diff options
Diffstat (limited to 'src/algebra')
92 files changed, 228 insertions, 225 deletions
diff --git a/src/algebra/aggcat.spad.pamphlet b/src/algebra/aggcat.spad.pamphlet index 8e9a0b23..e58fac69 100644 --- a/src/algebra/aggcat.spad.pamphlet +++ b/src/algebra/aggcat.spad.pamphlet @@ -1565,17 +1565,17 @@ UnaryRecursiveAggregate(S:Type): Category == RecursiveAggregate S with less?(l, n) == i := n::Integer - while i > 0 and not empty? l repeat (l := rest l; i := i - 1) - i > 0 + while positive? i and not empty? l repeat (l := rest l; i := i - 1) + positive? i more?(l, n) == i := n::Integer - while i > 0 and not empty? l repeat (l := rest l; i := i - 1) + while positive? i and not empty? l repeat (l := rest l; i := i - 1) zero?(i) and not empty? l size?(l, n) == i := n::Integer - while not empty? l and i > 0 repeat (l := rest l; i := i - 1) + while not empty? l and positive? i repeat (l := rest l; i := i - 1) empty? l and zero? i #x == diff --git a/src/algebra/algext.spad.pamphlet b/src/algebra/algext.spad.pamphlet index 01657494..b5e2d470 100644 --- a/src/algebra/algext.spad.pamphlet +++ b/src/algebra/algext.spad.pamphlet @@ -147,7 +147,7 @@ SimpleAlgebraicExtension(R:CommutativeRing, i:Integer := k rem size() p:Integer := size()$R ans:$ := 0 - for j in 0.. while i > 0 repeat + for j in 0.. while positive? i repeat h := i rem p -- index(p) = 0$R if h ~= 0 then diff --git a/src/algebra/algfunc.spad.pamphlet b/src/algebra/algfunc.spad.pamphlet index b32e1f56..bf4c4b71 100644 --- a/src/algebra/algfunc.spad.pamphlet +++ b/src/algebra/algfunc.spad.pamphlet @@ -222,25 +222,25 @@ AlgebraicallyClosedFunctionSpace(R: IntegralDomain): zeroOf(p:$, x:Symbol) == n := numer(f := univariate(p, kernel(x)$Kernel($))) - degree denom f > 0 => error "zeroOf: variable appears in denom" + positive? degree denom f => error "zeroOf: variable appears in denom" degree n = 0 => error "zeroOf: constant expression" zeroOf(n, x) rootOf(p:$, x:Symbol) == n := numer(f := univariate(p, kernel(x)$Kernel($))) - degree denom f > 0 => error "roofOf: variable appears in denom" + positive? degree denom f => error "roofOf: variable appears in denom" degree n = 0 => error "rootOf: constant expression" rootOf(n, x) zerosOf(p:$, x:Symbol) == n := numer(f := univariate(p, kernel(x)$Kernel($))) - degree denom f > 0 => error "zerosOf: variable appears in denom" + positive? degree denom f => error "zerosOf: variable appears in denom" degree n = 0 => empty() zerosOf(n, x) rootsOf(p:$, x:Symbol) == n := numer(f := univariate(p, kernel(x)$Kernel($))) - degree denom f > 0 => error "roofsOf: variable appears in denom" + positive? degree denom f => error "roofsOf: variable appears in denom" degree n = 0 => empty() rootsOf(n, x) @@ -358,7 +358,7 @@ AlgebraicFunction(R, F): Exports == Implementation where (r := retractIfCan(p)@Union(F, "failed")) case "failed" => inrootof(p, k::F) n := numer(f := univariate(r::F, k)) - degree denom f > 0 => error "roofOf: variable appears in denom" + positive? degree denom f => error "roofOf: variable appears in denom" inrootof(n, k::F) dvalg(l, x) == @@ -368,7 +368,7 @@ AlgebraicFunction(R, F): Exports == Implementation where ialg l == f := univariate(p := first l, retract(x := second l)@K) - degree denom f > 0 => error "roofOf: variable appears in denom" + positive? degree denom f => error "roofOf: variable appears in denom" inrootof(numer f, x) operator op == diff --git a/src/algebra/allfact.spad.pamphlet b/src/algebra/allfact.spad.pamphlet index c0b520d5..c45d662c 100644 --- a/src/algebra/allfact.spad.pamphlet +++ b/src/algebra/allfact.spad.pamphlet @@ -192,7 +192,7 @@ MPolyCatRationalFunctionFactorizer(E,OV,R,PRF) : C == T ---- push x back from the coefficient domain ---- pushuconst(r:F,x:OV):PRF == xs:SE:=convert x - degree(denom r,xs)>0 => error "bad polynomial form" + positive? degree(denom r,xs) => error "bad polynomial form" inv((denom r)::F)*pushucoef(univariate(numer r,xs),x) diff --git a/src/algebra/array1.spad.pamphlet b/src/algebra/array1.spad.pamphlet index 0a521e77..48ee917f 100644 --- a/src/algebra/array1.spad.pamphlet +++ b/src/algebra/array1.spad.pamphlet @@ -199,8 +199,8 @@ IndexedFlexibleArray(S:Type, mn: Integer): Exports == Implementation where growAdding(r, b, s) == b = 0 => r - #r > 0 => growAndFill(r, b, (r.f).0) - #s > 0 => growAndFill(r, b, (s.f).0) + positive?(#r) => growAndFill(r, b, (r.f).0) + positive?(#s) => growAndFill(r, b, (s.f).0) error "no default filler element" growAndFill(r, b, x) == diff --git a/src/algebra/bags.spad.pamphlet b/src/algebra/bags.spad.pamphlet index 69f6d509..38c5ab33 100644 --- a/src/algebra/bags.spad.pamphlet +++ b/src/algebra/bags.spad.pamphlet @@ -276,7 +276,7 @@ Heap(S:OrderedSet): Exports == Implementation where -- Williams' insertion algorithm O(log n) j := (#r) :: Integer r:=concat!(r,concat(x,empty()$Rep)) - while j > 0 repeat + while positive? j repeat i := (j-1) quo 2 if r(i) >= x then leave r(j) := r(i) diff --git a/src/algebra/catdef.spad.pamphlet b/src/algebra/catdef.spad.pamphlet index 2b6ff9d2..26aa0469 100644 --- a/src/algebra/catdef.spad.pamphlet +++ b/src/algebra/catdef.spad.pamphlet @@ -90,7 +90,7 @@ AbelianGroup(): Category == Join(CancellationAbelianMonoid, LeftLinearSet Intege if not (% has Ring) then n:Integer * x:% == zero? n => 0 - n>0 => double(n pretend PositiveInteger,x) + positive? n => double(n pretend PositiveInteger,x) double((-n) pretend PositiveInteger,-x) @ @@ -1015,8 +1015,10 @@ GcdDomain(): Category == IntegralDomain with c1:= content(p1); c2:= content(p2) p1:= (p1 exquo c1)::SUP % p2:= (p2 exquo c2)::SUP % - if (e1:=minimumDegree p1) > 0 then p1:=(p1 exquo monomial(1,e1))::SUP % - if (e2:=minimumDegree p2) > 0 then p2:=(p2 exquo monomial(1,e2))::SUP % + if positive?(e1:=minimumDegree p1) then + p1:=(p1 exquo monomial(1,e1))::SUP % + if positive?(e2:=minimumDegree p2) then + p2:=(p2 exquo monomial(1,e2))::SUP % e1:=min(e1,e2); c1:=gcd(c1,c2) p1:= degree p1 = 0 or degree p2 = 0 => monomial(c1,0) diff --git a/src/algebra/combfunc.spad.pamphlet b/src/algebra/combfunc.spad.pamphlet index f1dc9583..d89697fd 100644 --- a/src/algebra/combfunc.spad.pamphlet +++ b/src/algebra/combfunc.spad.pamphlet @@ -518,7 +518,7 @@ dummy variable is introduced to make the indexing variable \lq local\rq. if R has RetractableTo(Z) and F has Algebra(Fraction(Z)) then iibinom l == (s:=retractIfCan(first l-second l)@Union(R,"failed")) case R and - (t:=retractIfCan(s)@Union(Z,"failed")) case Z and t > 0 => + (t:=retractIfCan(s)@Union(Z,"failed")) case Z and positive? t => ans:=1::F for i in 1..t repeat ans:=ans*(second l+i::R::F) diff --git a/src/algebra/complet.spad.pamphlet b/src/algebra/complet.spad.pamphlet index 5ac5d928..d6d6244d 100644 --- a/src/algebra/complet.spad.pamphlet +++ b/src/algebra/complet.spad.pamphlet @@ -79,7 +79,7 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where n:Integer * x:% == x case inf => - n > 0 => x + positive? n => x negative? n => [not(x.inf)] error "Undefined product" [n * x.fin] @@ -103,7 +103,7 @@ OrderedCompletion(R:SetCategory): Exports == Implementation where characteristic == characteristic$R fininf(b, r) == - r > 0 => [b] + positive? r => [b] negative? r => [not b] error "Undefined product" diff --git a/src/algebra/crfp.spad.pamphlet b/src/algebra/crfp.spad.pamphlet index 1ac1ba20..8bbd8ee9 100644 --- a/src/algebra/crfp.spad.pamphlet +++ b/src/algebra/crfp.spad.pamphlet @@ -306,7 +306,7 @@ ComplexRootFindingPackage(R, UP): public == private where -- next we check if one of these centers is a root centerIsRoot : Boolean := false for i in 1..maxIndex lp repeat - if (mD := minimumDegree lp.i) > 0 then + if positive? (mD := minimumDegree lp.i) then pp : UP := monomial(1,1)-monomial(listOfCenters.i-u,0) centerIsRoot := true fp := fp * irreducibleFactor(pp,mD) @@ -418,7 +418,7 @@ ComplexRootFindingPackage(R, UP): public == private where divisorCascade(p, tp, info) == lfae : L FAE := nil() - for i in 1..degree tp while (degree tp > 0) repeat + for i in 1..degree tp while positive? degree tp repeat -- USE monicDivide !!! qr : Record(quotient: UP, remainder: UP) := divide(p,tp) factor1 : UP := tp diff --git a/src/algebra/curve.spad.pamphlet b/src/algebra/curve.spad.pamphlet index 57fd38d3..d69d6bfe 100644 --- a/src/algebra/curve.spad.pamphlet +++ b/src/algebra/curve.spad.pamphlet @@ -305,7 +305,7 @@ FunctionFieldCategory(F, UP, UPUP): Category == Definition where infValue f == zero? f => 0 - (n := infOrder f) > 0 => 0 + positive?(n := infOrder f) => 0 zero? n => (leadingCoefficient numer f) / (leadingCoefficient denom f) error "f not locally integral at infinity" diff --git a/src/algebra/ddfact.spad.pamphlet b/src/algebra/ddfact.spad.pamphlet index 46ef51c6..2fbc0ca5 100644 --- a/src/algebra/ddfact.spad.pamphlet +++ b/src/algebra/ddfact.spad.pamphlet @@ -225,7 +225,7 @@ DistinctDegreeFactorize(F,FP): C == T if (lcm := leadingCoefficient m) ~=1 then m := (inv lcm)*m --is x**d factor of m? - if (d := minimumDegree m)>0 then + if positive?(d := minimumDegree m) then m := (monicDivide (m,monomial(1,d))).quotient factlist := [[monomial(1,1),d]$ParFact] d:=degree m diff --git a/src/algebra/defaults.spad.pamphlet b/src/algebra/defaults.spad.pamphlet index 8de63814..e5e47e40 100644 --- a/src/algebra/defaults.spad.pamphlet +++ b/src/algebra/defaults.spad.pamphlet @@ -160,7 +160,7 @@ FiniteLinearAggregateSort(S, V): Exports == Implementation where g := 1 while g <= (n-m) repeat g := 3*g+1 g := g quo 3 - while g > 0 repeat + while positive? g repeat for i in m+g..n repeat j := i-g while j >= m and l(qelt(r, j+g), qelt(r, j)) repeat diff --git a/src/algebra/defintef.spad.pamphlet b/src/algebra/defintef.spad.pamphlet index 0253ac93..34eb5e03 100644 --- a/src/algebra/defintef.spad.pamphlet +++ b/src/algebra/defintef.spad.pamphlet @@ -118,7 +118,7 @@ ElementaryFunctionDefiniteIntegration(R, F): Exports == Implementation where -- returns true if a > b, false if a < b, "failed" if can't decide moreThan(a, b) == (r := retractIfCan(a)@Union(F, "failed")) case "failed" => -- infinite - whatInfinity(a) > 0 + positive? whatInfinity(a) (u := retractIfCan(r::F)@Union(Fraction Z, "failed")) case "failed" => "failed" u::Fraction(Z) > b @@ -171,11 +171,11 @@ ElementaryFunctionDefiniteIntegration(R, F): Exports == Implementation where z := (r := retractIfCan(a)@Union(F, "failed")) case "failed" => sign(f, x, a) sign(f, x, r::F, "right") - (b1 := z case Z) and z::Z > 0 => true + (b1 := z case Z) and positive?