diff --git a/README.md b/README.md
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
---
-title: SLOANE(1) Sloane User Manual | Version 2.0.0
-date: 2 Jan 2015
+title: SLOANE(1) Sloane User Manual | Version 2.0.1
+date: 7 Jan 2015
---
# NAME
@@ -10,14 +10,16 @@
# SYNOPSIS
-sloane [-a|--all] [-k KEYS] [-n N] [--url] [--local] [TERMS...]
+sloane [-a|--all] [-k KEYS] [-n N] [--url] [--local] TERMS...
-sloane [--filter] [--invert]
+sloane -A NUMBER
-sloane [--transform NAME] [--list-transforms]
+sloane --filter [--invert]
-sloane [--update] [--version] [--help]
+sloane --transform NAME
+sloane (--list-transforms | --update | --version | --help)
+
# DESCRIPTION
The `sloane` command searches Sloane's On-Line Encyclopedia of Integer
@@ -71,6 +73,10 @@
--local
: Grep for a sequence in the local database.
+-A *NUMBER*
+: Fetch the sequence with this number from the local database. Prints
+ the sequence, but nothing else, to sdout.
+
--filter
: Read sequences from stdin and return those that are in the local
database.
@@ -124,7 +130,11 @@
firefox `sloane --url -n 3 "(2+2)-free posets"`
-In the final example the local cache is used to filter out sequences
+To retrieve sequence A022493 from the local database use the `-A` option:
+
+ sloane -A022493
+
+In the final example the local database is used to filter out sequences
from the standard input that are in OEIS:
sloane --filter < ".sloane"
return Config
- { nameVer = "sloane 2.0.0"
+ { nameVer = "sloane 2.0.1"
, home = h
, sloaneDir = dsloane
, sloaneDB = dsloane "sloane.db"
diff --git a/Sloane/DB.hs b/Sloane/DB.hs
--- a/Sloane/DB.hs
+++ b/Sloane/DB.hs
@@ -6,6 +6,8 @@
module Sloane.DB
( DB
+ , ANumber
+ , Seq
, Reply
, update
, read
@@ -14,6 +16,7 @@
, null
, insert
, lookup
+ , lookupSeq
, grep
, take
, aNumbers
@@ -41,6 +44,7 @@
import System.Directory
type ANumber = Text
+type Seq = Text
type Key = Char
type Entry = Text
type Reply = Map Key Entry
@@ -101,6 +105,9 @@
lookup :: ANumber -> DB -> Maybe Reply
lookup = M.lookup
+
+lookupSeq :: ANumber -> DB -> Maybe Seq
+lookupSeq anum db = lookup anum db >>= M.lookup 'S'
grep :: Text -> DB -> DB
grep q = M.filter $ \reply ->
diff --git a/Sloane/GF.hs b/Sloane/GF.hs
--- a/Sloane/GF.hs
+++ b/Sloane/GF.hs
@@ -87,6 +87,7 @@
nthRootApprox :: Integer -> GF -> [GF]
nthRootApprox n f@(Series (1:_)) =
iterateUntilFixed (nthRootNext n f) (Series [1])
+nthRootApprox _ _ = error "GF has constant term different from 1"
nthRootNext :: Integer -> GF -> GF -> GF
nthRootNext n f g = Series (take (1 + 2*degree f) ds)
@@ -106,6 +107,7 @@
nthRoot1 n f@(Series (1:_)) =
let css = transpose (map coeffs (nthRootApprox n f))
in Series $ map fromJust (takeWhile isJust (map saddlePoint css))
+nthRoot1 _ _ = error "GF has constant term different from 1"
nthRoot :: Integer -> GF -> GF
nthRoot _ (Series []) = Series []
@@ -116,19 +118,14 @@
(^^^) :: GF -> Rational -> GF
(^^^) f r = case (numerator r, denominator r) of
(n, 1) -> f ^^ n
- (0, _) -> ogf [1]
+ (0, _) -> ogf [1::Int]
(n, k) -> nthRoot k f ^^ n
--- XXX: Seems correct, but isn't producing anything
--- nthRoot :: Integer -> GF -> GF
--- nthRoot n f = sum [ (f-1)^k * fromRational (bin n k) | k<-[0..]]
