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remove TABs, fix some doctests

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2009年01月01日-SienaTutorials
- Worksheet09-CombinatoricsIteratorsGenerators.rst
2012年10月29日-CIMPA-Bobo
- dynamique.rst
2021年10月18日-CIMPA-Bobo
- combinatoire-des-mots.rst
- dynamique.rst

4 files changed

+34

-182

lines changed

`‎2009年01月01日-SienaTutorials/Worksheet09-CombinatoricsIteratorsGenerators.rst`

Lines changed: 11 additions & 156 deletions

Original file line number	Diff line number	Diff line change
`@@ -15,15 +15,15 @@ Documentation/Resources`
`15`	`15`
`16`	`16`	`::`
`17`	`17`
`18`		`- sage: sage.combinat.`
	`18`	`+ sage: sage.combinat. # not tested`
`19`	`19`
`20`	`20`	`::`
`21`	`21`
`22`		`- sage: sage.combinat.sf.`
	`22`	`+ sage: sage.combinat.sf. # not tested`
`23`	`23`
`24`	`24`	`::`
`25`	`25`
`26`		`- sage: sage.combinat.words.`
	`26`	`+ sage: sage.combinat.words. # not tested`
`27`	`27`
`28`	`28`	`- There is a chapter on Combinatorics in the Reference Manual.`
`29`	`29`
@@ -44,33 +44,17 @@ The Python command ``iter`` returns an iterator from an object (the object its
`44`	`44`
`45`	`45`	`sage: it = iter([1,2,3])`
`46`	`46`	`sage: it`
`47`		`- <listiterator object at 0x35a3950>`
`48`		`-`
`49`		`-.. end of output`
`50`		`-`
`51`		`-::`
	`47`	`+ <list_iterator object at ...>`
`52`	`48`
`53`	`49`	`sage: next(it)`
`54`	`50`	`1`
`55`	`51`
`56`		`-.. end of output`
`57`		`-`
`58`		`-::`
`59`		`-`
`60`	`52`	`sage: next(it)`
`61`	`53`	`2`
`62`	`54`
`63`		`-.. end of output`
`64`		`-`
`65`		`-::`
`66`		`-`
`67`	`55`	`sage: next(it)`
`68`	`56`	`3`
`69`	`57`
`70`		`-.. end of output`
`71`		`-`
`72`		`-::`
`73`		`-`
`74`	`58`	`sage: next(it)`
`75`	`59`	`Traceback (most recent call last):`
`76`	`60`	`...`
@@ -89,61 +73,29 @@ A generator is a function that is used to define an iterator. Instead of ``
`89`	`73`	`....: yield b`
`90`	`74`	`....: a, b = b, a+b`
`91`	`75`
`92`		`-`
`93`		`-.. end of output`
`94`		`-`
`95`		`-::`
`96`		`-`
`97`	`76`	`sage: f = fibonacci_iterator()`
`98`	`77`
`99`		`-`
`100`		`-.. end of output`
`101`		`-`
`102`		`-::`
`103`		`-`
`104`	`78`	`sage: next(f)`
`105`	`79`	`1`
`106`	`80`
`107`		`-.. end of output`
`108`		`-`
`109`		`-::`
`110`		`-`
`111`	`81`	`sage: next(f)`
`112`	`82`	`1`
`113`	`83`
`114`		`-.. end of output`
`115`		`-`
`116`		`-::`
`117`		`-`
`118`	`84`	`sage: next(f)`
`119`	`85`	`2`
`120`	`86`
`121`		`-.. end of output`
`122`		`-`
`123`		`-::`
`124`		`-`
`125`	`87`	`sage: next(f)`
`126`	`88`	`3`
`127`	`89`
`128`		`-.. end of output`
`129`		`-`
`130`		`-::`
`131`		`-`
`132`	`90`	`sage: next(f)`
`133`	`91`	`5`
`134`	`92`
`135`		`-.. end of output`
`136`		`-`
`137`		`-::`
`138`		`-`
`139`	`93`	`sage: next(f)`
`140`	`94`	`8`
`141`	`95`
`142`		`-.. end of output`
`143`		`-`
`144`	`96`
`145`	`97`	`Project Euler Problem 2 <http://projecteuler.net/index.php?section=problems&id=2>`_
`146`		`-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`
	`98`	`+~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~`
`147`	`99`
`148`	`100`	`Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:`
`149`	`101`
`@@ -158,22 +110,12 @@ Find the sum of all the even\-valued terms in the sequence which do not exceed f`
`158`	`110`
`159`	`111`	`sage: result = 0`
`160`	`112`
`161`		`-`