(z::Z) => true z := (r := retractIfCan(b)@Union(F, "failed")) case "failed" => sign(f, x, b) sign(f, x, r::F, "left") - (b2 := z case Z) and z::Z > 0 => true + (b2 := z case Z) and positive?(z::Z) => true b1 and b2 => ((w := checkFor0(numer f, k, a, b)) case "failed") or (w::B) => "failed" false diff --git a/src/algebra/defintrf.spad.pamphlet b/src/algebra/defintrf.spad.pamphlet index f86baafa..9122f812 100644 --- a/src/algebra/defintrf.spad.pamphlet +++ b/src/algebra/defintrf.spad.pamphlet @@ -181,7 +181,8 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where i case halfinf => empty?(l := realZeros p) => empty() bounds:REC := - i.halfinf.dir > 0 => [i.halfinf.endpoint, "max"/[t.right for t in l]] + positive?(i.halfinf.dir) => + [i.halfinf.endpoint, "max"/[t.right for t in l]] ["min"/[t.left for t in l], i.halfinf.endpoint] l := [u::REC for t in l | (u := refine(p, t, bounds)) case REC] incl? => l @@ -227,7 +228,7 @@ DefiniteIntegrationTools(R, F): Exports == Implementation where (ea := infeval(p, a)) case "failed" => "failed" (eb := infeval(p, b)) case "failed" => "failed" (s := sign(ea::F * eb::F)) case "failed" => "failed" - s::Z > 0 + positive?(s::Z) -- returns true if p has a positive root. Include 0 is incl0? is true posRoot(p, incl0?) == diff --git a/src/algebra/divisor.spad.pamphlet b/src/algebra/divisor.spad.pamphlet index 4dc651e8..42056811 100644 --- a/src/algebra/divisor.spad.pamphlet +++ b/src/algebra/divisor.spad.pamphlet @@ -349,7 +349,7 @@ ModularHermitianRowReduction(R): Exports == Implementation where normalizedDivide(n:R, d:R):Record(quotient:R, remainder:R) == qr := divide(n, d) qr.remainder >= 0 => qr - d > 0 => + positive? d => qr.remainder := qr.remainder + d qr.quotient := qr.quotient - 1 qr diff --git a/src/algebra/dpolcat.spad.pamphlet b/src/algebra/dpolcat.spad.pamphlet index 1ec8f105..64ca21c2 100644 --- a/src/algebra/dpolcat.spad.pamphlet +++ b/src/algebra/dpolcat.spad.pamphlet @@ -330,7 +330,7 @@ DifferentialPolynomialCategory(R:Ring,S:OrderedSet, "max"/[order v for v in variables p] order (p:$,s:S):NonNegativeInteger == ground? p => 0 - empty? (vv:= [order v for v in variables p | (variable v) = s ]) =>0 + empty? (vv:= [order v for v in variables p | (variable v) = s ]) => 0 "max"/vv degree (p, s) == diff --git a/src/algebra/efstruc.spad.pamphlet b/src/algebra/efstruc.spad.pamphlet index 414217a8..7f9829db 100644 --- a/src/algebra/efstruc.spad.pamphlet +++ b/src/algebra/efstruc.spad.pamphlet @@ -481,11 +481,11 @@ ElementaryFunctionStructurePackage(R,F): Exports == Implementation where factdeprel(l, k) == ((r := retractIfCan(n := first argument k)@Union(Z, "failed")) - case Z) and (r::Z > 0) => [factorial(r::Z)::F] + case Z) and positive?(r::Z) => [factorial(r::Z)::F] for x in l repeat m := first argument x ((r := retractIfCan(n - m)@Union(Z, "failed")) case Z) and - (r::Z > 0) => return([*/[(m + i::F) for i in 1..r] * x::F]) + positive?(r::Z) => return([*/[(m + i::F) for i in 1..r] * x::F]) [true] else diff --git a/src/algebra/efuls.spad.pamphlet b/src/algebra/efuls.spad.pamphlet index 728522ce..b20867e0 100644 --- a/src/algebra/efuls.spad.pamphlet +++ b/src/algebra/efuls.spad.pamphlet @@ -220,7 +220,7 @@ ElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS):_ lc := coefficient(uls,ord) (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => (1/2) * pi() - (rat :: RN) > 0 => (1/2) * pi() + positive?(rat :: RN) => (1/2) * pi() (-1/2) * pi() (1/2) * pi() return "failed" @@ -238,7 +238,7 @@ ElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS):_ RATS => lc := coefficient(uls,ord) (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => 0 - (rat :: RN) > 0 => 0 + positive?(rat :: RN) => 0 TRANSFCN => pi() return "failed" 0 @@ -321,7 +321,7 @@ ElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS):_ lc := coefficient(uls,ord) (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => (1/2) * pi() - (rat :: RN) > 0 => (1/2) * pi() + positive?(rat :: RN) => (1/2) * pi() (-1/2) * pi() (1/2) * pi() error "atan: series expansion involves transcendental constants" @@ -342,7 +342,7 @@ ElementaryFunctionsUnivariateLaurentSeries(Coef,UTS,ULS):_ RATS => lc := coefficient(uls,ord) (rat := retractIfCan(lc)@Union(RN,"failed")) case "failed" => 0 - (rat :: RN) > 0 => 0 + positive?(rat :: RN) => 0 TRANSFCN => pi() error "acot: series expansion involves transcendental constants" 0 diff --git a/src/algebra/expexpan.spad.pamphlet b/src/algebra/expexpan.spad.pamphlet index 0166357c..332e8ca9 100644 --- a/src/algebra/expexpan.spad.pamphlet +++ b/src/algebra/expexpan.spad.pamphlet @@ -342,7 +342,7 @@ UnivariatePuiseuxSeriesWithExponentialSingularity(R,FE,var,cen):_ domTerm := termInfo.%term (type := termInfo.%type) = "series" => -- find limit of series term - (ord := order(pSeries := coeff domTerm,1)) > 0 => 0 + positive?(ord := order(pSeries := coeff domTerm,1)) => 0 coef := coefficient(pSeries,ord) member?(var,variables coef) => "failed" ord = 0 => coef :: OFE @@ -447,7 +447,7 @@ ExponentialExpansion(R,FE,var,cen): Exports == Implementation where seriesQuotientLimit(num,den) == -- limit of the quotient of two series series := num / den - (ord := order(series,1)) > 0 => 0 + positive?(ord := order(series,1)) => 0 coef := coefficient(series,ord) member?(var,variables coef) => "failed" ord = 0 => coef :: OFE diff --git a/src/algebra/f02.spad.pamphlet b/src/algebra/f02.spad.pamphlet index 81f1df5e..3a9be77d 100644 --- a/src/algebra/f02.spad.pamphlet +++ b/src/algebra/f02.spad.pamphlet @@ -489,7 +489,7 @@ NagEigenPackage(): Exports == Implementation where zero? ncolbArg and not wantqArg and not wantpArg => 2*tem zero? ncolbArg and wantpArg and not wantqArg => 3*tem not wantpArg => - ncolbArg >0 or wantqArg => 3*tem + positive? ncolbArg or wantqArg => 3*tem 5*tem cLen : Integer := mArg >= nArg => diff --git a/src/algebra/ffpoly2.spad.pamphlet b/src/algebra/ffpoly2.spad.pamphlet index 2e2796c5..76c5780f 100644 --- a/src/algebra/ffpoly2.spad.pamphlet +++ b/src/algebra/ffpoly2.spad.pamphlet @@ -101,7 +101,7 @@ FiniteFieldPolynomialPackage2(F,GF):Exports == Implementation where beta:=Frobenius(beta) trModp:=trModp +$(SUP F) beta *$(SUP F) map(coerce,qexp.i)$SUPF2 -- if it is of degree 0, it doesn't help us finding a root - if degree(trModp)$(SUP F) > 0 then + if positive? degree(trModp)$(SUP F) then -- for all elements gf of GF do for j in 1..sizeGF repeat -- compute gcd(trace(beta * x) + gf,stillToFactor) diff --git a/src/algebra/float.spad.pamphlet b/src/algebra/float.spad.pamphlet index e3e0b5a9..917d4490 100644 --- a/src/algebra/float.spad.pamphlet +++ b/src/algebra/float.spad.pamphlet @@ -274,7 +274,7 @@ Float(): atan(x,y) == x = 0 => - y > 0 => pi()/2 + positive? y => pi()/2 negative? y => -pi()/2 0 -- Only count on first quadrant being on principal branch. @@ -338,7 +338,7 @@ Float(): -- the running time is O( sqrt p M(p) ) assuming |x| < 1 k := ISQRT (bits()-100)::I quo 4 k := max(0,2 + k + order x) - if k > 0 then (inc k; x := x / 3**k::N) + if positive? k then (inc k; x := x / 3**k::N) r := sinSeries x for i in 1..k repeat r := itimes(3,r)-shift(r**3,2) bits p @@ -373,7 +373,7 @@ Float(): -- need to increase precision by more than k, otherwise recursion -- causes loss of accuracy. -- Michael Monagan suggests adding a factor of log(k) - if k > 0 then (inc(k+length(k)**2); x := shift(x,-k)) + if positive? k then (inc(k+length(k)**2); x := shift(x,-k)) r := cosSeries x for i in 1..k repeat r := shift(r*r,1)-1 bits p @@ -543,9 +543,9 @@ Float(): -- results in an overall running time of O( sqrt p M(p) ) k := ISQRT (p-100)::I quo 3 k := max(0,2 + k + order x) - if k > 0 then (inc k; x := shift(x,-k)) + if positive? k then (inc k; x := shift(x,-k)) e := expSeries x - if k > 0 then e := square(e,k) + if positive? k then e := square(e,k) bits p e * e1 @@ -609,7 +609,7 @@ Float(): chop(x,p) == e : I := LENGTH x.mantissa - p - if e > 0 then x := [shift2(x.mantissa,-e),x.exponent+e] + if positive? e then x := [shift2(x.mantissa,-e),x.exponent+e] x float(m,e) == normalize [m,e] float(m,e,b) == @@ -620,10 +620,10 @@ Float(): m := x.mantissa m = 0 => 0 e : I := LENGTH m - bits() - if e > 0 then + if positive? e then y := shift2(m,1-e) if odd? y then - y := (if y>0 then y+1 else y-1) quo 2 + y := (if positive? y then y+1 else y-1) quo 2 if LENGTH y > bits() then y := y quo 2 e := e+1 @@ -636,7 +636,7 @@ Float(): order x = order y and sign x = sign y and zero? (x - y) x < y == y.mantissa = 0 => negative? x.mantissa - x.mantissa = 0 => y.mantissa > 0 + x.mantissa = 0 => positive? y.mantissa negative? x and positive? y => true negative? y and positive? x => false order x < order y => positive? x @@ -794,13 +794,13 @@ Float(): chop10(x,p) == e : I := floorLength10 x.mantissa - p - if e > 0 then x := [x.mantissa quo 10**e::N,x.exponent+e] + if positive? e then x := [x.mantissa quo 10**e::N,x.exponent+e] x normalize10(x,p) == ma := x.mantissa ex := x.exponent e : I := length10 ma - p - if e > 0 then + if positive? e then ma := ma quo 10**(e-1)::N ex := ex + e (ma,r) := divide(ma, 10) @@ -926,7 +926,7 @@ Float(): s := convert(m)@S; n := #s; o := n + e -- Note: at least one digit is displayed after the decimal point -- and trailing zeroes after the decimal point are dropped - if o > 0 and o <= max(n,d) then + if positive? o and o <= max(n,d) then -- fixed format: add trailing zeroes before the decimal point if o > n then s := concat(s, new((o-n)::N,zero)) t := rightTrim(s(o + minIndex s .. n + minIndex s - 1), zero) @@ -960,7 +960,7 @@ Float(): OUTMODE() = "floating" => floating f OUTMODE() = "general" => general f empty()$String - if b > 0 then bits(b::PositiveInteger) + if positive? b then bits(b::PositiveInteger) s = empty()$String => error "bad output mode" s diff --git a/src/algebra/formula.spad.pamphlet b/src/algebra/formula.spad.pamphlet index 19011081..750bf710 100644 --- a/src/algebra/formula.spad.pamphlet +++ b/src/algebra/formula.spad.pamphlet @@ -231,7 +231,7 @@ ScriptFormulaFormat(): public == private where lss > len => l := concat(ss,l)$List(S) ls := ls + lss + 1 s := concat(s,concat(ss," ")$S)$S - if ls > 0 then l := concat(s,l)$List(S) + if positive? ls then l := concat(s,l)$List(S) reverse l group str == @@ -403,7 +403,7 @@ ScriptFormulaFormat(): public == private where %integer?(expr)$Foreign(Builtin) => i := expr : Integer if negative? i or (i > 9) then group str else str - (i := position(str,specialStrings)) > 0 => + positive?