3j%UdZddlmZddlmZddlmZddlZddlm Z m Z ddl Z ddl Z ddl ZddlZddlmZddlmZdd lmZdd lmZdd lmZej,d ZGd dej0ZGddej0ZGddej0ZGddej0ZGddej0ZdZdZdZ dZ!dZ"eee e!e"gZ#dZ$e%e jLdgzZ'd4dZ(dZ)d5d6d Z*d5d!Z+d"Z,d7d#Z-d$Z.Gd%d&Z/Gd'd(Z0Gd)d*Z1Gd+d,Z2Gd-d.Z3Gd/d0ejhZ5gZ6d1e7d2<e8d3k(rddlZejre5yy)8a A comprehensive, object model of the Xenakis Sieve. :class:`music21.sieve.Sieve` objects can be created from high-level string notations, and used to generate line segments in various representation. Additional functionality is available through associated objects. The :class:`music21.sieve.Sieve` class permits generation segments in four formats. >>> a = sieve.Sieve('3@2|7@1') >>> a.segment() [1, 2, 5, 8, 11, 14, 15, 17, 20, 22, 23, 26, 29, 32, 35, 36, 38, 41, 43, 44, 47, 50, 53, 56, 57, 59, 62, 64, 65, 68, 71, 74, 77, 78, 80, 83, 85, 86, 89, 92, 95, 98, 99] >>> a.segment(segmentFormat='binary') [0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1] >>> a.segment(segmentFormat='width') [1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 3, 1, 2, 3, 2, 1, 3, 3, 3, 3, 1] >>> len(a.segment(segmentFormat='unit')) 43 A :class:`music21.sieve.CompressionSegment` can be used to derive a Sieve from a ny sequence of integers. >>> a = sieve.CompressionSegment([3, 4, 5, 6, 7, 8, 13, 19]) >>> str(a) '6@1|7@6|8@5|9@4|10@3|11@8' The :class:`music21.sieve.PitchSieve` class provides a quick generation of :class:`music21.pitch.Pitch` lists from Sieves. >>> a = sieve.PitchSieve('13@3|13@6|13@9', 'c1', 'c10', 'f#4') >>> pitches = a() >>> ', '.join([str(p) for p in pitches]) 'F#1, A1, C2, G2, B-2, C#3, G#3, B3, D4, A4, C5, E-5, B-5, C#6, E6, B6, D7, F7, C8, E-8, F#8, C#9, E9, G9' ) annotations) literal_eval)IterableN)gcdlcm)common) environment) exceptions21)interval)pitchsievec eZdZy) UnitExceptionN__name__ __module__ __qualname__:/DATA/.local/lib/python3.12/site-packages/music21/sieve.pyrrIrrc eZdZy)ResidualExceptionNrrrrrrMrrrc eZdZy)SieveExceptionNrrrrrrQrrrc eZdZy)CompressionSegmentExceptionNrrrrrrUrrrc eZdZy)PitchSieveExceptionNrrrrrrYrrr{}&|^-@c#Ki}d} |j|d}|||z}||vr ||z}||vr |||<n||z}|||<||k\r||dz}Fw)a Yields the sequence of prime numbers via the Sieve of Eratosthenes. rather than creating a fixed list of a range (z) and crossing out multiples of sequential candidates, this algorithm stores primes under their next possible candidate, thus allowing the generation of primes in sequence without storing a complete range (z). Create a dictionary. Each entry in the dictionary is a key:item pair of (key) the largest multiple of this prime so far found and (item) the prime. The dictionary only has as many entries as found primes. If a candidate is not a key in the dictionary, it is not a multiple of any already-found prime; it is thus a prime. a new entry is added to the dictionary, with the square of the prime as the key. The square of the prime is the next possible multiple to be found. To use this generator, create an instance and then call the .next() method on the instance. >>> a = sieve.eratosthenes() >>> next(a) 2 >>> next(a) 3 We can also specify a starting value for the sequence, skipping over initial primes smaller than this number: >>> a = sieve.eratosthenes(95) >>> next(a) 97 >>> next(a) 101 N)pop)firstCandidateDqpnextMults r eratosthenesr0psF A A  EE!TN =1uHa-#a<a-AhK1uHAhKN" E) s ,AAcvt|}|dvry|dz}|dvrygd}|dkr||vryy|D] }||zdk(s y|d z d }}|d zs|d z}|d z}|d zstd D]U}ttjd |d z ||}|d k(r-td |D]}||d z k(rFt|d |}yy) a Returns True if an integer is likely prime or False if it is likely composite using the Rabin Miller primality test. See also here: http://www.4dsolutions.net/ocn/numeracy2.html >>> sieve.rabinMiller(234) False >>> sieve.rabinMiller(5) True >>> sieve.rabinMiller(4) False >>> sieve.rabinMiller(97 * 