest lscopy vector reverse gamma structuralConstants(ls:L S, mt: M FRAC POLY R) == nn := #(ls) - nrows(mt) ^= nn or ncols(mt) ^= nn => + nrows(mt) ~= nn or ncols(mt) ~= nn => error "structuralConstants: size of second argument does not _ agree with number of generators" gamma : L M FRAC(POLY R) := [] @@ -524,14 +524,14 @@ agree with number of generators" for j in 1..nn repeat r := qelt(mt,i,j) q := denom(r) - totalDegree(q,ls) ^= 0 => + totalDegree(q,ls) ~= 0 => error "structuralConstants: entries of second argument _ must be (linear) polynomials in the generators" p := numer(r) totalDegree(p,ls) > 1 => error "structuralConstants: entries of second argument _ must be linear polynomials in the generators" - if (c := coefficient(p, s, 1) ) ^= 0 then qsetelt_!(mat,i,j,c/q) + if (c := coefficient(p, s, 1) ) ~= 0 then qsetelt_!(mat,i,j,c/q) gamma := cons(mat, gamma) lscopy := rest lscopy vector reverse gamma diff --git a/src/algebra/naalgc.spad.pamphlet b/src/algebra/naalgc.spad.pamphlet index b48429ca..f6b470c1 100644 --- a/src/algebra/naalgc.spad.pamphlet +++ b/src/algebra/naalgc.spad.pamphlet @@ -653,7 +653,7 @@ FiniteRankNonAssociativeAlgebra(R:CommutativeRing): lrx case "failed" => "failed" rrx := rightRecip x rrx case "failed" => "failed" - (lrx :: %) ^= (rrx :: %) => "failed" + (lrx :: %) ~= (rrx :: %) => "failed" lrx :: % @@ -1005,7 +1005,7 @@ FramedNonAssociativeAlgebra(R:CommutativeRing): ++ Error: if shape of matrix doesn't fit. --attributes --attributes - --separable <=> discriminant() ^= 0 + --separable <=> discriminant() ~= 0 add V ==> Vector diff --git a/src/algebra/newpoint.spad.pamphlet b/src/algebra/newpoint.spad.pamphlet index b6b32e30..27301539 100644 --- a/src/algebra/newpoint.spad.pamphlet +++ b/src/algebra/newpoint.spad.pamphlet @@ -65,7 +65,7 @@ Point(R:Ring) : Exports == Implementation where dimension p == (# p)::PI -- Vector returns NonNegativeInteger...? convert(l:List R):% == point(l) cross(p0, p1) == - #p0 ^=3 or #p1^=3 => error "Arguments to cross must be three dimensional" + #p0 ~=3 or #p1~=3 => error "Arguments to cross must be three dimensional" point [p0.2 * p1.3 - p1.2 * p0.3, _ p1.1 * p0.3 - p0.1 * p1.3, _ p0.1 * p1.2 - p1.1 * p0.2] @@ -567,7 +567,7 @@ SubSpace(n:PI,R:Ring) : Exports == Implementation where (leaf? s1 and leaf? s2) => (s1.pt = s2.pt) and (s1.property = s2.property) and (s1.levelField = s2.levelField) -- note that the ordering of children is important - #s1.childrenField ^= #s2.childrenField => false + #s1.childrenField ~= #s2.childrenField => false and/[c1 = c2 for c1 in s1.childrenField for c2 in s2.childrenField] and (s1.property = s2.property) and (s1.levelField = s2.levelField) coerce(space:%):O == diff --git a/src/algebra/nlinsol.spad.pamphlet b/src/algebra/nlinsol.spad.pamphlet index f181a478..c69d5633 100644 --- a/src/algebra/nlinsol.spad.pamphlet +++ b/src/algebra/nlinsol.spad.pamphlet @@ -68,7 +68,7 @@ RetractSolvePackage(Q, R): Exports == Implementation where "failed" up := univariate(p, s := u::SY) ans:FQ := 0 - while up ^= 0 repeat + while up ~= 0 repeat (v := PQIfCan leadingCoefficient up) case "failed" => return "failed" ans := ans + monomial(1, s, degree up)$PQ * (v::FQ) up := reductum up diff --git a/src/algebra/nlode.spad.pamphlet b/src/algebra/nlode.spad.pamphlet index 2f7f672d..b43c0102 100644 --- a/src/algebra/nlode.spad.pamphlet +++ b/src/algebra/nlode.spad.pamphlet @@ -101,7 +101,7 @@ NonLinearFirstOrderODESolver(R, F): Exports == Implementation where r := denom(f := m / n)::F (not freeOf?(r, y := ky::F)) or (d := degree(p := univariate(numer f, ky))) < 2 - or degree(pp := reductum p) ^= 1 or reductum(pp) ^= 0 + or degree(pp := reductum p) ~= 1 or reductum(pp) ~= 0 or (not freeOf?(a := (leadingCoefficient(pp)::F), y)) or (not freeOf?(b := (leadingCoefficient(p)::F), y)) => "failed" [a / r, b / r, d] diff --git a/src/algebra/npcoef.spad.pamphlet b/src/algebra/npcoef.spad.pamphlet index ef842223..c89d9382 100644 --- a/src/algebra/npcoef.spad.pamphlet +++ b/src/algebra/npcoef.spad.pamphlet @@ -63,7 +63,7 @@ NPCoef(BP,E,OV,R,P) : C == T where changed:Boolean:=true ltochange:List(NNI):=empty() ltodel:List(NNI):=empty() - while changed and ndet^=1 repeat + while changed and ndet~=1 repeat changed :=false dt:=#tablecoef for i in 1..dt while ^changed repeat @@ -104,7 +104,7 @@ NPCoef(BP,E,OV,R,P) : C == T where #termlist=1 => vterm:=termlist.first for elterm in vterm while doit<2 repeat - (cu1:=elterm.pcoef)^=0 => cfu:=cu1*cfu + (cu1:=elterm.pcoef)~=0 => cfu:=cu1*cfu doit:=doit+1 poselt:=position(elterm,vterm):NNI doit=2 or (pp:=tterm.coefu exquo cfu) case "failed" => "failed" @@ -148,7 +148,7 @@ NPCoef(BP,E,OV,R,P) : C == T where for celt in ctdet repeat if celt.cfpos.expt=cfexp then celt.cfpos.pcoef:=cfcoef - if (and/[cc.pcoef ^=0 for cc in celt]) then + if (and/[cc.pcoef ~=0 for cc in celt]) then k:=position(celt,ctdet):NNI lterase:=cons(k,lterase) cterm.coefu:=(cterm.coefu - */[cc.pcoef for cc in celt]) diff --git a/src/algebra/numeigen.spad.pamphlet b/src/algebra/numeigen.spad.pamphlet index 310fe945..3f314958 100644 --- a/src/algebra/numeigen.spad.pamphlet +++ b/src/algebra/numeigen.spad.pamphlet @@ -198,7 +198,7 @@ InnerNumericEigenPackage(K,F,Par) : C == T charpol(A:MK) : SUK == dimA :PI := (nrows A):PI - dimA ^= ncols A => error " The matrix is not square" + dimA ~= ncols A => error " The matrix is not square" B:Matrix SUK :=zero(dimA,dimA) for i in 1..dimA repeat for j in 1..dimA repeat B(i,j):=A(i,j)::SUK diff --git a/src/algebra/numsolve.spad.pamphlet b/src/algebra/numsolve.spad.pamphlet index b640b925..edb7898c 100644 --- a/src/algebra/numsolve.spad.pamphlet +++ b/src/algebra/numsolve.spad.pamphlet @@ -148,7 +148,7 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where p0 := primitivePart multivariate(vec.0, mainvar) p1 := primitivePart(multivariate(vec.1, mainvar),mainvar) zero? p1 or - gcd(p0, leadingCoefficient(univariate(p1,mainvar))) ^=1 => + gcd(p0, leadingCoefficient(univariate(p1,mainvar))) ~=1 => innerSolve(cons(0,lp),empty(),lv,eps) findGenZeros([p1, p0], reverse lv, eps) @@ -161,15 +161,15 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where DP:=DirectProduct(#lv,NonNegativeInteger) dmp:=DistributedMultivariatePolynomial(lv,K) lq:L dmp:=[] - if ld^=[] then + if ld~=[] then lq:= [(pToDmp(q1)$PolToPol(lv,K)) pretend dmp for q1 in ld] partRes:=groebSolve(lnp,lvv)$GroebnerSolve(lv,K,K) pretend (L L dmp) partRes=list [] => [] -- remove components where denominators vanish - if lq^=[] then + if lq~=[] then gb:=GroebnerInternalPackage(K,DirectProduct(#lv,NNI),OV,dmp) partRes:=[pr for pr in partRes| - and/[(redPol(fq,pr pretend List(dmp))$gb) ^=0 + and/[(redPol(fq,pr pretend List(dmp))$gb) ~=0 for fq in lq]] -- select the components in "generic" form @@ -182,7 +182,7 @@ InnerNumericFloatSolvePackage(K,F,Par): Cat == Cap where "and"/[("max"/degree(f,rrlvv))=1 for f in res1] => listGen:=concat(res pretend (L dmp),listGen) result:L L F := [] - if listGen^=[] then + if listGen~=[] then listG :L L P K:= [[dmpToP(pf)$PolToPol(lv,K) for pf in pr] for pr in listGen] result:= @@ -286,14 +286,14 @@ FloatingRealPackage(Par): Cat == Cap where -- real zeros of the system of polynomial lp -- realRoots(lp:L RFI,lv:L SE,eps: Par) : L L Par == lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)^=1] + lden:=[dp for p in lp |(dp:=denom p)~=1] innerSolve(lnum,lden,lv,eps)$INFSP(I,Par,Par) solve(lp:L RFI,eps : Par) : L L EQ P Par == lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)^=1] + lden:=[dp for p in lp |(dp:=denom p)~=1] lv:="setUnion"/[variables np for np in lnum] - if lden^=[] then + if lden~=[] then lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden]) [makeEq(numres,lv) for numres in innerSolve(lnum,lden,lv,eps)$INFSP(I,Par,Par)] @@ -301,9 +301,9 @@ FloatingRealPackage(Par): Cat == Cap where solve(le:L EQ RFI,eps : Par) : L L EQ P Par == lp:=[lhs ep - rhs ep for ep in le] lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)^=1] + lden:=[dp for p in lp |(dp:=denom p)~=1] lv:="setUnion"/[variables np for np in lnum] - if lden^=[] then + if lden~=[] then lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden]) [makeEq(numres,lv) for numres in innerSolve(lnum,lden,lv,eps)$INFSP(I,Par,Par)] @@ -406,14 +406,14 @@ FloatingComplexPackage(Par): Cat == Cap where -- find the complex zeros of an univariate polynomial -- complexRoots(lp:L FPK,lv:L SE,eps:Par) : L L C Par == lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)^=1] + lden:=[dp for p in lp |(dp:=denom p)~=1] innerSolve(lnum,lden,lv,eps)$INFSP(K,C Par,Par) complexSolve(lp:L FPK,eps : Par) : L L EQ P C Par == lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)^=1] + lden:=[dp for p in lp |(dp:=denom p)~=1] lv:="setUnion"/[variables np for np in lnum] - if lden^=[] then + if lden~=[] then lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden]) [[equation(x::(P C Par),r::(P C Par)) for x in lv for r in nres] for nres in innerSolve(lnum,lden,lv,eps)$INFSP(K,C Par,Par)] @@ -421,9 +421,9 @@ FloatingComplexPackage(Par): Cat == Cap where complexSolve(le:L EQ FPK,eps : Par) : L L EQ P C Par == lp:=[lhs ep - rhs ep for ep in le] lnum:=[numer p for p in lp] - lden:=[dp for p in lp |(dp:=denom p)^=1] + lden:=[dp for p in lp |(dp:=denom p)~=1] lv:="setUnion"/[variables np for np in lnum] - if lden^=[] then + if lden~=[] then lv:=setUnion(lv,"setUnion"/[variables dp for dp in lden]) [[equation(x::(P C Par),r::(P C Par)) for x in lv for r in nres] for nres in innerSolve(lnum,lden,lv,eps)$INFSP(K,C Par,Par)] diff --git a/src/algebra/numtheor.spad.pamphlet b/src/algebra/numtheor.spad.pamphlet index b5cf7404..6df112a7 100644 --- a/src/algebra/numtheor.spad.pamphlet +++ b/src/algebra/numtheor.spad.pamphlet @@ -126,12 +126,12 @@ Using the half extended Euclidean algorithm we compute 1/a mod b. borg:I:=b c1:I := 1 d1:I := 0 - while b ^= 0 repeat + while b ~= 0 repeat q:I := a quo b r:I := a-q*b (a,b):=(b,r) (c1,d1):=(d1,c1-q*d1) - a ^= 1 => error("moduli are not relatively prime") + a ~= 1 => error("moduli are not relatively prime") positiveRemainder(c1,borg) @ @@ -287,7 +287,7 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where jacobi : (I,I) -> I ++ \spad{jacobi(a,b)} returns the Jacobi symbol \spad{J(a/b)}. ++ When b is odd, \spad{J(a/b) = product(L(a/p) for p in factor b )}. - ++ Note: by convention, 0 is returned if \spad{gcd(a,b) ^= 1}. + ++ Note: by convention, 0 is returned if \spad{gcd(a,b) ~= 1}. ++ Iterative \spad{O(log(b)^2)} version coded by Michael Monagan June 1987. legendre : (I,I) -> I ++ \spad{legendre(a,p)} returns the Legendre symbol \spad{L(a/p)}. @@ -560,7 +560,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where MonicQuotient: (SUP(I),SUP(I)) -> SUP(I) MonicQuotient (a,b) == - leadingCoefficient(b) ^= 1 => error "divisor must be monic" + leadingCoefficient(b) ~= 1 => error "divisor must be monic" b = 1 => a da := degree a db := degree b -- assertion: degree b > 0 diff --git a/src/algebra/odealg.spad.pamphlet b/src/algebra/odealg.spad.pamphlet index 29a358d9..32425c96 100644 --- a/src/algebra/odealg.spad.pamphlet +++ b/src/algebra/odealg.spad.pamphlet @@ -89,7 +89,7 @@ SystemODESolver(F, LO): Exports == Implementation where m:N := 0 -- number of Solutions part:V := new(n, 0) -- count first the different solutions - for sol in sols repeat m := m + count(#1 ^= 0, sol.basis)$List(F) + for sol in sols repeat m := m + count(#1 ~= 0, sol.basis)$List(F) SolMatrix:MF := new(n, m, 0) m := 0 for sol in reverse_! sols repeat @@ -136,7 +136,7 @@ SystemODESolver(F, LO): Exports == Implementation where offset := minIndex v - (mr := minRowIndex m) while r >= mr and every?(zero?, row(m, r))$Vector(LO) repeat r := r - 1 r < mr => error "backsolve: system has a 0 matrix" - (c := firstnonzero(m, r)) ^= maxColIndex m => + (c := firstnonzero(m, r)) ~= maxColIndex m => error "backsolve: undetermined system" rec := solve(m(r, c), v(r + offset)) dim := (r - mr + 1)::N @@ -151,7 +151,7 @@ SystemODESolver(F, LO): Exports == Implementation where while r > mr repeat r := r - 1 c := c - 1 - firstnonzero(m, r) ^= c => error "backsolve: undetermined system" + firstnonzero(m, r) ~= c => error "backsolve: undetermined system" degree(eq := m(r, c)) > 0 => error "backsolve: pivot of order > 0" a := leadingCoefficient(eq)::F if part? then @@ -189,7 +189,7 @@ SystemODESolver(F, LO): Exports == Implementation where -- returns the index of the first nonzero entry in row r of m firstnonzero(m, r) == for c in minColIndex m .. maxColIndex m repeat - m(r, c) ^= 0 => return c + m(r, c) ~= 0 => return c error "firstnonzero: zero row" -- computes +/[m(r, i) v(i) for i ranging over the last n columns of m] @@ -225,12 +225,12 @@ SystemODESolver(F, LO): Exports == Implementation where if i > nrows then leave x rown := minr - 1 for k in i .. nrows repeat - if (x(k, j) ^= 0) and ((rown = minr - 1) or + if (x(k, j) ~= 0) and ((rown = minr - 1) or degree x(k,j) < degree x(rown,j)) then rown := k rown = minr - 1 => "enuf" x := swapRows_!(x, i, rown) swap_!(w, i + offset, rown + offset) - for k in i+1 .. nrows | x(k, j) ^= 0 repeat + for k in i+1 .. nrows | x(k, j) ~= 0 repeat l := rightLcm(x(i,j), x(k,j)) a := rightQuotient(l, x(i, j)) b := rightQuotient(l, x(k, j)) diff --git a/src/algebra/odeef.spad.pamphlet b/src/algebra/odeef.spad.pamphlet index 734344a9..e33f827e 100644 --- a/src/algebra/odeef.spad.pamphlet +++ b/src/algebra/odeef.spad.pamphlet @@ -56,7 +56,7 @@ ReductionOfOrder(F, L): Exports == Impl where ithcoef(eq, i, s) == ans:F := 0 - while eq ^= 0 repeat + while eq ~= 0 repeat j := degree eq ans := ans + localbinom(j, i) * locals(s,j,i) * leadingCoefficient eq eq := reductum eq @@ -213,7 +213,7 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where up := univariate(p, k := first l) l := rest l ans:P2 := 0 - while up ^= 0 repeat + while up ~= 0 repeat ans := ans + monomial(upmp(leadingCoefficient up, l), k, degree up) up := reductum up ans @@ -284,7 +284,7 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where ulodo(eq, k) == op:LQ := 0 - while eq ^= 0 repeat + while eq ~= 0 repeat op := op + monomial(univariate(leadingCoefficient eq, k), degree eq) eq := reductum eq op @@ -294,7 +294,7 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where op := ulodo(eq, k) empty? remove_!(k, varselect(kernels g, x)) => -- i.e. rhs is rational rc := ratDsolve(op, univariate(g, k)) - rc.particular case "failed" => -- this implies g ^= 0 + rc.particular case "failed" => -- this implies g ~= 0 doVarParams(eq, g, homosolve(eq, op, rc.basis, k, x), x) [multivariate(rc.particular::RF, k), homosolve(eq, op, rc.basis, k, x)] doVarParams(eq, g, homosolve(eq, op, ratDsolve(op, 0).basis, k, x), x) @@ -316,7 +316,7 @@ ElementaryFunctionLODESolver(R, F, L): Exports == Implementation where localmap(f, op) == ans:L := 0 - while op ^= 0 repeat + while op ~= 0 repeat ans := ans + monomial(f leadingCoefficient op, degree op) op := reductum op ans @@ -475,7 +475,7 @@ ElementaryFunctionODESolver(R, F): Exports == Implementation where p := rec.left Lx := LinearOrdinaryDifferentialOperator(F, diff x) op:Lx := 0 - while p ^= 0 repeat + while p ~= 0 repeat op := op + monomial(leadingCoefficient p, degree p) p := reductum p solve(op, rec.right, x, a, y0)$ElementaryFunctionLODESolver(R, F, Lx) @@ -495,7 +495,7 @@ ElementaryFunctionODESolver(R, F): Exports == Implementation where p := rec.left Lx := LinearOrdinaryDifferentialOperator(F, diff x) op:Lx := 0 - while p ^= 0 repeat + while p ~= 0 repeat op := op + monomial(leadingCoefficient p, degree p) p := reductum p (uuu := solve(op, rec.right, x)$ElementaryFunctionLODESolver(R, F, Lx)) @@ -504,7 +504,7 @@ ElementaryFunctionODESolver(R, F): Exports == Implementation where -- returns [M, v] s.t. the equations are D x = M x + v parseSYS(eqs, ly, x) == - (n := #eqs) ^= #ly => "failed" + (n := #eqs) ~= #ly => "failed" m:M := new(n, n, 0) v:V := new(n, 0) xx := x::F diff --git a/src/algebra/oderf.spad.pamphlet b/src/algebra/oderf.spad.pamphlet index 6573a809..096c8973 100644 --- a/src/algebra/oderf.spad.pamphlet +++ b/src/algebra/oderf.spad.pamphlet @@ -48,7 +48,7 @@ BalancedFactorisation(R, UP): Exports == Implementation where */[balSqfr1(f.factor, n, b) for f in factors balSqfr(a,n,rest l)] balancedFactorisation(a:UP, l:List UP) == - empty?