(i := position(str,specialStrings)) => specialStringsInFormula.i str l : L E := (expr pretend L E) diff --git a/src/algebra/fparfrac.spad.pamphlet b/src/algebra/fparfrac.spad.pamphlet index b769ba05..f6495e21 100644 --- a/src/algebra/fparfrac.spad.pamphlet +++ b/src/algebra/fparfrac.spad.pamphlet @@ -141,7 +141,7 @@ FullPartialFractionExpansion(F, UP): Exports == Implementation where lvar := concat(makeVariable(u, m), lvar) lval := concat(inv((m+1)::F) * q, lval) qq := q0 quo gcd(pp, q0) -- new center - if (degree(qq) > 0) then + if positive? degree(qq) then ans := concat([(n + 1 - m)::N, qq, (pp * bm * cn * cm) rem qq], ans) cm := (c * cm) rem q0 -- cm = c**m modulo q now um := u1 * um -- um = u**m now diff --git a/src/algebra/free.spad.pamphlet b/src/algebra/free.spad.pamphlet index f87666b0..34d06a9a 100644 --- a/src/algebra/free.spad.pamphlet +++ b/src/algebra/free.spad.pamphlet @@ -344,7 +344,7 @@ FreeMonoid(S: SetCategory): FreeMonoidCategory(S) == FMdefinition where lb := listOfMonoms b na: Integer := #la nb: Integer := #lb - while na > 0 and nb > 0 repeat + while positive? na and positive? nb repeat la.first.gen > lb.first.gen => return false la.first.gen < lb.first.gen => return true if la.first.exp = lb.first.exp then @@ -504,8 +504,8 @@ InnerFreeAbelianMonoid(S: SetCategory, E:CancellationAbelianMonoid, un:E): if E has OrderedAbelianMonoid then highCommonTerms(f, g) == - makeMulti [[x.gen, min(x.exp, n)] for x in listOfMonoms f | - (n := coefficient(x.gen, g)) > 0] + makeMulti [[x.gen, min(x.exp, n)] for x in listOfMonoms f + | positive?(n := coefficient(x.gen, g))] @ \section{domain FAMONOID FreeAbelianMonoid} @@ -555,12 +555,12 @@ FreeAbelianGroup(S:SetCategory): Exports == Implementation where a < b == zero? a => zero? b => false - (inmax terms b).exp > 0 + positive?((inmax terms b).exp) ta := inmax terms a zero? b => negative? ta.exp ta := inmax terms a tb := inmax terms b - ta.gen < tb.gen => tb.exp > 0 + ta.gen < tb.gen => positive? tb.exp ta.gen > tb.gen => negative? ta.exp ta.exp < tb.exp => true ta.exp > tb.exp => false diff --git a/src/algebra/fs2expxp.spad.pamphlet b/src/algebra/fs2expxp.spad.pamphlet index 15b46ca9..4b549c83 100644 --- a/src/algebra/fs2expxp.spad.pamphlet +++ b/src/algebra/fs2expxp.spad.pamphlet @@ -236,7 +236,7 @@ FunctionSpaceToExponentialExpansion(R,FE,x,cen):_ -- converts an integral power to an exponential expansion (b := iExprToXXP(fcn,posCheck?)) case %problem => b xxp := b.%expansion - n > 0 => [xxp ** n] + positive? n => [xxp ** n] -- a Puiseux series will be reciprocated only if n < 0 and -- numerator of 'xxp' has exactly one monomial numberOfMonomials(num := numer xxp) > 1 => [xxp ** n] @@ -345,7 +345,7 @@ FunctionSpaceToExponentialExpansion(R,FE,x,cen):_ negative?(deg := order(ups,1)) => -- this "can't happen" error "exp of function with sigularity" - deg > 0 => [exp(ups)] + positive? deg => [exp(ups)] lc := coefficient(ups,0); varOpList := opsInvolvingX lc not opInOpList?("log" :: Symbol,varOpList) => [exp(ups)] -- try to fix exp(lc) if necessary @@ -425,7 +425,7 @@ FunctionSpaceToExponentialExpansion(R,FE,x,cen):_ upxs := f :: UPXS negative? (deg := order(upxs,1)) => stateProblem(fcnName,"essential singularity") - deg > 0 => [fcn(upxs) :: UPXS :: XXP] + positive? deg => [fcn(upxs) :: UPXS :: XXP] lc := coefficient(upxs,0); xOpList := opsInvolvingX lc null xOpList => [fcn(upxs) :: UPXS :: XXP] opInOpList?("log" :: SY,xOpList) => diff --git a/src/algebra/fs2ups.spad.pamphlet b/src/algebra/fs2ups.spad.pamphlet index 6014ae65..1fd0835e 100644 --- a/src/algebra/fs2ups.spad.pamphlet +++ b/src/algebra/fs2ups.spad.pamphlet @@ -273,7 +273,7 @@ FunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x):_ powerToUPS(fcn,n,posCheck?,atanFlag) == -- converts an integral power to a power series (b := exprToUPS(fcn,posCheck?,atanFlag)) case %problem => b - n > 0 => [(b.%series) ** n] + positive? n => [(b.%series) ** n] -- check lowest order coefficient when n < 0 ups := b.%series; deg := degree ups if (coef := coefficient(ups,deg)) = 0 then @@ -545,7 +545,7 @@ FunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x):_ -- (b) the lowest order coefficient is a product of exponentials -- and functions not involving x (b := exprToGenUPS(fcn,posCheck?,atanFlag)) case %problem => b - n > 0 => [(b.%series) ** n] + positive? n => [(b.%series) ** n] -- check lowest order coefficient when n < 0 ups := b.%series; deg := degree ups if (coef := coefficient(ups,deg)) = 0 then @@ -636,7 +636,7 @@ FunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x):_ -- a power series. negative?(deg := order(ups,1)) => stateProblem("exp","essential singularity") - deg > 0 => [exp ups] + positive? deg => [exp ups] lc := coefficient(ups,0); xOpList := opsInvolvingX lc not opInOpList?("log" :: SY,xOpList) => [exp ups] -- try to fix exp(lc) if necessary @@ -698,7 +698,7 @@ FunctionSpaceToUnivariatePowerSeries(R,FE,Expon,UPS,TRAN,x):_ ups := series.%series negative?(deg := order(ups,1)) => stateProblem(fcnName,"essential singularity") - deg > 0 => [fcn(ups) :: UPS] + positive? deg => [fcn(ups) :: UPS] lc := coefficient(ups,0); xOpList := opsInvolvingX lc null xOpList => [fcn(ups) :: UPS] opInOpList?("log" :: SY,xOpList) => diff --git a/src/algebra/galfact.spad.pamphlet b/src/algebra/galfact.spad.pamphlet index 56778a4f..43d4e9cb 100644 --- a/src/algebra/galfact.spad.pamphlet +++ b/src/algebra/galfact.spad.pamphlet @@ -602,7 +602,7 @@ GaloisGroupFactorizer(UP): Exports == Implementation where f := -f -- is x**d factor of f - if (d := minimumDegree f) > 0 then + if positive?(d := minimumDegree f) then f := monicDivide(f,monomial(1,d)).quotient factorlist := [[monomial(1,1),d]$ParFact] @@ -672,7 +672,7 @@ GaloisGroupFactorizer(UP): Exports == Implementation where f := -f -- is x**d factor of f - if (maxd := minimumDegree f) > 0 then + if positive?(maxd := minimumDegree f) then f := monicDivide(f,monomial(1,maxd)).quotient factorlist := [[monomial(1,1),maxd]$ParFact] r := max(2,r-maxd)::N diff --git a/src/algebra/gaussian.spad.pamphlet b/src/algebra/gaussian.spad.pamphlet index d32a353a..d8ac1583 100644 --- a/src/algebra/gaussian.spad.pamphlet +++ b/src/algebra/gaussian.spad.pamphlet @@ -109,7 +109,7 @@ ComplexCategory(R:CommutativeRing): Category == factorSquareFreePolynomial pp == pnorm:=normPolynomial pp k:R:=0 - while degree gcd(pnorm,differentiate pnorm)>0 repeat + while positive? degree gcd(pnorm,differentiate pnorm) repeat k:=k+1 pnorm:=normPolynomial elt(pp,monomial(1,1)-monomial(complex(0,k),0)) diff --git a/src/algebra/gdpoly.spad.pamphlet b/src/algebra/gdpoly.spad.pamphlet index 59004a5b..b169c548 100644 --- a/src/algebra/gdpoly.spad.pamphlet +++ b/src/algebra/gdpoly.spad.pamphlet @@ -74,7 +74,7 @@ GeneralDistributedMultivariatePolynomial(vl,R,E): public == private where zero?(p) => "failed" for v in vl repeat vv := variable(v)::OV - if degree(p,vv)>0 then return vv + if positive? degree(p,vv) then return vv "failed" ground?(p) == mainVariable(p) case "failed" diff --git a/src/algebra/ghensel.spad.pamphlet b/src/algebra/ghensel.spad.pamphlet index b5a1c513..baf7e85c 100644 --- a/src/algebra/ghensel.spad.pamphlet +++ b/src/algebra/ghensel.spad.pamphlet @@ -127,7 +127,7 @@ 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 positive? dfn and (factlist := genFact(fln,factlist))~=[] repeat auxfl := [] while factlist~=[] repeat auxl := factlist.first @@ -153,7 +153,7 @@ GeneralHenselPackage(RP,TP):C == T where factlist := [term for term in factlist | not member?(poly,term)] fln := aux factlist := auxfl - if dfn > 0 then finallist := cons(m,finallist) + if positive? dfn then finallist := cons(m,finallist) finallist @ diff --git a/src/algebra/gpol.spad.pamphlet b/src/algebra/gpol.spad.pamphlet index ff4b05e1..9cbcfd1b 100644 --- a/src/algebra/gpol.spad.pamphlet +++ b/src/algebra/gpol.spad.pamphlet @@ -119,7 +119,7 @@ LaurentPolynomial(R, UP): Exports == Implementation where p + q == zero? q => p zero? p => q - (d := order p - order q) > 0 => + positive?(d := order p - order q) => gpol(poly(p) * monomial(1, d::N) + poly q, order q) negative? d => gpol(poly(p) + poly(q) * monomial(1, (-d)::N), order p) mkgpol(order p, poly(p) + poly q) diff --git a/src/algebra/interval.spad.pamphlet b/src/algebra/interval.spad.pamphlet index 7fbd9fe8..94eea0f5 100644 --- a/src/algebra/interval.spad.pamphlet +++ b/src/algebra/interval.spad.pamphlet @@ -128,7 +128,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa contains?(u:%,f:R):Boolean == (f > inf(u)) and (f < sup(u)) - positive?(u:%):Boolean == inf(u) > 0 + positive?(u:%):Boolean == positive? inf(u) negative?(u:%):Boolean == negative? sup(u) a:% < b:% == @@ -161,7 +161,7 @@ Interval(R:Join(FloatingPointSystem,TranscendentalFunctionCategory)): IntervalCa a:Integer * b:% == - if (a > 0) then + if positive? a then qinterval(a*inf(b),a*sup(b)) else if negative? a then qinterval(a*sup(b),a*inf(b)) diff --git a/src/algebra/intfact.spad.pamphlet b/src/algebra/intfact.spad.pamphlet index f8655319..4c4be09d 100644 --- a/src/algebra/intfact.spad.pamphlet +++ b/src/algebra/intfact.spad.pamphlet @@ -299,7 +299,7 @@ IntegerRoots(I:IntegerNumberSystem): Exports == Implementation where z:I := 1 n1:= (n-1)::NNI x: I - while z > 0 repeat + while positive? z repeat x := y xn:= x**n1 y := (n1*x*xn+a) quo (n*xn) @@ -459,7 +459,7 @@ IntegerFactorizationPackage(I): Exports == Implementation where return makeFR(1, ls) m : Integer for m in 0.. while zero?(n rem d) repeat n := n quo d - if m>0 then ls := concat!(ls, ["prime",d,convert m]$FFE) + if positive? m then ls := concat!(ls, ["prime",d,convert m]$FFE) d := d+s BasicMethod n == diff --git a/src/algebra/intrf.spad.pamphlet b/src/algebra/intrf.spad.pamphlet index d4e2b859..79e22b48 100644 --- a/src/algebra/intrf.spad.pamphlet +++ b/src/algebra/intrf.spad.pamphlet @@ -70,7 +70,7 @@ SubResultantPackage(R, UP): Exports == Implementation where -- Hum it seems that Lionel returns [] when min(|p1|,|p2|) = 0 zero?(degree(p1)) => res.degree(p2) := p2 - if degree(p2) > 0 + if positive? degree(p2) then res.((degree(p2)-1)::NonNegativeInteger) := p1 res.0 := (leadingCoefficient(p1)**(degree p2)) :: UP @@ -79,7 +79,7 @@ SubResultantPackage(R, UP): Exports == Implementation where res.0 := 1 res zero?(degree(p2)) => - if degree(p1) > 0 + if positive? degree(p1) then res.