2) False >>> sieve.rabinMiller(6 ** 4 + 1) # prime True >>> sieve.rabinMiller(123986234193) # divisible by 3, runs fast False )r(T)r)F)r4 %)+/5;=CGIOSYadrr) r()absrangepowrandomrandint) nmprimesprimesriyjs r rabinMillerr[s. AAF{ AA;F Cx ; u9> q5!qA!e a E!e2Y q!a%(!Q / 6 q!AAEzAq! A  rcx|D]"}tj|rtdg}||j|d}|d}n8t t j |}|j|d}|d}t||dzD])}||vr|jd|jd+|S)a Treat a sequence of integers as defining contiguous binary integers, where provided values are 1's and excluded values are zero. For instance, running [3, 10, 12] through this method gives a 1 for the first entry (signifying 3), 0s for the next six entries (signifying 4-9), a 1 (for 10), a 0 (for 11), and a 1 (for 12). >>> sieve.discreteBinaryPad([3, 10, 12]) [1, 0, 0, 0, 0, 0, 0, 1, 0, 1] >>> sieve.discreteBinaryPad([3, 4, 5]) [1, 1, 1] znon-integer value foundrr)) risNumrsortlistcopydeepcopyrNappend)seriesfixRangexdiscreteminValmaxVal seriesAlts rdiscreteBinaryPadrks"||A 9: :H !"v./ 12 66A: & ; OOA  OOA  ' Orcj||j|d}|d}nt|}t|}||z }g}t|dkDrY|D]R}||z }t j |r t |}|dk7r|j||z B|jdT|S|jd|S)a3 Given a list of numbers, create a proportional spacing across the unit interval. The first entry will always be 0 and the last 1, other entries will be spaced according to their distance between these two units. For instance, for 0, 3, 4 the middle entry will be 0.75 since 3 is 3/4 of the distance between 0 and 4: >>> sieve.unitNormRange([0, 3, 4]) [0.0, 0.75, 1.0] but for [1, 3, 4], it will be 0.666... because 3 is 2/3 of the distance between 1 and 4 >>> sieve.unitNormRange([1, 3, 4]) [0.0, 0.666..., 1.0] rr]r))r_minmaxlenrr^floatrc)rdreminFoundmaxFoundspanunitvaldifs r unitNormRangerws$ A;B<v;v; h D D 6{QC.C||C Cjqy C$J' A K A Krc|dkrdgS|dk(rddgSg}d|dz z }t|dz D]}|j||z|jd|S)a9 Given a certain number of parts, return a list unit-interval values between 0 and 1, with as many divisions as parts; 0 and 1 are always inclusive. >>> sieve.unitNormEqual(3) [0.0, 0.5, 1] If parts is 0 or 1, then a single entry of [0] is given: >>> sieve.unitNormEqual(1) [0] r)rr()rNrc)partsrtsteprYs r unitNormEqualr{Asg zs !1v EAIuqy!A KKD !" A rc||k(rgS||kr|}|}n|}|}d}g}|}||kr!|j|||z }|dz }||kr!|r t|S|S)a Given a step size and an a/b min/max range, calculate number of parts to fill step through inclusive a,b, then return a unit interval list of values necessary to cover region. Note that returned values are, by default, normalized within the unit interval. >>> sieve.unitNormStep(0.5, 0, 1) [0.0, 0.5, 1] >>> sieve.unitNormStep(0.5, -1, 1) [0.0, 0.25, 0.5, 0.75, 1] >>> sieve.unitNormStep(0.5, -1, 1, normalized=False) [-1, -0.5, 0.0, 0.5, 1.0] >>> post = sieve.unitNormStep(0.25, 0, 20) >>> len(post) 81 >>> post = sieve.unitNormStep(0.25, 0, 20, normalized=False) >>> len(post) 81 rr))rcr{) rzab normalizedrhricountvaluesrfs r unitNormStepr[s2 Av 1u E FA v+ a T    v+U## rcnd}|dk(rd}|S||k(rd}|S|dkr||z|z}|dk(r |S|dz}|dkr|S)Nrr)'r)c1c2grus r _meziriacrsq A Qw  H r  H %ir6R-Cax HAA %i Hrc(eZdZdZddZdZddZy) PrimeSegmentcNg|_||_||_|jy)a A generator of prime number segments, given a start value and desired length of primes. >>> ps = sieve.PrimeSegment(3, 20) >>> ps() [3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73] N)segstartlength _fillRange)selfrrs r__init__zPrimeSegment.__init__s#   rNcg}d}|dzdk(r||kDr|dk(r|dz}n|dz }n|} t|r"|j|t||k\r |S||k(r |S||kDr|dk(r|dz}n|dz }n|dk(r|dz}n|dz }\)z scan all number in range and return a list of primes provide a max to force stoppage at certain point before the maximum length direction determines which way things go. r(rupr))r[rcro)rrrstop directionr _oddBoundaryrRs r_fillRabinMillerzPrimeSegment._fillRabinMillers 19>el2D AIAIA1~ 1 s8v% Dy <$AAAA$AAAA!rc|jdkr|jt|j|jdd}|Dcgc]}| }}t ||jkr5|jd|jt |z dd}||z|_y||_y|j|j|jdd|_ycc}w)z2 fill positive and negative range rdownNr)rrrMrror)rsegNegrfsegPoss rrzPrimeSegment._fillRanges ::>**3tzz?DKKFSF"()&Qqb&F)6{T[[(..q$++F 2K9=tE!F?!,,TZZdDQDH*s Cc~|jd|jdg}|dvrt|j|S|dk(rt|j|S|dvr[g}tt |jdz D]3}|j |j|dz|j|z 5|S|jS)z assumes that min and max values are derived from found primes means that primes will always be at boundaries rr]binbinaryrtwidwidthr))rrkrwrNrorc)r segmentFormatzrrXs r__call__zPrimeSegment.