1Math::NumSeq(3) User Contributed Perl Documentation Math::NumSeq(3)
2
6 Math::NumSeq -- number sequences
7
9 # only a base class, use one of the actual classes, such as
10 use Math::NumSeq::Squares;
11 my $seq = Math::NumSeq::Squares->new;
12 my ($i, $value) = $seq->next;
13
15 This is a base class for some number sequences. Sequence objects can
16 iterate through values and some sequences have random access and/or a
17 predicate test.
18 The idea is to generate things like squares or primes in a generic way.
20 Some sequences, like squares, are so easy there's no need for a class
21 except for the genericness. Other sequences are trickier and an
22 iterator is a good way to go through values. The iterating tries to be
23 progressive, so not calculating too far ahead yet doing reasonable size
24 chunks for efficiency.
25 Sequence values have an integer index "i" starting either from i=0 or
27 i=1 or whatever best suits the sequence. The values can be anything,
28 positive, negative, fractional, etc.
29 The intention is that all modules "Math::NumSeq::Foo" are sequence
31 classes, and that supporting things are deeper, such as under
32 "Math::NumSeq::Something::Helper" or "Math::NumSeq::Base::SharedStuff".
33 Number Types
35 The various methods try to support "Math::BigInt" and similar
36 overloaded number types. So for instance "pred()" might be applied to
37 test a big value, or "ith()" on a bigint to preserve precision from
38 some rapidly growing sequence. Infinities and NaNs give some kind of
39 NaN or infinite return (some unspecified kind as yet).
40
42 In the following "Foo" is one of the subclass names.
43 "$seq = Math::NumSeq::Foo->new (key=>value,...)"
45 Create and return a new sequence object.
46 Iterating
48 "($i, $value) = $seq->next()"
49 Return the next index and value in the sequence.
50 Most sequences are infinite and for them there's always a next
52 value. But if $seq is finite then at the end the return is no
53 values. So for example
54 while (my ($i, $value) = $seq->next) {
56 print "$i $value\n";
57 }
58 "$seq->rewind()"
60 Rewind the sequence to its starting point. The next call to
61 "next()" will be the initial "$i,$value" again.
62 See "Optional Methods" below for possible arbitrary "seeks".
64 "$i = $seq->tell_i()"
66 Return the current i position. This is the i which the next call
67 to "next()" will return.
68 Information
70 "$i = $seq->i_start()"
71 Return the first index $i in the sequence. This is the position
72 "rewind()" returns to.
73 "$str = $seq->description()"
75 Return a human-readable description of the sequence. This might be
76 translated into the locale language, though there's no message
77 translations yet.
78 "$value = $seq->values_min()"
80 "$value = $seq->values_max()"
81 Return the minimum or maximum value taken by values in the
82 sequence, or "undef" if unknown or infinity.
83 "$ret = $seq->characteristic($key)"
85 Return something if the sequence has $key (a string)
86 characteristic, or "undef" if not. This is intended as a loose set
87 of features or properties a sequence can have to describe itself.
88 digits integer or undef, the radix if seq is digits
90 count boolean, true if values are counts of something
91 smaller boolean, true if value[i] < i generally
92 integer boolean, true if all values are integers
93 increasing boolean, true if value[i+1] > value[i] always
95 non_decreasing boolean, true if value[i+1] >= value[i] always
96 increasing_from_i integer, i for which value[i+1] > value[i]
97 non_decreasing_from_i integer, i for which value[i+1] >= value[i]
98 value_is_radix boolean, value is radix for i
100 "value_is_radix" means each value is a radix applying to the i
102 index. For example "RepdigitRadix" value is a radix for which i is
103 a repdigit. These values might also be 0 or 1 or -1 or some such
104 non-radix to indicate no radix.
105 "$str = $seq->oeis_anum()"
107 Return the A-number (a string) for $seq in Sloane's Online
108 Encyclopedia of Integer Sequences, or return "undef" if not in the
109 OEIS or not known. For example
110 my $seq = Math::NumSeq::Squares->new;
112 my $anum = $seq->oeis_anum;
113 # gives $anum = "A000290"
114 The web page for that is then
116 <http://oeis.org/A000290>
118 Sometimes the OEIS has duplicates, ie. two A-numbers which are the
120 same sequence. When that's accidental or historical
121 "$seq->oeis_anum()" is whichever is reckoned the primary one.
122 "$aref = Math::NumSeq::Foo->parameter_info_array()"
124 "@list = Math::NumSeq::Foo->parameter_info_list()"
125 Return an arrayref or list describing the parameters taken by a
126 given class. This meant to help making widgets etc for user
127 interaction in a GUI. Each element is a hashref
128 {
130 name => parameter key arg for new()
131 share_key => string, or undef
132 description => human readable string
133 type => string "integer","boolean","enum" etc
134 default => value
135 minimum => number, or undef
136 maximum => number, or undef
137 width => integer, suggested display size
138 choices => for enum, an arrayref
139 choices_display => for enum, an arrayref
140 }
141 "type" is a string, one of
143 "integer"
145 "enum"
146 "boolean"
147 "string"
148 "filename"
149 "filename" is separate from "string" since it might require subtly
151 different handling to ensure it reaches Perl as a byte string,
152 whereas a "string" type might in principle take Perl wide chars.