((degree(p1)-1)::NonNegativeInteger) := p2 res.0 := (leadingCoefficient(p2)**(degree p1)) :: UP @@ -264,7 +264,7 @@ TranscendentalHermiteIntegration(F, UP): Exports == Implementation where p:UP := 0 mult:UP := 1 qhat := (q exquo (g0 := g := gcd(q, differentiate q)))::UP - while(degree(qbar := g) > 0) repeat + while positive? degree(qbar := g) repeat qbarhat := (qbar exquo (g := gcd(qbar, differentiate qbar)))::UP qtil:= - ((qhat * (derivation qbar)) exquo qbar)::UP bc := @@ -457,7 +457,7 @@ TranscendentalIntegration(F, UP): Exports == Implementation where error "monomIntPoly: monomial must have degree 2 or more" l := leadingCoefficient dt ans:UP := 0 - while (n := 1 + degree(p)::Z - d) > 0 repeat + while positive?(n := 1 + degree(p)::Z - d) repeat ans := ans + (term := monomial(leadingCoefficient(p) / (n * l), n::N)) p := p - derivation term -- degree(p) must drop here [ans, p] @@ -598,7 +598,7 @@ TranscendentalIntegration(F, UP): Exports == Implementation where explimintfrac(f, derivation, lu) == zero? f => [0, empty()] degree numer f >= degree denom f => error "Not a proper fraction" - order(denom f, monomial(1,1)) > 0 => error "Not integral at t = 0" + positive? order(denom f, monomial(1,1)) => error "Not integral at t = 0" r := HermiteIntegrate(f, derivation) zero?(r.logpart) => [r.answer, empty()] eta' := coefficient(derivation monomial(1, 1), 1) @@ -669,7 +669,7 @@ TranscendentalIntegration(F, UP): Exports == Implementation where gqr.remainder / (denom g))) case "failed" => "failed" zero?(gqr.remainder) => -- the following FAIL cannot occur if the primitives are all logs - degree(gqr.quotient) > 0 => FAIL + positive? degree(gqr.quotient) => FAIL (u3 := primintegratepoly(fqr.quotient, extendedint, retract derivation monomial(1, 1))) case UPUP => "failed" [u1.ratpart + u3.answer::RF, u3.a0] @@ -701,7 +701,7 @@ TranscendentalIntegration(F, UP): Exports == Implementation where primintegratepoly(p, extendedint, t') == zero? p => [0, 0$F] ans:UP := 0 - while (d := degree p) > 0 repeat + while positive?(d := degree p) repeat (ans1 := extendedint leadingCoefficient p) case "failed" => return([ans, p]) p := reductum p - monomial(d * t' * ans1.ratpart, (d - 1)::N) diff --git a/src/algebra/irexpand.spad.pamphlet b/src/algebra/irexpand.spad.pamphlet index 1441447a..6661642a 100644 --- a/src/algebra/irexpand.spad.pamphlet +++ b/src/algebra/irexpand.spad.pamphlet @@ -110,7 +110,7 @@ IntegrationResultToFunction(R, F): Exports == Implementation where sqrn := s.ans1 * rootSimp sqrt(-s.ans2) nn := lgp + d * sqrn * ilog(e, f * sqrn, setUnion(setUnion(kernels a, kernels b), kernels p0)) - sqr.sgn > 0 => [pp] + positive? sqr.sgn => [pp] negative? sqr.sgn => [nn] [pp, nn] diff --git a/src/algebra/laplace.spad.pamphlet b/src/algebra/laplace.spad.pamphlet index e961658a..9bbabadb 100644 --- a/src/algebra/laplace.spad.pamphlet +++ b/src/algebra/laplace.spad.pamphlet @@ -97,7 +97,7 @@ LaplaceTransform(R, F): Exports == Implementation where atn(f, t) == if ((v := isExpt f) case Record(var:K, exponent:Integer)) then w := v::Record(var:K, exponent:Integer) - (w.exponent > 0) and + positive?(w.exponent) and ((vv := symbolIfCan(w.var)) case SE) and (vv::SE = t) => return [1, w.exponent::PI] (u := isTimes f) case List(F) => diff --git a/src/algebra/laurent.spad.pamphlet b/src/algebra/laurent.spad.pamphlet index ada65fa0..131e9eb5 100644 --- a/src/algebra/laurent.spad.pamphlet +++ b/src/algebra/laurent.spad.pamphlet @@ -211,7 +211,7 @@ UnivariateLaurentSeriesConstructor(Coef,UTS):_ (expDiff := getExpon(x) - getExpon(y)) = 0 => getUTS(x) = getUTS(y) abs(expDiff) > _$streamCount$Lisp => false - expDiff > 0 => + positive? expDiff => getUTS(x) * monom(1,expDiff :: NNI) = getUTS(y) getUTS(y) * monom(1,(- expDiff) :: NNI) = getUTS(x) @@ -381,7 +381,7 @@ UnivariateLaurentSeriesConstructor(Coef,UTS):_ zero? n => zero? x => error "0 ** 0 is undefined" 1 - n > 0 => laurent(n * getExpon(x),getUTS(x) ** (n :: NNI)) + positive? n => laurent(n * getExpon(x),getUTS(x) ** (n :: NNI)) xInv := inv x; minusN := (-n) :: NNI laurent(minusN * getExpon(xInv),getUTS(xInv) ** minusN) diff --git a/src/algebra/listgcd.spad.pamphlet b/src/algebra/listgcd.spad.pamphlet index 69d50396..fac17b6d 100644 --- a/src/algebra/listgcd.spad.pamphlet +++ b/src/algebra/listgcd.spad.pamphlet @@ -118,7 +118,7 @@ HeuGcd (BP):C == T empty? lind => member?(1,listdeg) => lincase(listdeg,listf) localgcd listf - or/[n>0 for n in listdeg] => cons(1$BP,listf) + or/[positive? n for n in listdeg] => cons(1$BP,listf) lclistf:List(Z):= [leadingCoefficient f for f in listf] d:=lintgcd(lclistf) d=1 => cons(1$BP,listf) @@ -181,7 +181,7 @@ HeuGcd (BP):C == T minpol:=1$BP -- extract a monomial gcd mdeg:= "min"/[minimumDegree f for f in listf] - if mdeg>0 then + if positive? mdeg then minpol1:= monomial(1,mdeg) listf:= [(f exquo minpol1)::BP for f in listf] minpol:=minpol*minpol1 diff --git a/src/algebra/lodop.spad.pamphlet b/src/algebra/lodop.spad.pamphlet index 3ebad1d2..53a38c6c 100644 --- a/src/algebra/lodop.spad.pamphlet +++ b/src/algebra/lodop.spad.pamphlet @@ -178,7 +178,7 @@ NonCommutativeOperatorDivision(P, F): PDcat == PDdef where leftGcd(a,b) == a = 0 =>b b = 0 =>a - while degree b > 0 repeat (a,b) := (b, leftRemainder(a,b)) + while positive? degree b repeat (a,b) := (b, leftRemainder(a,b)) if b=0 then a else b -- l = leftLcm(a,b) means l = a*aa l = b*bb Uses leftDivide. leftLcm(a,b) == diff --git a/src/algebra/manip.spad.pamphlet b/src/algebra/manip.spad.pamphlet index fe59129a..4735b5e7 100644 --- a/src/algebra/manip.spad.pamphlet +++ b/src/algebra/manip.spad.pamphlet @@ -353,7 +353,7 @@ AlgebraicManipulations(R, F): Exports == Implementation where n := (retract(second arg)@Integer)::NonNegativeInteger ans:F := 0 q := univariate(p, k) - while (d := degree q) > 0 repeat + while positive?(d := degree q) repeat term := one?(g := gcd(d, n)) => monomial(1, k, d) monomial(1, kernel(operator k, [a,(n quo g)::F], height k), d quo g) diff --git a/src/algebra/matfuns.spad.pamphlet b/src/algebra/matfuns.spad.pamphlet index f8768acb..23617e39 100644 --- a/src/algebra/matfuns.spad.pamphlet +++ b/src/algebra/matfuns.spad.pamphlet @@ -114,7 +114,7 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ transpose x copy x y := rowEchelon y; i := maxRowIndex y - while rk > 0 and rowAllZeroes?(y,i) repeat + while positive? rk and rowAllZeroes?(y,i) repeat i := i - 1 rk := (rk - 1) :: NonNegativeInteger rk :: NonNegativeInteger @@ -131,7 +131,7 @@ InnerMatrixLinearAlgebraFunctions(R,Row,Col,M):_ basis : List Col := nil() rk := nrow; row := maxR -- compute rank = # rows - # rows of all zeroes - while rk > 0 and rowAllZeroes?(x,row) repeat + while positive? rk and rowAllZeroes?(x,row) repeat rk := (rk - 1) :: NonNegativeInteger row := (row - 1) :: NonNegativeInteger -- if maximal rank, return zero vector @@ -681,7 +681,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where copy x y := fractionFreeGauss! y i := maxRowIndex y - while rk > 0 and rowAllZeroes?(y,i) repeat + while positive? rk and rowAllZeroes?(y,i) repeat i := i - 1 rk := (rk - 1) :: NonNegativeInteger rk :: NonNegativeInteger @@ -694,7 +694,7 @@ MatrixLinearAlgebraFunctions(R,Row,Col,M):Exports == Implementation where normalizedDivide(n:R, d:R):Record(quotient:R, remainder:R) == qr := divide(n, d) qr.remainder >= 0 => qr - d > 0 => + positive? d => qr.remainder := qr.remainder + d qr.quotient := qr.quotient - 1 qr diff --git a/src/algebra/mathml.spad.pamphlet b/src/algebra/mathml.spad.pamphlet index 5cc0d658..ba186863 100644 --- a/src/algebra/mathml.spad.pamphlet +++ b/src/algebra/mathml.spad.pamphlet @@ -599,7 +599,7 @@ returning Void. I really only need the one coerce function. nargs : I := #args -- sayTeX$Lisp concat ["1: ",stringify first le," : ",string(nargs)$S] s : S := concat ["{",sop] - if nargs > 0 then + if positive? nargs then for a in args repeat -- sayTeX$Lisp concat ["2: ",stringify a] s1 : S := exprex a @@ -679,7 +679,7 @@ returning Void. I really only need the one coerce function. endS:S := concat ["</",name,">"] level:I := 1 --sayTeX$Lisp "eltLimit: element name: "name - while (level > 0) repeat + while positive? level repeat startI := position(startS,mathML,pI)$String endI := position(endS,mathML,pI)$String @@ -777,7 +777,7 @@ have to be switched by swapping names. len : I := #str plusminus : S := "<mo>+</mo><mo>-</mo>" pos : I := position(plusminus,str,1) - if pos > 0 then + if positive? pos then ustart:US := segment(1,pos-1)$US uend:US := segment(pos+20,len)$US str := concat [str.ustart,"<mo>-</mo>",str.uend] @@ -943,7 +943,7 @@ have to be switched by swapping names. while k < #numLS + 1 repeat if numLS.k = string i then j := j + 1 k := k+1 - if j > 0 then + if positive? j then tmpS := stringify args.i if j = 1 then s := s"<mo>∂</mo><mi>"tmpS"</mi>" @@ -1035,7 +1035,7 @@ have to be switched by swapping names. commaS : S := stringify first rest rest rest atomE commaTest : S := "," i : I := 0 - while position(commaTest,commaS,1) > 0 repeat + while positive? position(commaTest,commaS,1) repeat i := i+1 commaTest := commaTest"," s : S := "<msup><mi>"funcS"</mi><mrow>" @@ -1064,7 +1064,7 @@ have to be switched by swapping names. commaS : S := stringify first rest rest rest atomE commaTest : S := "," ndiffs : I := 0 - while position(commaTest,commaS,1) > 0 repeat + while positive? position(commaTest,commaS,1) repeat ndiffs := ndiffs+1 commaTest := commaTest"," s : S := "<mfrac><mrow><msup><mo>ⅆ</mo><mn>"string(ndiffs)"</mn></msup><mi>"funcS"</mi></mrow><mrow><mo>ⅆ</mo><msup><mi>"formatMml(first args,minPrec)"</mi><mn>"string(ndiffs)"</mn></msup></mrow></mfrac><mo>⁡</mo><mo>(</mo><mi>"formatMml(first args,minPrec)"</mi><mo>)</mo>" @@ -1154,7 +1154,7 @@ have to be switched by swapping names. -- %A for the bound variable and puts the original variable used -- in the input command as a superscript on the integral sign. -- I'm assuming that the axiom variable is 2 characters. - while (i := position(varRS,integrand,i+1)) > 0 repeat + while positive?