__call__s XXa[$((2, ' - -$TXXq1 1 f $ 1- - . .C3txx=1,- DHHQUOdhhqk9;.J88Or)NrN)rrrrrrrrrrrrs #JR$rrceZdZdZddZdZdZdZddZddZ d Z dd Z dd Z d Z d ZdZdZdZdZdZdZdZy)Residuala object that represents a modulus and a start point each object stores a range of integers (self._z) from which sections are drawn this range of integers can be changed whenever the section os drawn >>> residual = sieve.Residual(3, 2) Nc|ttd}||_||_|dvr t d||_|jdk(r||_n||jz|_gd|_d|_y)NrK)rr)z)negative value must be 0, 1, or a Booleanrintrrtrr) r`rN_z_mr_neg_shift_segmentFormatOptions_segmentFormat)rrSshiftnegrs rrzResidual.__init__sq 9U3Z A f #$OP P 77a<DK$''/DK%B"#rc||_y)zJ z is the range of integers to use when generating a list Nrrrs rsetZz Residual.setZ%s rc>tt||dz|_y)zv z is the range of integers to use when generating a list convenience function that fixes max r)Nr`rNrrminIntmaxInts r setZRangezResidual.setZRange+ uVVaZ01rc|jj}||jvrtd|||_y)Nzformat not in format options: )striplowerrrrrfmts rsetSegmentFormatzResidual.setSegmentFormat2s?iik! $,, ,#&DSE$JK K!rc| |j}| |j}g}|jdk(r|S||jz|jz}|D]&}|||jzk(s|j |(|j r0t j|}|D]}|j||}n|}|dvr t||S|dk(r t||S|dvr|jgt|dz z}|S|dvr|St|d)a get a residual subset of this modulus at this n within the integer range provided by z format can be 'int' or 'bin', for integer or binary >>> a = sieve.Residual(3, 2) >>> a.segment(3) [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98] >>> a.segment(3, range(3, 15)) [5, 8, 11, 14] rrrtrr))rintegerz( not a valid sieve segmentFormat string.) rrrrrcrrarbremoverkrwror) rrRrrsubsetvaluecompSetrrs rsegmentzResidual.segment:s 9A   //M 77a<M _ 'EEDGGO# e$ 99mmA&Gu% CC - -$S!, , f $ a( ( . .77)s3x!|,CJ 0 0J#}o5]$^_ _rc|jS)z period is M; obvious, but nice for completeness >>> a = sieve.Residual(3, 2) >>> a.period() 3 )rrs rperiodzResidual.periodis wwrctj|j}tj|j}tj|j}t ||||j Sr)rarrrrr)rrSrrs rraz Residual.copytsM IIdgg  $++&ii "5#tww//rc(|j|||S)a calls self.segment(); uses _segmentFormat >>> a = sieve.Residual(3, 2) >>> a() [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98] )rrrRrrs rrzResidual.__call__|s||Aq-00rc|dk(rN|jdk7r|jd|jd}n|jd}|jrd|}|S|jd|j}|jrd|}|S)zG does not show any logical operator but unary negation classicrz(n+)z(n)r%r&)rrr)rstylerepStrs r representzResidual.represents I {{a GG9C }A6 GG9CyyVH  y$++/FyyVH rc"|jS)z str representation using M(n + shift) style notation >>> a = sieve.Residual(3, 2) >>> str(a) '3@2' rrs r__str__zResidual.__str__s~~rc|y|j|jk(r3|j|jk(r|j|jk(ryy)zF ==, compare residual classes in terms of m and shift rr)rrrrothers r__eq__zResidual.__eq__sB = GGuxx KK5<</II+rc\|j|jkry|j|jkDry|j|jk(r_|j|jkry|j|jkDry|j|jk7r|jdk(ryyyy)z allow comparison based on m and shift; if all equal look at neg Still being used internally even though __cmp__ is not used in Python 3 r]r)rNrrs r__cmp__zResidual.__cmp__s 77UXX  WWuxx  WW {{U\\)u||+99 *yyA~! !rc.|j|dk(ryy)Nr]TFrrs r__lt__zResidual.__lt__s << " $rc.|j|dk(ryy)Nr)TFrrs r__gt__zResidual.__gt__s << ! #rc||jrd}nd}t|j|j||jS)z8 unary neg operators; return neg object rr))rrrrr)rrs r__neg__zResidual.__neg__s2 99CCc477;;rcN|js |jr td|j|j|j|j|j\}}t |j t |j z}t|}t||d|S)a  &, produces an intersection of two Residual classes returns a new Residual class cannot be done if R under complementation >>> a = sieve.Residual(3, 2) >>> b = sieve.Residual(5, 1) >>> c = a & b >>> str(c) '15@11' z3complemented Residual objects cannot be intersectedr) rr_cmpIntersectionrrsetrr`r)rrrSrRzSetrs r__and__zResidual.