Lines Matching refs:FE
5 ++ Related Domains: ExponentialExpansion, UnivariatePuiseuxSeries(FE, x, cen)
14 FunctionSpaceToExponentialExpansion(R, FE, x, cen) : _
18 FE : Join(AlgebraicallyClosedField, TranscendentalFunctionCategory, _
21 cen : FE
27 K ==> Kernel FE
32 PCL ==> PolynomialCategoryLifting(IndexedExponents K, K, R, SMP, FE)
36 UTS ==> UnivariateTaylorSeries(FE, x, cen)
37 ULS ==> UnivariateLaurentSeries(FE, x, cen)
38 UPXS ==> UnivariatePuiseuxSeries(FE, x, cen)
39 EFULS ==> ElementaryFunctionsUnivariateLaurentSeries(FE, UTS, ULS)
40 EFUPXS ==> ElementaryFunctionsUnivariatePuiseuxSeries(FE, ULS, UPXS, EFULS)
41 TEXPP ==> TaylorSeriesExpansionPuiseux(FE, UTS, ULS, UPXS)
42 FS2UPS ==> FunctionSpaceToUnivariatePowerSeries(R, FE, RN, UPXS, EFUPXS,
44 EXPUPXS ==> ExponentialOfUnivariatePuiseuxSeries(FE, x, cen)
45 UPXSSING ==> UnivariatePuiseuxSeriesWithExponentialSingularity(R, FE, x, cen)
46 XXP ==> ExponentialExpansion(R, FE, x, cen)
50 SIGNEF ==> ElementaryFunctionSign(R, FE)
53 exprToXXP : (FE, B) -> XResult
59 localAbs : FE -> FE
61 ++ on whether or not FE has a function \spad{abs}. This should be
69 ratIfCan : FE -> Union(RN,"failed")
72 newElem : FE -> FE
73 smpElem : SMP -> FE
74 k2Elem : K -> FE
75 iExprToXXP : (FE, B) -> XResult
76 listToXXP : (L FE, B, XXP, (XXP, XXP) -> XXP) -> XResult
77 isNonTrivPower : FE -> Union(Record(val:FE,exponent:I),"failed")
79 powerToXXP : (FE, I, B) -> XResult
82 nthRootToXXP : (FE, NNI, B) -> XResult
83 genPowerToXXP : (L FE, B) -> XResult
87 expToXXP : (FE, B) -> XResult
89 logToXXP : (FE, B) -> XResult
90 applyIfCan : (UPXS -> Union(UPXS,"failed"),FE,S,B) -> XResult
91 applyBddIfCan : (FE,UPXS -> Union(UPXS,"failed"),FE,S,B) -> XResult
92 tranToXXP : (K, FE, B) -> XResult
95 opsInvolvingX : FE -> L BOP
97 exponential? : FE -> B
98 productOfNonZeroes? : FE -> B
99 atancotToXXP : (FE, FE, B, I) -> XResult
130 smpElem p == map(k2Elem, (x1 : R) : FE +-> x1::FE, p)$PCL
136 empty?(args := [newElem a for a in argument k]) => k :: FE
143 is?(k, 'sinh) => (ez - iez) / (2 :: FE)
144 is?(k, 'cosh) => (ez + iez) / (2 :: FE)
150 is?(k, 'atanh) => log((z + 1) / (1 - z)) / (2 :: FE)
151 is?(k, 'acoth) => log((z + 1) / (z - 1)) / (2 :: FE)
169 (sum := isPlus fcn) case L(FE) =>
170 listToXXP(sum :: L(FE), posCheck?, 0, (y1 : XXP, y2 : XXP) : XXP
172 (prod := isTimes fcn) case L(FE) =>
173 listToXXP(prod :: L(FE), posCheck?, 1, (y1 : XXP, y2 : XXP) : XXP
175 (expt := isNonTrivPower fcn) case Record(val : FE, exponent : I) =>
176 power := expt :: Record(val : FE, exponent : I)
201 power := expt :: Record(val : FE, exponent : I)
276 deg := (nInv :: FE) * (degree num)
283 deg := (nInv :: FE) * (degree den)
315 [monomial(ker :: FE, 0)$UPXS :: XXP]
316 empty?(args := argument ker) => [monomial(ker :: FE, 0)$UPXS :: XXP]
342 expCoef := normalize(exp lc, x)$ElementaryFunctionStructurePackage(R, FE)
379 logTerm : FE :=
380 mon : FE := (x :: FE) - (cen :: FE)
381 pow : FE := mon ^ (deg :: FE)
383 term1 : FE := (deg :: FE) * log(mon)
469 for term in (prod :: L(FE)) repeat
482 applyBddIfCan(ker :: FE,sinIfCan,arg,"sin",posCheck?)
484 applyBddIfCan(ker :: FE,cosIfCan,arg,"cos",posCheck?)
490 atancotToXXP(ker :: FE, arg, posCheck?, 1)
492 atancotToXXP(ker :: FE, arg, posCheck?, -1)
501 if FE has abs : FE -> FE then
506 signOfExpression : FE -> FE
522 cc : FE :=
524 (rn := ratIfCan(ord :: FE)) case "failed" =>
531 posNegPi2 := signOfExpression(lc) * pi()/(2 :: FE)
533 pi()/(2 :: FE) - posNegPi2
535 plusMinus = 1 => -pi()/(2 :: FE)
537 plusMinus = 1 => pi()/(2 :: FE)