(i := position(varRS,integrand,i+1)) repeat u1 := segment(1,i-1)$US u2 := segment(i+2,#integrand)$US integrand := concat [integrand.u1,bvarS,integrand.u2] @@ -1253,10 +1253,10 @@ have to be switched by swapping names. -- Note that since the resulting MathML <mfrac>s are nested we need -- to handle the whole continued fraction at once, i.e. we can't -- just look for, e.g., {{ZAG}{1}{6}} - (#args > 1) and (position("ZAG",stringify first rest args,1) > 0) => + (#args > 1) and positive? position("ZAG",stringify first rest args,1) => tmpS : S := stringify first args - position("ZAG",tmpS,1) > 0 => formatZag(args) --- position("ZAG",tmpS,1) > 0 => formatZag1(args) + positive? position("ZAG",tmpS,1) => formatZag(args) +-- positive? position("ZAG",tmpS,1) => formatZag1(args) concat [formatMml(first args,minPrec) "<mo>+</mo>" formatZag(rest args)] -- At least for the ops "*","+","-" we need to test to see if a sigma or pi -- is one of their arguments because we might need parentheses as indicated @@ -1313,7 +1313,7 @@ have to be switched by swapping names. #args > 1 => "<mfrac>"formatMml(first rest tmpZag,minPrec)"<mrow><mn>"formatMml(first rest rest tmpZag,minPrec)"</mn><mo>+</mo>"formatZag(rest args)"</mrow></mfrac>" (first args = "...":: E)@Boolean => "<mo>…</mo>" op:S := stringify first args - position("ZAG",op,1) > 0 => + positive? position("ZAG",op,1) => "<mfrac>"formatMml(first rest tmpZag,minPrec)formatMml(first rest rest tmpZag,minPrec)"</mfrac>" error "formatZag: Last argument in ZAG construct has unknown operator: "op @@ -1356,15 +1356,15 @@ have to be switched by swapping names. -- ExponentialE str = "%i" => "<mi>ⅈ</mi>" -- ImaginaryI - len > 0 and str.1 = char "%" => concat(concat("<mi>",str),"</mi>") + positive? len and str.1 = char "%" => concat(concat("<mi>",str),"</mi>") len > 1 and digit? str.1 => concat ["<mn>",str,"</mn>"] -- should handle floats -- presumably this is a literal string - len > 0 and str.1 = char "_"" => + positive? len and str.1 = char "_"" => concat(concat("<mtext>",str),"</mtext>") len = 1 and str.1 = char " " => " " - (i := position(str,specialStrings)) > 0 => + positive?(i := position(str,specialStrings)) => specialStringsInMML.i - (i := position(char " ",str)) > 0 => + positive?(i := position(char " ",str)) => -- We want to preserve spacing, so use a roman font. -- What's this for? Leave the \rm in for now so I can see -- where it arises. Removed 2007-02-14 @@ -1378,10 +1378,10 @@ have to be switched by swapping names. nargs : I := #args -- need to test here in case first l is SUPERSUB case and then -- pass first l and args to formatSuperSub. - position("SUPERSUB",op,1) > 0 => + positive? position("SUPERSUB",op,1) => formatSuperSub(first l,args,minPrec) -- now test for SUB - position("SUB",op,1) > 0 => + positive? position("SUB",op,1) => formatSub1(first l,args,minPrec) -- special cases diff --git a/src/algebra/mfinfact.spad.pamphlet b/src/algebra/mfinfact.spad.pamphlet index 5292b222..55153b57 100644 --- a/src/algebra/mfinfact.spad.pamphlet +++ b/src/algebra/mfinfact.spad.pamphlet @@ -109,7 +109,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T factorlist:L SUParFact :=empty() mdeg :=minimumDegree um ---- is the Mindeg > 0? ---- - if mdeg>0 then + if positive? mdeg then f1:SUP P:=monomial(1,mdeg) um:=(um exquo f1)::SUP P factorlist:=cons([monomial(1,1),mdeg],factorlist) @@ -173,7 +173,7 @@ MultFiniteFactorize(OV,E,F,PG) : C == T factorlist:L MParFact :=empty() ---- is the Mindeg > 0? ---- lmdeg :=minimumDegree(m,lvar) - or/[n>0 for n in lmdeg] => simplify(m,dx,lvar,lmdeg) + or/[positive? n for n in lmdeg] => simplify(m,dx,lvar,lmdeg) ---- Make the polynomial square-free ---- om:=pushup(m,basicVar) sqfacs:=squareFree(om) diff --git a/src/algebra/mkfunc.spad.pamphlet b/src/algebra/mkfunc.spad.pamphlet index e3e81eea..288a3a82 100644 --- a/src/algebra/mkfunc.spad.pamphlet +++ b/src/algebra/mkfunc.spad.pamphlet @@ -178,7 +178,7 @@ InputForm(): conv [convert("*"::Symbol), s1, s2]$List(%) s1:% ** n:Integer == - s1 = 0 and n > 0 => 0 + s1 = 0 and positive? n => 0 s1 = 1 or zero? n => 1 one? n => s1 conv [convert("**"::Symbol), s1, convert n]$List(%) diff --git a/src/algebra/moddfact.spad.pamphlet b/src/algebra/moddfact.spad.pamphlet index dc68773e..14795411 100644 --- a/src/algebra/moddfact.spad.pamphlet +++ b/src/algebra/moddfact.spad.pamphlet @@ -103,7 +103,7 @@ ModularDistinctDegreeFactorizer(U):C == T where exptmod(u1,i,u2) == negative? i => error("negative exponentiation not allowed for exptMod") ans:= 1$EMR - while i > 0 repeat + while positive? i repeat if odd?(i) then ans:= (ans * u1) rem u2 i:= i quo 2 u1:= (u1 * u1) rem u2 @@ -116,14 +116,14 @@ ModularDistinctDegreeFactorizer(U):C == T where ddfactor(u) == if (c:= lc(u)) ~= 1$I then u:= makeMonic(u) ans:= sepfact(ddfact(u)) - cons(c::EMR,[makeMonic(f) for f in ans | degree(f) > 0]) + cons(c::EMR,[makeMonic(f) for f in ans | positive? degree(f)]) gcd(u,v,q) == gcd(reduce(u,q),reduce(v,q))::U factor(u,q) == v:= reduce(u,q) dv:= reduce(differentiate(u),q) - degree gcd(v,dv) > 0 => + positive? degree gcd(v,dv) => error("Modular factor: polynomial must be squarefree") ans:= ddfactor v [f::U for f in ans] @@ -138,7 +138,7 @@ ModularDistinctDegreeFactorizer(U):C == T where repeat w:= exptmod(w,p,u) g:= gcd(w - m,u) - if degree g > 0 then + if positive? degree g then g:= makeMonic(g) ans:= [[g,d],:ans] u:= (u quo g) @@ -179,7 +179,7 @@ ModularDistinctDegreeFactorizer(U):C == T where x:U:= monomial(1,1) -- for small primes find linear factors by exhaustion d=1 and p < 1000 => - for i in 0.. while du > 0 repeat + for i in 0.. while positive? du repeat if u(i::U) = 0 then ans := cons(reduce(x-(i::U),p),ans) du := du-1 @@ -230,7 +230,7 @@ ModularDistinctDegreeFactorizer(U):C == T where p:=modulus(t) d:= d - 1 tt:=t - while d > 0 repeat + while positive? d repeat tt:= (tt + (t:=exptmod(t,p,u))) rem u d:= d - 1 tt diff --git a/src/algebra/modgcd.spad.pamphlet b/src/algebra/modgcd.spad.pamphlet index a30dd0cc..b094a863 100644 --- a/src/algebra/modgcd.spad.pamphlet +++ b/src/algebra/modgcd.spad.pamphlet @@ -77,7 +77,7 @@ InnerModularGcd(R,BP,pMod,nextMod):C == T modularGcdPrimitive(listf : List BP) :BP == empty? listf => 0$BP g := first listf - for f in rest listf | not zero? f while degree g > 0 repeat + for f in rest listf | not zero? f while positive? degree g repeat g:=modGcdPrimitive(g,f) g @@ -89,7 +89,7 @@ InnerModularGcd(R,BP,pMod,nextMod):C == T minpol:=1$BP -- extract a monomial gcd mdeg:= "min"/[minimumDegree f for f in listf] - if mdeg>0 then + if positive? mdeg then minpol1:= monomial(1,mdeg) listf:= [(f exquo minpol1)::BP for f in listf] minpol:=minpol*minpol1 diff --git a/src/algebra/mring.spad.pamphlet b/src/algebra/mring.spad.pamphlet index 46e50c7d..6adb05f8 100644 --- a/src/algebra/mring.spad.pamphlet +++ b/src/algebra/mring.spad.pamphlet @@ -106,7 +106,7 @@ MonoidRing(R: Ring, M: Monoid): MRcategory == MRdefinition where p:Integer := size()$R n:Integer := size()$M ans:% := 0 - for j in 0.. while i > 0 repeat + for j in 0.. while positive? i repeat h := i rem p -- we use index(p) = 0$R if h ~= 0 then diff --git a/src/algebra/mset.spad.pamphlet b/src/algebra/mset.spad.pamphlet index 22e633de..351eefee 100644 --- a/src/algebra/mset.spad.pamphlet +++ b/src/algebra/mset.spad.pamphlet @@ -154,10 +154,10 @@ Multiset(S: SetCategory): MultisetAggregate S with ((n := t.e) <= max) => remove!(e,t) ms.count := ms.count-n - max > 0 => + positive? max => t.e := n-max ms.count := ms.count-max - (n := n+max) > 0 => + positive?(n := n+max) => t.e := -max ms.count := ms.count-n ms @@ -169,10 +169,10 @@ Multiset(S: SetCategory): MultisetAggregate S with ((n := t.e) <= max) => remove!(e,t) ms.count := ms.count-n - max > 0 => + positive? max => t.e := n-max ms.count := ms.count-max - (n := n+max) > 0 => + positive?(n := n+max) => t.e := -max ms.count := ms.count-n ms @@ -245,7 +245,7 @@ Multiset(S: SetCategory): MultisetAggregate S with n := 0 for e in keys t1 repeat m := min(t1.e,t2.e) - m > 0 => + positive? m => m := t1.e + t2.e t.e := m n := n + m @@ -259,7 +259,7 @@ Multiset(S: SetCategory): MultisetAggregate S with for e in keys t1 repeat k1 := t1.e k2 := t2.e - k1 > 0 and k2 = 0 => + positive? k1 and k2 = 0 => t.e := k1 n := n + k1 n = 0 => empty() diff --git a/src/algebra/multfact.spad.pamphlet b/src/algebra/multfact.spad.pamphlet index 376da187..b6009e97 100644 --- a/src/algebra/multfact.spad.pamphlet +++ b/src/algebra/multfact.spad.pamphlet @@ -117,7 +117,7 @@ InnerMultFact(OV,E,R,P) : C == T factorlist:L SUParFact :=empty() mdeg :=minimumDegree um ---- is the Mindeg > 0? ---- - if mdeg>0 then + if positive? mdeg then f1:USP:=monomial(1,mdeg) um:=(um exquo f1)::USP factorlist:=cons([monomial(1,1),mdeg],factorlist) @@ -383,7 +383,7 @@ InnerMultFact(OV,E,R,P) : C == T factorlist:L MParFact :=empty() lmdeg :=minimumDegree(m,lvar) ---- is the Mindeg > 0? ---- - or/[n>0 for n in lmdeg] => simplify(m,lvar,lmdeg,ufactor) + or/[positive? n for n in lmdeg] => simplify(m,lvar,lmdeg,ufactor) sqfacs := squareFree m lcont := unit sqfacs diff --git a/src/algebra/newpoly.spad.pamphlet b/src/algebra/newpoly.spad.pamphlet index 573a085f..459ef7b3 100644 --- a/src/algebra/newpoly.spad.pamphlet +++ b/src/algebra/newpoly.spad.pamphlet @@ -1400,7 +1400,7 @@ RecursivePolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, V:OrderedSet): Ca if ground?(tpol) then n := retract(ground(tpol))@INT - if n > 0 + if positive? n then stpol := concat(" +",convert(n)@String)$String else diff --git a/src/algebra/numode.spad.pamphlet b/src/algebra/numode.spad.pamphlet index 84415e34..4a88a636 100644 --- a/src/algebra/numode.spad.pamphlet +++ b/src/algebra/numode.spad.pamphlet @@ -203,7 +203,7 @@ NumericalOrdinaryDifferentialEquations(): Exports == Implementation where --compute the derivative derivs(dydx,y,x) --if overshoot, the set h accordingly - if (x + step.tryValue - x2) > 0.0 then + if positive?(x + step.tryValue - x2) then step.tryValue := x2 - x --find the correct scaling for i in 1..m repeat diff --git a/src/algebra/odealg.spad.pamphlet b/src/algebra/odealg.spad.pamphlet index 653dece6..1a3d355d 100644 --- a/src/algebra/odealg.spad.pamphlet +++ b/src/algebra/odealg.spad.pamphlet @@ -152,7 +152,7 @@ SystemODESolver(F, LO): Exports == Implementation where r := r - 1 c := c - 1 firstnonzero(m, r) ~= c => error "backsolve: undetermined system" - degree(eq := m(r, c)) > 0 => error "backsolve: pivot of order > 0" + positive? degree(eq := m(r, c)) => error "backsolve: pivot of order > 0" a := leadingCoefficient(eq)::F if part? then part(r + offset) := (v(r + offset) - applyLodo(m, r, part, n)) / a diff --git a/src/algebra/oderf.spad.pamphlet b/src/algebra/oderf.spad.pamphlet index f104bc74..2fb8bf0a 100644 --- a/src/algebra/oderf.spad.pamphlet +++ b/src/algebra/oderf.spad.pamphlet @@ -462,7 +462,7 @@ RationalLODE(F, UP): Exports == Implementation where ratDsolve0(op, g) == zero? degree op => [inv(leadingCoefficient(op)::RF) * g, empty()] - minimumDegree op > 0 => + positive? minimumDegree op => sol := ratDsolve0(monicRightDivide(op, monomial(1, 1)).quotient, g) b:List(RF) := [1] for f in sol.basis repeat diff --git a/src/algebra/opalg.spad.pamphlet b/src/algebra/opalg.spad.pamphlet index 759f9136..4c7a08fe 100644 --- a/src/algebra/opalg.spad.pamphlet +++ b/src/algebra/opalg.spad.pamphlet @@ -103,7 +103,7 @@ ModuleOperator(R: Ring, M:LeftModule(R)): Exports == Implementation where x:$ ** i:Integer == i = 0 => 1 - i > 0 => expt(x,i pretend PositiveInteger)$RepeatedSquaring($) + positive? i => expt(x,i pretend PositiveInteger)$RepeatedSquaring($) (inv(retract(x)@TERM)) ** (-i) evaluateInverse(f, g) == @@ -171,7 +171,7 @@ ModuleOperator(R: Ring, M:LeftModule(R)): Exports == Implementation where for rec in reverse! factors m repeat e := rec.exp g := rec.gen - e > 0 => + positive? e => for i in 1..e repeat r := opeval(g, r) negative? e => for i in 1..