__and__s{ ::#$YZ Z$$TWWehh U\\R1477|c%((m+ J1a##rcy)z ``|``, not sure if this can be implemented i.e., a union of two Residual classes can not be expressed as a single Residual, that is intersections can always be reduced, whereas unions cannot be reduced. Nrrs r__or__zResidual.__or__s rc&t||}||z}||z}d}d} |dk7r|dk7r ||z}||z}n|| fS|dk7r||z |zdk7r|| fS|dk7r||z |zdk(r||k7r ||k(r|} |}| |fS||z|z} t||} || ||z z|zz| z}| |fS)z compression by intersection find m,n such that the intersection of two Residuals can be reduced to one Residual. Xenakis p 273. rr))rr) rm1m2n1n2drrn3m3rs rrzResidual._cmpIntersections BK 1W 1W   7rQwbBbBr6M 6R1})r6M !V"r'Q!+"(rBBr6Mb1B"b!AR"W *+r1Br6Mr)rrNrNNreturnrr)rrr__doc__rrrrrrrarrrrrrrrrrrrrrrrsc$* 2"-`^0 1"  6  <$* rrc>eZdZdZd dZd dZdZdZdZdZ d Z y) CompressionSegmenta Utility to convert from a point sequence to sieve. A z range can be supplied to explicitly provide the complete sieve segment, both positive and negative values. all values in the z range not in the segment are interpreted as negative values. thus, there is an essential dependency on the z range and the realized sieve. No matter the size of the z range, there is a modulus at which one point in the segment can be found. As such, any segment can be reduced to, at a minimum, a residual for each point in the segment, each, for the supplied z, providing a segment with one point. The same segment can then have multiplied logical string representations, depending on the provided z. >>> a = sieve.CompressionSegment([3, 4, 5, 6, 7, 8, 13, 19]) >>> str(a) '6@1|7@6|8@5|9@4|10@3|11@8' >>> b = sieve.CompressionSegment([0, 2, 4, 6, 8]) >>> str(b) '2@0' >>> c = sieve.CompressionSegment([0, 2, 4, 5, 7, 9, 11, 12]) >>> str(c) '5@2|5@4|6@5|7@0' Ncttj|}|jg|_|D],}||jvs|jj |.t |jdkr td|j|t |j|_ |jy#t$r}td|d}~wwxYw)Nr)z'segment must have more than one elementz*no Residual classes found for this z range) r`rarbr__matchrcror_zUpdater_maxMod_processAssertionError)rsrcrnum assertErrors rrzCompressionSegment.__init__=s4==%&   C$++% ""3' t{{ q -.WX X a477|   MMO -<  s6C C! CC!c|M|j|j|s td||_|jd|jd}}y|jd|jd}}t t ||dz|_y)Nz-z range must be a superset of desired segmentrr]r))_subsetrrrr`rN)rrzMinzMaxs rrzCompressionSegment._zUpdateWs =<< Q/1CEEDGTWWR[$DQR$D5q23DGrc|jS)z >>> a = sieve.CompressionSegment([3, 4, 5, 6, 7, 8]) >>> b = a() >>> str(b[0]) '1@0' ) _residualsrs rrzCompressionSegment.__call__fsrcg}t|jdk(rt|jd}|S|jD]}|jt|dj |}|S)Nr)rr#)ror strrcjoin)rresStrresObjs rrzCompressionSegment.__str__pse t 1 $+,F  // c&k**XXf%F rcHd}|D] }||vs|dz}|t|k(ryy)zM True if sub is part of set; assumes no redundancies in each rr))ro)rsubthisSet commonNumrfs rr zCompressionSegment._subset{s7 AG|%M  C rcd}||jkr`t||d|j}|}|j||r||fS|j||r||fS|dz}||jkr`t d|j)z_ given a point, and SieveSegment, find a modulus and shift that match. r)rza mod was not found less than )rrrr r)rrRpartwholerSobjrs r_findzCompressionSegment._finds $,,1aDGG,C%C||C&Cxc5)CxAA$,,=dll^LMMrcg|_tj|j}d}|r|dz}|d}|j|||j\}}| t d||jvr8|jj ||D]}||vs|j ||sn|r|jjy)a take a copy of match; move through each value of this list as if it were n; for each n test each modulo (from 1 to len(z) + 1) to find a residual. when found (one will be found), keep it; remove the found segments from the match, and repeat. rr)rNz_find() returned a None object)r rarrrrcrr_)rmatchmaxToRunrRrrrfs rrzCompressionSegment._processs $++& MHaAzz!UDKK8HC{12RSS$//)&&s+AEz Q rr) rrrrrrrrr rrrrrrrs+:4 4 N&rrc*eZdZdZd'd(dZdZdZdZdZd'dZ d Z d Z d Z d Z d ZdZdZdZdZdZdZdZdZd)dZdZdZd*dZdZdZd'dZdZd'dZdZ d Z! d+ d,d!Z"d-d"Z#d.d#Z$ d/ d0d$Z%d1d%Z&d&Z'y)2Sievez Create a sieve segment from a sieve logical string of any complexity. >>> a = sieve.Sieve('3@11') >>> b = sieve.Sieve('2&4&8|5') >>> c = sieve.Sieve('(5|2)&4&8') Ncv|%t|trttd}n|t j |r ||_d|_d|_d|_ gd|_ d|_ i|_ d|_ d|_d|_d|_d|_||_|j$|j'yy) NrKexprrFrr]) isinstancerr`rNr isListLiker_state_expTyperr_nonCompressible_resLib_resId_expTree _expPeriod_cmpTree _cmpPeriod_usrStr_load)rusrStrrs rrzSieve.