diff options
Diffstat (limited to 'src/algebra/intrf.spad.pamphlet')
| -rw-r--r-- | src/algebra/intrf.spad.pamphlet | 34 |
1 files changed, 17 insertions, 17 deletions
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] @ |