(-e) repeat r := opInvEval(g, r) diff --git a/src/algebra/outform.spad.pamphlet b/src/algebra/outform.spad.pamphlet index b73ef8c3..28fbbdb4 100644 --- a/src/algebra/outform.spad.pamphlet +++ b/src/algebra/outform.spad.pamphlet @@ -157,7 +157,7 @@ NumberFormats(): NFexports == NFimplementation where m0:String := concat(new(i,plen),concat("I",new(i,pren))) mm := concat([m0 for j in 1..d]$List(String)) -- strictly speaking the blank is gratuitous - if #s > 0 then s := concat(" ", s) + if positive?(#s) then s := concat(" ", s) s := concat(mm, s) s diff --git a/src/algebra/pade.spad.pamphlet b/src/algebra/pade.spad.pamphlet index 08d7bdbc..f46e79e4 100644 --- a/src/algebra/pade.spad.pamphlet +++ b/src/algebra/pade.spad.pamphlet @@ -145,7 +145,7 @@ PadeApproximants(R,PS,UP): Exports == Implementation where zero? gps => constInner 0 -- Normalize so numerator or denominator has constant term. ldeg:= min(order dps,order gps) - if ldeg > 0 then + if positive? ldeg then dps := divOutDegree(dps,ldeg) gps := divOutDegree(gps,ldeg) padeInner(l,m,gps,dps) diff --git a/src/algebra/pattern.spad.pamphlet b/src/algebra/pattern.spad.pamphlet index fd008b3e..c5a667e6 100644 --- a/src/algebra/pattern.spad.pamphlet +++ b/src/algebra/pattern.spad.pamphlet @@ -255,7 +255,7 @@ Pattern(R:SetCategory): Exports == Implementation where 0 == taggedElt(PAT_ZERO, empty()) p:% ** n:NonNegativeInteger == - p = 0 and n > 0 => 0 + p = 0 and positive? n => 0 p = 1 or zero? n => 1 one? n => p mkPat(constant? p, [[p, n]$REC], 1 + (p.lev)) diff --git a/src/algebra/pdecomp.spad.pamphlet b/src/algebra/pdecomp.spad.pamphlet index 1e6f1829..b449e437 100644 --- a/src/algebra/pdecomp.spad.pamphlet +++ b/src/algebra/pdecomp.spad.pamphlet @@ -53,7 +53,7 @@ PolynomialDecomposition(UP, F): PDcat == PDdef where for i in 0.. while f ~= 0 repeat fr := divide(f, h) f := fr.quotient; r := fr.remainder - degree r > 0 => return "failed" + positive? degree r => return "failed" g := g + r * monomial(1, i) g diff --git a/src/algebra/permgrps.spad.pamphlet b/src/algebra/permgrps.spad.pamphlet index 29b849a9..ee5c746a 100644 --- a/src/algebra/permgrps.spad.pamphlet +++ b/src/algebra/permgrps.spad.pamphlet @@ -281,11 +281,11 @@ PermutationGroup(S:SetCategory): public == private where randomElement : V NNI := group.randomInteger words := nil()$(L NNI) if wordProblem then words := word.(randomInteger::NNI) - if maxLoops > 0 then + if positive? maxLoops then numberOfLoops : I := 1 + (random()$Integer rem maxLoops) else numberOfLoops : I := maxLoops - while numberOfLoops > 0 repeat + while positive? numberOfLoops repeat randomInteger : I := 1 + (random()$Integer rem numberOfGenerators) randomElement := times ( group.randomInteger , randomElement ) if wordProblem then words := append ( word.(randomInteger::NNI) , words) @@ -331,7 +331,7 @@ PermutationGroup(S:SetCategory): public == private where word := nil()$(L NNI) oorb := o.orb osvc := o.svc - while degree > 0 repeat + while positive? degree repeat p := osvc.ppt negative? p => return [ xelt , word ] x := group.p @@ -368,7 +368,7 @@ PermutationGroup(S:SetCategory): public == private where group2 := nil()$(L V NNI) words3 := nil()$(L L NNI) j : I := 15 - while j > 0 repeat + while positive? j repeat -- find generators for the stabilizer ran := ranelt ( group , words , maxLoops ) str := strip ( ran.elt , ort , group , words ) @@ -520,7 +520,7 @@ PermutationGroup(S:SetCategory): public == private where for j in (i-1)..1 by -1 while noresult repeat s := gporb.j.svc p := gporb.j.orb.1 - while ( degree > 0 ) and noresult repeat + while positive? degree and noresult repeat entry := s.(z.p) if negative? entry then if entry = -1 then leave @@ -567,7 +567,7 @@ PermutationGroup(S:SetCategory): public == private where group2 := brace()$(FSET PERM S) gp : L PERM S := group.gens for gen in gp repeat - if degree gen > 0 then insert!(gen, group2) + if positive? degree gen then insert!(gen, group2) group2 knownGroup? (gp : %) : Void == @@ -659,7 +659,7 @@ PermutationGroup(S:SetCategory): public == private where randomInteger : I := 1 + (random()$Integer rem numberOfGenerators) randomElement := gp.randomInteger numberOfLoops : I := 1 + (random()$Integer rem maximalNumberOfFactors) - while numberOfLoops > 0 repeat + while positive? numberOfLoops repeat randomInteger : I := 1 + (random()$Integer rem numberOfGenerators) randomElement := gp.randomInteger * randomElement numberOfLoops := numberOfLoops - 1 @@ -710,7 +710,7 @@ PermutationGroup(S:SetCategory): public == private where orbits ( gp ) == spp := support gp orbits := nil()$(L FSET S) - while cardinality spp > 0 repeat + while positive? cardinality spp repeat el := extract! spp orbitSet := orbit ( gp , el ) orbits := cons ( orbitSet , orbits ) diff --git a/src/algebra/pfbr.spad.pamphlet b/src/algebra/pfbr.spad.pamphlet index 5919c7ec..5fb79179 100644 --- a/src/algebra/pfbr.spad.pamphlet +++ b/src/algebra/pfbr.spad.pamphlet @@ -149,7 +149,7 @@ PolynomialFactorizationByRecursionUnivariate(R, S): public == private where substns:= randomR() zero? elt(leadingCoefficient pp,substns ) => "next" ppR:=map( elt(#1,substns),pp) - degree gcd(ppR,differentiate ppR)>0 => "next" + positive? degree gcd(ppR,differentiate ppR) => "next" leave [substns,ppR] raise(supR) == map(#1:R::S,supR) @@ -160,7 +160,7 @@ PolynomialFactorizationByRecursionUnivariate(R, S): public == private where -- returns "failed" if the substitution is bad, else a factorization ppR:=map(elt(#1,r),pp) degree ppR < degree pp => "failed" - degree gcd(ppR,differentiate ppR) >0 => "failed" + positive? degree gcd(ppR,differentiate ppR) => "failed" factors:= fDown:=factorSquareFreePolynomial ppR [raise (unit fDown * factorList(fDown).first.fctr), @@ -384,7 +384,7 @@ PolynomialFactorizationByRecursion(R,E, VarSet:OrderedSet, S): public == -- returns "failed" if the substitution is bad, else a factorization ppR:=map(eval(#1,first lvpp,r),pp) degree ppR < degree pp => "failed" - degree gcd(ppR,differentiate ppR) >0 => "failed" + positive? degree gcd(ppR,differentiate ppR) => "failed" factors:= empty? rest lvpp => fDown:=factorSquareFreePolynomial map(retract(#1)::R,ppR) @@ -434,7 +434,7 @@ PolynomialFactorizationByRecursion(R,E, VarSet:OrderedSet, S): public == substns:= [randomR() for v in lvpp] zero? eval(leadingCoefficient pp,lvpp,substns ) => "next" ppR:=map((retract eval(#1,lvpp,substns))::R,pp) - degree gcd(ppR,differentiate ppR)>0 => "next" + positive? degree gcd(ppR,differentiate ppR) => "next" leave [substns,ppR] chooseSLPEViableSubstitutions(lvpolys,lpolys,pp) == @@ -450,7 +450,7 @@ PolynomialFactorizationByRecursion(R,E, VarSet:OrderedSet, S): public == for u in lpolys] uu:=lpolysR while not empty? uu repeat - "or"/[ degree(gcd(uu.first,v))>0 for v in uu.rest] => leave + "or"/[positive? degree(gcd(uu.first,v)) for v in uu.rest] => leave uu:=rest uu not empty? uu => "next" leave diff --git a/src/algebra/plot.spad.pamphlet b/src/algebra/plot.spad.pamphlet index fdeeafed..d03da277 100644 --- a/src/algebra/plot.spad.pamphlet +++ b/src/algebra/plot.spad.pamphlet @@ -387,7 +387,7 @@ Plot(): Exports == Implementation where todo1 := rest todo1 todo2 := rest todo2 if not null todo1 then (t := first(todo1); p := first(todo2)) - n > 0 => + positive? n => NUMFUNEVALS := NUMFUNEVALS + n t := curve.knots; p := curve.points xRange := select(p,xCoord,min) .. select(p,xCoord,max) diff --git a/src/algebra/plot3d.spad.pamphlet b/src/algebra/plot3d.spad.pamphlet index 44429031..aa98d794 100644 --- a/src/algebra/plot3d.spad.pamphlet +++ b/src/algebra/plot3d.spad.pamphlet @@ -343,7 +343,7 @@ Plot3D(): Exports == Implementation where todo2 := concat!(todo2, p) todo1 := rest todo1; todo2 := rest todo2 if not null todo1 then (t := first(todo1); p := first(todo2)) - if n > 0 then + if positive? n then NUMFUNEVALS := NUMFUNEVALS + n t := curve.knots; p := curve.points xRg := select(p,xCoord,min) .. select(p,xCoord,max) diff --git a/src/algebra/poly.spad.pamphlet b/src/algebra/poly.spad.pamphlet index 42c1eab2..d055f03d 100644 --- a/src/algebra/poly.spad.pamphlet +++ b/src/algebra/poly.spad.pamphlet @@ -142,7 +142,7 @@ PolynomialRing(R:Ring,E:OrderedAbelianMonoid): T == C 0$R recip(p) == null p => "failed" - p.first.k > 0$E => "failed" + positive? p.first.k => "failed" (u:=recip(p.first.c)) case "failed" => "failed" (u::R)::% @@ -499,7 +499,7 @@ SparseUnivariatePolynomial(R:Ring): UnivariatePolynomialCategory(R) with multivariate(supp:SparseUnivariatePolynomial(%),v:SingletonAsOrderedSet) == zero? supp => 0 lc:=leadingCoefficient supp - degree lc > 0 => error "bad form polynomial" + positive? degree lc => error "bad form polynomial" monomial(leadingCoefficient lc,degree supp) + multivariate(reductum supp,v) if R has FiniteFieldCategory and R has PolynomialFactorizationExplicit then @@ -907,7 +907,7 @@ UnivariatePolynomialSquareFree(RC:IntegralDomain,P):C == T di:=(di exquo pi)::P - differentiate(ci) pi:=gcd(ci,di) i:=i+1 - degree(pi) > 0 => + positive? degree(pi) => lcp:=(lcp exquo (leadingCoefficient(pi)**i))::RC lffe:=[["sqfr",pi,i],:lffe] makeFR(lcp::P,lffe) diff --git a/src/algebra/polycat.spad.pamphlet b/src/algebra/polycat.spad.pamphlet index 140fc069..d3107611 100644 --- a/src/algebra/polycat.spad.pamphlet +++ b/src/algebra/polycat.spad.pamphlet @@ -538,7 +538,7 @@ PolynomialCategory(R:Ring, E:OrderedAbelianMonoidSup, VarSet:OrderedSet): vars:=rest vars d:=degree(p,v) ans:% := 0 - while (d>0) repeat + while positive? d repeat (dd:=(d::Integer exquo ch::Integer)) case "failed" => return nothing cp:=coefficient(p,v,d) @@ -880,7 +880,7 @@ UnivariatePolynomialCategory(R:Ring): Category == if R has CommutativeRing then differentiate(x:%, deriv:R -> R, x':%) == d:% := 0 - while (dg := degree x) > 0 repeat + while positive?