__init__s 9FC0U3Z A Y6,,V4 /4  #%B" %,.     << # JJL $rctj|jr<|j|j |j|j y|j|j |j yr)rr%r/ _resClear_initLoadSegment_initCompression _initParsers rr0z Sieve._loads^   T\\ * NN   ! !$,, /  ! ! # NN  OO   ! ! #rcd|_t|jvs6t|jvs$t|jvst |jvr |j n |jd|_d}|jrd}|S|jdk(rd}|S|jdk(rd}|S#t$r d|_YJwxYw#t$r+ |j n#t$r d|_YnwxYwYwxYw)Ncomplexr)simpler#zno compression possibler intersection) r'NEGr+LGROUPRGROUPXOR _cmpSegment IndexErrorr(r TypeError)rmethods rr5zSieve._initCompressions" 4== T]]*T]]*$--' *  " .%%' (   .F  ]]i 'F ]]h &#F ' *()% *  ..$$&!.,-D). .sHB2#C2CC C<C#"C<#C63C<5C66C<;C<c|jd}|jd}t|}||k(r||_||_y||_t||_y)zb Lazy period initialization, called only when needed from public period() method. r"cmpN)_resPeriodListrr,r.)rmListExpmListCmplcmExps r _initPeriodzSieve._initPeriod/sU&&u-&&u-h x $DO$DO$DO!8nDOrcd|_y)z7 Set this Sieve to its expanded state. r"N)r&rs rexpandz Sieve.expand?s  rc|7||jk7r(||_|jd|j|jryd|_y)z9 Set this sieve to its compressed state. NrD)rr3r5r(r&rs rcompresszSieve.compressEsE =Q$''\DG NN5 !  ! ! #  DKrcd|jdi}|j-|j|jdj|d<|S|j|d<|S)zH Provides a dictionary data representation for exchange logStrr"rr)rrr) _resKeyStrr)rdatas r_getParameterDatazSieve._getParameterDataUs` dnnU+  77? T__Q%78::DI DI rc||_y)zu Set the z as a list. The z is the range of integers to use when generating a sieve segment. Nrrs rrz Sieve.setZds rc>tt||dz|_y)z Set the z as a min and max value. The z is the range of integers to use when generating a sieve segment. r)Nrrs rrzSieve.setZRangekrrc|jj}||jvrtd|||_y)Nzcannot set to format: )rrrrrrs rrzSieve.setSegmentFormatrs?iik! d00 0 #9#!?@ @!rc|j}djtt|dtg}|d}t ||S)z9 unary neg operators; return neg object. r#rOr)rRrr;r<r=r )rdataSelfr1rs rrz Sieve.__neg__}sN))+   X      SMVQrc |j}|j}djt|dttt|dtg}t |dt |dz}t |}t||S)z &, produces an intersection of two >>> a = sieve.Sieve('3@11') >>> b = sieve.Sieve('2&4&8|5') >>> c = sieve.Sieve('(5|2)&4&8') >>> d = a & b >>> str(d) '{2@0&4@0&8@0|5@0}&{3@2}' r#rOr)rRrr<r=ANDrr`r rrrW dataOtherr1rrs rrz Sieve.__and__s))+++-   h     X    8C=!C #$77 JVQrc |j}|j}djt|dttt|dtg}t |dt |dz}t |}t||S)z ``|``, produces a union >>> a = sieve.Sieve('3@11') >>> b = sieve.Sieve('2&4&8|5') >>> d = a | b >>> str(d) '{2@0&4@0&8@0|5@0}|{3@2}' r#rOr)rRrr<r=ORrr`r rZs rrz Sieve.__or__s))+++-   h     X    8C=!C #$77 JVQrc |j}|j}djt|dttt|dtg}t |dt |dz}t |}t||S)z4 ^, produces exclusive disjunction. r#rOr)rRrr<r=r>rr`r rZs r__xor__z Sieve.__xor__s))+++-   h     X    8C=!C #$77 JVQrcd}tj|rt|dddS|j}|sy|j dr|j dd}|j dr|j dd}|j t d}|j td}|ddk(rd }|d dj}nd}|sy t|}d}tj|rt|}d}n0tj|r|d}t|d kDr|d }nd}|||d S#tttf$rYywxYw) ai process an arg string for proper Residual creation valid syntax for Mod, shift pairs: all valid: MsubN, M@N, M,N, M if M is given alone, shift is assumed to be 0 this method assumes that all brackets have been replaced with parentheses returns a dictionary of args suitable for creating a Residual class r)rSrRrNr,r&r#r%r))rSrr)rr^rrfindreplacer<r=r NameError SyntaxErrorrAr%ro)rr1rSrargsrs r_parseResidualzSieve._parseResidualsS  << V1Q7 7 ;;u ^^E3/F ;;s ^^C-F++ !9 CABZ%%'FC  'D << D AE   t $QA4y1}Q ; 2  s D66E  E ctj|rt|}|d}|jddk\r|j dt }|jddk\r|j dt }|jddk\r|j dt }|jddk\r|j dt }|jddk\r|j dt }|jd dk\r|j d t}|jd dk\r|j d t}|jd dk\r|j d t}|jd dk\r|j d t}|jd dk\r|j d t}|j dd}|S)a provide synonyms for logical symbols:: intersection == and, &, * union == or, |, + not == not, - the native format for str representation uses only ``&``, ``|``, ``-``; this method converts all other string representations all brackets and braces are replaced with parenthesis parentheses are only used for the internal representation on string representation, braces are restored z@0andr*or+xorr$not[](r r#) rr^rrbrcrYr]r;r<r=)rr1s r _parseLogiczSieve._parseLogics << [Fxr]F ;;u  "^^E3/F ;;s q ^^C-F ;;t  !