(ll := select(#1 ^= 0, l)) => + empty?(ll := select(#1 ~= 0, l)) => error "balancedFactorisation: 2nd argument is empty or all 0" sa := squareFree a unit(sa) * */[balSqfr(f.factor,f.exponent,ll) for f in factors sa]) @@ -226,7 +226,7 @@ PrimitiveRatDE(F, UP, L, LQ): Exports == Implementation where cd := splitDenominator coefficients op f := cd.den / gcd(cd.num) l:L := 0 - while op ^= 0 repeat + while op ~= 0 repeat l := l + monomial(retract(f * leadingCoefficient op), degree op) op := reductum op [l, [f * g for g in lg]] @@ -261,7 +261,7 @@ PrimitiveRatDE(F, UP, L, LQ): Exports == Implementation where lamb:List(N) := [d := degree l] lf:List(UP) := [a := leadingCoefficient l] mup := d::Z - order(a, c) - while (l := reductum l) ^= 0 repeat + while (l := reductum l) ~= 0 repeat a := leadingCoefficient l if (m := (d := degree l)::Z - order(a, c)) > mup then mup := m @@ -511,10 +511,10 @@ RationalLODE(F, UP): Exports == Implementation where regularPoint(l, lg) == a := leadingCoefficient(l) * commonDenominator lg - coefficient(a, 0) ^= 0 => 0 + coefficient(a, 0) ~= 0 => 0 for i in 1.. repeat - a(j := i::F) ^= 0 => return i - a(-j) ^= 0 => return(-i) + a(j := i::F) ~= 0 => return i + a(-j) ~= 0 => return(-i) unitlist(i, q) == v := new(q, 0)$Vector(F) @@ -535,7 +535,7 @@ RationalLODE(F, UP): Exports == Implementation where for i in 1..q]$List(RF) a1 := inv(leadingCoefficient(op)::RF) part := [UTS2UP(dd * ode(RF2UTS(a1 * g)$tools + f #1, e)$solver, n)$tools - /$RF d for g in lg | g ^= 0]$List(RF) + /$RF d for g in lg | g ~= 0]$List(RF) [hom, part] nzero? v == @@ -553,7 +553,7 @@ RationalLODE(F, UP): Exports == Implementation where lamb:List(N) := [d := degree l] lf:List(UP) := [a := leadingCoefficient l] mup := degree(a)::Z - d - while (l := reductum l) ^= 0 repeat + while (l := reductum l) ~= 0 repeat a := leadingCoefficient l if (m := degree(a)::Z - (d := degree l)) > mup then mup := m @@ -809,7 +809,7 @@ ConstantLODE(R, F, L): Exports == Implementation where homoBasis(op, x) == p:SUP := 0 - while op ^= 0 repeat + while op ~= 0 repeat p := p + monomial(leadingCoefficient op, degree op) op := reductum op b:List(F) := empty() diff --git a/src/algebra/op.spad.pamphlet b/src/algebra/op.spad.pamphlet index 19d4218e..8b195cbe 100644 --- a/src/algebra/op.spad.pamphlet +++ b/src/algebra/op.spad.pamphlet @@ -156,9 +156,9 @@ BasicOperator(): Exports == Implementation where -- property EQUAL? contains a function f: (BOP, BOP) -> Boolean -- such that f(o1, o2) is true iff o1 = o2 op1 = op2 == - name(op1) ^= name(op2) => false - op1.narg ^= op2.narg => false - brace(keys properties op1)^=$Set(String) brace(keys properties op2) => false + name(op1) ~= name(op2) => false + op1.narg ~= op2.narg => false + brace(keys properties op1)~=$Set(String) brace(keys properties op2) => false (func := property(op1, EQUAL?)) case None => ((func::None) pretend (($, $) -> Boolean)) (op1, op2) true @@ -172,14 +172,14 @@ BasicOperator(): Exports == Implementation where -- property LESS? contains a function f: (BOP, BOP) -> Boolean -- such that f(o1, o2) is true iff o1 < o2 op1 < op2 == - (w1 := weight op1) ^= (w2 := weight op2) => w1 < w2 - op1.narg ^= op2.narg => op1.narg < op2.narg - name(op1) ^= name(op2) => name(op1) < name(op2) + (w1 := weight op1) ~= (w2 := weight op2) => w1 < w2 + op1.narg ~= op2.narg => op1.narg < op2.narg + name(op1) ~= name(op2) => name(op1) < name(op2) n1 := #(k1 := brace(keys(properties op1))$Set(String)) n2 := #(k2 := brace(keys(properties op2))$Set(String)) - n1 ^= n2 => n1 < n2 + n1 ~= n2 => n1 < n2 not zero?(n1 := #(d1 := difference(k1, k2))) => - n1 ^= (n2 := #(d2 := difference(k2, k1))) => n1 < n2 + n1 ~= (n2 := #(d2 := difference(k2, k1))) => n1 < n2 inspect(d1) < inspect(d2) (func := property(op1, LESS?)) case None => ((func::None) pretend (($, $) -> Boolean)) (op1, op2) diff --git a/src/algebra/openmath.spad.pamphlet b/src/algebra/openmath.spad.pamphlet index 2ad57181..c186a2fd 100644 --- a/src/algebra/openmath.spad.pamphlet +++ b/src/algebra/openmath.spad.pamphlet @@ -150,7 +150,7 @@ ExpressionToOpenMath(R: Join(OpenMath, OrderedSet, Ring)): with outputOMArith1(dev, "power", args) outputOMDefsum(dev: OpenMathDevice, args: List Expression R): Void == - #args ^= 5 => error "Unexpected number of arguments to a defsum" + #args ~= 5 => error "Unexpected number of arguments to a defsum" OMputApp(dev) OMputSymbol(dev, "arith1", "sum") outputOMIntInterval(dev, args.4, args.5) @@ -158,7 +158,7 @@ ExpressionToOpenMath(R: Join(OpenMath, OrderedSet, Ring)): with OMputEndApp(dev) outputOMDefprod(dev: OpenMathDevice, args: List Expression R): Void == - #args ^= 5 => error "Unexpected number of arguments to a defprod" + #args ~= 5 => error "Unexpected number of arguments to a defprod" OMputApp(dev) OMputSymbol(dev, "arith1", "product") outputOMIntInterval(dev, args.4, args.5) @@ -166,7 +166,7 @@ ExpressionToOpenMath(R: Join(OpenMath, OrderedSet, Ring)): with OMputEndApp(dev) outputOMDefint(dev: OpenMathDevice, args: List Expression R): Void == - #args ^= 5 => error "Unexpected number of arguments to a defint" + #args ~= 5 => error "Unexpected number of arguments to a defint" OMputApp(dev) OMputSymbol(dev, "calculus1", "defint") outputOMInterval(dev, args.4, args.5) @@ -174,7 +174,7 @@ ExpressionToOpenMath(R: Join(OpenMath, OrderedSet, Ring)): with OMputEndApp(dev) outputOMInt(dev: OpenMathDevice, args: List Expression R): Void == - #args ^= 3 => error "Unexpected number of arguments to a defint" + #args ~= 3 => error "Unexpected number of arguments to a defint" OMputApp(dev) OMputSymbol(dev, "calculus1", "int") outputOMLambda(dev, eval(args.1, args.2, args.3), args.3) diff --git a/src/algebra/ore.spad.pamphlet b/src/algebra/ore.spad.pamphlet index 1c567ebf..ebdc406a 100644 --- a/src/algebra/ore.spad.pamphlet +++ b/src/algebra/ore.spad.pamphlet @@ -30,7 +30,7 @@ UnivariateSkewPolynomialCategory(R:Ring): ++ \spad{l = sum(monomial(a(i),i), i = 0..n)}. minimumDegree: $ -> NonNegativeInteger ++ minimumDegree(l) is the smallest \spad{k} such that - ++ \spad{a(k) ^= 0} if + ++ \spad{a(k) ~= 0} if ++ \spad{l = sum(monomial(a(i),i), i = 0..n)}. leadingCoefficient: $ -> R ++ leadingCoefficient(l) is \spad{a(n)} if @@ -146,14 +146,14 @@ UnivariateSkewPolynomialCategory(R:Ring): coefficients l == ans:List(R) := empty() - while l ^= 0 repeat + while l ~= 0 repeat ans := concat(leadingCoefficient l, ans) l := reductum l ans a:R * y:% == z:% := 0 - while y ^= 0 repeat + while y ~= 0 repeat z := z + monomial(a * leadingCoefficient y, degree y) y := reductum y z @@ -165,7 +165,7 @@ UnivariateSkewPolynomialCategory(R:Ring): if R has IntegralDomain then l exquo a == ans:% := 0 - while l ^= 0 repeat + while l ~= 0 repeat (u := (leadingCoefficient(l) exquo a)) case "failed" => return "failed" ans := ans + monomial(u::R, degree l) @@ -205,7 +205,7 @@ UnivariateSkewPolynomialCategory(R:Ring): a0 := a u0:% := v:% := 1 v0:% := u:% := 0 - while b ^= 0 repeat + while b ~= 0 repeat qr := leftDivide(a, b) (a, b) := (b, qr.remainder) (u0, u):= (u, u0 - u * qr.quotient) @@ -216,7 +216,7 @@ UnivariateSkewPolynomialCategory(R:Ring): zero? a => b zero? b => a degree a < degree b => ncgcd(b, a, ncrem) - while b ^= 0 repeat (a, b) := (b, ncrem(a, b)) + while b ~= 0 repeat (a, b) := (b, ncrem(a, b)) a extended(a, b, eea) == @@ -240,7 +240,7 @@ UnivariateSkewPolynomialCategory(R:Ring): a0 := a u0:% := v:% := 1 v0:% := u:% := 0 - while b ^= 0 repeat + while b ~= 0 repeat qr := rightDivide(a, b) (a, b) := (b, qr.remainder) (u0, u):= (u, u0 - qr.quotient * u) @@ -392,7 +392,7 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where times(x, y, sigma, delta) == zero? y => 0 z:C := 0 - while x ^= 0 repeat + while x ~= 0 repeat z := z + termPoly(leadingCoefficient x, degree x, y, sigma, delta) x := reductum x z @@ -402,7 +402,7 @@ UnivariateSkewPolynomialCategoryOps(R, C): Exports == Implementation where (u := subtractIfCan(n, 1)) case "failed" => a * y n1 := u::N z:C := 0 - while y ^= 0 repeat + while y ~= 0 repeat m := degree y b := leadingCoefficient y z := z + termPoly(a, n1, monomial(sigma b, m + 1), sigma, delta) diff --git a/src/algebra/outform.spad.pamphlet b/src/algebra/outform.spad.pamphlet index 9b2c13fe..8fd70793 100644 --- a/src/algebra/outform.spad.pamphlet +++ b/src/algebra/outform.spad.pamphlet @@ -180,17 +180,17 @@ NumberFormats(): NFexports == NFimplementation where n := romval ord c -- (I)=1000, ((I))=10000, (((I)))=100000, etc if n < 0 then - c ^= pren => + c ~= pren => error ["Improper character in Roman numeral: ",c] nprens: PI := 1 while c = pren and i >= minIndex s repeat c := s.i; i := i-1 if c = pren then nprens := nprens+1 - c ^= ichar => + c ~= ichar => error "Improper Roman numeral: (x)" for k in 1..nprens while i >= minIndex s repeat c := s.i; i := i-1 - c ^= plen => + c ~= plen => error "Improper Roman numeral: unbalanced ')'" n := 10**(nprens + 2) if n < Max then @@ -420,8 +420,8 @@ OutputForm(): SetCategory with --% Specific applications "=": ($, $) -> $ ++ f = g creates the equivalent infix form. - "^=": ($, $) -> $ - ++ f ^= g creates the equivalent infix form. + "~=": ($, $) -> $ + ++ f ~= g creates the equivalent infix form. "<": ($, $) -> $ ++ f < g creates the equivalent infix form. ">": ($, $) -> $ @@ -571,7 +571,7 @@ OutputForm(): SetCategory with vconcat(a,b) == [eform VCONCAT, a, b] vconcat l == cons(eform VCONCAT, l) - a ^= b == [sform "^=", a, b] + a ~= b == [sform "~=", a, b] a < b == [sform "<", a, b] a > b == [sform ">", a, b] a <= b == [sform "<=", a, b] @@ -793,7 +793,7 @@ Note that this code is not included in the generated catdef.spad file. (SPADCALL |n| (- |m| 1) (QREFELT $ 46)) (QREFELT $ 45))))) (DEFUN |OUTFORM;matrix;L$;29| (|ll| $) - (PROG (#0=#:G1430 |l| #1=#:G1431 |lv|) + (PROG (#0=#:G1437 |l| #1=#:G1438 |lv|) (RETURN (SEQ (LETT |lv| (PROGN @@ -824,7 +824,7 @@ Note that this code is not included in the generated catdef.spad file. (CONS (|OUTFORM;eform| 'AGGSET $) |l|)) (DEFUN |OUTFORM;blankSeparate;L$;33| (|l| $) - (PROG (|c| |u| #0=#:G1439 |l1|) + (PROG (|c| |u| #0=#:G1446 |l1|) (RETURN (SEQ (LETT |c| (|OUTFORM;eform| 'CONCATB $) |OUTFORM;blankSeparate;L$;33|) @@ -913,8 +913,8 @@ Note that this code is not included in the generated catdef.spad file. (DEFUN |OUTFORM;vconcat;L$;49| (|l| $) (CONS (|OUTFORM;eform| 'VCONCAT $) |l|)) -(DEFUN |OUTFORM;^=;3$;50| (|a| |b| $) - (LIST (|OUTFORM;sform| "^=" $) |a| |b|)) +(DEFUN |OUTFORM;~=;3$;50| (|a| |b| $) + (LIST (|OUTFORM;sform| "~=" $) |a| |b|)) (DEFUN |OUTFORM;<;3$;51| (|a| |b| $) (LIST (|OUTFORM;sform| "<" $) |a| |b|)) @@ -978,7 +978,7 @@ Note that this code is not included in the generated catdef.spad file. (DEFUN |OUTFORM;empty;$;71| ($) (LIST (|OUTFORM;eform| 'NOTHING $))) (DEFUN |OUTFORM;infix?;$B;72| (|a| $) - (PROG (#0=#:G1484 |e|) + (PROG (#0=#:G1491 |e|) (RETURN (SEQ (EXIT (SEQ (LETT |e| (COND @@ -1087,7 +1087,7 @@ Note that this code is not included in the generated catdef.spad file. (LIST (|OUTFORM;eform| 'TAG $) |a| |b|)) (DEFUN |OUTFORM;differentiate;$Nni$;95| (|a| |nn| $) - (PROG (#0=#:G1514 |r| |s|) + (PROG (#0=#:G1521 |r| |s|) (RETURN (SEQ (COND ((ZEROP |nn|) |a|) @@ -1139,7 +1139,7 @@ Note that this code is not included in the generated catdef.spad file. (DEFUN |OutputForm| () (PROG () (RETURN - (PROG (#0=#:G1528) + (PROG (#0=#:G1535) (RETURN (COND ((LETT #0# (HGET |$ConstructorCache| '|OutputForm|) @@ -1199,7 +1199,7 @@ Note that this code is not included in the generated catdef.spad file. |OUTFORM;scripts;$L$;44| (|NonNegativeInteger|) (47 . |#|) (|List| $$) (52 . |append|) |OUTFORM;supersub;$L$;45| |OUTFORM;hconcat;L$;47| |OUTFORM;vconcat;L$;49| - |OUTFORM;^=;3$;50| |OUTFORM;<;3$;51| |OUTFORM;>;3$;52| + |OUTFORM;~=;3$;50| |OUTFORM;<;3$;51| |OUTFORM;>;3$;52| |OUTFORM;<=;3$;53| |OUTFORM;>=;3$;54| |OUTFORM;+;3$;55| |OUTFORM;-;3$;56| |OUTFORM;-;2$;57| |OUTFORM;*;3$;58| |OUTFORM;/;3$;59| |OUTFORM;**;3$;60| |OUTFORM;div;3$;61| @@ -1226,23 +1226,23 @@ Note that this code is not included in the generated catdef.spad file. |OUTFORM;prod;3$;100| |OUTFORM;prod;4$;101| |OUTFORM;int;2$;102| |OUTFORM;int;3$;103| |OUTFORM;int;4$;104| (|SingleInteger|)) - '#(~= 78 |zag| 84 |width| 90 |vspace| 99 |vconcat| 104 - |supersub| 115 |superHeight| 121 |super| 126 |sum| 132 - |subHeight| 150 |sub| 155 |string| 161 |slash| 166 - |semicolonSeparate| 172 |scripts| 177 |rspace| 183 |root| - 189 |right| 200 |rem| 211 |rarrow| 217 |quote| 223 |quo| - 228 |prod| 234 |print| 252 |prime| 257 |presuper| 268 - |presub| 274 |prefix| 280 |postfix| 286 |pile| 292 |paren| - 297 |overlabel| 307 |overbar| 313 |over| 318 |outputForm| - 324 |or| 344 |not| 350 |messagePrint| 355 |message| 360 - |matrix| 365 |left| 370 |latex| 381 |label| 386 |int| 392 - |infix?| 410 |infix| 415 |hspace| 428 |height| 433 - |hconcat| 442 |hash| 453 |exquo| 458 |empty| 464 |elt| 468 - |dot| 474 |div| 485 |differentiate| 491 |commaSeparate| - 497 |coerce| 502 |center| 507 |bracket| 518 |brace| 528 - |box| 538 |blankSeparate| 543 |binomial| 548 |assign| 554 - |and| 560 ^= 566 SEGMENT 572 >= 583 > 589 = 595 <= 607 < - 613 / 619 - 625 + 636 ** 642 * 648) + '#(~= 78 |zag| 90 |width| 96 |vspace| 105 |vconcat| 110 + |supersub| 121 |superHeight| 127 |super| 132 |sum| 138 + |subHeight| 156 |sub| 161 |string| 167 |slash| 172 + |semicolonSeparate| 178 |scripts| 183 |rspace| 189 |root| + 195 |right| 206 |rem| 217 |rarrow| 223 |quote| 229 |quo| + 234 |prod| 240 |print| 258 |prime| 263 |presuper| 274 + |presub| 280 |prefix| 286 |postfix| 292 |pile| 298 |paren| + 303 |overlabel| 313 |overbar| 319 |over| 324 |outputForm| + 330 |or| 350 |not| 356 |messagePrint| 361 |message| 366 + |matrix| 371 |left| 376 |latex| 387 |label| 392 |int| 398 + |infix?