--- where
--- -- bin n k = {1/n choose k}
--- bin n k = product [(1-i*n+n) % i | i<-[1..k] ] / (n%1)^k
-
+-- XXX: Deprecate and use (^^^(1%2)) instead?
squareRoot :: GF -> GF
squareRoot = Series . map toRational . squareRoot' . map fromRational . coeffs
+-- XXX: Deprecate?
squareRoot' :: [Double] -> [Double]
squareRoot' [] = []
squareRoot' (c:ct) = ds
diff --git a/Sloane/Transform.hs b/Sloane/Transform.hs
--- a/Sloane/Transform.hs
+++ b/Sloane/Transform.hs
@@ -19,6 +19,8 @@
, tCONVi
, tEXPCONV
, tDIFF
+ , tMOBIUS
+ , tMOBIUSi
, tEULER
, tEXP
, tLOG
@@ -159,6 +161,31 @@
tDIFF :: NamedTransform
tDIFF = NT "DIFF" (\cs -> zipWith (-) (drop 1 cs) cs)
+-- The Mobius function of the poset of integers under divisibility
+mobius :: Integer -> Integer -> Integer
+mobius a b
+ | a == b = 1
+ | b `rem` a == 0 = -sum [ mobius a c | c <- [a..b-1], b `rem` c == 0 ]
+ | otherwise = 0
+
+-- The number theoretical Mobius function
+mu :: Integer -> Integer
+mu = mobius 1
+
+tMOBIUS :: NamedTransform
+tMOBIUS = NT "MOBIUS" $ \cs ->
+ [ sum [mu (n `div` k) % 1 * (cs !! (fromInteger k-1))
+ | k<-[1..n], n `rem` k == 0
+ ]
+ | (n,_) <- zip [1..] cs
+ ]
+
+tMOBIUSi :: NamedTransform
+tMOBIUSi = NT "MOBIUSi" $ \cs ->
+ [ sum [ (cs !! (fromInteger k-1)) | k<-[1..n], n `rem` k == 0 ]
+ | (n,_) <- zip [1..] cs
+ ]
+
tEULER :: NamedTransform
tEULER = NT "EULER" (\cs ->
let f = product $ zipWith (\n c -> (1 - x^n)^^^c) [1::Int ..] cs
@@ -238,6 +265,8 @@
, tCONVi
, tEXPCONV
, tDIFF
+ , tMOBIUS
+ , tMOBIUSi
, tEULER
-- , tEULERi
, tEXP
diff --git a/sloane.1 b/sloane.1
--- a/sloane.1
+++ b/sloane.1
@@ -1,17 +1,19 @@
-.TH "SLOANE" "1" "2 Jan 2015" "Sloane User Manual" "Version 2.0.0"
+.TH "SLOANE" "1" "7 Jan 2015" "Sloane User Manual" "Version 2.0.1"
.SH NAME
.PP
sloane \- a command line interface to Sloane\[aq]s On\-Line Encyclopedia
of Integer Sequences
.SH SYNOPSIS
.PP
-sloane [\-a|\-\-all] [\-k KEYS] [\-n N] [\-\-url] [\-\-local] [TERMS...]
+sloane [\-a|\-\-all] [\-k KEYS] [\-n N] [\-\-url] [\-\-local] TERMS...
.PP
-sloane [\-\-filter] [\-\-invert]
+sloane \-A NUMBER
.PP
-sloane [\-\-transform NAME] [\-\-list\-transforms]
+sloane \-\-filter [\-\-invert]
.PP
-sloane [\-\-update] [\-\-version] [\-\-help]
+sloane \-\-transform NAME
+.PP
+sloane (\-\-list\-transforms | \-\-update | \-\-version | \-\-help)
.SH DESCRIPTION
.PP
The \f[C]sloane\f[] command searches Sloane\[aq]s On\-Line Encyclopedia
@@ -95,6 +97,12 @@
.RS
.RE
.TP
+.B \-A \f[I]NUMBER\f[]
+Fetch the sequence with this number from the local database.