^^D"-F ;;s q ^^C,F ;;u  "^^C,F ;;u  "^^E3/F ;;s q ^^C0F ;;s q ^^C0F ;;s q ^^C0F ;;s q ^^C0FR( rcZt|}t|jdd}d|dS)zF return string necessary to instantiate a set object. rrr#zset(r)r`reprrc)rvalLists r_setInstantiateStrzSieve._setInstantiateStrCs2w-w-''R0gYa  rcd|dS)Nzr)rresIds rrPzSieve._resKeyStrKsE7!}rc |dvr td|dk(r5g}|jD]"}||jvs|j|$|S|dk(r5g}|jD]"}||jvs|j|$|Sy)z5 get residual keys based on library. )rDr"zstate must be 'cmp' or 'exp'rDr"N)rr)r-rcr+)rstatelibKeyskeys r_resKeyszSieve._resKeysNs  & !?@ @ E>G||$--'NN3'$N e^G||$--'NN3'$N rcg}|j|D]5}|j|j}||vs%|j|7|j |S)z For all residual classes, get the period, or the value of M, and return these in a list. Remove any redundant values and sort. )rr)rrcr_)rr|mListr~r.s rrEzSieve._resPeriodListasU =='C S!((*A~ Q(   rc0|jdj|}|%dj|}d|}td|dt|d|d|d|j}||j |j |<|j |S)z create a residual object, store in expResidualLib return a string id representation this uses self._z at initialization. r#z cannot parse zbad residual class notation: (rrSrr)rgrrrrr)rP)rrzrresDictjoinedmsgrs r _resCreatezSieve._resCreatens %%bggfo6 ?WWV_F!&*C #A#!JK K'#,(8!%.$''306 T__U+,u%%rc`||j|j|<|j|Sr)r)rP)rrzrs r _resAssignzSieve._resAssigns(/5 T__U+,u%%rc| |j}tj|s|td||j|||}|j |S)z this is where residuals are converted to set evaluating strings z should not be stored; should be a temporary value z"z must be a list of integers, not )rrr%rr)rw)rrzrRrrvs r _resToSetStrzSieve._resToSetStrs_ 9A  #  #EaU!KL L%$,,u%a+&&w//rc,|jdz|_y)z' increment the _resId. r)N)r*rs r_resIdIncrementzSieve._resIdIncrementskkAo rc,tt|jj}|D];}|j |}||j vs#||j vs2tdt|jj|_y)z reset self._resId to the next available number may need to re-label some residual classes if gaps develop ids should be contiguous integer sequence zgap in residual keysN) rNror)keysrPr-r+rr*)riValsrXtestKeys r _resResetIdzSieve._resResetIdsv c$,,++-./Aooa(Gdmm+t}}0L$%;<< $,,++-. rc|i|_d|_y|dk(r6|j|}|D]}|j|=|jy|dk(r t dy)NrrDr"z1Expanded residual classes should never be cleared)r)r*rrr)rr|cmpKeysr~s rr3zSieve._resClearsf =DLDK e^mmE*GLL%     e^ !TU Urcfg|_t||j}|j|j|_|}|D]G}|jj|j |j ||j Itj|j|_y)z= load from a segments reload _resId. N) r+rrrcrr*rr]r)rusrDatasegObjunionrs rr4zSieve._initLoadSegments  #GTWW5 77?iiDGF MM f!E F  " . rci|_d|_g|_|jt j |j }d} |t|k(rn||}|dk(rd}n||dz }|t|dz k(rd}n||dz}|tvr"|jj||dz}n|tk(r|d}td|d|tk(r||tvrd}td|d|tk(rX|V|tk(rM|)|tttt fvrd }td |d|jj||dz }n|t"j$vs |tk(rg}t j|} d} || | ztk(r|jt| dz} | | zt|k(rn1|| | z} | tvs | tk(rn|j| | dz} C|jj|j'|jd j)||j+|| z}n|dz}|js td d j)|j|_y) zV process usrStr string into proper argument dictionaries for Residual rr)Nz(negation cannot be used without operandsz"badly formed logical string (a): (rz,negation cannot be used as a binary operatorz"badly formed logical string (b): (z6negation must be of a group and isolated by delimitersz"badly formed logical string (c): (r#zno residual classes defined)r)r*r+rsrarbr/roBOUNDSrcr;rRESIDUALr<rYr]r>stringdigitsrrr) rrrOrXchar charPreviouscharNextrrsubStartsubLensubChars rr6zSieve._initParses    !!$-- "=> CK!9DAv# %a!e} CK!O#!!a%=v~ $$T*E!1@$'I#a%PQQ#+"."h.D$'I#a%PQQ#+*&(!,(b#0FFRC(+McURS)TUU $$T*Q &$#+99Q<(V+,3MM#&#aZF 6)c&k9$X%67G&(GsN g.!'! $$T__T[["''&/%RS$$&JEOR|| !