| 416 |infix| 421 |hspace| 434 |height| 439 + |hconcat| 448 |hash| 459 |exquo| 464 |empty| 470 |elt| 474 + |dot| 480 |div| 491 |differentiate| 497 |commaSeparate| + 503 |coerce| 508 |center| 513 |bracket| 524 |brace| 534 + |box| 544 |blankSeparate| 549 |binomial| 554 |assign| 560 + |and| 566 SEGMENT 572 >= 583 > 589 = 595 <= 607 < 613 / + 619 - 625 + 636 ** 642 * 648) 'NIL (CONS (|makeByteWordVec2| 1 '(0 0 0)) (CONS '#(|SetCategory&| |BasicType&| NIL) @@ -1254,42 +1254,42 @@ Note that this code is not included in the generated catdef.spad file. 54 1 6 9 0 66 1 6 0 0 67 1 6 2 0 68 1 6 70 0 71 2 72 0 0 0 73 1 72 0 0 101 1 25 0 10 110 1 124 10 123 125 1 10 0 - 0 126 2 0 9 0 0 1 2 0 0 0 0 115 0 0 - 19 35 1 0 19 0 30 1 0 0 19 44 1 0 0 - 49 76 2 0 0 0 0 45 2 0 0 0 49 74 1 0 - 19 0 33 2 0 0 0 0 63 2 0 0 0 0 129 3 - 0 0 0 0 0 130 1 0 0 0 128 1 0 19 0 32 - 2 0 0 0 0 62 1 0 0 0 105 2 0 0 0 0 - 119 1 0 0 49 52 2 0 0 0 49 69 2 0 0 - 19 19 46 1 0 0 0 116 2 0 0 0 0 117 1 - 0 0 0 43 2 0 0 0 19 40 2 0 0 0 0 89 2 - 0 0 0 0 122 1 0 0 0 106 2 0 0 0 0 90 - 3 0 0 0 0 0 133 1 0 0 0 131 2 0 0 0 0 - 132 1 0 7 0 8 2 0 0 0 70 112 1 0 0 0 - 109 2 0 0 0 0 65 2 0 0 0 0 64 2 0 0 0 - 49 100 2 0 0 0 0 104 1 0 0 49 50 1 0 - 0 49 61 1 0 0 0 60 2 0 0 0 0 113 1 0 - 0 0 107 2 0 0 0 0 118 1 0 0 10 29 1 0 - 0 23 24 1 0 0 21 22 1 0 0 19 20 2 0 0 - 0 0 93 1 0 0 0 94 1 0 7 10 14 1 0 0 - 10 13 1 0 0 47 48 1 0 0 0 42 2 0 0 0 - 19 39 1 0 10 0 1 2 0 0 0 0 121 3 0 0 - 0 0 0 136 2 0 0 0 0 135 1 0 0 0 134 1 - 0 9 0 98 2 0 0 0 49 102 3 0 0 0 0 0 - 103 1 0 0 19 36 0 0 19 34 1 0 19 0 31 - 1 0 0 49 75 2 0 0 0 0 37 1 0 137 0 1 - 2 0 0 0 0 91 0 0 0 12 2 0 0 0 49 99 2 - 0 0 0 70 111 1 0 0 0 108 2 0 0 0 0 88 - 2 0 0 0 70 127 1 0 0 49 51 1 0 17 0 - 18 1 0 0 0 41 2 0 0 0 19 38 1 0 0 0 - 58 1 0 0 49 59 1 0 0 49 57 1 0 0 0 56 - 1 0 0 0 114 1 0 0 49 55 2 0 0 0 0 97 - 2 0 0 0 0 120 2 0 0 0 0 92 2 0 0 0 0 - 77 1 0 0 0 96 2 0 0 0 0 95 2 0 0 0 0 - 81 2 0 0 0 0 79 2 0 0 0 0 16 2 0 9 0 - 0 15 2 0 0 0 0 80 2 0 0 0 0 78 2 0 0 - 0 0 86 1 0 0 0 84 2 0 0 0 0 83 2 0 0 - 0 0 82 2 0 0 0 0 87 2 0 0 0 0 85))))) + 0 126 2 0 0 0 0 77 2 0 9 0 0 1 2 0 0 + 0 0 115 0 0 19 35 1 0 19 0 30 1 0 0 + 19 44 1 0 0 49 76 2 0 0 0 0 45 2 0 0 + 0 49 74 1 0 19 0 33 2 0 0 0 0 63 2 0 + 0 0 0 129 3 0 0 0 0 0 130 1 0 0 0 128 + 1 0 19 0 32 2 0 0 0 0 62 1 0 0 0 105 + 2 0 0 0 0 119 1 0 0 49 52 2 0 0 0 49 + 69 2 0 0 19 19 46 1 0 0 0 116 2 0 0 0 + 0 117 1 0 0 0 43 2 0 0 0 19 40 2 0 0 + 0 0 89 2 0 0 0 0 122 1 0 0 0 106 2 0 + 0 0 0 90 3 0 0 0 0 0 133 1 0 0 0 131 + 2 0 0 0 0 132 1 0 7 0 8 2 0 0 0 70 + 112 1 0 0 0 109 2 0 0 0 0 65 2 0 0 0 + 0 64 2 0 0 0 49 100 2 0 0 0 0 104 1 0 + 0 49 50 1 0 0 49 61 1 0 0 0 60 2 0 0 + 0 0 113 1 0 0 0 107 2 0 0 0 0 118 1 0 + 0 10 29 1 0 0 23 24 1 0 0 21 22 1 0 0 + 19 20 2 0 0 0 0 93 1 0 0 0 94 1 0 7 + 10 14 1 0 0 10 13 1 0 0 47 48 1 0 0 0 + 42 2 0 0 0 19 39 1 0 10 0 1 2 0 0 0 0 + 121 3 0 0 0 0 0 136 2 0 0 0 0 135 1 0 + 0 0 134 1 0 9 0 98 2 0 0 0 49 102 3 0 + 0 0 0 0 103 1 0 0 19 36 0 0 19 34 1 0 + 19 0 31 1 0 0 49 75 2 0 0 0 0 37 1 0 + 137 0 1 2 0 0 0 0 91 0 0 0 12 2 0 0 0 + 49 99 2 0 0 0 70 111 1 0 0 0 108 2 0 + 0 0 0 88 2 0 0 0 70 127 1 0 0 49 51 1 + 0 17 0 18 1 0 0 0 41 2 0 0 0 19 38 1 + 0 0 0 58 1 0 0 49 59 1 0 0 49 57 1 0 + 0 0 56 1 0 0 0 114 1 0 0 49 55 2 0 0 + 0 0 97 2 0 0 0 0 120 2 0 0 0 0 92 1 0 + 0 0 96 2 0 0 0 0 95 2 0 0 0 0 81 2 0 + 0 0 0 79 2 0 0 0 0 16 2 0 9 0 0 15 2 + 0 0 0 0 80 2 0 0 0 0 78 2 0 0 0 0 86 + 1 0 0 0 84 2 0 0 0 0 83 2 0 0 0 0 82 + 2 0 0 0 0 87 2 0 0 0 0 85))))) '|lookupComplete|)) (MAKEPROP '|OutputForm| 'NILADIC T) diff --git a/src/algebra/pade.spad.pamphlet b/src/algebra/pade.spad.pamphlet index de1a71b2..475212ef 100644 --- a/src/algebra/pade.spad.pamphlet +++ b/src/algebra/pade.spad.pamphlet @@ -162,7 +162,7 @@ PadeApproximants(R,PS,UP): Exports == Implementation where (l,m) := (m,l) plist := concat(0,plist) alist := concat(0,alist) - -- Ensure l >= m, maintaining coef(dps,0)^=0. + -- Ensure l >= m, maintaining coef(dps,0)~=0. if l < m then -- (a<n>*x**n + a<n+1>*x**n+1 + ...)/b -- = x**n/b + (a<n> + a<n+1>*x + ...)/b diff --git a/src/algebra/padic.spad.pamphlet b/src/algebra/padic.spad.pamphlet index a75faa77..e17fe7dc 100644 --- a/src/algebra/padic.spad.pamphlet +++ b/src/algebra/padic.spad.pamphlet @@ -116,7 +116,7 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where modPInfo n == dv := divide(n,p) r0 := dv.remainder; q := dv.quotient - if (r := modP r0) ^= r0 then q := q + ((r0 - r) quo p) + if (r := modP r0) ~= r0 then q := q + ((r0 - r) quo p) [r,q] invModP: I -> I @@ -135,7 +135,7 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where n : I := _$streamCount$Lisp for i in 0..n repeat empty? st => return true - frst st ^= 0 => return false + frst st ~= 0 => return false st := rst st empty? st @@ -143,7 +143,7 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where st := stream x for i in 0..1000 repeat empty? st => return 0 - frst st ^= 0 => return i + frst st ~= 0 => return i st := rst st error "order: series has more than 1000 leading zero coefs" @@ -293,13 +293,13 @@ InnerPAdicInteger(p,unBalanced?): Exports == Implementation where n : NNI ; count : NNI := _$streamCount$Lisp l : L OUT := empty() for n in 0..count while not empty? st repeat - if frst(st) ^= 0 then + if frst(st) ~= 0 then l := concat(termOutput(n :: I,frst st),l) st := rst st if showAll?() then for n in (count + 1).. while explicitEntries? st and _ not eq?(st,rst st) repeat - if frst(st) ^= 0 then + if frst(st) ~= 0 then l := concat(termOutput(n pretend I,frst st),l) st := rst st l := @@ -515,13 +515,13 @@ PAdicRationalConstructor(p,PADIC): Exports == Implementation where empty? uu => 0 :: OUT n : NNI ; count : NNI := _$streamCount$Lisp for n in 0..count while not empty? uu repeat - if frst(uu) ^= 0 then + if frst(uu) ~= 0 then l := concat(termOutput((n :: I) + m,frst(uu)),l) uu := rst uu if showAll?() then for n in (count + 1).. while explicitEntries? uu and _ not eq?(uu,rst uu) repeat - if frst(uu) ^= 0 then + if frst(uu) ~= 0 then l := concat(termOutput((n::I) + m,frst(uu)),l) uu := rst uu l := diff --git a/src/algebra/patmatch1.spad.pamphlet b/src/algebra/patmatch1.spad.pamphlet index 381bbf30..1ee6220f 100644 --- a/src/algebra/patmatch1.spad.pamphlet +++ b/src/algebra/patmatch1.spad.pamphlet @@ -283,7 +283,7 @@ PatternMatchKernel(S, E): Exports == Implementation where -- matches the ordered lists ls and lp. patternMatchArg(ls, lp, l) == - #ls ^= #lp => failed() + #ls ~= #lp => failed() for p in lp for s in ls repeat generic? p and failed?(l := addMatch(p,s,l)) => return failed() for p in lp for s in ls repeat @@ -518,7 +518,7 @@ PatternMatchTools(S, R, P): Exports == Implementation where patternMatchTimes(ls, lp, l, pmatch) == member?(mn1, lp) => (u := negConstant ls) case "failed" => failed() - if (u::P ^= -1::P) then ls := concat(-u::P, ls) + if (u::P ~= -1::P) then ls := concat(-u::P, ls) patternMatch(remove(u::P,ls), remove(mn1,lp), */#1, l, pmatch) patternMatch(ls, lp, */#1, l, pmatch) diff --git a/src/algebra/pattern.spad.pamphlet b/src/algebra/pattern.spad.pamphlet index e22e9207..fe011879 100644 --- a/src/algebra/pattern.spad.pamphlet +++ b/src/algebra/pattern.spad.pamphlet @@ -195,7 +195,7 @@ Pattern(R:SetCategory): Exports == Implementation where generic? p == symbol? p and bitSet?(p.pat.sym.tag, SYM_GENERIC) multiple? p == symbol? p and bitSet?(p.pat.sym.tag,SYM_MULTIPLE) optional? p == symbol? p and bitSet?(p.pat.sym.tag,SYM_OPTIONAL) - bitSet?(a, b) == And(a, b) ^= 0 + bitSet?(a, b) == And(a, b) ~= 0 coerce(p:%):O == PAT2O(p.pat) p1:% ** p2:% == taggedElt(PAT_EXPT, [p1, p2]) LPAT2O(f, l) == reduce(f, [x::O for x in l])$List(O) diff --git a/src/algebra/pdecomp.spad.pamphlet b/src/algebra/pdecomp.spad.pamphlet index 37057fc4..8f60ecd0 100644 --- a/src/algebra/pdecomp.spad.pamphlet +++ b/src/algebra/pdecomp.spad.pamphlet @@ -20,7 +20,7 @@ PolynomialComposition(UP: UnivariatePolynomialCategory(R), R: Ring): with == add compose(g, h) == r: UP := 0 - while g ^= 0 repeat + while g ~= 0 repeat r := leadingCoefficient(g)*h**degree(g) + r g := reductum g r @@ -50,7 +50,7 @@ PolynomialDecomposition(UP, F): PDcat == PDdef where PDdef == add leftFactor(f, h) == g: UP := 0 - for i in 0.. while f ^= 0 repeat + for i in 0.. while f ~= 0 repeat fr := divide(f, h) f := fr.quotient; r := fr.remainder degree r > 0 => return "failed" @@ -59,7 +59,7 @@ PolynomialDecomposition(UP, F): PDcat == PDdef where decompose(f, dg, dh) == df := degree f - dg*dh ^= df => "failed" + dg*dh ~= df => "failed" h := rightFactorCandidate(f, dh) g := leftFactor(f, h) g case "failed" => "failed" diff --git a/src/algebra/perm.spad.pamphlet b/src/algebra/perm.spad.pamphlet index 23f24341..141f9c58 100644 --- a/src/algebra/perm.spad.pamphlet +++ b/src/algebra/perm.spad.pamphlet @@ -224,10 +224,10 @@ domain. perm smallerCycle?(cyca: L S, cycb: L S): B == - #cyca ^= #cycb => + #cyca ~= #cycb => #cyca < #cycb for i in cyca for j in cycb repeat - i ^= j => return smaller?(i, j) + i ~= j => return smaller?(i, j) false shorterCycle?(cyca: L S, cycb: L S): B == @@ -235,7 +235,7 @@ domain. permord(pa: RECCYPE, pb : RECCYPE): B == for i in pa.cycl for j in pb.cycl repeat - i ^= j => return smallerCycle?(i, j) + i ~= j => return smallerCycle?(i, j) #pa.cycl < #pb.cycl coerceToCycle(p: %, doSorting?: B): L L S == @@ -249,7 +249,7 @@ domain. preim := rest preim nextEltInCycle := first im im := rest im - while nextEltInCycle ^= firstEltInCycle repeat + while nextEltInCycle ~= firstEltInCycle repeat nextCycle := cons(nextEltInCycle, nextCycle) i := position(nextEltInCycle, preim) preim := delete(preim,i) @@ -325,18 +325,18 @@ removes fixed points from its result. degree p == #movedPoints p p = q == - #(preimp := p.1) ^= #(preimq := q.1) => false + #(preimp := p.1) ~= #(preimq := q.1) => false for i in 1..maxIndex preimp repeat pos := position(preimp.i, preimq) pos = 0 => return false - (p.2).i ^= (q.2).pos => return false + (p.2).i ~= (q.2).pos => return false true orbit(p ,el) == -- start with a 1-element list: out : Set S := brace list el el2 := eval(p, el) - while el2 ^= el repeat + while el2 ~= el repeat -- be carefull: insert adds one element -- as side effect to out insert_!(el2, out) @@ -365,7 +365,7 @@ removes fixed points from its result. pacyc:= coerceToCycle(pa,true) pbcyc:= coerceToCycle(pb,true) for i in pacyc for j in pbcyc repeat - i ^= j => return smallerCycle? ( i, j ) + i ~= j => return smallerCycle? ( i, j ) maxIndex pacyc < maxIndex pbcyc coerce(lls : L L S): % == coerceCycle lls @@ -410,11 +410,11 @@ removes fixed points from its result. preim := nil()$(L S) im := nil()$(L S) for pair in loP repeat - if first pair ^= second pair then + if first pair ~= second pair then preim := cons(first pair, preim) im := cons(second pair, im) duplicates?(preim) or duplicates?(im) or brace(preim)$(Set S) _ - ^= brace(im)$(Set S) => + ~= brace(im)$(Set S) => error "coerceListOfPairs: the input cannot be interpreted as a permutation" [preim, im] @@ -439,7 +439,7 @@ removes fixed points from its result. el := imOfq.j -- if the composition fixes the element, we don't -- have to do anything - if el ^= preimOfp.i then + if el ~= preimOfp.i then preimOfqp := cons(preimOfp.i, preimOfqp) imOfqp := cons(el, imOfqp) -- we drop the parts of q which have to do with p diff --git a/src/algebra/perman.spad.pamphlet b/src/algebra/perman.spad.pamphlet index bc2f63f1..2fa6e43d 100644 --- a/src/algebra/perman.spad.pamphlet +++ b/src/algebra/perman.spad.pamphlet @@ -135,7 +135,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")): ++ some modifications are necessary: ++ \item 2. if {\em n > 6} and R is an integral domain with characteristic ++ different from 2 (the algorithm works if and only 2 is not a - ++ zero-divisor of R and {\em characteristic()$R ^= 2}, + ++ zero-divisor of R and {\em characteristic()$R ~= 2}, ++ but how to check that for any given R ?), ++ the local function {\em permanent2} is called; ++ \item 3. else, the local function {\em permanent3} is called @@ -166,7 +166,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")): -- For the meaning of the elements of vv, see GRAY. w : V R := new(n,0$R) j := 1 -- Will be the number of the element changed in subset - while j ^= (n+1) repeat -- we sum over all subsets of (1,...,n) + while j ~= (n+1) repeat -- we sum over all subsets of (1,...,n) sgn := -sgn b := sgn if vv.1.j = 1 then k := -1 @@ -211,7 +211,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")): b := b * w.i a := a+b j := 1 -- Will be the number of the element changed in subset - while j ^= n repeat -- we sum over all subsets of (1,...,n-1) + while j ~= n repeat -- we sum over all subsets of (1,...,n-1) sgn := -sgn b := sgn if vv.1.j = 1 then k := -1 @@ -256,7 +256,7 @@ Permanent(n : PositiveInteger, R : Ring with commutative("*")): b := b *$R w.i a := a +$R b j := 1 -- Will be the number of the element changed in subset - while j ^= n repeat -- we sum over all subsets of (1,...,n-1) + while j ~= n repeat -- we sum over all subsets of (1,...,n-1) sgn := -sgn b := sgn if vv.1.j = 1 then k := -1 diff --git a/src/algebra/permgrps.spad.pamphlet b/src/algebra/permgrps.spad.pamphlet index 0b3fa62d..ee97d7ed 100644 --- a/src/algebra/permgrps.spad.pamphlet +++ b/src/algebra/permgrps.spad.pamphlet @@ -218,7 +218,7 @@ PermutationGroup(S:SetCategory): public == private where flag := false while pointer > 1 repeat pointer := ( pointer - 1 )::NNI - if newlw.pointer ^= test then + if newlw.pointer ~= test then -- don't get a trivial element, try next test := newlw.pointer anzahl := 1 @@ -294,7 +294,7 @@ PermutationGroup(S:SetCategory): public == private where testIdentity ( p : V NNI ) : B == -- internal test for identity - for i in 1..degree repeat qelt(p,i) ^= i => return false + for i in 1..degree repeat qelt(p,i) ~= i => return false true pointList(group : %) : L S == @@ -346,14 +346,14 @@ PermutationGroup(S:SetCategory): public == private where ort := orbitWithSvc ( group , i ) k := ort.orb k1 := # k - if k1 ^= 1 then leave + if k1 ~= 1 then leave gpsgs := nil()$(L V NNI) words2 := nil()$(L L NNI) gplength : NNI := #group - for jj in 1..gplength repeat if (group.jj).i ^= i then leave + for jj in 1..gplength repeat if (group.jj).i ~= i then leave for k in 1..gplength repeat el2 := group.k - if el2.i ^= i then + if el2.i ~= i then gpsgs := cons ( el2 , gpsgs ) if wordProblem then words2 := cons ( words.k , words2 ) else @@ -432,7 +432,7 @@ PermutationGroup(S:SetCategory): public == private where pt2 := baseLength - j + 1 sgs2 := append ( sgs2 , out.j ) obs2 := orbitWithSvc ( sgs2 , baseOfGroup.pt2 ) - if # obs2.orb ^= orbitLength.j then + if # obs2.orb ~= orbitLength.j then test := false leave if test then @@ -541,7 +541,7 @@ PermutationGroup(S:SetCategory): public == private where word := shortenWord ( word , group ) if newBasePoint then for i in 1..degree repeat - if z.i ^= i then + if z.i ~= i then baseOfGroup := append ( baseOfGroup , [ i ] ) leave out := cons (list z, out ) @@ -739,7 +739,7 @@ PermutationGroup(S:SetCategory): public == private where subgroup ( gp1 , gp2 ) gp1 = gp2 == - movedPoints gp1 ^= movedPoints gp2 => false + movedPoints gp1 ~= movedPoints gp2 => false if #(gp1.gens) <= #(gp2.gens) then not subgroup ( gp1 , gp2 ) => return false else @@ -1007,7 +1007,7 @@ PermutationGroupExamples():public == private where mathieu11(l:L I):PERMGRP I == -- permutations derived from the ATLAS l:=removeDuplicates l - #l ^= 11 => error "Exactly 11 integers for mathieu11 needed !" + #l ~= 11 => error "Exactly 11 integers for mathieu11 needed !" a:L L I:=[[l.1,l.10],[l.2,l.8],[l.3,l.11],[l.5,l.7]] llli2gp [a,[[l.1,l.4,l.7,l.6],[l.2,l.11,l.10,l.9]]] @@ -1016,7 +1016,7 @@ PermutationGroupExamples():public == private where mathieu12(l:L I):PERMGRP I == -- permutations derived from the ATLAS l:=removeDuplicates l - #l ^= 12 => error "Exactly 12 integers for mathieu12 needed !" + #l ~= 12 => error "Exactly 12 integers for mathieu12 needed !" a:L L I:= [[l.1,l.2,l.3,l.4,l.5,l.6,l.7,l.8,l.9,l.10,l.11]] llli2gp [a,[[l.1,l.6,l.5,l.8,l.3,l.7,l.4,l.2,l.9,l.10],[l.11,l.12]]] @@ -1026,7 +1026,7 @@ PermutationGroupExamples():public == private where mathieu22(l:L I):PERMGRP I == -- permutations derived from the ATLAS l:=removeDuplicates l - #l ^= 22 => error "Exactly 22 integers for mathieu22 needed !" + #l ~= 22 => error "Exactly 22 integers for mathieu22 needed !" a:L L I:=[[l.1,l.2,l.4,l.8,l.16,l.9,l.18,l.13,l.3,l.6,l.12], _ [l.5,l.10,l.20,l.17,l.11,l.22,l.21,l.19,l.15,l.7,l.14]] b:L L I:= [[l.1,l.2,l.6,l.18],[l.3,l.15],[l.5,l.8,l.21,l.13], _ @@ -1038,7 +1038,7 @@ PermutationGroupExamples():public == private where mathieu23(l:L I):PERMGRP I == -- permutations derived from the ATLAS l:=removeDuplicates l - #l ^= 23 => error "Exactly 23 integers for mathieu23 needed !" + #l ~= 23 => error "Exactly 23 integers for mathieu23 needed !" a:L L I:= [[l.1,l.2,l.3,l.4,l.5,l.6,l.7,l.8,l.9,l.10,l.11,l.12,l.13,l.14,_ l.15,l.16,l.17,l.18,l.19,l.20,l.21,l.22,l.23]] b:L L I:= [[l.2,l.16,l.9,l.6,l.8],[l.3,l.12,l.13,l.18,l.4], _ @@ -1050,7 +1050,7 @@ PermutationGroupExamples():public == private where mathieu24(l:L I):PERMGRP I == -- permutations derived from the ATLAS l:=removeDuplicates l - #l ^= 24 => error "Exactly 24 integers for mathieu24 needed !" + #l ~= 24 => error "Exactly 24 integers for mathieu24 needed !" a:L L I:= [[l.1,l.16,l.10,l.22,l.24],[l.2,l.12,l.18,l.21,l.7], _ [l.4,l.5,l.8,l.6,l.17],[l.9,l.11,l.13,l.19,l.15]] b:L L I:= [[l.1,l.22,l.13,l.14,l.6,l.20,l.3,l.21,l.8,l.11],[l.2,l.10], _ @@ -1062,7 +1062,7 @@ PermutationGroupExamples():public == private where janko2(l:L I):PERMGRP I == -- permutations derived from the ATLAS l:=removeDuplicates l - #l ^= 100 => error "Exactly 100 integers for janko2 needed !" + #l ~= 100 => error "Exactly 100 integers for janko2 needed !" a:L L I:=[ _ [l.2,l.3,l.4,l.5,l.6,l.7,l.8], _ [l.9,l.10,l.11,l.12,l.13,l.14,l.15], _ diff --git a/src/algebra/pfr.spad.pamphlet b/src/algebra/pfr.spad.pamphlet index 8286147e..eeaa4c2f 100644 --- a/src/algebra/pfr.spad.pamphlet +++ b/src/algebra/pfr.spad.pamphlet @@ -147,9 +147,9 @@ PartialFraction(R: EuclideanDomain): Cat == Capsule where coefs := (i :: Record(coef1: R, coef2: R)) c : % := copypf 0$% d : % - if coefs.coef2 ^= 0$R then + if coefs.coef2 ~= 0$R then c := normalizeFracTerm ([coefs.coef2, t.den]$fTerm) - if coefs.coef1 ^= 0$R then + if coefs.coef1 ~= 0$R then d := normalizeFracTerm ([coefs.coef1, s.den]$fTerm) c.whole := c.whole + d.whole not (null d.fract) => c.fract := append(d.fract,c.fract) @@ -200,7 +200,7 @@ PartialFraction(R: EuclideanDomain): Cat == Capsule where e = 1 => l := cons(s,l) f := nthFactor(s.den,1) d := degree(sp := padicallyExpand(f,s.num)) - while (sp ^= 0$SUPR) repeat + while (sp ~= 0$SUPR) repeat l := cons([leadingCoefficient sp,nilFactor(f,e-d)]$fTerm, l) d := degree(sp := reductum sp) [b.whole, sort(LessThan,l)]$% @@ -282,7 +282,7 @@ PartialFraction(R: EuclideanDomain): Cat == Capsule where padicallyExpand(p,qr.quotient) a = b == - a.whole ^= b.whole => false -- must verify this + a.whole ~= b.whole => false -- must verify this (null a.fract) => null b.fract => a.whole = b.whole false diff --git a/src/algebra/pgcd.spad.pamphlet b/src/algebra/pgcd.spad.pamphlet index 8cee7ec0..e37aa5d0 100644 --- a/src/algebra/pgcd.spad.pamphlet +++ b/src/algebra/pgcd.spad.pamphlet @@ -122,9 +122,9 @@ PolynomialGcdPackage(E,OV,R,P):C == T where member?(lval,ltry) => "new point" ltry:=cons(lval,ltry) uf1:SUP:=completeEval(p1,lvr,lval) - degree uf1 ^= d1 => "new point" + degree uf1 ~= d1 => "new point" uf2:SUP:= completeEval(p2,lvr,lval) - degree uf2 ^= d2 => "new point" + degree uf2 ~= d2 => "new point" u:=gcd(uf1,uf2) du:=degree u --the univariate gcd is 1 @@ -141,7 +141,7 @@ PolynomialGcdPackage(E,OV,R,P):C == T where dd=d1 => if ^((f:=p2 exquo p1) case "failed") then return [[u],ltry,p1]$UTerm - if dd^=d2 then dd:=(dd-1)::NNI + if dd~=d2 then dd:=(dd-1)::NNI dd=d2 => if ^((f:=p1 exquo p2) case "failed") then @@ -183,7 +183,7 @@ PolynomialGcdPackage(E,OV,R,P):C == T where (gd1,gd2):=(l,l) ul:=completeEval(l,lvar1,lval) dl:=degree ul - if degree gcd(ul,differentiate ul) ^=0 then + if degree gcd(ul,differentiate ul) ~=0 then newchoice:=good(l,lvar1,ltry) ul:=newchoice.upol ltry:=newchoice.inval @@ -195,7 +195,7 @@ PolynomialGcdPackage(E,OV,R,P):C == T where d:SUP:=gcd(cons(ul,ulist)) if degree d =0 then return gd1 lquo:=(ul exquo d)::SUP - if degree lquo ^=0 then + if degree lquo ~=0 then lgcd:=gcd(cons(leadingCoefficient l,lcpol)) (gdl:=lift(l,d,lquo,lgcd,lvar1,ldeg,lval)) case "failed" => return notCoprime(g,p2,ldeg,lvar1,ltry) @@ -321,7 +321,7 @@ PolynomialGcdPackage(E,OV,R,P):C == T where df:=degree f leadlist:List(P):=[] - if lgcd^=1 then + if lgcd~=1 then leadpol:=true f:=lgcd*f ldeg:=[n0+n1 for n0 in ldeg for n1 in degree(lgcd,lvar)] @@ -335,7 +335,7 @@ PolynomialGcdPackage(E,OV,R,P):C == T where "failed" plist := pl :: List SUPP (p0:SUPP,p1:SUPP):=(plist.first,plist.2) - if completeEval(p0,lvar,lval) ^= lg.first then + if completeEval(p0,lvar,lval) ~= lg.first then (p0,p1):=(p1,p0) ^leadpol => p0 p0 exquo content(p0) diff --git a/src/algebra/pinterp.spad.pamphlet b/src/algebra/pinterp.spad.pamphlet index d8c1482f..0d3c9a04 100644 --- a/src/algebra/pinterp.spad.pamphlet +++ b/src/algebra/pinterp.spad.pamphlet @@ -24,13 +24,13 @@ PolynomialInterpolationAlgorithms(F, P): Cat == Body where Body ==> add LagrangeInterpolation(lx, ly) == - #lx ^= #ly => + #lx ~= #ly => error "Different number of points and values." ip: P := 0 for xi in lx for yi in ly for i in 0.. repeat pp: P := 1 xp: F := 1 - for xj in lx for j in 0.. | i ^= j repeat + for xj in lx for j in 0.. | i ~= j repeat pp := pp * (monomial(1,1) - monomial(xj,0)) xp := xp * (xi - xj) ip := ip + (yi/xp) * pp diff --git a/src/algebra/pleqn.spad.pamphlet b/src/algebra/pleqn.spad.pamphlet index 8b0569f3..057c9bc3 100644 --- a/src/algebra/pleqn.spad.pamphlet +++ b/src/algebra/pleqn.spad.pamphlet @@ -225,7 +225,7 @@ ParametricLinearEquations(R,Var,Expon,GR): ++ pr2dmp(p) converts p to target domain hasoln: (Fgb, L GR) -> Rec8 ++ hasoln(g, l) tests whether the quasi-algebraic set - ++ defined by p = 0 for p in g and q ^= 0 for q in l + ++ defined by p = 0 for p in g and q ~= 0 for q in l ++ is empty or not and returns a simplified definition ++ of the quasi-algebraic set -- this is now done in QALGSET package @@ -325,7 +325,7 @@ ParametricLinearEquations(R,Var,Expon,GR): w:L GF:=sys.vec p:V GF:=new(n,0) pbas:L V GF:=[] - if k ^= 0 then + if k ~= 0 then augmat:M GF:=zero(k,n+1) for i in rss for i1 in 1.. repeat for j in nss for j1 in 1.. repeat @@ -387,7 +387,7 @@ ParametricLinearEquations(R,Var,Expon,GR): bsolve (coeff, w, h, outname, mode) == r:=nrows coeff -- n:=ncols coeff - r ^= #w => error "number of rows unequal on lhs and rhs" + r ~= #w => error "number of rows unequal on lhs and rhs" newfile:FNAME rksoln:File Rec3 count:I:=0 @@ -613,7 +613,7 @@ ParametricLinearEquations(R,Var,Expon,GR): for nss in nextSublist(n, k) until found repeat matsub := mat(rss, nss) pretend SM(j, GR) detmat := determinant(matsub) - if detmat ^= 0 then + if detmat ~= 0 then found:= (ground? detmat) detmat:=sqfree detmat neweqn:Rec:=construct(detmat,rss,nss) diff --git a/src/algebra/plot.spad.pamphlet b/src/algebra/plot.spad.pamphlet index ea92ae66..01877c29 100644 --- a/src/algebra/plot.spad.pamphlet +++ b/src/algebra/plot.spad.pamphlet @@ -260,7 +260,7 @@ Plot(): Exports == Implementation where NUMFUNEVALS := NUMFUNEVALS + 1 t := c := reverse_! c; p := q := reverse_! q s := (h-l)/(minPoints()::F-1) - if (first t) ^= l then + if (first t) ~= l then t := c := concat(l,c) p := q := concat(f l,p) NUMFUNEVALS := NUMFUNEVALS + 1 diff --git a/src/algebra/plot3d.spad.pamphlet b/src/algebra/plot3d.spad.pamphlet index 804a1207..575498d5 100644 --- a/src/algebra/plot3d.spad.pamphlet +++ b/src/algebra/plot3d.spad.pamphlet @@ -218,7 +218,7 @@ Plot3D(): Exports == Implementation where NUMFUNEVALS := NUMFUNEVALS + 1 t := c := reverse_! c; p := q := reverse_! q s := (h-l)/(MINPOINTS::F-1) - if (first t) ^= l then + if (first t) ~= l then t := c := concat(l,c); p := q := concat(f l,p) NUMFUNEVALS := NUMFUNEVALS + 1 while not null rest t repeat diff --git a/src/algebra/poltopol.spad.pamphlet b/src/algebra/poltopol.spad.pamphlet index b1f1801d..296c0027 100644 --- a/src/algebra/poltopol.spad.pamphlet +++ b/src/algebra/poltopol.spad.pamphlet @@ -79,7 +79,7 @@ MPolyCatFunctions3(Vars1,Vars2,E1,E2,R,PR1,PR2): C == T where up := univariate(p, x1::Vars1) x2 := f(x1::Vars1) ans:PR2 := 0 - while up ^= 0 repeat + while up ~= 0 repeat ans := ans + monomial(map(f,leadingCoefficient up),x2,degree up) up := reductum up ans diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet index ad0206cd..fe9eb615 100644 --- a/src/algebra/poly.spad.pamphlet +++ b/src/algebra/poly.spad.pamphlet @@ -54,7 +54,7 @@ FreeModule(R:Ring,S:OrderedSet): -- one? r => x (r = 1) => x --map(r*#1,x) - [[u.k,a] for u in x | (a:=r*u.c) ^= 0$R] + [[u.k,a] for u in x | (a:=r*u.c) ~= 0$R] if R has EntireRing then x * r == zero? r => 0 @@ -68,7 +68,7 @@ FreeModule(R:Ring,S:OrderedSet): -- one? r => x (r = 1) => x --map(r*#1,x) - [[u.k,a] for u in x | (a:=u.c*r) ^= 0$R] + [[u.k,a] for u in x | (a:=u.c*r) ~= 0$R] coerce(x) : OutputForm == null x => (0$R) :: OutputForm @@ -288,7 +288,7 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C -- null p2 => 0 -- zero?(p1.first.k) => p1.first.c * p2 -- one? p2 => p1 --- +/[[[t1.k+t2.k,r]$Term for t2 in p2 | (r:=t1.c*t2.c) ^= 0] +-- +/[[[t1.k+t2.k,r]$Term for t2 in p2 | (r:=t1.c*t2.c) ~= 0] -- for t1 in reverse(p1)] -- -- This 'reverse' is an efficiency improvement: -- -- reduces both time and space [Abbott/Bradford/Davenport] @@ -348,7 +348,7 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C while not null p1 and p1.first.k > e2 repeat (rout:=[p1.first,:rout]; p1:=p1.rest) --use PUSH and POP? null p1 or p1.first.k < e2 => rout:=[[e2,c2],:rout] - if (u:=p1.first.c + c2) ^= 0 then rout:=[[e2, u],:rout] + if (u:=p1.first.c + c2) ~= 0 then rout:=[[e2, u],:rout] p1:=p1.rest NRECONC(rout,p1)$Lisp if R has approximate then @@ -501,7 +501,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with while not null p1 and p1.first.k > e2 repeat (rout:=[p1.first,:rout]; p1:=p1.rest) --use PUSH and POP? null p1 or p1.first.k < e2 => rout:=[[e2,c2],:rout] - if (u:=p1.first.c + c2) ^= 0 then rout:=[[e2, u],:rout] + if (u:=p1.first.c + c2) ~= 0 then rout:=[[e2, u],:rout] p1:=p1.rest NRECONC(rout,p1)$Lisp @@ -600,7 +600,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with while not null p1 and p1.first.k > e2 repeat (rout:=[p1.first,:rout]; p1:=p1.rest) --use PUSH and POP? null p1 or p1.first.k < e2 => rout:=[[e2,c2],:rout] - if (u:=p1.first.c + c2) ^= 0 then rout:=[[e2, u],:rout] + if (u:=p1.first.c + c2) ~= 0 then rout:=[[e2, u],:rout] p1:=p1.rest NRECONC(rout,p1)$Lisp pseudoRemainder(p1,p2) == @@ -651,7 +651,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with monicDivide(p1:%,p2:%) == null p2 => error "monicDivide: division by 0" - leadingCoefficient p2 ^= 1 => error "Divisor Not Monic" + leadingCoefficient p2 ~= 1 => error "Divisor Not Monic" p2 = 1 => [p1,0] null p1 => [0,0] degree p1 < (n:=degree p2) => [0,p1] @@ -679,7 +679,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with -- p:=pseudoRemainder(p1,p2) -- co:=1$R; -- e:= (p1.first.k - p2.first.k):NonNegativeInteger --- while not null p and p.first.k ^= 0 repeat +-- while not null p and p.first.k ~= 0 repeat -- p1:=p2; p2:=p; p:=pseudoRemainder(p1,p2) -- null p or p.first.k = 0 => "enuf" -- co:=(p1.first.c ** e exquo co ** max(0, (e-1))::NonNegativeInteger)::R @@ -727,7 +727,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with n:=p2.first.k p2:=p2.rest rout:=empty()$List(Term) - while p1 ^= 0 repeat + while p1 ~= 0 repeat (u:=subtractIfCan(p1.first.k, n)) case "failed" => leave rout:=[[u, ct * p1.first.c], :rout] p1:=fmecg(p1.rest, rout.first.k, rout.first.c, p2) @@ -938,7 +938,7 @@ UnivariatePolynomialSquareFree(RC:IntegralDomain,P):C == T makeFR(u,[["sqfr",c,1]]) i:NonNegativeInteger:=0; lffe:List FF:=[] lcp := leadingCoefficient p - while degree(ci)^=0 repeat + while degree(ci)~=0 repeat ci:=(ci exquo pi)::P di:=(di exquo pi)::P - differentiate(ci) pi:=gcd(ci,di) @@ -960,7 +960,7 @@ UnivariatePolynomialSquareFree(RC:IntegralDomain,P):C == T di := (p exquo ci)::P i:NonNegativeInteger:=0; lffe:List FF:=[] dunit : P := 1 - while degree(di)^=0 repeat + while degree(di)~=0 repeat diprev := di di := gcd(ci,di) ci:=(ci exquo di)::P @@ -1081,7 +1081,7 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where cont1:=cont1*((unit listfin1)**uexp) pfaclist:=append(flistfin1,pfaclist) cont:=cont*cont1 - cont ^= 1 => + cont ~= 1 => sqp := squareFree cont pfaclist:= append (factorList sqp,pfaclist) makeFR(unit(sqp)*coefficient(unit squf,0),pfaclist) @@ -1090,7 +1090,7 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where squareFree(p:P) == mv:=mainVariable p mv case "failed" => makeFR(p,[])$Factored(P) - characteristic$RC ^=0 => finSqFr(p,variables p) + characteristic$RC ~=0 => finSqFr(p,variables p) up:=univariate(p,mv) cont := content up up := (up exquo cont)::SUP @@ -1098,7 +1098,7 @@ PolynomialSquareFree(VarSet:OrderedSet,E,RC:GcdDomain,P):C == T where pfaclist:List FF := [[u.flg,multivariate(u.fctr,mv),u.xpnt] for u in factorList squp] - cont ^= 1 => + cont ~= 1 => sqp := squareFree cont makeFR(unit(sqp)*coefficient(unit squp,0), append(factorList sqp, pfaclist)) diff --git a/src/algebra/polycat.spad.pamphlet b/src/algebra/polycat.spad.pamphlet index bb940038..05ee03f9 100644 --- a/src/algebra/polycat.spad.pamphlet +++ b/src/algebra/polycat.spad.pamphlet @@ -361,7 +361,7 @@ PolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, VarSet:OrderedSet): -- concat(leadingMonomial p, monomials reductum p) -- replaced by sequential version for efficiency, by WMSIT, 7/30/90 ml:= empty$List(%) - while p ^= 0 repeat + while p ~= 0 repeat ml:=concat(leadingMonomial p, ml) p:= reductum p reverse ml @@ -408,7 +408,7 @@ PolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, VarSet:OrderedSet): ground? p => 0 u := univariate(p, mainVariable(p)::VarSet) d: NonNegativeInteger := 0 - while u ^= 0 repeat + while u ~= 0 repeat d := max(d, degree u + totalDegree leadingCoefficient u) u := reductum u d @@ -418,7 +418,7 @@ PolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, VarSet:OrderedSet): d: NonNegativeInteger := 0 w: NonNegativeInteger := 0 if member?