153 For "enum" the "choices" field is an arrayref of possible values,
155 such as
156 { name => "flavour",
158 type => "enum",
159 choices => ["strawberry","chocolate"],
160 }
161 "choices_display", if provided, is human-readable strings for those
163 choices, possibly translated into another language (though there's
164 no translations yet).
165 "minimum" and "maximum" are omitted (or "undef") if there's no hard
167 limit on the parameter.
168 "share_key" is designed to indicate when parameters from different
170 NumSeq classes can be a single control widget in a GUI etc.
171 Normally the "name" is enough, but when the same name has slightly
172 different meanings in different classes a "share_key" keeps
173 different meanings separate.
174 Optional Methods
176 The following methods are only implemented for some sequences since
177 it's sometimes difficult to generate an arbitrary numbered element etc.
178 Check "$seq->can('ith')" etc before using.
179 "$seq->seek_to_i($i)"
181 "$seq->seek_to_value($value)"
182 Move the current i so "next()" will return $i or $value on the next
183 call. If $value is not in the sequence then move so as to return
184 the next higher value which is.
185 Usually "seek_to_value()" only makes sense for sequences where all
187 values are distinct, so that a value is an unambiguous location.
188 "$value = $seq->ith($i)"
190 Return the $i'th value in the sequence. Only some sequence classes
191 implement this method.
192 "($v0, $v1) = $seq->ith_pair($i)"
194 Return two values "ith($i)" and "ith($i+1)" from the sequence.
195 This method can be used whenever "ith()" exists.
196 "$seq->can('ith_pair')" says whether "ith_pair()" can be used (and
197 gives a coderef).
198 For some sequences a pair of values can be calculated with less
200 work than two separate "ith()" calls.
201 "$bool = $seq->pred($value)"
203 Return true if $value occurs in the sequence. For example for the
204 squares this returns true if $value is a square or false if not.
205 "$i = $seq->value_to_i($value)"
207 "$i = $seq->value_to_i_ceil($value)"
208 "$i = $seq->value_to_i_floor($value)"
209 Return the index i of $value. If $value is not in the sequence
210 then "value_to_i()" returns "undef", or "value_to_i_ceil()" returns
211 the i of the next higher value which is, "value_to_i_floor()" the i
212 of the next lower value.
213 These methods usually only make sense for monotonic increasing
215 sequences, or perhaps non-decreasing so with some repeating values.
216 "$i = $seq->value_to_i_estimate($value)"
218 Return an estimate of the i corresponding to $value.
219 The accuracy of this estimate is unspecified, but can at least hint
221 at the growth rate of the sequence. For example if making an
222 "intersection" checking for given values in the sequence then if
223 the estimated i is small it may be fastest to go through the
224 sequence by "next()" and compare, rather than apply "pred()" to
225 each target.
226
228 Math::NumSeq::Squares, Math::NumSeq::Cubes, Math::NumSeq::Pronic,
229 Math::NumSeq::Triangular, Math::NumSeq::Polygonal,
230 Math::NumSeq::Tetrahedral, Math::NumSeq::StarNumbers,
231 Math::NumSeq::Powerful, Math::NumSeq::PowerPart,
232 Math::NumSeq::PowerFlip
233 Math::NumSeq::Even, Math::NumSeq::Odd, Math::NumSeq::All,
235 Math::NumSeq::AllDigits, Math::NumSeq::ConcatNumbers,
236 Math::NumSeq::Runs
237 Math::NumSeq::Primes, Math::NumSeq::TwinPrimes,
239 Math::NumSeq::SophieGermainPrimes, Math::NumSeq::AlmostPrimes,
240 Math::NumSeq::DeletablePrimes, Math::NumSeq::Emirps,
241 Math::NumSeq::MobiusFunction, Math::NumSeq::LiouvilleFunction,
242 Math::NumSeq::DivisorCount, Math::NumSeq::GoldbachCount,
243 Math::NumSeq::LemoineCount, Math::NumSeq::PythagoreanHypots
244 Math::NumSeq::PrimeFactorCount, Math::NumSeq::AllPrimeFactors
246 Math::NumSeq::ErdosSelfridgeClass, Math::NumSeq::PrimeIndexOrder,
