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| author | dos-reis <gdr@axiomatics.org> | 2011-03-12 17:04:43 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-03-12 17:04:43 +0000 |
| commit | 52fddea19454dc2b9bcb54c6edd5a4cd4f5765a9 (patch) | |
| tree | 4b13ccc6d57c7c1ee615c83615b246c98eae388a /src/algebra/numtheor.spad.pamphlet | |
| parent | 42d38bee45a64edfc12641053e58581c20584363 (diff) | |
| download | open-axiom-52fddea19454dc2b9bcb54c6edd5a4cd4f5765a9.tar.gz | |
* src/algebra/: Systematically use negative? when comparing for
less than 0.
Diffstat (limited to 'src/algebra/numtheor.spad.pamphlet')
| -rw-r--r-- | src/algebra/numtheor.spad.pamphlet | 28 |
1 files changed, 14 insertions, 14 deletions
diff --git a/src/algebra/numtheor.spad.pamphlet b/src/algebra/numtheor.spad.pamphlet index a4174263..98a30591 100644 --- a/src/algebra/numtheor.spad.pamphlet +++ b/src/algebra/numtheor.spad.pamphlet @@ -213,7 +213,7 @@ or \[14\] <<chineseRemainder(x1,m1,x2,m2)>>= chineseRemainder(x1,m1,x2,m2) == - m1 < 0 or m2 < 0 => error "moduli must be positive" + negative? m1 or negative? m2 => error "moduli must be positive" x1 := positiveRemainder(x1,m1) x2 := positiveRemainder(x2,m2) x1 + m1 * positiveRemainder(((x2-x1) * inverse(m1,m2)),m2) @@ -325,7 +325,7 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where harmonic n == s:I; h:RN - n < 0 => error("harmonic not defined for negative integers") + negative? n => error("harmonic not defined for negative integers") if n >= H.Hn then (s,h) := H else (s := 0; h := 0) for k in s+1..n repeat h := h + 1/k H.Hn := n @@ -334,7 +334,7 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where fibonacci n == n = 0 => 0 - n < 0 => (odd? n => 1; -1) * fibonacci(-n) + negative? n => (odd? n => 1; -1) * fibonacci(-n) f1, f2 : I (f1,f2) := (0,1) for k in length(n)-2 .. 0 by -1 repeat @@ -344,7 +344,7 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where f2 euler n == - n < 0 => error "euler not defined for negative integers" + negative? n => error "euler not defined for negative integers" odd? n => 0 l := (#E) :: I n < l => E(n) @@ -361,7 +361,7 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where E(n) bernoulli n == - n < 0 => error "bernoulli not defined for negative integers" + negative? n => error "bernoulli not defined for negative integers" odd? n => n = 1 => -1/2 0 @@ -399,7 +399,7 @@ IntegerNumberTheoryFunctions(): Exports == Implementation where -- then J(d/n) = chi(n) for n > 0. -- Reference: Hecke, Vorlesungen ueber die Theorie der Algebraischen -- Zahlen. - if b < 0 then b := -b + if negative? b then b := -b b = 0 => error "second argument of jacobi may not be 0" b = 1 => 1 even? b and positiveRemainder(a,4) > 1 => @@ -581,7 +581,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where cyclotomic n == --++ cyclotomic polynomial denoted phi[n](x) p:I; q:I; r:I; s:I; m:NNI; c:SUP(I); t:SUP(I) - n < 0 => error "cyclotomic not defined for negative integers" + negative? n => error "cyclotomic not defined for negative integers" n = 0 => x k := n; s := p := 1 c := x - 1 @@ -598,7 +598,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where euler n == p : SUP(RN); t : SUP(RN); c : RN; s : I - n < 0 => error "euler not defined for negative integers" + negative? n => error "euler not defined for negative integers" if n < E.En then (s,p) := (0$I,1$SUP(RN)) else (s,p) := E -- (s,p) := if n < E.En then (0,1) else E for i in s+1 .. n repeat @@ -611,7 +611,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where bernoulli n == p : SUP RN; t : SUP RN; c : RN; s : I - n < 0 => error "bernoulli not defined for negative integers" + negative? n => error "bernoulli not defined for negative integers" if n < B.Bn then (s,p) := (0$I,1$SUP(RN)) else (s,p) := B -- (s,p) := if n < B.Bn then (0,1) else B for i in s+1 .. n repeat @@ -631,7 +631,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where hermite n == s : I; p : SUP(I); q : SUP(I) - n < 0 => error "hermite not defined for negative integers" + negative? n => error "hermite not defined for negative integers" -- (s,p,q) := if n < H.Hn then (0,1,x) else H if n < H.Hn then (s := 0; p := 1; q := x) else (s,p,q) := H for k in s+1 .. n repeat (p,q) := (2*x*p-2*(k-1)*q,p) @@ -642,7 +642,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where legendre n == s:I; t:I; p:SUP(RN); q:SUP(RN) - n < 0 => error "legendre not defined for negative integers" + negative? n => error "legendre not defined for negative integers" -- (s,p,q) := if n < P.Pn then (0,1,y) else P if n < P.Pn then (s := 0; p := 1; q := y) else (s,p,q) := P for k in s+1 .. n repeat @@ -655,7 +655,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where laguerre n == k:I; s:I; t:I; p:SUP(I); q:SUP(I) - n < 0 => error "laguerre not defined for negative integers" + negative? n => error "laguerre not defined for negative integers" -- (s,p,q) := if n < L.Ln then (0,1,x) else L if n < L.Ln then (s := 0; p := 1; q := x) else (s,p,q) := L for k in s+1 .. n repeat @@ -668,7 +668,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where chebyshevT n == s : I; p : SUP(I); q : SUP(I) - n < 0 => error "chebyshevT not defined for negative integers" + negative? n => error "chebyshevT not defined for negative integers" -- (s,p,q) := if n < CT.Tn then (0,1,x) else CT if n < CT.Tn then (s := 0; p := 1; q := x) else (s,p,q) := CT for k in s+1 .. n repeat (p,q) := ((2*x*p - q),p) @@ -679,7 +679,7 @@ PolynomialNumberTheoryFunctions(): Exports == Implementation where chebyshevU n == s : I; p : SUP(I); q : SUP(I) - n < 0 => error "chebyshevU not defined for negative integers" + negative? n => error "chebyshevU not defined for negative integers" if n < U.Un then (s := 0; p := 1; q := 0) else (s,p,q) := U for k in s+1 .. n repeat (p,q) := ((2*x*p - q),p) U.Un := n |