(v, lv) then w:=1 - while u ^= 0 repeat + while u ~= 0 repeat d := max(d, w*(degree u) + totalDegree(leadingCoefficient u,lv)) u := reductum u d @@ -2960,7 +2960,7 @@ UnivariatePolynomialCategory(R:Ring): Category == if R has Algebra Fraction Integer then integrate p == ans:% := 0 - while p ^= 0 repeat + while p ~= 0 repeat l := leadingCoefficient p d := 1 + degree p ans := ans + inv(d::Fraction(Integer)) * monomial(l, d) @@ -4326,7 +4326,7 @@ UnivariatePolynomialCategoryFunctions2(R,PR,S,PS): Exports == Impl where Impl ==> add map(f, p) == ans:PS := 0 - while p ^= 0 repeat + while p ~= 0 repeat ans := ans + monomial(f leadingCoefficient p, degree p) p := reductum p ans @@ -4365,14 +4365,14 @@ CommuteUnivariatePolynomialCategory(R, UP, UPUP): Exports == Impl where -- converts P(x,y) to P(y,x) swap poly == ans:UPUP := 0 - while poly ^= 0 repeat + while poly ~= 0 repeat ans := ans + makePoly(leadingCoefficient poly, degree poly) poly := reductum poly ans makePoly(poly, d) == ans:UPUP := 0 - while poly ^= 0 repeat + while poly ~= 0 repeat ans := ans + monomial(monomial(leadingCoefficient poly, d), degree poly) poly := reductum poly diff --git a/src/algebra/primelt.spad.pamphlet b/src/algebra/primelt.spad.pamphlet index baee4e62..cc1d9bf4 100644 --- a/src/algebra/primelt.spad.pamphlet +++ b/src/algebra/primelt.spad.pamphlet @@ -93,7 +93,7 @@ PrimitiveElement(F): Exports == Implementation where ll := nil()$List(UP) for v in lv repeat ((u := findUniv(l, v, w)) case "failed") or - (degree(p := univariate(u::P, v)) ^= 1) => return "failed" + (degree(p := univariate(u::P, v)) ~= 1) => return "failed" (bc := extendedEuclidean(univariate leadingCoefficient p, pw,1)) case "failed" => error "Should not happen" ll := concat(map(#1, diff --git a/src/algebra/prtition.spad.pamphlet b/src/algebra/prtition.spad.pamphlet index 6b3cd538..0148ff2d 100644 --- a/src/algebra/prtition.spad.pamphlet +++ b/src/algebra/prtition.spad.pamphlet @@ -166,7 +166,7 @@ SymmetricPolynomial(R:Ring) == PolynomialRing(R,Partition) add zero?(p1.first.k) => p1.first.c * p2 -- one? p2 => p1 (p2 = 1) => p1 - +/[[[t1.k+t2.k,r]$Term for t2 in p2 | (r:=t1.c*t2.c) ^= 0] + +/[[[t1.k+t2.k,r]$Term for t2 in p2 | (r:=t1.c*t2.c) ~= 0] for t1 in reverse(p1)] -- This 'reverse' is an efficiency improvement: -- reduces both time and space [Abbott/Bradford/Davenport] diff --git a/src/algebra/pscat.spad.pamphlet b/src/algebra/pscat.spad.pamphlet index 0c94186a..58d549c6 100644 --- a/src/algebra/pscat.spad.pamphlet +++ b/src/algebra/pscat.spad.pamphlet @@ -299,13 +299,13 @@ UnivariateTaylorSeriesCategory(Coef): Category == Definition where n : NNI ; count : NNI := _$streamCount$Lisp l : L OUT := empty() for n in 0..count while not empty? uu repeat - if frst(uu) ^= 0 then + if frst(uu) ~= 0 then l := concat(termOutput(n :: I,frst uu,vv),l) uu := rst uu if showAll?() then for n in (count + 1).. while explicitEntries? uu and _ not eq?(uu,rst uu) repeat - if frst(uu) ^= 0 then + if frst(uu) ~= 0 then l := concat(termOutput(n :: I,frst uu,vv),l) uu := rst uu l := diff --git a/src/algebra/pseudolin.spad.pamphlet b/src/algebra/pseudolin.spad.pamphlet index 3eb384b4..fb6d38a5 100644 --- a/src/algebra/pseudolin.spad.pamphlet +++ b/src/algebra/pseudolin.spad.pamphlet @@ -96,19 +96,19 @@ PseudoLinearNormalForm(K:Field): Exports == Implementation where while j <= N and M(i, j) = 0 repeat j := j + 1 if j <= N then -- expand companionblock by lemma 5 - if j ^= i+1 then + if j ~= i+1 then -- perform first a permutation E := permutationMatrix(N, i+1, j) M := changeBase(M, E, sig, der) B := B*E Binv := E*Binv - -- now is M(i, i+1) ^= 0 + -- now is M(i, i+1) ~= 0 E := mulMatrix(N, i+1, siginv inv M(i,i+1)) M := changeBase(M, E, sig, der) B := B*E Binv := inv(E)*Binv for j in 1..N repeat - if j ^= i+1 then + if j ~= i+1 then E := addMatrix(N, i+1, j, siginv(-M(i,j))) M := changeBase(M, E, sig, der) B := B*E diff --git a/src/algebra/puiseux.spad.pamphlet b/src/algebra/puiseux.spad.pamphlet index 3d1f8162..8b4bb665 100644 --- a/src/algebra/puiseux.spad.pamphlet +++ b/src/algebra/puiseux.spad.pamphlet @@ -546,13 +546,13 @@ UnivariatePuiseuxSeries(Coef,var,cen): Exports == Implementation where empty? uu => 0 :: OUT n : NNI; count : NNI := _$streamCount$Lisp for n in 0..count while not empty? uu repeat - if frst(uu) ^= 0 then + if frst(uu) ~= 0 then l := concat(termOutput((n :: I) * rat + m,frst uu,xxx),l) uu := rst uu if showAll?() then for n in (count + 1).. while explicitEntries? uu and _ not eq?(uu,rst uu) repeat - if frst(uu) ^= 0 then + if frst(uu) ~= 0 then l := concat(termOutput((n :: I) * rat + m,frst uu,xxx),l) uu := rst uu l := diff --git a/src/algebra/qalgset.spad.pamphlet b/src/algebra/qalgset.spad.pamphlet index 7f5a0371..e6dfe5aa 100644 --- a/src/algebra/qalgset.spad.pamphlet +++ b/src/algebra/qalgset.spad.pamphlet @@ -75,7 +75,7 @@ QuasiAlgebraicSet(R, Var,Expon,Dpoly) : C == T quasiAlgebraicSet: (List Dpoly, Dpoly) -> $ ++ quasiAlgebraicSet(pl,q) returns the quasi-algebraic set ++ with defining equations p = 0 for p belonging to the list pl, and - ++ defining inequation q ^= 0. + ++ defining inequation q ~= 0. status: $ -> Status ++ status(s) returns true if the quasi-algebraic set is empty, ++ false if it is not, and "failed" if not yet known @@ -151,7 +151,7 @@ QuasiAlgebraicSet(R, Var,Expon,Dpoly) : C == T q=0$newPoly => 0$Dpoly dq:newExpon:=degree q n:NNI:=selectfirst (dq) - n^=0 => "failed" + n~=0 => "failed" ((g:=oldpoly reductum q) case "failed") => "failed" monomial(leadingCoefficient q,selectsecond dq)$Dpoly + (g::Dpoly) diff --git a/src/algebra/radix.spad.pamphlet b/src/algebra/radix.spad.pamphlet index d26f7b52..02fd8169 100644 --- a/src/algebra/radix.spad.pamphlet +++ b/src/algebra/radix.spad.pamphlet @@ -193,7 +193,7 @@ RadixExpansion(bb): Exports == Implementation where radixInt(n,bas) == rits: List I := nil() - while abs n ^= 0 repeat + while abs n ~= 0 repeat qr := divide(n,bas) n := qr.quotient rits := concat(qr.remainder,rits) @@ -226,7 +226,7 @@ RadixExpansion(bb): Exports == Implementation where ritsi := rits ritsn := rits; for i in 1..n repeat ritsn := rest ritsn i := 0 - while first(ritsi) ^= first(ritsn) repeat + while first(ritsi) ~= first(ritsn) repeat ritsi := rest ritsi ritsn := rest ritsn i := i + 1 diff --git a/src/algebra/rdeef.spad.pamphlet b/src/algebra/rdeef.spad.pamphlet index 662c1f27..812a7e44 100644 --- a/src/algebra/rdeef.spad.pamphlet +++ b/src/algebra/rdeef.spad.pamphlet @@ -74,7 +74,7 @@ IntegrationTools(R:OrderedSet, F:FunctionSpace R): Exp == Impl where -- true if x should be considered before y in the tower better?(x, y) == - height(y) ^= height(x) => height(y) < height(x) + height(y) ~= height(x) => height(y) < height(x) has?(operator y, ALGOP) or (is?(y, "exp"::SE) and not is?(x, "exp"::SE) and not has?(operator x, ALGOP)) @@ -136,7 +136,7 @@ IntegrationTools(R:OrderedSet, F:FunctionSpace R): Exp == Impl where if u case ANS then rc := u::ANS ans := ans + rc.special - if rc.integrand ^= 0 then + if rc.integrand ~= 0 then ir0 := intPatternMatch(rc.integrand, x, int, pmint) ans := ans + ratpart ir0 lg := concat(logpart ir0, lg) @@ -435,7 +435,7 @@ ElementaryRischDE(R, F): Exports == Implementation where dc - db boundAt0(twr, f0, nb, nc, x, t, limitedint) == - nb ^= 0 => min(0, nc - min(0, nb)) + nb ~= 0 => min(0, nc - min(0, nb)) l1 := logdiff(twr, l0 := tower f0) (if0 := limitedint(f0, [first argument u for u in l1])) case "failed" => error "Risch's theorem violated" diff --git a/src/algebra/rderf.spad.pamphlet b/src/algebra/rderf.spad.pamphlet index 33dcd1dd..f8d8d0b3 100644 --- a/src/algebra/rderf.spad.pamphlet +++ b/src/algebra/rderf.spad.pamphlet @@ -117,7 +117,7 @@ TranscendentalRischDE(F, UP): Exports == Implementation where q:UP := 0 db := (degree bb)::Z lb := leadingCoefficient bb - while cc ^= 0 repeat + while cc ~= 0 repeat d < 0 or (n := (degree cc)::Z - db) < 0 or n > d => return [q, true] r := monomial((leadingCoefficient cc) / lb, n::N) cc := cc - bb * r - derivation r @@ -130,7 +130,7 @@ TranscendentalRischDE(F, UP): Exports == Implementation where -- dtm1 = degree(Dt) - 1 SPDEnocancel2(bb, cc, d, dtm1, lt, derivation) == q:UP := 0 - while cc ^= 0 repeat + while cc ~= 0 repeat d < 0 or (n := (degree cc)::Z - dtm1) < 0 or n > d => return [[q, true]] if n > 0 then r := monomial((leadingCoefficient cc) / (n * lt), n::N) @@ -139,7 +139,7 @@ TranscendentalRischDE(F, UP): Exports == Implementation where q := q + r else -- n = 0 so solution must have degree 0 db:N := (zero? bb => 0; degree bb); - db ^= degree(cc) => return [[q, true]] + db ~= degree(cc) => return [[q, true]] zero? db => return [[bb, cc, 0, 1, q]] r := leadingCoefficient(cc) / leadingCoefficient(bb) cc := cc - r * bb - derivation(r::UP) @@ -162,7 +162,7 @@ TranscendentalRischDE(F, UP): Exports == Implementation where v := polyRDE(u.a, bb, cc, n, differentiate).ans [v.ans / u.t, v.nosol] --- return an a bound on the degree of a solution of A P'+ B P = C,A ^= 0 +-- return an a bound on the degree of a solution of A P'+ B P = C,A ~= 0 -- cancellation at infinity is possible -- base case: F' = 0 getBound(a, b, dc) == diff --git a/src/algebra/realzero.spad.pamphlet b/src/algebra/realzero.spad.pamphlet index 27374130..e6c16ca1 100644 --- a/src/algebra/realzero.spad.pamphlet +++ b/src/algebra/realzero.spad.pamphlet @@ -122,7 +122,7 @@ RealZeroPackage(Pol): T == C where append(append(J, L), K) PosZero(F : Pol) == --F is square free, primitive - --and F(0) ^= 0; returns isoList for positive + --and F(0) ~= 0; returns isoList for positive --roots of F b : Integer := rootBound(F) @@ -184,7 +184,7 @@ RealZeroPackage(Pol): T == C where d := degree(F) cc : Integer := 1 G : Pol := monomial(leadingCoefficient F,d) - while (F:=reductum(F)) ^= 0 repeat + while (F:=reductum(F)) ~= 0 repeat n := degree(F) cc := cc*(c**(d-n):NonNegativeInteger) G := G + monomial(cc * leadingCoefficient(F), n) @@ -195,7 +195,7 @@ RealZeroPackage(Pol): T == C where -- --computes Pol G such that G(x) = F(x+1) -- G : Pol := F -- n : Integer := 1 --- while (F := differentiate(F)) ^= 0 repeat +-- while (F := differentiate(F)) ~= 0 repeat -- if not ((tempF := F exquo n) case "failed") then F := tempF -- G := G + F -- n := n + 1 diff --git a/src/algebra/reclos.spad.pamphlet b/src/algebra/reclos.spad.pamphlet index b0400ad1..82687d55 100644 --- a/src/algebra/reclos.spad.pamphlet +++ b/src/algebra/reclos.spad.pamphlet @@ -115,7 +115,7 @@ RealPolynomialUtilitiesPackage(TheField,ThePols) : PUB == PRIV where sylvesterSequence(p1,p2) == res : List(ThePols) := [p1] - while (p2 ^= 0) repeat + while (p2 ~= 0) repeat res := cons(p2 , res) (p1 , p2) := (p2 , -(p1 rem p2)) if degree(p1) > 0 @@ -138,7 +138,7 @@ RealPolynomialUtilitiesPackage(TheField,ThePols) : PUB == PRIV where -- lsg := sign(first(l)) -- for term in l repeat -- if ^( (sg := sign(term) ) = 0 ) then --- if (sg ^= lsg) then res := res + 1 +-- if (sg ~= lsg) then res := res + 1 -- lsg := sg -- res @@ -261,7 +261,7 @@ RealRootCharacterizationCategory(TheField, ThePols ) : Category == PUB where defPol := definingPolynomial(rootChar) d := principalIdeal([defPol,toInv]) zero?(d.generator,rootChar) => "failed" - if (degree(d.generator) ^= 0 ) + if (degree(d.generator) ~= 0 ) then defPol := (defPol exquo (d.generator))::ThePols d := principalIdeal([defPol,toInv]) @@ -890,7 +890,7 @@ RightOpenIntervalRootCharacterization(TheField,ThePolDom) : PUB == PRIV where -- lsg := sign(coefficient(p,0)) -- l := [ sign(i) for i in reverse!(coefficients(p))] -- for sg in l repeat --- if (sg ^= lsg) then res := res + 1 +-- if (sg ~= lsg) then res := res + 1 -- lsg := sg -- res @ diff --git a/src/algebra/rep1.spad.pamphlet b/src/algebra/rep1.spad.pamphlet index b65c7675..47e3638e 100644 --- a/src/algebra/rep1.spad.pamphlet +++ b/src/algebra/rep1.spad.pamphlet @@ -233,7 +233,7 @@ RepresentationPackage1(R): public == private where symmetricTensors (a : M R, n : PI) == m : NNI := nrows a - m ^= ncols a => + m ~= ncols a => error("Input to symmetricTensors is no square matrix") n = 1 => a @@ -253,7 +253,7 @@ RepresentationPackage1(R): public == private where beta := unrankImproperPartitions1(n,m,j-1)$SGCF g := invContent(beta) colemanMatrix := nextColeman(alpha,beta,nullMatrix)$SGCF - while colemanMatrix ^= nullMatrix repeat + while colemanMatrix ~= nullMatrix repeat gamma := inverseColeman(alpha,beta,colemanMatrix)$SGCF help : R := calcCoef(beta,colemanMatrix)::R for k in 1..n repeat diff --git a/src/algebra/rep2.spad.pamphlet b/src/algebra/rep2.spad.pamphlet index 64fec1fc..01c39568 100644 --- a/src/algebra/rep2.spad.pamphlet +++ b/src/algebra/rep2.spad.pamphlet @@ -326,7 +326,7 @@ RepresentationPackage2(R): public == private where -- will the rank change if we add this nextVector -- to the basis so far computed? addedToBasis : M R := vertConcat(basis, nextVector) - if rank addedToBasis ^= nrows basis then + if rank addedToBasis ~= nrows basis then basis := rowEchelon addedToBasis -- add vector w to basis updateFurtherElts : L V R := _ [(lm.i*w)::V R for i in 1..maxIndex lm] @@ -355,7 +355,7 @@ RepresentationPackage2(R): public == private where -- will the rank change if we add this nextVector -- to the basis so far computed? addedToBasis : M R := vertConcat(basis, nextVector) - if rank addedToBasis ^= nrows basis then + if rank addedToBasis ~= nrows basis then standardBasis := cons(entries w, standardBasis) basis := rowEchelon addedToBasis -- add vector w to basis updateFurtherElts : L V R := _ @@ -381,7 +381,7 @@ RepresentationPackage2(R): public == private where rankOfSubmodule : I := # submodule -- R-Rank of submodule submoduleRepresentation : L M R := nil() factormoduleRepresentation : L M R := nil() - if n ^= rankOfSubmodule then + if n ~= rankOfSubmodule then messagePrint " A proper cyclic submodule is found." if doSplitting? then -- no else !! submoduleIndices : L I := [i for i in 1..rankOfSubmodule] @@ -502,12 +502,12 @@ RepresentationPackage2(R): public == private where -- test singularity of x0 and x1 rk0 : NNI := rank x0 rk1 : NNI := rank x1 - rk0 ^= rk1 => + rk0 ~= rk1 => messagePrint "Dimensions of kernels differ" foundResult := true result := false -- can assume dimensions are equal - rk0 ^= n - 1 => + rk0 ~= n - 1 => -- not of any use here if kernel not one-dimensional if randomelements then messagePrint "Random element in generated algebra does" @@ -528,7 +528,7 @@ RepresentationPackage2(R): public == private where aG0,kernel0.1) baseChange1 : M R := standardBasisOfCyclicSubmodule(_ aG1,kernel1.1) - (ncols baseChange0) ^= (ncols baseChange1) => + (ncols baseChange0) ~= (ncols baseChange1) => messagePrint " Dimensions of generated cyclic submodules differ" foundResult := true result := false @@ -539,7 +539,7 @@ RepresentationPackage2(R): public == private where foundResult := true result := true for j in 1..numberOfGenerators while result repeat - if (aG0.j*transitionM) ^= (transitionM*aG1.j) then + if (aG0.j*transitionM) ~= (transitionM*aG1.j) then result := false transitionM := zero(1 ,1) messagePrint " There is no isomorphism, as the only possible one" @@ -594,7 +594,7 @@ RepresentationPackage2(R): public == private where messagePrint " one-dimensional kernel" kernel : L V R := nullSpace x if n=#cyclicSubmodule(aG, first kernel) then - result := (irreducibilityTestInternal(aG,x,false)).1 ^= nil()$(L M R) + result := (irreducibilityTestInternal(aG,x,false)).1 ~= nil()$(L M R) -- result := not null? first irreducibilityTestInternal(aG,x,false) -- this down't compile !! else -- we found a proper submodule result := false @@ -690,7 +690,7 @@ RepresentationPackage2(R): public == private where algebraGenerators.2 , x) -- test singularity of x n : NNI := #row(x, 1) -- degree of representation - if (rank x) ^= n then -- x singular + if (rank x) ~= n then -- x singular if randomelements then messagePrint "Random element in generated algebra is singular" else diff --git a/src/algebra/rf.spad.pamphlet b/src/algebra/rf.spad.pamphlet index 26220e4c..c8e40f71 100644 --- a/src/algebra/rf.spad.pamphlet +++ b/src/algebra/rf.spad.pamphlet @@ -91,8 +91,8 @@ PolynomialCategoryQuotientFunctions(E, V, R, P, F): mymerge(variables numer f, variables denom f) isPower f == - (den := denom f) ^= 1 => - numer f ^= 1 => "failed" + (den := denom f) ~= 1 => + numer f ~= 1 => "failed" (ur := isExpt den) case "failed" => [den::F, -1] r := ur::Record(var:V, exponent:NonNegativeInteger) [r.var::P::F, - (r.exponent::Integer)] @@ -127,7 +127,7 @@ PolynomialCategoryQuotientFunctions(E, V, R, P, F): concat_!