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| author | dos-reis <gdr@axiomatics.org> | 2011-10-25 03:47:29 +0000 |
|---|---|---|
| committer | dos-reis <gdr@axiomatics.org> | 2011-10-25 03:47:29 +0000 |
| commit | 2092a554d70524bc90440d96367e32c9ede28ee8 (patch) | |
| tree | f60d455b9d03bfe6454bb2ae33b82114aeb3f91b /src/algebra/special.spad.pamphlet | |
| parent | 99aeb02edd1614d30e308a9267325f138617d58f (diff) | |
| download | open-axiom-2092a554d70524bc90440d96367e32c9ede28ee8.tar.gz | |
* algebra/perman.spad.pamphlet (Permanent): Specify type of local
variable j.
* algebra/patmatch1.spad.pamphlet (PatternMatchTools): Tidy.
* algebra/padic.spad.pamphlet: Restrict type of literal constants.
* algebra/sttf.spad.pamphlet: Likewise.
* algebra/puiseux.spad.pamphlet: Likewise.
* algebra/odealg.spad.pamphlet (SystemODESolver) [applyLodo0]:
Specify type of local variable ans.
* algebra/numtheor.spad.pamphlet (IntegerNumberTheoryFunctions): Tidy.
* algebra/naalgc.spad.pamphlet (MonadWithUnit) [rightPower]:
Specify type of local variable res.
[leftPower]: Likewise.
* algebra/lodop.spad.pamphlet (NonCommutativeOperatorDivision)
[leftLcm]: Specify type of local variable v.
* algebra/intfact.spad.pamphlet (IntegerRoots) [approxSqrt]:
Specify type of local variables old and new.
* algebra/elfuts.spad.pamphlet
(EllipticFunctionsUnivariateTaylorSeries): Restrict types of
literal constants.
* algebra/ffnb.spad.pamphlet
(FiniteFieldNormalBasisExtensionByPolynomial): Likewise.
* algebra/fnla.spad.pamphlet (FreeNilpotentLie): Likewise.
* algebra/intaux.spad.pamphlet (IntegrationResult): Likewise.
* algebra/defintef.spad.pamphlet
(ElementaryFunctionDefiniteIntegration) [checkSMP]: Specify type
in the definition of local variable n.
* algebra/combinat.spad.pamphlet (IntegerCombinatoricFunctions):
Tidy definition of local variables.
* algebra/clifford.spad.pamphlet (CliffordAlgebra): Specify type in
the definition of local variables k, exchanges, bz.
* algebra/catdef.spad.pamphlet (CartesianTensor): Specify type in the
definition of local varibles rx and offz.
Remove useless variables zol, xol, oly, and zoly.
Diffstat (limited to 'src/algebra/special.spad.pamphlet')
| -rw-r--r-- | src/algebra/special.spad.pamphlet | 12 |
1 files changed, 8 insertions, 4 deletions
diff --git a/src/algebra/special.spad.pamphlet b/src/algebra/special.spad.pamphlet index 8a619f7b..b8c1c293 100644 --- a/src/algebra/special.spad.pamphlet +++ b/src/algebra/special.spad.pamphlet @@ -294,7 +294,8 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where laguerreL(n, x) == n = 0 => 1 - (p1, p0) := (-x + 1, 1) + p0: R := 1 + p1: R := -x + 1 for i in 1..n-1 repeat (p1, p0) := ((2*i::R + 1 - x)*p1 - i**2*p0, p1) p1 @@ -312,19 +313,22 @@ OrthogonalPolynomialFunctions(R: CommutativeRing): Exports == Impl where p1 chebyshevT(n, x) == n = 0 => 1 - (p1, p0) := (x, 1) + p0: R := 1 + p1: R := x for i in 1..n-1 repeat (p1, p0) := (2*x*p1 - p0, p1) p1 chebyshevU(n, x) == n = 0 => 1 - (p1, p0) := (2*x, 1) + p0: R := 1 + p1: R := 2*x for i in 1..n-1 repeat (p1, p0) := (2*x*p1 - p0, p1) p1 hermiteH(n, x) == n = 0 => 1 - (p1, p0) := (2*x, 1) + p0: R := 1 + p1: R := 2*x for i in 1..n-1 repeat (p1, p0) := (2*x*p1 - 2*i*p0, p1) p1 |