`162`		`-.. end of output`
`163`		`-`
`164`		`-::`
`165`		`-`
`166`	`113`	`sage: for f in fibonacci_iterator():`
`167`	`114`	`....: if f > 4000000:`
`168`	`115`	`....: break`
`169`	`116`	`....: if is_even(f):`
`170`	`117`	`....: result += f`
`171`	`118`
`172`		`-`
`173`		`-.. end of output`
`174`		`-`
`175`		`-::`
`176`		`-`
`177`	`119`	`sage: result`
`178`	`120`	`4613732`
`179`	`121`
`@@ -193,17 +135,9 @@ There are many objects in Sage that model sets of combinatorial objects.`
`193`	`135`	`sage: P`
`194`	`136`	`Standard permutations of 3`
`195`	`137`
`196`		`-.. end of output`
`197`		`-`
`198`		`-::`
`199`		`-`
`200`	`138`	`sage: P.cardinality()`
`201`	`139`	`6`
`202`	`140`
`203`		`-.. end of output`
`204`		`-`
`205`		`-::`
`206`		`-`
`207`	`141`	`sage: P.list()`
`208`	`142`	`[[1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], [3, 2, 1]]`
`209`	`143`
`@@ -216,21 +150,13 @@ There are many objects in Sage that model sets of combinatorial objects.`
`216`	`150`
`217`	`151`	`.. end of output`
`218`	`152`
`219`		`-`
`220`	`153`	`::`
`221`	`154`
`222`		`- sage: time P = Permutations(7, avoiding=[2,1,4,3])`
`223`		`- sage: P`
`224`		`- Time: CPU 0.00 s, Wall: 0.00 s`
	`155`	`+ sage: P = Permutations(7, avoiding=[2,1,4,3]); P`
`225`	`156`	`Standard permutations of 7 avoiding [[2, 1, 4, 3]]`
`226`	`157`
`227`		`-.. end of output`
`228`		`-`
`229`		`-::`
`230`		`-`
`231`		`- sage: time P.cardinality()`
	`158`	`+ sage: P.cardinality()`
`232`	`159`	`2761`
`233`		`- Time: CPU 4.10 s, Wall: 4.20 s`
`234`	`160`
`235`	`161`	`.. end of output`
`236`	`162`
`@@ -309,21 +235,13 @@ There are many objects in Sage that model sets of combinatorial objects.`
`309`	`235`
`310`	`236`	`::`
`311`	`237`
`312`		`- sage: W = Words("ab")`
	`238`	`+ sage: W = Words("ab", finite=True)`
`313`	`239`	`sage: W`
`314`		`- Words over Ordered Alphabet ['a', 'b']`
`315`		`-`
`316`		`-.. end of output`
`317`		`-`
`318`		`-::`
	`240`	`+ Finite words over {'a', 'b'}`
`319`	`241`
`320`	`242`	`sage: W.cardinality()`
`321`	`243`	`+Infinity`
`322`	`244`
`323`		`-.. end of output`
`324`		`-`
`325`		`-::`
`326`		`-`
`327`	`245`	`sage: it = iter(W)`
`328`	`246`	`sage: for a in range(16):`
`329`	`247`	`....: print(next(it))`
`@@ -352,18 +270,7 @@ There are many objects in Sage that model sets of combinatorial objects.`
`352`	`270`
`353`	`271`	`sage: P = posets()`
`354`	`272`	`sage: P`
`355`		`- Posets`
`356`		`-`
`357`		`-.. end of output`
`358`		`-`
`359`		`-::`
`360`		`-`
`361`		`- sage: P.cardinality()`
`362`		`- +Infinity`
`363`		`-`
`364`		`-.. end of output`
`365`		`-`
`366`		`-::`
	`273`	`+ Category of posets`
`367`	`274`
`368`	`275`	`sage: it = iter(P)`
`369`	`276`	`sage: for a in range(10):`
`@@ -395,10 +302,6 @@ Sage supports several ways of creating new combinatorial classes from objects.`
`395`	`302`	`sage: C`
`396`	`303`	`Combinations of [1, 2, 3] of length 2`
`397`	`304`
`398`		`-.. end of output`
`399`		`-`
`400`		`-::`
`401`		`-`
`402`	`305`	`sage: C.list()`
`403`	`306`	`[[1, 2], [1, 3], [2, 3]]`
`404`	`307`
`@@ -411,10 +314,6 @@ Sage supports several ways of creating new combinatorial classes from objects.`
`411`	`314`	`sage: S`
`412`	`315`	`Subsets of {1, 2, 3} of size 2`
`413`	`316`
`414`		`-.. end of output`
`415`		`-`
`416`		`-::`
`417`		`-`
`418`	`317`	`sage: S.list()`