(l::List(F), d) isPlus f == - denom f ^= 1 => "failed" + denom f ~= 1 => "failed" (s := isPlus numer f) case "failed" => "failed" [x::F for x in s] diff --git a/src/algebra/riccati.spad.pamphlet b/src/algebra/riccati.spad.pamphlet index 30485093..877d0403 100644 --- a/src/algebra/riccati.spad.pamphlet +++ b/src/algebra/riccati.spad.pamphlet @@ -128,7 +128,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where lc := leadingDenomRicDE(c, op) if finite? then lc := select_!(#1.deg <= b, lc) for rec in lc repeat - for r in zeros(c, rec.eq) | r ^= 0 repeat + for r in zeros(c, rec.eq) | r ~= 0 repeat rcn := r /$RF (c ** rec.deg) neweq := changeVar(op, rcn) sols := padicsol(c, neweq, (rec.deg-1)::N, true, zeros) @@ -163,7 +163,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where constantCoefficientOperator(op, m) == ans:UP := 0 - while op ^= 0 repeat + while op ~= 0 repeat if degree(p := leadingCoefficient op) = m then ans := ans + monomial(leadingCoefficient p, degree op) op := reductum op @@ -179,7 +179,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where i := first(rec.ij) m := i * (d := rec.deg) + nu coefficient(l, i::N) ans:List(Z) := empty() - for j in 0..n | (f := coefficient(l, j)) ^= 0 repeat + for j in 0..n | (f := coefficient(l, j)) ~= 0 repeat if ((k := (j * d + nu f)) > m) then return empty() else if (k = m) then ans := concat(j, ans) ans @@ -226,8 +226,8 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where innerlb(l, nu) == lb:List(IJ) := empty() n := degree l - for i in 0..n | (li := coefficient(l, i)) ^= 0repeat - for j in i+1..n | (lj := coefficient(l, j)) ^= 0 repeat + for i in 0..n | (li := coefficient(l, i)) ~= 0repeat + for j in i+1..n | (lj := coefficient(l, j)) ~= 0 repeat u := (nu li - nu lj) exquo (i-j) if (u case Z) and ((b := u::Z) > 0) then lb := concat([[i, j], b::N], lb) @@ -257,7 +257,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where lc := leadingCoefficientRicDE l if finite? then lc := select_!(#1.deg <= b, lc) for rec in lc repeat - for a in zeros(rec.eq) | a ^= 0 repeat + for a in zeros(rec.eq) | a ~= 0 repeat atn:UP := monomial(a, rec.deg) neweq := changeVar(l, atn) sols := polysol(neweq, (rec.deg - 1)::N, true, zeros) @@ -430,8 +430,8 @@ RationalRicDE(F, UP): Exports == Implementation where ans:List(POL) := [[0, l]] empty?(lc := leadingCoefficientRicDE l) => ans rec := first lc -- one with highest degree - for a in zeros(rec.eq) | a ^= 0 repeat - if (p := newtonSolution(l, a, rec.deg, zeros)) ^= 0 then + for a in zeros(rec.eq) | a ~= 0 repeat + if (p := newtonSolution(l, a, rec.deg, zeros)) ~= 0 then ans := concat([p, changeVar(l, p)], ans) ans @@ -439,7 +439,7 @@ RationalRicDE(F, UP): Exports == Implementation where reverseUP p == ans:UTS := 0 n := degree(p)::Z - while p ^= 0 repeat + while p ~= 0 repeat ans := ans + monomial(leadingCoefficient p, (n - degree p)::N) p := reductum p ans @@ -454,11 +454,11 @@ RationalRicDE(F, UP): Exports == Implementation where m:Z := 0 aeq:UPS := 0 op := l - while op ^= 0 repeat + while op ~= 0 repeat mu := degree(op) * n + degree leadingCoefficient op op := reductum op if mu > m then m := mu - while l ^= 0 repeat + while l ~= 0 repeat c := leadingCoefficient l d := degree l s:UTS := monomial(1, (m - d * n - degree c)::N)$UTS * reverseUP c diff --git a/src/algebra/rinterp.spad.pamphlet b/src/algebra/rinterp.spad.pamphlet index 41fa6c59..a945c303 100644 --- a/src/algebra/rinterp.spad.pamphlet +++ b/src/algebra/rinterp.spad.pamphlet @@ -56,9 +56,9 @@ the denominator. In fact, we could also leave -- for example -- $k$ unspecified and determine it as $k=[[#xlist]]-m-1$: I don't know whether this would be better. <<RINTERP Implementation>>= - #xlist ^= #ylist => + #xlist ~= #ylist => error "Different number of points and values." - #xlist ^= m+k+1 => + #xlist ~= m+k+1 => error "wrong number of points" @ diff --git a/src/algebra/rule.spad.pamphlet b/src/algebra/rule.spad.pamphlet index ce3011bc..98e0ee8d 100644 --- a/src/algebra/rule.spad.pamphlet +++ b/src/algebra/rule.spad.pamphlet @@ -113,7 +113,7 @@ RewriteRule(Base, R, F): Exports == Implementation where -- appear?(x, [p1,...,pn]) is true if x appears as a variable in -- a composite pattern pi. appear?(x, l) == - for p in l | p ^= x repeat + for p in l | p ~= x repeat member?(x, variables p) => return true false diff --git a/src/algebra/setorder.spad.pamphlet b/src/algebra/setorder.spad.pamphlet index 198d8d85..1e62721b 100644 --- a/src/algebra/setorder.spad.pamphlet +++ b/src/algebra/setorder.spad.pamphlet @@ -83,7 +83,7 @@ UserDefinedPartialOrdering(S:SetCategory): with less?(a, b) == for x in deref llow repeat - x = a => return(a ^= b) + x = a => return(a ~= b) x = b => return false aa := bb := false$Boolean for x in deref lhigh repeat @@ -91,7 +91,7 @@ UserDefinedPartialOrdering(S:SetCategory): with bb => return false aa := true if x = b then - aa => return(a ^= b) + aa => return(a ~= b) bb := true aa => false bb => true diff --git a/src/algebra/sgcf.spad.pamphlet b/src/algebra/sgcf.spad.pamphlet index b2740766..c871cb18 100644 --- a/src/algebra/sgcf.spad.pamphlet +++ b/src/algebra/sgcf.spad.pamphlet @@ -234,7 +234,7 @@ SymmetricGroupCombinatoricFunctions(): public == private where k < 0 => nonZeros k >= numberOfImproperPartitions(n,m) => nonZeros cm : I := m --cm gives the depth of the tree - while n ^= 0 repeat + while n ~= 0 repeat s : I := 0 cm := cm - 1 for y in n..1 by -1 repeat --determination of the next son @@ -374,7 +374,7 @@ SymmetricGroupCombinatoricFunctions(): public == private where vrest : V I := new(ncol,0) cnull : M I := new(1,1,0) coleman := copy C - if coleman ^= cnull then + if coleman ~= cnull then -- look for the first row of "coleman" that has a succeeding -- partition, this can be atmost row nrow-1 i : NNI := (nrow-1)::NNI @@ -416,7 +416,7 @@ SymmetricGroupCombinatoricFunctions(): public == private where nextPartition(gamma:L I,part:V I,number:I) == n : NNI := #gamma vnull : V I := vector(nil()$(L I)) -- empty vector - if part ^= vnull then + if part ~= vnull then i : NNI := 2 sum := part(1) while (part(i) = gamma(i)) or (sum = 0) repeat diff --git a/src/algebra/sign.spad.pamphlet b/src/algebra/sign.spad.pamphlet index a9c3a5c3..627b6c36 100644 --- a/src/algebra/sign.spad.pamphlet +++ b/src/algebra/sign.spad.pamphlet @@ -186,7 +186,7 @@ RationalFunctionSign(R:GcdDomain): Exports == Implementation where listSign(l, s) == for term in l repeat (u := termSign term) case "failed" => return "failed" - u::Integer ^= s => return "failed" + u::Integer ~= s => return "failed" s termSign term == diff --git a/src/algebra/smith.spad.pamphlet b/src/algebra/smith.spad.pamphlet index 8c89d9ef..dd3ff8ca 100644 --- a/src/algebra/smith.spad.pamphlet +++ b/src/algebra/smith.spad.pamphlet @@ -99,7 +99,7 @@ SmithNormalForm(R,Row,Col,M) : Exports == Implementation where m1:= nrows m n1:= ncols m for i in 1..m1 repeat - for j in 1..n1 | (j ^= i) repeat + for j in 1..n1 | (j ~= i) repeat if not zero?(m(i,j)) then return false true @@ -111,14 +111,14 @@ SmithNormalForm(R,Row,Col,M) : Exports == Implementation where m -- elementary operation of second kind: add to row i-- - -- a*row j (i^=j) -- + -- a*row j (i~=j) -- elRow2(m : M,a:R,i:I,j:I) : M == vec:= map(a*#1,row(m,j)) vec:=map("+",row(m,i),vec) setRow!(m,i,vec) m -- elementary operation of second kind: add to column i -- - -- a*column j (i^=j) -- + -- a*column j (i~=j) -- elColumn2(m : M,a:R,i:I,j:I) : M == vec:= map(a*#1,column(m,j)) vec:=map("+",column(m,i),vec) @@ -157,7 +157,7 @@ SmithNormalForm(R,Row,Col,M) : Exports == Implementation where lastStep(sf : SmithForm) : SmithForm == m:=sf.Smith m1:=min(nrows m,ncols m) - for i in 1..m1 while (mii:=m(i,i)) ^=0 repeat + for i in 1..m1 while (mii:=m(i,i)) ~=0 repeat for j in i+1..m1 repeat if (m(j,j) exquo mii) case "failed" then return lastStep(ijDivide(sf,i,j)) diff --git a/src/algebra/solvefor.spad.pamphlet b/src/algebra/solvefor.spad.pamphlet index 7095d4e1..faf51c7d 100644 --- a/src/algebra/solvefor.spad.pamphlet +++ b/src/algebra/solvefor.spad.pamphlet @@ -131,7 +131,7 @@ PolynomialSolveByFormulas(UP, F): PSFcat == PSFdef where error concat("Polynomial must be of degree ", n::String) needLcoef(cn: F): Boolean == - cn ^= 0 => true + cn ~= 0 => true error "Leading coefficient must not be 0." needChar0(): Boolean == @@ -253,7 +253,7 @@ PolynomialSolveByFormulas(UP, F): PSFcat == PSFdef where -- t0 := the cubic resolvent of x**3-p*x**2-4*r*x+4*p*r-q**2 -- The roots of the translated polynomial are those of -- two quadratics. (What about rt=0 ?) - -- rt=0 can be avoided by picking a root ^= p of the cubic + -- rt=0 can be avoided by picking a root ~= p of the cubic -- polynomial above. This is always possible provided that -- the input is squarefree. In this case the two other roots -- are +(-) 2*r**(1/2). diff --git a/src/algebra/solvelin.spad.pamphlet b/src/algebra/solvelin.spad.pamphlet index 9c35d201..4700ce1a 100644 --- a/src/algebra/solvelin.spad.pamphlet +++ b/src/algebra/solvelin.spad.pamphlet @@ -213,7 +213,7 @@ LinearSystemPolynomialPackage(R, E, OV, P): Cat == Capsule where poly2vect(p : P, vs : List OV) : Record(coefvec: V F, reductum: F) == coefs := new(#vs, 0)$(V F) - for v in vs for i in 1.. while p ^= 0 repeat + for v in vs for i in 1.. while p ~= 0 repeat u := univariate(p, v) degree u = 0 => "next v" coefs.i := (c := leadingCoefficient u)::F diff --git a/src/algebra/solverad.spad.pamphlet b/src/algebra/solverad.spad.pamphlet index 59e92725..ee9e0b68 100644 --- a/src/algebra/solverad.spad.pamphlet +++ b/src/algebra/solverad.spad.pamphlet @@ -165,7 +165,7 @@ RadicalSolvePackage(R): Cat == Capsule where lv1:L Kernel(RE):=[kernel rlv.first] rlv1:=rlv.rest p1:=par.rest - while p1^=[] repeat + while p1~=[] repeat res1:=cons(eval(p1.first,lv1,res1),res1) p1:=p1.rest lv1:=cons(kernel rlv1.first,lv1) @@ -199,7 +199,7 @@ RadicalSolvePackage(R): Cat == Capsule where rpRes:=[reverse res for res in parRes] listGen:= [res for res in rpRes|isGeneric?(res,rlv)] result:L L RE:=[] - if listGen^=[] then + if listGen~=[] then result:="append"/[findGenZeros(res,rlv) for res in listGen] for res in listGen repeat rpRes:=delete(rpRes,position(res,rpRes)) diff --git a/src/algebra/space.spad.pamphlet b/src/algebra/space.spad.pamphlet index 1f1235d2..3d269880 100644 --- a/src/algebra/space.spad.pamphlet +++ b/src/algebra/space.spad.pamphlet @@ -616,7 +616,7 @@ ThreeSpace(R:Ring):Exports == Implementation where numCurves := numCurves + 1 (#kid = 2) and _ (#children first kid = 1) and _ - (#children first rest kid ^= 1) => + (#children first rest kid ~= 1) => numPolys := numPolys + 1 numConstructs := numConstructs + 1 -- otherwise, a mathematical surface is assumed diff --git a/src/algebra/special.spad.pamphlet b/src/algebra/special.spad.pamphlet index 1765eebd..bb41d3df 100644 --- a/src/algebra/special.spad.pamphlet +++ b/src/algebra/special.spad.pamphlet @@ -381,7 +381,7 @@ NumberTheoreticPolynomialFunctions(R: CommutativeRing): Exports == Impl where cyclotomic(k, x) == p: SUP(I) := cyclotomic(k) r: R := 0 - while p ^= 0 repeat + while p ~= 0 repeat d := degree p c := leadingCoefficient p p := reductum p @@ -392,7 +392,7 @@ NumberTheoreticPolynomialFunctions(R: CommutativeRing): Exports == Impl where eulerE(k, x) == p: SUP(RN) := euler(k) r: R := 0 - while p ^= 0 repeat + while p ~= 0 repeat d := degree p c := leadingCoefficient p p := reductum p @@ -401,7 +401,7 @@ NumberTheoreticPolynomialFunctions(R: CommutativeRing): Exports == Impl where bernoulliB(k, x) == p: SUP(RN) := bernoulli(k) r: R := 0 - while p ^= 0 repeat + while p ~= 0 repeat d := degree p c := leadingCoefficient p p := reductum p diff --git a/src/algebra/stream.spad.pamphlet b/src/algebra/stream.spad.pamphlet index 4edd8509..8bd55a61 100644 --- a/src/algebra/stream.spad.pamphlet +++ b/src/algebra/stream.spad.pamphlet @@ -1031,7 +1031,7 @@ Stream(S): Exports == Implementation where not empty? x and frst x = first l and x = rst x x0 := x for s in l repeat - empty? x or s ^= frst x => return false + empty? x or s ~= frst x => return false x := rst x eq?(x,x0) diff --git a/src/algebra/string.spad.pamphlet b/src/algebra/string.spad.pamphlet index d881d0a6..09adfaf7 100644 --- a/src/algebra/string.spad.pamphlet +++ b/src/algebra/string.spad.pamphlet @@ -599,17 +599,17 @@ the coercion. n := maxIndex pattern p := position(dontcare, pattern, m := minIndex pattern)::N p = m-1 => pattern = target - (p ^= m) and not prefix?(pattern(m..p-1), target) => false + (p ~= m) and not prefix?(pattern(m..p-1), target) => false i := p -- index into target q := position(dontcare, pattern, p + 1)::N - while q ^= m-1 repeat + while q ~= m-1 repeat s := pattern(p+1..q-1) i := position(s, target, i)::N i = m-1 => return false i := i + #s p := q q := position(dontcare, pattern, q + 1)::N - (p ^= n) and not suffix?(pattern(p+1..n), target) => false + (p ~= n) and not suffix?(pattern(p+1..n), target) => false true @ diff --git a/src/algebra/sttaylor.spad.pamphlet b/src/algebra/sttaylor.spad.pamphlet index 27a16ec0..a16e32ce 100644 --- a/src/algebra/sttaylor.spad.pamphlet +++ b/src/algebra/sttaylor.spad.pamphlet @@ -465,7 +465,7 @@ StreamTaylorSeriesOperations(A): Exports == Implementation where powerre: (A,ST A,ST A) -> ST A powerre(s,x,c) == delay empty? x => zro() - frst x^=1 => error "**:constant coefficient should be 1" + frst x~=1 => error "**:constant coefficient should be 1" concat(frst x,finteg((s+1)*(c*deriv x))-rst x * c) power(s,x) == YS(powerre(s,x,#1)) diff --git a/src/algebra/sum.spad.pamphlet b/src/algebra/sum.spad.pamphlet index e6b315bc..e866dc11 100644 --- a/src/algebra/sum.spad.pamphlet +++ b/src/algebra/sum.spad.pamphlet @@ -55,7 +55,7 @@ InnerPolySum(E, V, R, P): Exports == Impl where up := univariate(p, v) lp := nil()$List(SUP P) ld := nil()$List(Z) - while up ^= 0 repeat + while up ~= 0 repeat ud := degree up; uc := leadingCoefficient up up := reductum up rec := pmul(uc, 1 / (ud+1) * bernoulli(ud+1)) @@ -186,12 +186,12 @@ GosperSummationMethod(E, V, R, P, Q): Exports == Impl where dz := degree zron mat: Matrix RQ := zero(dz+1, (k+1)::NonNegativeInteger) vec: Vector RQ := new(dz+1, 0) - while zron ^= 0 repeat + while zron ~= 0 repeat cz := leadingCoefficient zron dz := degree zron zron := reductum zron mz := univariate(cz, mv) - while mz ^= 0 repeat + while mz ~= 0 repeat cmz := leadingCoefficient(mz)::RQ dmz := degree mz mz := reductum mz @@ -259,7 +259,7 @@ GosperSummationMethod(E, V, R, P, Q): Exports == Impl where not monomial? nom => error "pCoef requires a monomial 2nd arg" vlist := variables nom - for v in vlist while p ^= 0 repeat + for v in vlist while p ~= 0 repeat unom:= univariate(nom,v) pow:=degree unom nom:=leadingCoefficient unom @@ -269,13 +269,13 @@ GosperSummationMethod(E, V, R, P, Q): Exports == Impl where linearAndNNIntRoot(mp, v) == p := univariate(mp, v) - degree p ^= 1 => "failed" + degree p ~= 1 => "failed" (p1 := retractIfCan(coefficient(p, 1))@Union(RN,"failed")) case "failed" or (p0 := retractIfCan(coefficient(p, 0))@Union(RN,"failed")) case "failed" => "failed" rt := -(p0::RN)/(p1::RN) - rt < 0 or denom rt ^= 1 => "failed" + rt < 0 or denom rt ~= 1 => "failed" numer rt @ diff --git a/src/algebra/symbol.spad.pamphlet b/src/algebra/symbol.spad.pamphlet index cde5e9ac..cb29a702 100644 --- a/src/algebra/symbol.spad.pamphlet +++ b/src/algebra/symbol.spad.pamphlet @@ -191,7 +191,7 @@ Symbol(): Exports == Implementation where -- Scripts ==> Record(sub:L,sup:L,presup:L,presub:L,args:L) latex e == s : String := (PNAME(name e)$Lisp) pretend String - if #s > 1 and s.1 ^= char "\" then + if #s > 1 and s.1 ~= char "\" then s := concat("\mbox{\it ", concat(s, "}")$String)$String not scripted? e => s ss : Scripts := scripts e diff --git a/src/algebra/syssolp.spad.pamphlet b/src/algebra/syssolp.spad.pamphlet index 2a7f1250..ef019257 100644 --- a/src/algebra/syssolp.spad.pamphlet +++ b/src/algebra/syssolp.spad.pamphlet @@ -146,13 +146,13 @@ SystemSolvePackage(R): Cat == Cap where push:=PushVariables(R,DP,OV,dmp) lq : L dmp lvv:L OV:=[variable(vv)::OV for vv in lv] - lq:=[pushup(df::dmp,lvv)$push for f in lf|(df:=denom f)^=1] + lq:=[pushup(df::dmp,lvv)$push for f in lf|(df:=denom f)~=1] lp:=[pushup(numer(f)::dmp,lvv)$push for f in lf] parRes:=groebSolve(lp,lvv)$GroebnerSolve(lv,P R,R) - if lq^=[] then + if lq~=[] then gb:=GroebnerInternalPackage(P R,DirectProduct(#lv,NNI),OV,dmp) parRes:=[pr for pr in parRes| - and/[(redPol(fq,pr pretend List(dmp))$gb) ^=0 + and/[(redPol(fq,pr pretend List(dmp))$gb) ~=0 for fq in lq]] [[retract pushdown(pf,lvv)$push for pf in pr] for pr in parRes] @@ -199,7 +199,7 @@ SystemSolvePackage(R): Cat == Cap where rec.particular case "failed" => "failed" rhs := rec.particular :: V F zeron:V F:=zero(#lv) - for p in rec.basis | p ^= zeron repeat + for p in rec.basis | p ~= zeron repeat sym := newInF(1) for i in 1..