(dg := degree x) repeat lc := leadingCoefficient x d := d + x' * monomial(dg * lc, (dg - 1)::NonNegativeInteger) + monomial(deriv lc, dg) @@ -896,7 +896,7 @@ UnivariatePolynomialCategory(R:Ring): Category == differentiate(x:%, deriv:R -> R, x':%) == d:% := 0 - while (dg := degree x) > 0 repeat + while positive?(dg := degree x) repeat lc := leadingCoefficient x d := d + monomial(deriv lc, dg) + lc * ncdiff(dg, x') x := reductum x @@ -904,7 +904,7 @@ UnivariatePolynomialCategory(R:Ring): Category == differentiate(x:%, deriv:R -> R) == differentiate(x, deriv, 1$%)$% differentiate(x:%) == d:% := 0 - while (dg := degree x) > 0 repeat + while positive?(dg := degree x) repeat d := d + monomial(dg * leadingCoefficient x, (dg - 1)::NonNegativeInteger) x := reductum x d diff --git a/src/algebra/primelt.spad.pamphlet b/src/algebra/primelt.spad.pamphlet index 1f18de1d..c72e09f6 100644 --- a/src/algebra/primelt.spad.pamphlet +++ b/src/algebra/primelt.spad.pamphlet @@ -83,7 +83,7 @@ PrimitiveElement(F): Exports == Implementation where findUniv(l, v, opt) == for p in l repeat - degree(p, v) > 0 and incl?(variables p, [v, opt]) => return p + positive? degree(p, v) and incl?(variables p, [v, opt]) => return p "failed" triangularLinearIfCan(l, lv, w) == diff --git a/src/algebra/prs.spad.pamphlet b/src/algebra/prs.spad.pamphlet index 7804b4fb..1155ee6d 100644 --- a/src/algebra/prs.spad.pamphlet +++ b/src/algebra/prs.spad.pamphlet @@ -889,7 +889,7 @@ PseudoRemainderSequence(R, polR) : Specification == Implementation where resultantReduit(P : polR, Q : polR) : R == UV := subResultantGcdEuclidean(P, Q) UVs : polR := UV.gcd - degree(UVs) > 0 => 0 + positive? degree(UVs) => 0 l : List(R) := concat(coefficients(UV.coef1), coefficients(UV.coef2)) return (LC(UVs) exquo gcd(l))::R @@ -897,7 +897,7 @@ PseudoRemainderSequence(R, polR) : Specification == Implementation where Record(coef1 : polR, coef2 : polR, resultantReduit : R) == UV := subResultantGcdEuclidean(P, Q) UVs : polR := UV.gcd - degree(UVs) > 0 => construct(0::polR, 0::polR, 0::R) + positive? degree(UVs) => construct(0::polR, 0::polR, 0::R) l : List(R) := concat(coefficients(UV.coef1), coefficients(UV.coef2)) gl : R := gcd(l) c1 : polR := (UV.coef1 exquo gl)::polR @@ -909,7 +909,7 @@ PseudoRemainderSequence(R, polR) : Specification == Implementation where Record(coef2 : polR, resultantReduit : R) == UV := subResultantGcdEuclidean(P, Q) UVs : polR := UV.gcd - degree(UVs) > 0 => construct(0::polR, 0::R) + positive? degree(UVs) => construct(0::polR, 0::R) l : List(R) := concat(coefficients(UV.coef1), coefficients(UV.coef2)) gl : R := gcd(l) c2 : polR := (UV.coef2 exquo gl)::polR diff --git a/src/algebra/random.spad.pamphlet b/src/algebra/random.spad.pamphlet index 0a650ee2..dc47310e 100644 --- a/src/algebra/random.spad.pamphlet +++ b/src/algebra/random.spad.pamphlet @@ -198,7 +198,7 @@ RandomIntegerDistributions(): with n := 0 mq := m -- m quo w**n - while (mqnext := mq quo w) > 0 repeat + while positive?(mqnext := mq quo w) repeat n := n + 1 mq := mqnext ridHack1(mq, n, w, l) diff --git a/src/algebra/rdeef.spad.pamphlet b/src/algebra/rdeef.spad.pamphlet index c7d5e368..b028efda 100644 --- a/src/algebra/rdeef.spad.pamphlet +++ b/src/algebra/rdeef.spad.pamphlet @@ -272,7 +272,7 @@ ElementaryRischDE(R, F): Exports == Implementation where else data := data1::Data f' := nfprime := n * differentiate(f, x) p:P := 1 - for v in data | (m := n * v.coeff) > 0 repeat + for v in data | positive?(m := n * v.coeff) repeat p := p * v.argument ** (m::N) f' := f' - m * differentiate(v.argument::F, x) / (v.argument::F) rec := baseRDE(univariate(f', k), univariate(p::F * g, k)) @@ -286,7 +286,7 @@ ElementaryRischDE(R, F): Exports == Implementation where tab.f := data := makeData(f, x, k) else data := data1::Data p:P := 1 - for v in data | (m := n * v.coeff) > 0 repeat + for v in data | positive?(m := n * v.coeff) repeat p := p * v.argument ** (m::N) f := f - v.coeff * log(v.argument::F) nfp := nfp - m * differentiate(v.argument::F, x) / (v.argument::F) @@ -318,9 +318,9 @@ ElementaryRischDE(R, F): Exports == Implementation where one?(degree(num := univariate(fnum, u))) then cf := (leadingCoefficient num) / fden if (n := retractIfCan(cf)@Union(Z, "failed")) case Z then - if degree(numer logand, k) > 0 then + if positive? degree(numer logand, k) then disasters := concat([n::Z, numer logand], disasters) - if degree(denom logand, k) > 0 then + if positive? degree(denom logand, k) then disasters := concat([-(n::Z), denom logand], disasters) disasters @@ -343,7 +343,7 @@ ElementaryRischDE(R, F): Exports == Implementation where (u := cc exquo aa) case "failed" => "failed" primintfldpoly(u::UP, extint(#1, t'), t') n := degree(cc)::Z - (db := degree(bb)::Z) - if ((da := degree(aa)::Z) = db) and (da > 0) then + if ((da := degree(aa)::Z) = db) and positive? da then lk0 := tower(f0 := - (leadingCoefficient bb) / (leadingCoefficient aa)) lk1 := logdiff(twr, lk0) diff --git a/src/algebra/rderf.spad.pamphlet b/src/algebra/rderf.spad.pamphlet index 1cd6563d..dbf1eddf 100644 --- a/src/algebra/rderf.spad.pamphlet +++ b/src/algebra/rderf.spad.pamphlet @@ -73,7 +73,7 @@ TranscendentalRischDE(F, UP): Exports == Implementation where (~b0?) and (baseCase? or degree(u.b) > max(0, n)) => answ := SPDEnocancel1(u.b, u.c, u.m, derivation) [[u.alpha * answ.ans + u.beta, answ.nosol]] - (n > 0) and (b0? or degree(u.b) < n) => + positive? n and (b0? or degree(u.b) < n) => uansw := SPDEnocancel2(u.b,u.c,u.m,n,leadingCoefficient dt,derivation) uansw case ans=> [[u.alpha * uansw.ans.ans + u.beta, uansw.ans.nosol]] [[uansw.eq.b, uansw.eq.c, uansw.eq.m, @@ -131,7 +131,7 @@ TranscendentalRischDE(F, UP): Exports == Implementation where q:UP := 0 while cc ~= 0 repeat negative? d or negative?(n := (degree cc)::Z - dtm1) or n > d => return [[q, true]] - if n > 0 then + if positive? n then r := monomial((leadingCoefficient cc) / (n * lt), n::N) cc := cc - bb * r - derivation r d := n - 1 diff --git a/src/algebra/rdesys.spad.pamphlet b/src/algebra/rdesys.spad.pamphlet index 6b62280d..b50f2b3f 100644 --- a/src/algebra/rdesys.spad.pamphlet +++ b/src/algebra/rdesys.spad.pamphlet @@ -111,7 +111,7 @@ TranscendentalRischDESystem(F, UP): Exports == Implementation where h := (h exquo g)::UP c1 := u1::UP c2 := u2::UP - (da := degree a) > 0 => + positive?(da := degree a) => (u := diophant(a, h, b, c1, c2)) case "failed" => "failed" rec := u::REC v := SPDEsys(a, b, h + derivation a, rec.z1 - derivation(rec.r1), diff --git a/src/algebra/realzero.spad.pamphlet b/src/algebra/realzero.spad.pamphlet index cee4a98e..5a049438 100644 --- a/src/algebra/realzero.spad.pamphlet +++ b/src/algebra/realzero.spad.pamphlet @@ -112,7 +112,7 @@ RealZeroPackage(Pol): T == C where F = 0 => error "ReZeroSqfr: zero polynomial" L : isoList := [] degree(F) = 0 => L - if (r := minimumDegree(F)) > 0 then + if positive?(r := minimumDegree(F)) then L := [[0,0]$Interval] tempF := F exquo monomial(1, r) if not (tempF case "failed") then @@ -140,7 +140,7 @@ RealZeroPackage(Pol): T == C where v = 1 => L := [[0,1]$Interval] G : Pol := transMultInv(2, F) H : Pol := transAdd1(G) - if minimumDegree H > 0 then + if positive? minimumDegree H then -- H has a root at 0 => F has one at 1/2, and G at 1 L := [[1/2,1/2]$Interval] Q : Pol := monomial(1, 1) @@ -277,7 +277,7 @@ RealZeroPackage(Pol): T == C where F := (F exquo (monomial(bd,1)-monomial(bn,0)))::Pol v:=elt(transMultInv(bd, F), bn) u:=elt(transMultInv(ad, F), an) - if u > 0 then (F:=-F;v:=-v) + if positive? u then (F:=-F;v:=-v) if negative? v then error [int, "is not a valid isolation interval for", F] if eps <= 0 then error "precision must be positive" @@ -289,7 +289,7 @@ RealZeroPackage(Pol): T == C where a := mid an := midn ad := midd - v > 0 => + positive? v => b := mid bn := midn bd := midd diff --git a/src/algebra/reclos.spad.pamphlet b/src/algebra/reclos.spad.pamphlet index c1359c1b..9c7e2ae7 100644 --- a/src/algebra/reclos.spad.pamphlet +++ b/src/algebra/reclos.spad.pamphlet @@ -118,7 +118,7 @@ RealPolynomialUtilitiesPackage(TheField,ThePols) : PUB == PRIV where while (p2 ~= 0) repeat res := cons(p2 , res) (p1 , p2) := (p2 , -(p1 rem p2)) - if degree(p1) > 0 + if positive? degree(p1) then p1 := unitCanonical(p1) res := [ term quo p1 for term in res ] @@ -247,7 +247,7 @@ RealRootCharacterizationCategory(TheField, ThePols ) : Category == PUB where negative? sign(toTest, rootChar) positive?(toTest, rootChar) == - sign(toTest, rootChar) > 0 + positive? sign(toTest, rootChar) rootOf(pol,n) == liste:List($):= allRootsOf(pol) @@ -633,7 +633,7 @@ RightOpenIntervalRootCharacterization(TheField,ThePolDom) : PUB == PRIV where lt := cons(t.int , lt) vi := sturmVariationsOf(reverse! lt)$UTIL o :Z := n - vl + vi - if o > 0 + if positive? o then sturmNthRoot(lp,int,r,vi,vr,o::N) else @@ -815,7 +815,7 @@ RightOpenIntervalRootCharacterization(TheField,ThePolDom) : PUB == PRIV where inv(leadingCoefficient(toTest))*reductum(toTest) delta := gcd(toTest,rootChar.defPol) newChar := [rootChar.low,rootChar.high,rootChar.defPol]$Rep - if degree(delta) > 0 + if positive? degree(delta) then if sign(delta.(rootChar.low) * delta.(rootChar.high)) <= 0 then diff --git a/src/algebra/regset.spad.pamphlet b/src/algebra/regset.spad.pamphlet index 3bb55e90..262a9789 100644 --- a/src/algebra/regset.spad.pamphlet +++ b/src/algebra/regset.spad.pamphlet @@ -977,7 +977,7 @@ RegularTriangularSetGcdPackage(R,E,V,P,TS): Exports == Implementation where ts := lpwt.tower lbwt := toseInvertible?(leadingCoefficient(p2,v),ts)@(List BWT) for bwt in lbwt repeat - (bwt.val = true) and (degree(p2,v) > 0) => + (bwt.val = true) and positive? degree(p2,v) => p3 := prem(p1, -p2) s: P := init(p2)**(mdeg(p1) - mdeg(p2))::N toSave := cons([[p2,p3,s],bwt.tower]$LpWT,toSave) diff --git a/src/algebra/riccati.spad.pamphlet b/src/algebra/riccati.spad.pamphlet index e581b129..a331e45e 100644 --- a/src/algebra/riccati.spad.pamphlet +++ b/src/algebra/riccati.spad.pamphlet @@ -228,7 +228,7 @@ PrimitiveRatRicDE(F, UP, L, LQ): Exports == Implementation where for i in 0..n | (li := coefficient(l, i)) ~= 0 repeat 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 + if (u case Z) and positive?