248 Math::NumSeq::PrimeIndexPrimes
249 Math::NumSeq::Totient, Math::NumSeq::TotientCumulative,
251 Math::NumSeq::TotientSteps, Math::NumSeq::TotientStepsSum,
252 Math::NumSeq::TotientPerfect, Math::NumSeq::DedekindPsiCumulative,
253 Math::NumSeq::DedekindPsiSteps, Math::NumSeq::Abundant,
254 Math::NumSeq::PolignacObstinate
255 Math::NumSeq::Factorials, Math::NumSeq::Primorials,
257 Math::NumSeq::Fibonacci, Math::NumSeq::LucasNumbers,
258 Math::NumSeq::FibonacciWord, Math::NumSeq::FibonacciRepresentations,
259 Math::NumSeq::PisanoPeriod, Math::NumSeq::PisanoPeriodSteps,
260 Math::NumSeq::Fibbinary, Math::NumSeq::FibbinaryBitCount
261 Math::NumSeq::Catalan, Math::NumSeq::BalancedBinary,
263 Math::NumSeq::Pell, Math::NumSeq::Tribonacci, Math::NumSeq::Perrin,
264 Math::NumSeq::SpiroFibonacci
265 Math::NumSeq::FractionDigits, Math::NumSeq::SqrtDigits,
267 Math::NumSeq::SqrtEngel, Math::NumSeq::SqrtContinued,
268 Math::NumSeq::SqrtContinuedPeriod, Math::NumSeq::AlgebraicContinued
269 Math::NumSeq::DigitCount, Math::NumSeq::DigitCountLow,
271 Math::NumSeq::DigitCountHigh
272 Math::NumSeq::DigitLength, Math::NumSeq::DigitLengthCumulative,
274 Math::NumSeq::SelfLengthCumulative, Math::NumSeq::DigitProduct,
275 Math::NumSeq::DigitProductSteps, Math::NumSeq::DigitSum,
276 Math::NumSeq::DigitSumModulo, Math::NumSeq::RadixWithoutDigit,
277 Math::NumSeq::RadixConversion, Math::NumSeq::MaxDigitCount
278 Math::NumSeq::Palindromes, Math::NumSeq::Xenodromes,
280 Math::NumSeq::Beastly, Math::NumSeq::Repdigits,
281 Math::NumSeq::RepdigitAny, Math::NumSeq::RepdigitRadix,
282 Math::NumSeq::UndulatingNumbers, Math::NumSeq::HarshadNumbers,
283 Math::NumSeq::MoranNumbers, Math::NumSeq::HappyNumbers,
284 Math::NumSeq::HappySteps
285 Math::NumSeq::CullenNumbers, Math::NumSeq::ProthNumbers,
287 Math::NumSeq::WoodallNumbers, Math::NumSeq::BaumSweet,
288 Math::NumSeq::GolayRudinShapiro,
289 Math::NumSeq::GolayRudinShapiroCumulative, Math::NumSeq::MephistoWaltz,
290 Math::NumSeq::HafermanCarpet, Math::NumSeq::KlarnerRado,
291 Math::NumSeq::UlamSequence, Math::NumSeq::ReRound,
292 Math::NumSeq::ReReplace, Math::NumSeq::LuckyNumbers
293 Math::NumSeq::CollatzSteps, Math::NumSeq::ReverseAdd,
295 Math::NumSeq::ReverseAddSteps, Math::NumSeq::JugglerSteps,
296 Math::NumSeq::SternDiatomic, Math::NumSeq::NumAronson,
297 Math::NumSeq::HofstadterFigure, Math::NumSeq::DuffinianNumbers
298 Math::NumSeq::Kolakoski, Math::NumSeq::GolombSequence,
300 Math::NumSeq::AsciiSelf, Math::NumSeq::Multiples, Math::NumSeq::Modulo
301 Math::NumSeq::Expression, Math::NumSeq::File, Math::NumSeq::OEIS
303 Math::NumSeq::AlphabeticalLength,
305 Math::NumSeq::AlphabeticalLengthSteps, Math::NumSeq::SevenSegments (in
306 the Math-NumSeq-Alpha dist)
307 Math::NumSeq::Aronson (in the Math-Aronson dist)
309 Math::NumSeq::PlanePathCoord, Math::NumSeq::PlanePathDelta,
311 Math::NumSeq::PlanePathTurn, Math::NumSeq::PlanePathN (in the Math-
312 PlanePath dist)
313 Other Modules Etc
315 Math::Sequence and Math::Series, for symbolic recursive sequence
316 definitions
317 math-image, for displaying images with the NumSeq sequences
319
321 http://user42.tuxfamily.org/math-numseq/index.html
322
324 Copyright 2010, 2011, 2012, 2013, 2014 Kevin Ryde
325 Math-NumSeq is free software; you can redistribute it and/or modify it
327 under the terms of the GNU General Public License as published by the
328 Free Software Foundation; either version 3, or (at your option) any
329 later version.
330 Math-NumSeq is distributed in the hope that it will be useful, but
332 WITHOUT ANY WARRANTY; without even the implied warranty of
333 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
334 General Public License for more details.
335 You should have received a copy of the GNU General Public License along
337 with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.
338perl v5.28.0 2014-06-29 Math::NumSeq(3)