#lv repeat rhs.i := rhs.i + sym*p.i diff --git a/src/algebra/taylor.spad.pamphlet b/src/algebra/taylor.spad.pamphlet index 7fa64c04..2005597a 100644 --- a/src/algebra/taylor.spad.pamphlet +++ b/src/algebra/taylor.spad.pamphlet @@ -97,7 +97,7 @@ InnerTaylorSeries(Coef): Exports == Implementation where n : I := _$streamCount$Lisp for i in 0..n repeat empty? st => return true - frst st ^= 0 => return false + frst st ~= 0 => return false st := rst st empty? st @@ -332,7 +332,7 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where while not empty? u and n > 0 repeat u := rst u n := (n - 1) :: NNI - empty? u or n ^= 0 => 0 + empty? u or n ~= 0 => 0 frst u elt(x:%,n:NNI) == coefficient(x,n) diff --git a/src/algebra/tex.spad.pamphlet b/src/algebra/tex.spad.pamphlet index 7577e3f4..adc11106 100644 --- a/src/algebra/tex.spad.pamphlet +++ b/src/algebra/tex.spad.pamphlet @@ -424,19 +424,19 @@ TexFormat(): public == private where args := rest args null args => concat(form)$S tmp : S := formatTex(first args, minPrec) - if (tmp ^= "") and (tmp ^= "{}") and (tmp ^= " ") then + if (tmp ~= "") and (tmp ~= "{}") and (tmp ~= " ") then form := append(form,[" \sb ",group tmp])$(List S) -- superscripts args := rest args null args => group concat(form)$S tmp : S := formatTex(first args, minPrec) - if (tmp ^= "") and (tmp ^= "{}") and (tmp ^= " ") then + if (tmp ~= "") and (tmp ~= "{}") and (tmp ~= " ") then form := append(form,[" \sp ",group tmp])$(List S) -- presuperscripts args := rest args null args => group concat(form)$S tmp : S := formatTex(first args, minPrec) - if (tmp ^= "") and (tmp ^= "{}") and (tmp ^= " ") then + if (tmp ~= "") and (tmp ~= "{}") and (tmp ~= " ") then form := append([" \sp ",group tmp],form)$(List S) prescript := true -- presubscripts @@ -446,7 +446,7 @@ TexFormat(): public == private where prescript => cons("{}",form) form tmp : S := formatTex(first args, minPrec) - if (tmp ^= "") and (tmp ^= "{}") and (tmp ^= " ") then + if (tmp ~= "") and (tmp ~= "{}") and (tmp ~= " ") then form := append([" \sb ",group tmp],form)$(List S) prescript := true group concat @@ -469,7 +469,7 @@ TexFormat(): public == private where p < 1 => error "unknown Tex unary op" opPrec := plexPrecs.p n : I := #args - (n ^= 2) and (n ^= 3) => error "wrong number of arguments for plex" + (n ~= 2) and (n ~= 3) => error "wrong number of arguments for plex" s : S := op = "SIGMA" => "\sum" op = "SIGMA2" => "\sum" @@ -480,12 +480,12 @@ TexFormat(): public == private where "????" hold := formatTex(first args,minPrec) args := rest args - if op ^= "INDEFINTEGRAL" then - if hold ^= "" then + if op ~= "INDEFINTEGRAL" then + if hold ~= "" then s := concat [s," \sb",group concat ["\displaystyle ",hold]] if not null rest args then hold := formatTex(first args,minPrec) - if hold ^= "" then + if hold ~= "" then s := concat [s," \sp",group concat ["\displaystyle ",hold]] args := rest args s := concat [s," ",formatTex(first args,minPrec)] diff --git a/src/algebra/transsolve.spad.pamphlet b/src/algebra/transsolve.spad.pamphlet index 168619fa..e9071b02 100644 --- a/src/algebra/transsolve.spad.pamphlet +++ b/src/algebra/transsolve.spad.pamphlet @@ -347,7 +347,7 @@ TransSolvePackage(R) : Exports == Implementation where exprtable:Table(RE,RE):=table() (isPlus(expr)) case "failed" => expr ans:RE:=0 - while expr ^= 0 repeat + while expr ~= 0 repeat loopexpr:RE:=leadingMonomial(numer(expr))::RE if testLog(loopexpr,Y) and (#tableXkernels(loopexpr,Y)=1) then exprr:=buildnexpr(loopexpr,Y) diff --git a/src/algebra/tree.spad.pamphlet b/src/algebra/tree.spad.pamphlet index 5a82ba59..27b0d061 100644 --- a/src/algebra/tree.spad.pamphlet +++ b/src/algebra/tree.spad.pamphlet @@ -261,13 +261,13 @@ Tree(S: SetCategory): T==C where cyclicEqual?(t1, t2) == cp1 := cyclicParents t1 cp2 := cyclicParents t2 - #cp1 ^= #cp2 or null cp1 => t1 = t2 + #cp1 ~= #cp2 or null cp1 => t1 = t2 cyclicEqual4?(t1, t2, cp1, cp2) cyclicEqual4?(t1, t2, cp1, cp2) == t1 case empty => t2 case empty t2 case empty => false - 0 ^= (k := eqMemberIndex(t1, cp1, 0)) => eq?(t2, cp2 . k) + 0 ~= (k := eqMemberIndex(t1, cp1, 0)) => eq?(t2, cp2 . k) value t1 = value t2 and "and"/[cyclicEqual4?(x,y,cp1,cp2) for x in children t1 for y in children t2] diff --git a/src/algebra/twofact.spad.pamphlet b/src/algebra/twofact.spad.pamphlet index f3e99f53..541157b7 100644 --- a/src/algebra/twofact.spad.pamphlet +++ b/src/algebra/twofact.spad.pamphlet @@ -43,7 +43,7 @@ NormRetractPackage(F, ExtF, SUEx, ExtP, n):C == T where Frobenius(ff:ExtP):ExtP == fft:ExtP:=0 - while ff^=0 repeat + while ff~=0 repeat fft:=fft + monomial(map(Frobenius, leadingCoefficient ff), degree ff) ff:=reductum ff @@ -51,10 +51,10 @@ NormRetractPackage(F, ExtF, SUEx, ExtP, n):C == T where retractIfCan(ff:ExtP):Union(P, "failed") == fft:P:=0 - while ff ^= 0 repeat + while ff ~= 0 repeat lc : SUEx := leadingCoefficient ff plc: SUP F := 0 - while lc ^= 0 repeat + while lc ~= 0 repeat lclc:ExtF := leadingCoefficient lc (retlc := retractIfCan lclc) case "failed" => return "failed" plc := plc + monomial(retlc::F, degree lc) @@ -159,7 +159,7 @@ TwoFactorize(F) : C == T pfaclist) unitPart := unit(nfacs)**uexp * unitPart pfaclist := cons(u,pfaclist) - cont ^= 1 => + cont ~= 1 => sqp := squareFree cont contlist:=[[w.flg,(w.fctr)::P,w.xpnt] for w in factorList sqp] pfaclist:= append(contlist, pfaclist) @@ -229,7 +229,7 @@ TwoFactorize(F) : C == T i:=i+1 zero? elt(lcm, vval) => "next value" umv := map(elt(#1,vval), m)$UPCF2(R, P, F, R) - degree(gcd(umv,differentiate umv))^=0 => "next val" + degree(gcd(umv,differentiate umv))~=0 => "next val" n := 1 look := false extField:=FiniteFieldExtension(F,n) @@ -237,7 +237,7 @@ TwoFactorize(F) : C == T TP:=SparseUnivariatePolynomial SUEx mm:TP:=0 m1:=m - while m1^=0 repeat + while m1~=0 repeat mm:=mm+monomial(map(coerce,leadingCoefficient m1)$UPCF2(F,R, extField,SUEx),degree m1) m1:=reductum m1 @@ -252,7 +252,7 @@ TwoFactorize(F) : C == T i:=i+1 elt(lcmm,val)=0 => "next value" umex := map(elt(#1,val), mm)$UPCF2(SUEx, TP, extField, SUEx) - degree(gcd(umex,differentiate umex))^=0 => "next val" + degree(gcd(umex,differentiate umex))~=0 => "next val" look:=false prime:SUEx:=monomial(1,1)-monomial(val,0) fumex:=factor(umex)$DistinctDegreeFactorize(extField,SUEx) @@ -273,7 +273,7 @@ TwoFactorize(F) : C == T while not empty? lfacth repeat ff := first lfacth lfacth := rest lfacth - if (c:=leadingCoefficient leadingCoefficient ff) ^=1 then + if (c:=leadingCoefficient leadingCoefficient ff) ~=1 then ff:=((inv c)::SUEx)* ff not ((ffu:= retractIfCan(ff)$Normp) case "failed") => lfactk := cons(ffu::P, lfactk) diff --git a/src/algebra/unifact.spad.pamphlet b/src/algebra/unifact.spad.pamphlet index 672a3c69..1e9f19d8 100644 --- a/src/algebra/unifact.spad.pamphlet +++ b/src/algebra/unifact.spad.pamphlet @@ -110,13 +110,13 @@ UnivariateFactorize(ZP) : public == private where lead := leadingCoefficient m trail := lead m := reductum m - while m ^= 0 repeat + while m ~= 0 repeat trail := leadingCoefficient m m:= reductum m fc := factor(c) :: Factored(Z) for r in factors fc repeat - if (r.exponent = 1) and (0 ^= (lead rem r.factor)) and - (0 ^= (trail rem (r.factor ** 2))) then return true + if (r.exponent = 1) and (0 ~= (lead rem r.factor)) and + (0 ~= (trail rem (r.factor ** 2))) then return true false negShiftz(n: Z,Modulus:PI): Z == @@ -136,7 +136,7 @@ UnivariateFactorize(ZP) : public == private where nm := (degree m)::NNI nmq2:NNI := nm quo 2 norm: Z := sqroot(+/[coefficient(m,k)**2 for k in 0..nm]) - if nmq2^=1 then nm := (nmq2-1):NNI + if nmq2~=1 then nm := (nmq2-1):NNI else nm := nmq2 bin0 := nm cbound := (bin0*norm+lcm)::PI @@ -173,7 +173,7 @@ UnivariateFactorize(ZP) : public == private where q:=nextPrime(q)$IntegerPrimesPackage(Z) pretend PI (rr:=lcm rem q) = 0$Z => "next prime" disc:=gcd(m,differentiate m,q) - (degree disc)^=0 => "next prime" + (degree disc)~=0 => "next prime" k := k+1 newdd := ddFact(m,q) ((n := numFactors(newdd)) < 9) => @@ -216,11 +216,11 @@ UnivariateFactorize(ZP) : public == private where d,d2: Z d := coefficient(m,1)**2-4*coefficient(m,0)*coefficient(m,2) d2 := sqroot(d) - (d-d2**2)^=0 => [m] + (d-d2**2)~=0 => [m] alpha: Z := coefficient(m,1)+d2 beta: Z := 2*coefficient(m,2) d := gcd(alpha,beta) - if d ^=1 then + if d ~=1 then alpha := alpha quo d beta := beta quo d m0: ZP := monomial(beta,1)+monomial(alpha,0) diff --git a/src/algebra/vector.spad.pamphlet b/src/algebra/vector.spad.pamphlet index 0406479e..04833f55 100644 --- a/src/algebra/vector.spad.pamphlet +++ b/src/algebra/vector.spad.pamphlet @@ -68,7 +68,7 @@ VectorCategory(R:Type): Category == OneDimensionalArrayAggregate R with add if R has AbelianSemiGroup then u + v == - (n := #u) ^= #v => error "Vectors must be of the same length" + (n := #u) ~= #v => error "Vectors must be of the same length" map(_+ , u, v) if R has AbelianMonoid then @@ -85,13 +85,13 @@ 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" + #u ~= #v => error "Vectors must be of the same length" _+/[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] cross(u, v) == - #u ^= 3 or #v ^= 3 => error "Vectors must be of length 3" + #u ~= 3 or #v ~= 3 => error "Vectors must be of length 3" construct [qelt(u, 2)*qelt(v, 3) - qelt(u, 3)*qelt(v, 2) , _ qelt(u, 3)*qelt(v, 1) - qelt(u, 1)*qelt(v, 3) , _ qelt(u, 1)*qelt(v, 2) - qelt(u, 2)*qelt(v, 1) ] diff --git a/src/algebra/view2D.spad.pamphlet b/src/algebra/view2D.spad.pamphlet index 858de376..a318364c 100644 --- a/src/algebra/view2D.spad.pamphlet +++ b/src/algebra/view2D.spad.pamphlet @@ -283,7 +283,7 @@ GraphImage (): Exports == Implementation where listOfListsOfPoints := [ l for l in listOfListsOfPoints | ^null l ] if (null listOfListsOfPoints) then error "GraphImage was given a list that contained no valid point lists" - if ((len := #listOfListsOfPoints) ^= givenLen) then + if ((len := #listOfListsOfPoints) ~= givenLen) then sayBrightly([" Warning: Ignoring pointless point list"::E]$List(E))$Lisp graf.llPoints := listOfListsOfPoints -- do point colors @@ -308,7 +308,7 @@ GraphImage (): Exports == Implementation where doOptions(graf) (s := #(graf.llPoints)) = 0 => error "You are trying to make a graph with no points" - key graf ^= 0 => + key graf ~= 0 => error "You are trying to draw over an existing graph" transform := coord(graf.optionsField,cartesian$COORDSYS)$DrawOptionFunctions0 graf.llPoints:= putColorInfo(graf.llPoints,graf.pointColors) @@ -818,7 +818,7 @@ TwoDimensionalViewport ():Exports == Implementation where move(viewport,xLoc,yLoc) == viewport.moveTo := [xLoc,yLoc] - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,MOVE)$Lisp checkViewport viewport => @@ -827,7 +827,7 @@ TwoDimensionalViewport ():Exports == Implementation where getI(VIEW)$Lisp -- acknowledge update(viewport,graph,slot) == - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,putGraph2D)$Lisp checkViewport viewport => @@ -837,7 +837,7 @@ TwoDimensionalViewport ():Exports == Implementation where resize(viewport,xSize,ySize) == viewport.size := [xSize,ySize] - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,RESIZE)$Lisp checkViewport viewport => @@ -852,7 +852,7 @@ TwoDimensionalViewport ():Exports == Implementation where error "Referring to a graph with too big an index" viewport.graphStatesField.graphIndex.deltaX := xTranslate viewport.graphStatesField.graphIndex.deltaY := yTranslate - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,TRANSLATE2D)$Lisp checkViewport viewport => @@ -868,7 +868,7 @@ TwoDimensionalViewport ():Exports == Implementation where error "Referring to a graph with too big an index" viewport.graphStatesField.graphIndex.scaleX := xScale -- check union (undefined?) viewport.graphStatesField.graphIndex.scaleY := yScale -- check union (undefined?) - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,SCALE2D)$Lisp checkViewport viewport => @@ -932,7 +932,7 @@ TwoDimensionalViewport ():Exports == Implementation where title(viewport,Title) == viewport.title := Title - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,TITLE)$Lisp checkViewport viewport => @@ -940,7 +940,7 @@ TwoDimensionalViewport ():Exports == Implementation where getI(VIEW)$Lisp -- acknowledge reset viewport == - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,SPADBUTTONPRESS)$Lisp checkViewport viewport => @@ -955,7 +955,7 @@ TwoDimensionalViewport ():Exports == Implementation where else status := no viewport.graphStatesField.graphIndex.axes := status -- check union (undefined?) - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,axesOnOff2D)$Lisp checkViewport viewport => @@ -967,7 +967,7 @@ TwoDimensionalViewport ():Exports == Implementation where if (graphIndex > maxGRAPHS) then error "Referring to a graph with too big an index" viewport.graphStatesField.graphIndex.axesColor := color - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,axesColor2D)$Lisp checkViewport viewport => @@ -984,7 +984,7 @@ TwoDimensionalViewport ():Exports == Implementation where else status := no viewport.graphStatesField.graphIndex.units := status -- check union (undefined?) - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,unitsOnOff2D)$Lisp checkViewport viewport => @@ -996,7 +996,7 @@ TwoDimensionalViewport ():Exports == Implementation where if (graphIndex > maxGRAPHS) then error "Referring to a graph with too big an index" viewport.graphStatesField.graphIndex.unitsColor := color - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,unitsColor2D)$Lisp checkViewport viewport => @@ -1013,7 +1013,7 @@ TwoDimensionalViewport ():Exports == Implementation where else