(b := u::Z) then lb := concat([[i, j], b::N], lb) lb diff --git a/src/algebra/seg.spad.pamphlet b/src/algebra/seg.spad.pamphlet index 19a475a4..c0795e9e 100644 --- a/src/algebra/seg.spad.pamphlet +++ b/src/algebra/seg.spad.pamphlet @@ -153,7 +153,7 @@ Segment(S:Type): SegmentCategory(S) with h := hi s inc := (incr s)::S zero? inc => error "Cannot expand a segment with an increment of zero" - if inc > 0 then + if positive? inc then while l <= h repeat lr := concat(l, lr) l := l + inc @@ -169,7 +169,7 @@ Segment(S:Type): SegmentCategory(S) with l := lo s h := hi s inc := (incr s)::S - if inc > 0 then + if positive? inc then while l <= h repeat lr := concat(f l, lr) l := l + inc @@ -225,7 +225,7 @@ SegmentFunctions2(R:Type, S:Type): public == private where l := lo r h := hi r inc := (incr r)::R - if inc > 0 then + if positive? inc then while l <= h repeat lr := concat(f(l), lr) l := l + inc diff --git a/src/algebra/sf.spad.pamphlet b/src/algebra/sf.spad.pamphlet index 1faaffe7..54dc881a 100644 --- a/src/algebra/sf.spad.pamphlet +++ b/src/algebra/sf.spad.pamphlet @@ -448,7 +448,7 @@ DoubleFloat(): Join(FloatingPointSystem, DifferentialRing, OpenMath, atan(x,y) == zero? x => - y > 0 => pi()/2 + positive? y => pi()/2 negative? y => -pi()/2 0 -- Only count on first quadrant being on principal branch. diff --git a/src/algebra/sgcf.spad.pamphlet b/src/algebra/sgcf.spad.pamphlet index fda88648..c6eb2ffd 100644 --- a/src/algebra/sgcf.spad.pamphlet +++ b/src/algebra/sgcf.spad.pamphlet @@ -186,7 +186,7 @@ SymmetricGroupCombinatoricFunctions(): public == private where numberOfImproperPartitionsInternal(n,m,cm) == n = 0 => binomial(m,cm)$ICF - cm = 0 and n > 0 => 0 + cm = 0 and positive? n => 0 s := 0 for i in 0..n-1 repeat s := s + numberOfImproperPartitionsInternal(i,m,cm-1) diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet index bc77952c..888a40f3 100644 --- a/src/algebra/si.spad.pamphlet +++ b/src/algebra/si.spad.pamphlet @@ -110,7 +110,7 @@ IntegerNumberSystem(): Category == -- iterates in order 0,1,-1,2,-2,3,-3,... nextItem n == zero? n => just 1 - n > 0 => just(-n) + positive? n => just(-n) just(1-n) patternMatch(x, p, l) == @@ -126,7 +126,7 @@ IntegerNumberSystem(): Category == r := x rem n r = 0 => r if negative? n then n:=-n - r > 0 => + positive? r => 2 * r > n => r - n r 2*r + n <= 0 => r + n diff --git a/src/algebra/sign.spad.pamphlet b/src/algebra/sign.spad.pamphlet index b96e13a3..3101d04c 100644 --- a/src/algebra/sign.spad.pamphlet +++ b/src/algebra/sign.spad.pamphlet @@ -100,7 +100,7 @@ InnerPolySign(R, UP): Exports == Implementation where signAround(p:UP, dir:Integer, rsign:R -> U) == zero? p => 0 (u := rsign leadingCoefficient p) case "failed" => "failed" - (dir > 0) or (even? degree p) => u::Integer + positive? dir or (even? degree p) => u::Integer - (u::Integer) @ diff --git a/src/algebra/solvedio.spad.pamphlet b/src/algebra/solvedio.spad.pamphlet index 54a9330e..f83c9cb6 100644 --- a/src/algebra/solvedio.spad.pamphlet +++ b/src/algebra/solvedio.spad.pamphlet @@ -119,10 +119,10 @@ DiophantineSolutionPackage(): Cat == Capsule where -- create vertices from node ind to other nodes v := zero(k)$VI for i in 1..k repeat - ind > 0 => + positive? ind => negative? coeffs.i => v.i := zeroNode + ind + coeffs.i - coeffs.i > 0 => + positive? coeffs.i => v.i := zeroNode + ind + coeffs.i [v, true] @@ -136,7 +136,7 @@ DiophantineSolutionPackage(): Cat == Capsule where k := if ind < graph.zeroNode then m else n for i in k..graph.dim repeat x := sol.i - v.i > 0 => -- vertex exists to other node + positive? v.i => -- vertex exists to other node sol.i := x + 1 v.i = graph.zeroNode => -- solution found verifyMinimality(sol, graph, flag) => @@ -174,7 +174,7 @@ DiophantineSolutionPackage(): Cat == Capsule where k := if ind < graph.zeroNode then m else n for i in k..graph.dim while flag repeat x := sol.i - x > 0 and v.i > 0 => -- vertex exists to other node + positive? x and positive? v.i => -- vertex exists to other node sol.i := (x - 1) :: NI v.i = graph.zeroNode => -- solution found flag := false diff --git a/src/algebra/sregset.spad.pamphlet b/src/algebra/sregset.spad.pamphlet index 0598921f..dc961607 100644 --- a/src/algebra/sregset.spad.pamphlet +++ b/src/algebra/sregset.spad.pamphlet @@ -564,7 +564,7 @@ SquareFreeRegularTriangularSetGcdPackage(R,E,V,P,TS): Exports == Implementation ts := lpwt.tower lbwt := stoseInvertible?(leadingCoefficient(p2,v),ts)@(List BWT) for bwt in lbwt repeat - (bwt.val = true) and (degree(p2,v) > 0) => + (bwt.val = true) and positive? degree(p2,v) => p3 := prem(p1, -p2) s: P := init(p2)**(mdeg(p1) - mdeg(p2))::N toSave := cons([[p2,p3,s],bwt.tower]$LpWT,toSave) diff --git a/src/algebra/stream.spad.pamphlet b/src/algebra/stream.spad.pamphlet index a51a1c51..8be08ff7 100644 --- a/src/algebra/stream.spad.pamphlet +++ b/src/algebra/stream.spad.pamphlet @@ -698,12 +698,12 @@ Stream(S): Exports == Implementation where getm(x,le,n) == explicitlyEmpty? x => le lazy? x => - n > 0 => + positive? n => empty? x => le getm(rst x,concat(frst(x) :: OUT,le),n - 1) concat(message("..."),le) eq?(x,rst x) => concat(overbar(frst(x) :: OUT),le) - n > 0 => getm(rst x,concat(frst(x) :: OUT,le),n - 1) + positive? n => getm(rst x,concat(frst(x) :: OUT,le),n - 1) concat(message("..."),le) streamCountCoerce x == @@ -731,7 +731,7 @@ Stream(S): Exports == Implementation where listm(x,le,n) == explicitlyEmpty? x => le lazy? x => - n > 0 => + positive? n => empty? x => le listm(rst x, concat(frst(x) :: OUT,le),n-1) concat(message("..."),le) @@ -1082,7 +1082,7 @@ Stream(S): Exports == Implementation where if S has SetCategory then output(n,x) == - (not(n>0))or empty? x => void() + (not(positive? n)) or empty? x => void() mathPrint(frst(x)::OUT)$Lisp output(n-1, rst x) diff --git a/src/algebra/sttaylor.spad.pamphlet b/src/algebra/sttaylor.spad.pamphlet index ed89b75d..2de808ad 100644 --- a/src/algebra/sttaylor.spad.pamphlet +++ b/src/algebra/sttaylor.spad.pamphlet @@ -498,7 +498,7 @@ Remarks: integer, we won't get a Taylor expansion and thus raise an error. <<package STTAYLOR StreamTaylorSeriesOperations>>= - if ord > 0 and negative? rn then + if positive? ord and negative? rn then error "**: negative power does not exist" @ diff --git a/src/algebra/sturm.spad.pamphlet b/src/algebra/sturm.spad.pamphlet index d1a5b484..30c438a1 100644 --- a/src/algebra/sturm.spad.pamphlet +++ b/src/algebra/sturm.spad.pamphlet @@ -290,8 +290,8 @@ SturmHabichtPackage(R,x): T == C where epsil(int1:NNI,elt1:R,elt2:R):INT == int1 = 0 => 0 odd? int1 => 0 - ct1:INT:=if elt1 > 0 then 1 else -1 - ct2:INT:=if elt2 > 0 then 1 else -1 + ct1:INT:=if positive? elt1 then 1 else -1 + ct2:INT:=if positive? elt2 then 1 else -1 ct3:NNI:=(int1 exquo 2)::NNI ct4:INT:=(ct1*ct2)::INT ((-1)**(ct3::NNI))*ct4 diff --git a/src/algebra/syssolp.spad.pamphlet b/src/algebra/syssolp.spad.pamphlet index 1561a89a..82218fa6 100644 --- a/src/algebra/syssolp.spad.pamphlet +++ b/src/algebra/syssolp.spad.pamphlet @@ -130,7 +130,7 @@ SystemSolvePackage(R): Cat == Cap where newInF(n: Integer):F==varInF new()$SE testDegree(f :P R , lv :L SE) : Boolean == - "or"/[degree(f,vv)>0 for vv in lv] + "or"/[positive? degree(f,vv) for vv in lv] ---- Exported Functions ---- -- solve a system of rational functions diff --git a/src/algebra/taylor.spad.pamphlet b/src/algebra/taylor.spad.pamphlet index e3e01da9..5c113a19 100644 --- a/src/algebra/taylor.spad.pamphlet +++ b/src/algebra/taylor.spad.pamphlet @@ -317,7 +317,7 @@ UnivariateTaylorSeries(Coef,var,cen): Exports == Implementation where coefficient(x,n) == -- Cannot use elt! Should return 0 if stream doesn't have it. u := stream x - while not empty? u and n > 0 repeat + while not empty? u and positive? n repeat u := rst u n := (n - 1) :: NNI empty? u or n ~= 0 => 0 diff --git a/src/algebra/tex.spad.pamphlet b/src/algebra/tex.spad.pamphlet index 3b296d57..99314dff 100644 --- a/src/algebra/tex.spad.pamphlet +++ b/src/algebra/tex.spad.pamphlet @@ -301,7 +301,7 @@ TexFormat(): public == private where lineConcat( line : S, lines: L S ) : L S == length := #line - if ( length > 0 ) then + if positive? length then -- If the last character is a backslash then split at "\ ". -- Reinstate the blank. @@ -367,7 +367,7 @@ TexFormat(): public == private where ls := ls + lss + 1 s := concat(s,concat(ss," ")$S)$S - if ls > 0 then l := lineConcat( s, l ) + if positive? ls then l := lineConcat( s, l ) reverse l @@ -606,14 +606,14 @@ TexFormat(): public == private where len > 1 and str.1 = char "%" and str.2 = char "%" => u : US := segment(3,len)$US concat(" \%\%",str.u) - len > 0 and str.1 = char "%" => concat(" \",str) + positive? len and str.1 = char "%" => concat(" \",str) len > 1 and digit? str.1 => group str -- should handle floats - len > 0 and str.1 = char "_"" => + positive? len and str.1 = char "_"" => concat(concat(" \mbox{\tt ",str),"} ") len = 1 and str.1 = char " " => "{\ }" - (i := position(str,specialStrings)) > 0 => + positive?(i := position(str,specialStrings)) => specialStringsInTeX.i - (i := position(char " ",str)) > 0 => + positive?(i := position(char " ",str)) => -- We want to preserve spacing, so use a roman font. concat(concat(" \mbox{\rm ",str),"} ") str diff --git a/src/algebra/tree.spad.pamphlet b/src/algebra/tree.spad.pamphlet index a4249665..9dbae5b9 100644 --- a/src/algebra/tree.spad.pamphlet +++ b/src/algebra/tree.spad.pamphlet @@ -103,7 +103,7 @@ Tree(S: SetCategory): T==C where t1 = t2 => 0 t2 case empty => -1 u := [n for t in children t2 | (n := distance1(t1,t)) >= 0] - #u > 0 => 1 + "min"/u + positive?(#u) => 1 + "min"/u -1 distance(t1,t2) == n := distance1(t1, t2) @@ -199,7 +199,7 @@ Tree(S: SetCategory): T==C where multipleOverbar((".")::OutputForm,eqMemberIndex(t, pl,0),pl) empty? children t => value t::OutputForm nodeForm := (value t)::OutputForm - if (k := eqMemberIndex(t, pl, 0)) > 0 then + if positive?(k := eqMemberIndex(t, pl, 0)) then nodeForm := multipleOverbar(nodeForm, k, pl) prefix(nodeForm, [coerce1(br,cons(t,parents),pl) for br in children t]) diff --git a/src/algebra/twofact.spad.pamphlet b/src/algebra/twofact.spad.pamphlet index eb0bad93..2161c9a2 100644 --- a/src/algebra/twofact.spad.pamphlet +++ b/src/algebra/twofact.spad.pamphlet @@ -176,7 +176,7 @@ TwoFactorize(F) : C == T ll:=[] unitPart:P cont:=content m - if degree(cont)>0 then + if positive? degree(cont) then m1:=m exquo cont m1 case "failed" => error "content doesn't divide" m:=m1 diff --git a/src/algebra/unifact.spad.pamphlet b/src/algebra/unifact.spad.pamphlet index 4d5d874b..ab5a3e8e 100644 --- a/src/algebra/unifact.spad.pamphlet +++ b/src/algebra/unifact.spad.pamphlet @@ -253,7 +253,7 @@ UnivariateFactorize(ZP) : public == private where m := -m -- is x**d factor of m? - if (d := minimumDegree m) >0 then + if positive?(d := minimumDegree m) then m := (monicDivide(m,monomial(1,d))).quotient factorlist := [[monomial(1,1),d]$ParFact] |