>? ? . rcvg|_tj|j}|jt}d}|D]}|dk(r |jt }t |dk(r|j|d}nPtt |dz D]6}|dk(r|j||}n|}|j||dz}||z}8|jj|j|j||jtj|j|_y)z9 an unbound sieve, intersection Residual rr#r)N)r-rar+splitr]rYror)rNrcrr*rr) rrOorListr:orGroupandListrXr}r~s rrzSieve._cmpIntersection!s  4==)b! G"}mmC(G7|q #||GAJ7 s7|a/0AAv LL4( WQU^4A#$q5L1 MM l!K L  ")* . rcdg|_|jd}|s tdt||j}|D]G}|jj |j |j||jItj|j|_y)z< a bound sieve, uss a newly created segment r"z/empty segment; segment compression not possibleN) r-rr@rrrcrr*rr]r)rrrrs rr?zSieve._cmpSegmentAs  ll5!NO O#C1hF MM f!E F  " . rc | |j}| |j}| |j}|dk(r tj|j}n'|dk(r tj|j }nd}|j |}tddd|}|j|}|jd|dz}|D]%} |j| |j| ||}'|jtd}|jtd } t|d d tiii} t#| } | j%|d vr t'| |S|dk(r t)| |S|dvr=g} t+t-| dz D]} | j/| | dz| | z !| S| S#t$r} t!d |d | d} ~ wwxYw)a Return a sieve segment in various formats. >>> a = sieve.Sieve('3@11') >>> a.segment('exp') [2, 5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59, 62, 65, 68, 71, 74, 77, 80, 83, 86, 89, 92, 95, 98] >>> c = sieve.Sieve('(5|2)&4&8') >>> c.segment('cmp', segmentFormat='wid') [8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8] Nr"rDr#r)rr%rqr __builtins__rzbadly formed logical string (rrtr)r&rrrar+r-rrrwrcrr<r=evalrrerr`r_rkrwrNrorc)rr|rRrrevalStrrrsetStrr~rserrXs rrz Sieve.segmentTs& =KKE 9A   //M E>ii .G e^ii .GG}}U#!Q1%((2//#v|4Cooc4+<+CC3i  - -$S!, , f $ a( ( . .C3s8a<( CAJQ/1)JJ#  /y:  sF,, G 5GG c|j}|jdk(r|j|dk(r |jS|dk(r |jSt d)aE Return the period of the sieve. >>> a = sieve.Sieve('3@11') >>> a.period() 3 >>> b = sieve.Sieve('2&4&8|5') >>> b.period() 40 >>> c = sieve.Sieve('(5|2)&4&8') >>> c.period() 40 * Changed in v9: state is taken from the object. r]r"rDzState must be exp or cmp)r&r,rIr. ValueError)rr|s rrz Sieve.periodsS(  ??b     E>?? " e^?? "78 8rc>|j|j|||Sr)rr&rs rrzSieve.__call__s||DKKA}==rc g}|}d}|dkr|} ||z} |dvr2|j|j|tt| | |} n1|j|j|tt| | d} || ddz}||z}|dz}t ||k\rn|dkr|d|} t | |k7r t d|dk(rt | t| d| d dzS|d vrt| t| d| d dzS| S) z Collect sieve segment points for the provided length and format. >>> a = sieve.Sieve('3@11') >>> a.collect(10, 100, 10, 'int') [102, 105, 108, 111, 114, 117, 120, 123, 126, 129] rrrrNr)z/desired length of sieve segment cannot be foundrtr]r)rr&r`rNrorrwrk) rrRzMinimumrrzStepfoundr. zExtendCountr r segmentPartialrs rcollectz Sieve.collects@*  U"Du9D 00!%dkk1.25t3D.E}"V"&dkk1.25t3D.Eu"NN1--EE A'!+L5zV##U"(GVn s8v  !RS S F " eCFCGaK&@A A / /$S%AB! *DE EJrcF| |j}|dk(r tj|j}n'|dk(r tj|j}nd}|j |}|D]0}|j ||j |j|}2|S)z style of None is use for users; adds | to single residuals style abs (absolute) does not add | tos single residual class r"rDr#)r&rar+r-rrcr)r)rr|rrrr~s rrzSieve.represents =KKE E>))DMM*C e^))DMM*CC}}U#C++c4<<#4#>#>u#EFC rc"|jSrrrs rrz Sieve.__str__s~~rr)r1zstr | list[str]rzlist[int] | None)r list[int])rN)NrNN)r|z*t.Literal['cmp'] | t.Literal['exp'] | Nonerrrr)rK) rRrrrrrrrrrrr)NN)(rrrrrr0r5rIrKrMrRrrrrrrr_rgrsrwrPrrErrrrrr3r4r6rr?rrrrrrrrrr r s%8 $> -   2"   6 6 .;z+\!& &"& 0& / V /$V/v/@/*9=  K5K  KZ9>> 9 99 9  9  9 9v* rr c>eZdZdZ d ddZdZddZy) PitchSieveat Quick utility generator of :class:`music21.pitch.Pitch` lists from :class:`music21.sieve.Sieve` objects. >>> ps = sieve.PitchSieve('6@0', 'c4', 'c8') >>> [str(p) for p in ps()] ['C4', 'F#4', 'C5', 'F#5', 'C6', 'F#6', 'C7', 'F#7', 'C8'] >>> a = sieve.PitchSieve('4@7') >>> [str(p) for p in a()] ['E-3', 'G3', 'B3', 'E-4', 'G4', 'B4'] Nc||_t|j|_|tj||_ntjd|_|tj||_ntjd|_|tj||_n$tj|j |_|t||_ y||_ y)Nc3c5) sieveStringr  sieveObjectr Pitch pitchLower pitchUpper pitchOriginrarbrpeld)rrrrrrs rrzPitchSieve.__init__(s '#((8(8"9  !#kk*5DO#kk$/DO  !#kk*5DO#kk$/DO  "${{;7D #}}T__=D  ?SzDHDHrc |jj}|jj}tt t |t |dz}|j j}|jdk(rI|j||}g}|D].