status := 0$I viewport.graphStatesField.graphIndex.connect := status -- check union (undefined?) - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,connectOnOff)$Lisp checkViewport viewport => @@ -1029,7 +1029,7 @@ TwoDimensionalViewport ():Exports == Implementation where else status := 0$I viewport.graphStatesField.graphIndex.points := status -- check union (undefined?) - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,pointsOnOff)$Lisp checkViewport viewport => @@ -1045,7 +1045,7 @@ TwoDimensionalViewport ():Exports == Implementation where else status := 0$I viewport.graphStatesField.graphIndex.spline := status -- check union (undefined?) - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,spline2D)$Lisp checkViewport viewport => @@ -1061,7 +1061,7 @@ TwoDimensionalViewport ():Exports == Implementation where else status := 0$I viewport.graphStatesField.graphIndex.showing := status -- check union (undefined?) - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,showing2D)$Lisp checkViewport viewport => @@ -1072,7 +1072,7 @@ TwoDimensionalViewport ():Exports == Implementation where controlPanel (viewport,onOff) == if onOff = "on" then viewport.flags.showCP := yes else viewport.flags.showCP := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,hideControl2D)$Lisp checkViewport viewport => @@ -1080,7 +1080,7 @@ TwoDimensionalViewport ():Exports == Implementation where getI(VIEW)$Lisp -- acknowledge close viewport == - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,closeAll2D)$Lisp checkViewport viewport => @@ -1101,7 +1101,7 @@ TwoDimensionalViewport ():Exports == Implementation where write(viewport:$,Filename:STR,thingsToWrite:L STR) == stringToSend : STR := "" - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW2D)$Lisp sendI(VIEW,writeView)$Lisp checkViewport viewport => diff --git a/src/algebra/view3D.spad.pamphlet b/src/algebra/view3D.spad.pamphlet index 226145a6..25f1f30c 100644 --- a/src/algebra/view3D.spad.pamphlet +++ b/src/algebra/view3D.spad.pamphlet @@ -596,7 +596,7 @@ ThreeDimensionalViewport(): Exports == Implementation where viewport.lighting.lightX := convert(Xlight)@SF viewport.lighting.lightY := convert(Ylight)@SF viewport.lighting.lightZ := convert(Zlight)@SF - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,lightDef)$Lisp checkViewport viewport => @@ -608,7 +608,7 @@ ThreeDimensionalViewport(): Exports == Implementation where axes (viewport,onOff) == if onOff = "on" then viewport.flags.axesOn := yes else viewport.flags.axesOn := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,axesOnOff)$Lisp checkViewport viewport => @@ -618,7 +618,7 @@ ThreeDimensionalViewport(): Exports == Implementation where diagonals (viewport,onOff) == if onOff = "on" then viewport.flags.diagonalsOn := yes else viewport.flags.diagonalsOn := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,diagOnOff)$Lisp checkViewport viewport => @@ -628,7 +628,7 @@ ThreeDimensionalViewport(): Exports == Implementation where outlineRender (viewport,onOff) == if onOff = "on" then viewport.flags.outlineRenderOn := yes else viewport.flags.outlineRenderOn := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,outlineOnOff)$Lisp checkViewport viewport => @@ -638,7 +638,7 @@ ThreeDimensionalViewport(): Exports == Implementation where controlPanel (viewport,onOff) == if onOff = "on" then viewport.flags.showCP := yes else viewport.flags.showCP := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,hideControl)$Lisp checkViewport viewport => @@ -655,14 +655,14 @@ ThreeDimensionalViewport(): Exports == Implementation where else if (how = "smooth") then -- smooth viewport.flags.style := smooth else viewport.flags.style := wireMesh - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,viewport.flags.style)$Lisp checkViewport viewport => getI(VIEW)$Lisp -- acknowledge reset viewport == - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,SPADBUTTONPRESS)$Lisp checkViewport viewport => @@ -670,7 +670,7 @@ ThreeDimensionalViewport(): Exports == Implementation where getI(VIEW)$Lisp -- acknowledge close viewport == - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,closeAll)$Lisp checkViewport viewport => @@ -678,7 +678,7 @@ ThreeDimensionalViewport(): Exports == Implementation where viewport.key := 0$I viewpoint (viewport:%):V == - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,queryVIEWPOINT)$Lisp checkViewport viewport => @@ -698,7 +698,7 @@ ThreeDimensionalViewport(): Exports == Implementation where viewpoint (viewport:%, viewpt:V):Void == viewport.viewpoint := viewpt - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,changeVIEWPOINT)$Lisp checkViewport viewport => @@ -744,7 +744,7 @@ ThreeDimensionalViewport(): Exports == Implementation where title (viewport,Title) == viewport.title := Title - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,TITLE)$Lisp checkViewport viewport => @@ -753,7 +753,7 @@ ThreeDimensionalViewport(): Exports == Implementation where colorDef (viewport,HueOffset,HueNumber) == viewport.colors := [h := (hue HueOffset),(hue HueNumber) - h] - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,COLORDEF)$Lisp checkViewport viewport => @@ -767,7 +767,7 @@ ThreeDimensionalViewport(): Exports == Implementation where move(viewport,xLoc,yLoc) == viewport.moveTo := [xLoc,yLoc] - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,MOVE)$Lisp checkViewport viewport => @@ -777,7 +777,7 @@ ThreeDimensionalViewport(): Exports == Implementation where resize(viewport,xSize,ySize) == viewport.size := [xSize,ySize] - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,RESIZE)$Lisp checkViewport viewport => @@ -800,7 +800,7 @@ ThreeDimensionalViewport(): Exports == Implementation where rotate(viewport:%,Theta:F,Phi:F) == viewport.viewpoint.theta := convert(Theta)@SF viewport.viewpoint.phi := convert(Phi)@SF - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,ROTATE)$Lisp checkViewport viewport => @@ -810,7 +810,7 @@ ThreeDimensionalViewport(): Exports == Implementation where zoom(viewport:%,Scale:F) == viewport.viewpoint.scale := convert(Scale)@SF - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,ZOOM)$Lisp checkViewport viewport => @@ -821,7 +821,7 @@ ThreeDimensionalViewport(): Exports == Implementation where viewport.viewpoint.scaleX := convert(ScaleX)@SF viewport.viewpoint.scaleY := convert(ScaleY)@SF viewport.viewpoint.scaleZ := convert(ScaleZ)@SF - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,zoomx)$Lisp checkViewport viewport => @@ -833,7 +833,7 @@ ThreeDimensionalViewport(): Exports == Implementation where translate(viewport,DeltaX,DeltaY) == viewport.viewpoint.deltaX := convert(DeltaX)@SF viewport.viewpoint.deltaY := convert(DeltaY)@SF - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,TRANSLATE)$Lisp checkViewport viewport => @@ -845,7 +845,7 @@ ThreeDimensionalViewport(): Exports == Implementation where if (Amount < 0$F) or (Amount > 1$F) then error "The intensity must be a value between 0 and 1, inclusively." viewport.lighting.translucence := convert(Amount)@SF - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,translucenceDef)$Lisp checkViewport viewport => @@ -860,7 +860,7 @@ ThreeDimensionalViewport(): Exports == Implementation where write(viewport:%,Filename:S,thingsToWrite:L S) == stringToSend : S := "" - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,writeView)$Lisp checkViewport viewport => @@ -879,7 +879,7 @@ ThreeDimensionalViewport(): Exports == Implementation where perspective (viewport,onOff) == if onOff = "on" then viewport.perspective.perspectiveField := yes else viewport.perspective.perspectiveField := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,perspectiveOnOff)$Lisp checkViewport viewport => @@ -889,7 +889,7 @@ ThreeDimensionalViewport(): Exports == Implementation where showRegion (viewport,onOff) == if onOff = "on" then viewport.flags.showRegionField := yes else viewport.flags.showRegionField := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,region3D)$Lisp checkViewport viewport => @@ -899,7 +899,7 @@ ThreeDimensionalViewport(): Exports == Implementation where showClipRegion (viewport,onOff) == if onOff = "on" then viewport.volume.clipRegionField := yes else viewport.volume.clipRegionField := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,clipRegionOnOff)$Lisp checkViewport viewport => @@ -909,7 +909,7 @@ ThreeDimensionalViewport(): Exports == Implementation where clipSurface (viewport,onOff) == if onOff = "on" then viewport.volume.clipSurfaceField := yes else viewport.volume.clipSurfaceField := no - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,clipSurfaceOnOff)$Lisp checkViewport viewport => @@ -918,7 +918,7 @@ ThreeDimensionalViewport(): Exports == Implementation where eyeDistance(viewport:%,EyeDistance:F) == viewport.perspective.eyeDistance := convert(EyeDistance)@SF - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,eyeDistanceData)$Lisp checkViewport viewport => @@ -927,7 +927,7 @@ ThreeDimensionalViewport(): Exports == Implementation where hitherPlane(viewport:%,HitherPlane:F) == viewport.perspective.hitherPlane := convert(HitherPlane)@SF - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,hitherPlaneData)$Lisp checkViewport viewport => @@ -937,7 +937,7 @@ ThreeDimensionalViewport(): Exports == Implementation where modifyPointData(viewport,anIndex,aPoint) == (n := dimension aPoint) < 3 => error "The point should have dimension of at least 3" viewport.space3D := modifyPointData(viewport.space3D,anIndex,aPoint) - (key(viewport) ^= 0$I) => + (key(viewport) ~= 0$I) => sendI(VIEW,typeVIEW3D)$Lisp sendI(VIEW,modifyPOINT)$Lisp checkViewport viewport => @@ -950,7 +950,7 @@ ThreeDimensionalViewport(): Exports == Implementation where getI(VIEW)$Lisp -- acknowledge -- print viewport == --- (key(viewport) ^= 0$I) => +-- (key(viewport) ~= 0$I) => -- sendI(VIEW,typeVIEW3D)$Lisp -- sendI(VIEW,printViewport)$Lisp -- checkViewport viewport => diff --git a/src/algebra/wtpol.spad.pamphlet b/src/algebra/wtpol.spad.pamphlet index c3ee8d28..af1414e0 100644 --- a/src/algebra/wtpol.spad.pamphlet +++ b/src/algebra/wtpol.spad.pamphlet @@ -55,14 +55,14 @@ WeightedPolynomials(R:Ring,VarSet: OrderedSet, E:OrderedAbelianMonoidSup, changeWeightLevel(n) == wtlevel:=n lookupList:List Record(var:VarSet, weight:NonNegativeInteger) - if #vl ^= #wl then error "incompatible length lists in WeightedPolynomial" + if #vl ~= #wl then error "incompatible length lists in WeightedPolynomial" lookupList:=[[v,n] for v in vl for n in wl] -- local operation innercoerce:(p,z) -> $ lookup:Varset -> NonNegativeInteger lookup v == l:=lookupList - while l ^= [] repeat + while l ~= [] repeat v = l.first.var => return l.first.weight l:=l.rest 0 diff --git a/src/algebra/xlpoly.spad.pamphlet b/src/algebra/xlpoly.spad.pamphlet index c863ac2f..6d79566d 100644 --- a/src/algebra/xlpoly.spad.pamphlet +++ b/src/algebra/xlpoly.spad.pamphlet @@ -243,7 +243,7 @@ LyndonWord(VarSet:OrderedSet):Public == Private where lyndon? w == w = 1$OFMON => false f: OFMON := rest w - while f ^= 1$OFMON repeat + while f ~= 1$OFMON repeat not lexico(w,f) => return false f := rest f true @@ -594,7 +594,7 @@ LiePolynomial(VarSet:OrderedSet, R:CommutativeRing) : Public == Private where LiePolyIfCan p == -- inefficace a cause de la rep. de XDPOLY not quasiRegular? p => "failed" p1: XDPOLY := p ; r:$ := 0 - while p1 ^= 0 repeat + while p1 ~= 0 repeat t: Record(k:WORD, c:R) := mindegTerm p1 w: WORD := t.k; coef:R := t.c (l := lyndonIfCan(w)$LWORD) case "failed" => return "failed" @@ -770,7 +770,7 @@ PoincareBirkhoffWittLyndonBasis(VarSet: OrderedSet): Public == Private where null x.rest retract x == - #x ^= 1 => error "cannot convert to Lyndon word" + #x ~= 1 => error "cannot convert to Lyndon word" x.first retractIfCan x == @@ -958,7 +958,7 @@ XPBWPolynomial(VarSet:OrderedSet,R:CommutativeRing): XDPcat == XDPdef where p.last.k = 1$BASIS => p.last.c 0$R - quasiRegular? p == (p=0) or (p.last.k ^= 1$BASIS) + quasiRegular? p == (p=0) or (p.last.k ~= 1$BASIS) quasiRegular p == p = 0 => p p.last.k = 1$BASIS => delete(p, maxIndex p) diff --git a/src/algebra/xpoly.spad.pamphlet b/src/algebra/xpoly.spad.pamphlet index 6ff416b1..160ee646 100644 --- a/src/algebra/xpoly.spad.pamphlet +++ b/src/algebra/xpoly.spad.pamphlet @@ -107,7 +107,7 @@ OrderedFreeMonoid(S: OrderedSet): OFMcategory == OFMdefinition where x: List REC := listOfMonoms(w)$Rep null x => "failed" fx: REC := first x - fx.gen ^= l => "failed" + fx.gen ~= l => "failed" fx.exp = 1 => makeMulti rest(x) makeMulti [[fx.gen, (fx.exp - 1)::NNI ]$REC, :rest x] @@ -288,7 +288,7 @@ FreeModule1(R:Ring,S:OrderedSet): FMcat == FMdef where monomials x == [ monom (t.k, t.c) for t in x] retractIfCan x == - numberOfMonomials(x) ^= 1 => "failed" + numberOfMonomials(x) ~= 1 => "failed" x.first.c = 1 => x.first.k "failed" @@ -578,7 +578,7 @@ XPolynomialRing(R:Ring,E:OrderedMonoid): T == C where constant? p == (p = 0) or (maxdeg(p) = 1$E) constant p == coef(p,1$E) - quasiRegular? p == (p=0) or (last p).k ^= 1$E + quasiRegular? p == (p=0) or (last p).k ~= 1$E quasiRegular p == quasiRegular?(p) => p [t for t in p | not(t.k = 1$E)] @@ -746,10 +746,10 @@ XDistributedPolynomial(vl:OrderedSet,R:Ring): XDPcat == XDPdef where x * shw(rest w1,w2) + y * shw(w1,rest w2) lquo(p:%,q:%):% == - +/ [r * t.c for t in q | (r := lquo(p,t.k)) ^= 0] + +/ [r * t.c for t in q | (r := lquo(p,t.k)) ~= 0] rquo(p:%,q:%):% == - +/ [r * t.c for t in q | (r := rquo(p,t.k)) ^= 0] + +/ [r * t.c for t in q | (r := rquo(p,t.k)) ~= 0] coef(p:%,q:%):R == p = 0 => 0$R @@ -839,14 +839,14 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where p2 case R => p1 * p2::R p1 case R => p1 * p2.c0 x:REGPOLY := construct [[t.k, a]$TERM for t in ListOfTerms(p1.reg) _ - | (a:= rquo(t.c,p2)) ^= 0$% ]$LTERMS + | (a:= rquo(t.c,p2)) ~= 0$% ]$LTERMS simplifie [coef(p1,p2) , x]$VPOLY trunc(p,n) == n = 0 or (p case R) => (constant p)::% n1: NNI := (n-1)::NNI lt: LTERMS := [[t.k, r]$TERM for t in ListOfTerms p.reg _ - | (r := trunc(t.c, n1)) ^= 0]$LTERMS + | (r := trunc(t.c, n1)) ~= 0]$LTERMS x: REGPOLY := construct lt simplifie [constant p, x]$VPOLY @@ -854,7 +854,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where constant? p => (constant p)::% vl: List VarSet := sort(#1 > #2, varList p) x : REGPOLY := _ - construct [[v, unexpand r]$TERM for v in vl| (r:=lquo(p,v)) ^= 0] + construct [[v, unexpand r]$TERM for v in vl| (r:=lquo(p,v)) ~= 0] [constant p, x]$VPOLY if R has CommutativeRing then @@ -999,7 +999,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where rquo(p:%, v:VarSet):% == p case R => 0 x:REGPOLY := construct [[t.k, a]$TERM for t in ListOfTerms(p.reg) - | (a:= rquo(t.c,v)) ^= 0 ] + | (a:= rquo(t.c,v)) ~= 0 ] simplifie [constant(coefficient(p.reg,v)) , x]$VPOLY rquo(p:%, w:WORD):% == @@ -1026,7 +1026,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where p case R => p = 0 => error "XRPOLY.mindeg: polynome nul !!" 1$WORD - p.c0 ^= 0 => 1$WORD + p.c0 ~= 0 => 1$WORD "min"/[(t.k) *$WORD mindeg(t.c) for t in ListOfTerms p.reg] maxdeg p == @@ -1042,7 +1042,7 @@ XRecursivePolynomial(VarSet:OrderedSet,R:Ring): Xcat == Xdef where map(fn,p) == p case R => fn(p::R) x:REGPOLY := construct [[t.k,a]$TERM for t in ListOfTerms p.reg - |(a := map(fn,t.c)) ^= 0$R] + |(a := map(fn,t.c)) ~= 0$R] simplifie [fn(p.c0),x]$VPOLY varList p == |