`419`	`318`	`[{1, 2}, {1, 3}, {2, 3}]`
`420`	`319`
`@@ -427,16 +326,8 @@ Sage supports several ways of creating new combinatorial classes from objects.`
`427`	`326`	`sage: S`
`428`	`327`	`Set partitions of ['a', 'b', 'c']`
`429`	`328`
`430`		`-.. end of output`
`431`		`-`
`432`		`-::`
`433`		`-`
`434`	`329`	`sage: S.list()`
`435`		`- [{{'a', 'c', 'b'}}, {{'c', 'b'}, {'a'}}, {{'c'}, {'a', 'b'}}, {{'a', 'c'}, {'b'}}, {{'c'}, {'b'}, {'a'}}]`
`436`		`-`
`437`		`-.. end of output`
`438`		`-`
`439`		`-::`
	`330`	`+ [{{'a', 'b', 'c'}}, ...]`
`440`	`331`
`441`	`332`	`sage: S.cardinality()`
`442`	`333`	`5`
`@@ -449,8 +340,6 @@ Example: Vexillary involutions`
`449`	`340`
`450`	`341`	`A vexillary involution is a permutation that:`
`451`	`342`
`452`		`-`
`453`		`-`
`454`	`343`	`#. avoids the pattern 2143;`
`455`	`344`
`456`	`345`	#. is an involution (that is, :math:`p = p^{-1}`).
`@@ -464,26 +353,13 @@ We can create the set of vexillary involutions of the set {1,2,3,4} in Sage by`
`464`	`353`	`sage: def is_involution(p):`
`465`	`354`	`....: return p == p.inverse()`
`466`	`355`
`467`		`-`
`468`		`-.. end of output`
`469`		`-`
`470`		`-::`
`471`		`-`
`472`	`356`	`sage: P = Permutations(4, avoiding=[2,1,4,3]).filter(is_involution)`
`473`	`357`	`sage: P`
`474`	`358`	`Filtered sublass of Standard permutations of 4 avoiding [[2, 1, 4, 3]]`
`475`	`359`
`476`		`-.. end of output`
`477`		`-`
`478`		`-::`
`479`		`-`
`480`	`360`	`sage: P.cardinality()`
`481`	`361`	`9`
`482`	`362`
`483`		`-.. end of output`
`484`		`-`
`485`		`-::`
`486`		`-`
`487`	`363`	`sage: P.list()`
`488`	`364`	`[[1, 2, 3, 4], [1, 2, 4, 3], [1, 3, 2, 4], [1, 4, 3, 2], [3, 4, 1, 2], [2, 1, 3, 4], [4, 2, 3, 1], [3, 2, 1, 4], [4, 3, 2, 1]]`
`489`	`365`
`@@ -497,17 +373,9 @@ We can create the set of vexillary involutions of the set {1,2,3,4} in Sage by`
`497`	`373`	`....: return P.cardinality()`
`498`	`374`
`499`	`375`
`500`		`-.. end of output`
`501`		`-`
`502`		`-::`
`503`		`-`
`504`	`376`	`sage: SL = sloane_find([number_of_vexillary_involutions(n) for n in range(1,7)])`
`505`	`377`	`Searching Sloane's online database...`
`506`	`378`
`507`		`-.. end of output`
`508`		`-`
`509`		`-::`
`510`		`-`
`511`	`379`	`sage: SL[0]`
`512`	`380`	`[1006, 'Motzkin numbers: number of ways of drawing any number of nonintersecting chords joining n (labeled) points on a circle.', [1, 1, 2, 4, 9, 21, 51, 127, 323, 835, 2188, 5798, 15511, 41835, 113634, 310572, 853467, 2356779, 6536382, 18199284, 50852019, 142547559, 400763223, 1129760415, 3192727797, 9043402501, 25669818476, 73007772802, 208023278209, 593742784829]]`
`513`	`381`
`@@ -604,26 +472,13 @@ At the very minimum, you should implement the following methods:`
`604`	`472`	`....: p = Permutation(p)`
`605`	`473`	`....: return len(p) == self._n and p.avoids([2,1,4,3]) and p == p.inverse()`
`606`	`474`
`607`		`-`
`608`		`-.. end of output`
`609`		`-`
`610`		`-::`
`611`		`-`
`612`	`475`	`sage: V = VexillaryInvolutions(4)`
`613`	`476`	`sage: V`
`614`	`477`	`Vexillary involutions of 4`
`615`	`478`
`616`		`-.. end of output`
`617`		`-`
`618`		`-::`
`619`		`-`
`620`	`479`	`sage: [2,1,3,4] in V`
`621`	`480`	`True`
`622`	`481`
`623`		`-.. end of output`
`624`		`-`
`625`		`-::`
`626`		`-`
`627`	`482`	`sage: [2,1,4,3] in V`
`628`	`483`	`False`
`629`	`484`