}tj}||_|j|0|St|j||d} tt t| }|j||d} g}t t| D]:} | | dk(s tj}| | |_|j|<|S)ag Return a sieve segment as a list of :class:`music21.pitch.Pitch` objects, mapped to the range between pitchLower and pitchUpper. >>> a = sieve.PitchSieve('4@7&5@4') >>> a() [] >>> a = sieve.PitchSieve('13@3|13@6|13@9', 'c1', 'c10') >>> ', '.join([str(p) for p in a()]) 'E-1, F#1, A1, E2, G2, B-2, F3, G#3, B3, F#4, A4, C5, G5, B-5, C#6, G#6, B6, D7, A7, C8, E-8, B-8, C#9, E9, B9' >>> a = sieve.PitchSieve('3@0', 'c4', 'c5', 'c4', 0.5) >>> a.eld 0.5 The following is a microtonal pitch sieve; presently these are not displayed; true values are [0, 1.5, 3.0, 4.5, 6.0, 7.5, 9.0, 10.5, 12.0] >>> pitches = a() >>> ', '.join([str(p) for p in pitches]) 'C4, C#~4, E-4, E~4, F#4, G~4, A4, B`4, C5' True values: [0.5, 2.0, 3.5, 5.0, 6.5, 8.0, 9.5, 11.0] >>> a = sieve.PitchSieve('3@0', 'c4', 'c5', 'c#4', 0.5) >>> pitches = a() >>> ', '.join([str(p) for p in pitches]) 'C~4, D4, E`4, F4, F#~4, G#4, A~4, B4' r)F)rr)rpsrr`rNrrrrr rrcrro) rminPSmaxPSrrRsieveSegIntegerssieveSegpsNumr.rvbinSegrXs rrzPitchSieve.__call__Hs0D"""" s5z3uqy>2 3      88q=#//15 H)KKM"*&#488UEeLGU3w<()A%%aE2FH3v;'!9> A"1:ADOOA& ( rcJ|jj}|dkrtt|dz}nd}|jd|d}g}t |D]8\}}t j ||jz}|j|:|s td|S)ax Return a list of Interval objects that defines the complete structure of this :class:`music21.sieve.Sieve`. >>> a = sieve.PitchSieve('3@0') >>> a.getIntervalSequence() [] >>> a = sieve.PitchSieve('3@0|7@0') >>> a.sieveObject.segment() [0, 3, 6, 7, 9, 12, 14, 15, 18, 21, 24, 27, 28, 30, 33, 35, 36, 39, 42, 45, 48, 49, 51, 54, 56, 57, 60, 63, 66, 69, 70, 72, 75, 77, 78, 81, 84, 87, 90, 91, 93, 96, 98, 99] >>> a.sieveObject.period() 21 >>> a.getIntervalSequence() [, , , , , , , , ] This is the PitchSieve for a major scale: >>> b = sieve.PitchSieve('(-3@2 & 4) | (-3@1 & 4@1) | (3@2 & 4@2) | (-3 & 4@3)') >>> b.getIntervalSequence() [, , , , , , ] iɚ;r)Nrr)rzinterval segment has no values) rrr`rN enumerater Intervalrrcr)rr.r widthSegmentspostrXr intervalObjs rgetIntervalSequencezPitchSieve.getIntervalSequencesP    # # % y=U1q5\"AA((AU(C (*!-0HAu"++EDHH,<=K KK $1 %&FG G r)NNNr))r str | Nonerrrrrz int | float)rzlist[interval.Interval])rrrrrrrrrrrrsL )-(,)-"# %&'   @>@=rrcBeZdZdZdZdZdZdZdZdZ dZ d Z y ) Testc(|jddy)NT) assertEqualrs r testDummyzTest.testDummys t$rcfd}|D]}|t|dzz }|dt|dz }|dz }|S)Nroz, rr(rp)rro)rlistInoutr.s rpitchOutz Test.pitchOutsEA 3q6D= C!CHqL! s  rcttd}gd}|D]$\}}}}t||}t||}||z}&y)Nr2))r2r3r(r4)rr3r)r2)r4rr2r()r) rr}testArgsrrrrr~rXs rtestIntersectionzTest.testIntersectionsC QK?&NBBR AR AAA'rc fgd}|D](}t|}|dttd}*y)N)z-5 | 4 & 4sub3 & 6 | 4 & 4z2 or 4 and 4 & 6 or 4 & 4r2)r(rr3)r)r3r6r8r)r r`rN)rrargtestObjdummys rtestSieveParsezTest.testSieveParses2CCjGAtE"I/Ercrtddd}td}|j|jf}|}y)Nz-5 | 4 & 4sub3 & 6b3zf#4)rrr)runused_testObjrrs rtestSievePitchzTest.testSievePitchs9#$8$F12""G$6$66 rcfgd}|D](}t|}tt|}|}*y)N))r2r3 ) rr3rr$*)rr3r7)r(r2rr4r rLr6r8r9r:rr;r<)rr(rr4r5rr6rrrr8r9r:r) r)r(r2rr4r3r5rrrL)iirr(r))rr r)rrfrrsObjrs r testTimePointzTest.testTimePoints3C$S)CS?DFErcttd}d}t||}|jt |dd}t||}|jt |dd}t||}|jt |dd}t||}|jt |d d }t||}|jt |d y) NrKz"3@2 & 4@1 | 2@0 & 3@1 | 3@3 | -4@2z3@2&4@1|2@0&3@1|3@0|-4@2z5-(3@2 & -4@1 & -(12@3 | 12@8) | (-2@0 & 3@1 | (3@3)))z)-{3@2&-4@1&-{12@3|12@8}|{-2@0&3@1|{3@0}}}z[(8@0 | 8@1 | 8@7) & (5@1 | 5@3)] | [(8@0 | 8@1 | 8@2) & 5@0] | [8@3 & (5@0 | 5@1 | 5@2 | 5@3 | 5@4)] | [8@4 & (5@0 | 5@1 | 5@2 | 5@3 | 5@4)] | [(8@5 | 8@6) & (5@2 | 5@3 | 5@4)] | (8@1 & 5@2) | (8@6 & 5@1)z{{8@0|8@1|8@7}&{5@1|5@3}}|{{8@0|8@1|8@2}&5@0}|{8@3&{5@0|5@1|5@2|5@3|5@4}}|{8@4&{5@0|5@1|5@2|5@3|5@4}}|{{8@5|8@6}&{5@2|5@3|5@4}}|{8@1&5@2}|{8@6&5@1}z4(-3@2 & 4) | (-3@1 & 4@1) | (3@2 & 4@2) | (-3 & 4@3)z*{-3@2&4@0}|{-3@1&4@1}|{3@2&4@2}|{-3@0&4@3}zV(-(13@3 | 13@5 | 13@7 | 13@9) & 11@2) | (-(11@4 | 11@8) & 13@9) | (13@0 | 13@1 | 13@6)zB{-{13@3|13@5|13@7|13@9}&11@2}|{-{11@4|11@8}&13@9}|{13@0|13@1|13@6})r`rNr rr)rrr1r}s r testSievezTest.testSieves s 5 &!  Q!;<H &!  Q!LMR &!  QI J H &!  Q!MN) &!  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