+Prints the sequence, but nothing else, to sdout.
+.RS
+.RE
+.TP
.B \-\-filter
Read sequences from stdin and return those that are in the local
database.
@@ -184,7 +192,16 @@
\f[]
.fi
.PP
-In the final example the local cache is used to filter out sequences
+To retrieve sequence A022493 from the local database use the
+\f[C]\-A\f[] option:
+.IP
+.nf
+\f[C]
+sloane\ \-A022493
+\f[]
+.fi
+.PP
+In the final example the local database is used to filter out sequences
from the standard input that are in OEIS:
.IP
.nf
diff --git a/sloane.cabal b/sloane.cabal
--- a/sloane.cabal
+++ b/sloane.cabal
@@ -1,5 +1,5 @@
Name: sloane
-Version: 2.0.0
+Version: 2.0.1
Synopsis: A command line interface to Sloane's On-Line Encyclopedia
of Integer Sequences
Description: A command line interface to Sloane's On-Line Encyclopedia
diff --git a/sloane.hs b/sloane.hs
--- a/sloane.hs
+++ b/sloane.hs
@@ -5,6 +5,7 @@
--
import Data.List (intercalate)
+import Data.Maybe (maybeToList)
import Data.Monoid
import Data.Text (Text)
import qualified Data.Text as T
@@ -14,12 +15,11 @@
import Network.Curl.Download (openURI)
import Options.Applicative
import Sloane.Config
-import Sloane.DB (DB)
+import Sloane.DB (DB, ANumber, Seq)
import qualified Sloane.DB as DB
import Sloane.Transform
type URL = String
-type Seq = Text
data Options = Options
{ full :: Bool -- Print all fields?
@@ -27,6 +27,7 @@
, limit :: Int -- Fetch at most this many entries
, url :: Bool -- Print URLs of found entries
, local :: Bool -- Lookup in local DB
+ , anumber :: Int -- Get the sequence with this number from the local DB
, filtr :: Bool -- Filter out sequences in local DB
, invert :: Bool -- Return sequences NOT in DB
, transform :: String -- Apply the named transform
@@ -80,6 +81,9 @@
clean = T.filter (`elem` " 0123456789-") . T.map tr
tr c = if c `elem` ";," then ' ' else c
+mkANumber :: Int -> ANumber
+mkANumber n = let s = show n in T.pack ('A' : replicate (6-length s) '0' ++ s)
+
filterDB :: Options -> DB -> IO [Seq]
filterDB opts db = filter match . parseSeqs <$> IO.getContents
where
@@ -111,6 +115,11 @@
<*> switch
( long "local"
<> help "Use the local database rather than oeis.org" )
+ <*> option auto
+ ( short 'A'
+ <> metavar "NUMBER"
+ <> value 0
+ <> help "Fetch the sequence with this number from the local database" )
<*> switch
( long "filter"
<> help ("Read sequences from stdin and return"
@@ -149,10 +158,13 @@
$ parserFailure pprefs pinfo ShowHelpText mempty
opts <- customExecParser pprefs pinfo
let tname = transform opts
+ let anum = anumber opts
+ let lookupSeq = maybeToList . DB.lookupSeq (mkANumber anum)
let sloane
| version opts = putStrLn . nameVer
| update opts = DB.update
| listTransforms opts = const $ mapM_ (putStrLn . name) transforms
+ | anum > 0 = \c -> lookupSeq <$> DB.read c >>= mapM_ IO.putStrLn
| filtr opts = \c -> DB.read c >>= filterDB opts >>= mapM_ IO.putStrLn
| null (terms opts) = const usage
| not (null tname) = const $ applyTransform opts tname