`‎2012年10月29日-CIMPA-Bobo/dynamique.rst`

Lines changed: 6 additions & 7 deletions

Original file line number	Diff line number	Diff line change
`@@ -31,7 +31,7 @@ Cas particuliers:`
`31`	`31`	- topologique: `X` compact, `T`: continu
`32`	`32`	- mesurable: `X` équipé d'une mesure `\mu` préservée par `T`:
`33`	`33`
`34`		-`\mu (T^{-1}(A)) = \mu(A)` pour tout `A` mesurable
	`34`	+`\mu (T^{-1}(A)) = \mu(A)` pour tout `A` mesurable
`35`	`35`
`36`	`36`	`Questions typiques:`
`37`	`37`
@@ -213,7 +213,7 @@ et `T_Y`.
`213`	`213`	`inférieur.`
`214`	`214`
`215`	`215`	- Induire l'application sur un cône d'angle `\pi/4` centré en - 1.
`216`		-- Recommencer avec `\pi/7`.
	`216`	+- Recommencer avec `\pi/7`.
`217`	`217`
`218`	`218`
`219`	`219`	`.. TOPIC:: Exercice`
@@ -224,11 +224,10 @@ et `T_Y`.
`224`	`224`	`.. math::`
`225`	`225`
`226`	`226`	`T(x,y)=`
`227`		`- \begin{cases}`
`228`		`- (1+a-y,x) & (x,y)\in A\\`
`229`		`- (x-1,1-y) & (x,y)\in B`
`230`		`- \end{cases}`
`231`		`-`
	`227`	`+ \begin{cases}`
	`228`	`+ (1+a-y,x) & (x,y)\in A\\`
	`229`	`+ (x-1,1-y) & (x,y)\in B`
	`230`	`+ \end{cases}`
`232`	`231`
`233`	`232`	#. Pour `a` rationnel, décrire la partition à l'étape `n`.
`234`	`233`

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`‎2009年01月01日-SienaTutorials/Worksheet09-CombinatoricsIteratorsGenerators.rst`

`‎2012年10月29日-CIMPA-Bobo/dynamique.rst`

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