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Module TI-Python: exploration module random + comparaisons

:32ti73: :32ti73e: :32ti73e2: :32ti76f: :32ti80: :32ti81: :32ti82: :32ti85: :32ti86: :32ti82s: :32ti82sf: :32ti82sfn: :32ti83: :32ti83p: :32ti83pb: :32ti83pr: :32ti83pfr: :32ti83pse: :32ti84p: :32ti84pse: :32ti84ppse: :32ti84pfr: :32ti84pcse: :32ti83pfrusb: :32ti82p: :32ti82a: :32ti84pce: :32ti83pce:
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Module TI-Python: exploration module random + comparaisons

Message non lude critor » 02 Déc 2018, 16:07

Cet article traitant du module
TI-Python
est préparé dans des conditions inconfortables : nous ne disposons pas du module, l'article est rédigé a posteriori et illustré à l’aide des photos de tests prises sur le stand de
Texas Instruments
aux journées APMEP 2018 puis congrès UdPPC 2018 avec le prototype.

Certaines photos ne correspondront pas exactement à ce qui a été rédigé, et les informations apportées peuvent être ou devenir inexactes. En vous priant de bien vouloir nous en excuser.

9931Dans un article précédent nous t'avons présenté le
TI-Python
, module externe permettant l'exécution de scripts
Python
sur ta
TI-83 Premium CE
. Nous t'avions annoncé la présence des modules
math
et
random
. Par la suite, nous avions exploré son module
builtins
puis son module
math
.

Lors de notre premier article nous n'avions pas pu t'illustrer ce qu'offrait le module
random
car ayant omis de le prendre en photo. Comme promis réparons aujourd'hui cela en explorant ce module à l'aide du script suivant :
Code: Tout sélectionner
#platforms: (0)TI-Nspire (1)NumWorks (2)Graph 90+E (3)Graph 75+E (4)TI-Python
plines=[29,12,  7, 9,11]
pcols =[53,99,509,32,32]
platform=0
try:
  import sys
  try:
    if sys.platform=='nspire': platform=0
    if sys.platform=='TI-Python Adapter': platform=4
  except: platform=3
except:
  try:
    import kandinsky
    platform=1
  except:
    platform=2

nlines=plines[platform]
ncols=pcols[platform]
curline=0

def mprint(*ls):
  global curline
  st=""
  for s in ls:
    if not(isinstance(s,str)):
      s=str(s)
    st=st+s
  stlines=1+int(len(st)/ncols)
  if curline+stlines>=nlines:
    input("Input to continue:")
    curline=0
  print(st)
  curline+=stlines

def sstr(obj):
  try:
    s=obj.__name__
  except:
    s=str(obj)
    a=s.find("'")
    b=s.rfind("'")
    if a>=0 and b!=a:
      s=s[a+1:b]
  return s

def explmod(pitm,pitmsl=[],reset=True):
  global curline
  if(reset):
    curline=0
    pitmsl=[sstr(pitm)]
  hd="."*(len(pitmsl)-1)
  spath=".".join(pitmsl)
  c=0
  for itms in sorted(dir(pitm)):
    c=c+1
    try:
      itm=eval(spath+"."+itms)
      mprint(hd+itms+"="+str(itm))
      if spath.rfind(itms)<0:
        pitmsl2=pitmsl.copy()
        pitmsl2.append(itms)
        c=c+explmod(itm,pitmsl2,False)
    except:
      mprint(hd+itms)
  if c>0:
    mprint(hd+"Total: "+str(c)+" item(s)")
  return c


Le script nous liste alors pas moins de 30 entrées retranscrites ci-dessous :
TI-Python a écrit:>>> from explmod import *
>>> import random
>>> explmod(random)
__name__='random'
.count()=<bound_method>
.endswith()=<bound_method>
.find()=<bound_method>
9998.format()=<bound_method>
.index()=<bound_method>
.isalpha()=<bound_method>
.isdigit()=<bound_method>
.islower()=<bound_method>
.isspace()=<bound_method>
.isupper()=<bound_method>
.join()=<bound_method>
.lower()=<bound_method>
.lstrip()=<bound_method>
9999.replace()=<bound_method>
.rfind()=<bound_method>
.rindex()=<bound_method>
.rsplit()=<bound_method>
.rstrip()=<bound_method>
.split()=<bound_method>
.startswith()=<bound_method>
.strip()=<bound_method>
.upper()=<bound_method>
9952Total: 22 item(s)
choice()=<function>
getrandbits()=<function>
randint()=<function>
random()=<function>
randrange()=<function>
seed()=<function>
uniform()=<function>
Total: 30 item(s)
30
>>>


Voici ci-dessous la comparaison de ce que renvoient les différents modèles disposant d'une implémentation
Python
en lançant ce même script :

Casio Graph 90+E
Casio Graph 35/75+E
NumWorks

TI-Python
pour
TI-83 Premium CE
__name__='random'
choice()
getrandbits()
randint()
random()
randrange()
seed()
uniform()
Total: 0
Total: 30


Et oui, égalité pour tout-le-monde sauf la
TI-Nspire
qui n'intègre pas le module
random
pourtant essentiel au lycée. :mj:
D'où le classement suivant :
  1. NumWorks
    ,
    Casio Graph 35+E/75+E
    ,
    Casio Graph 90+E
    et module
    TI-Python
    pour
    TI-83 Premium CE
    avec
    30
    entrées
  2. TI-Nspire
    avec
    0
    entrées
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Re: Module TI-Python: exploration module random + comparaiso

Message non lude Adriweb » 02 Déc 2018, 16:51

Notons cela dit que Vogtinator prévoit de mettre à jour le MicroPython Nspire pour utiliser la dernière version - on peut donc supposer que tout ce qui manque (et plus) sera dispo :)
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Re: Module TI-Python: exploration module random + comparaiso

Message non lude parisse » 02 Déc 2018, 16:52

Je renouvelle ma demande que KhiCAS pour Casio Graph 90+e soit mentionne dans les comparaisons Python. C'est d'autant plus legitime ici que les modules random des constructeurs sont des versions allegees du module random de Python (micro-random). Le module random de Python comporte ainsi des commandes comme shuffle, sample, ou des generateurs selon des lois, dont la loi normale ou exponentielle, non disponibles dans micro-random.
Comme shuffle, sample fonctionnent a l'identique dans KhiCAS, et comme KhiCAS propose ses propres generateurs selon diverses lois de proba (par exemple randnorm ou randexp), le classement devrait etre:
1. KhiCAS pour Casio Graph 90+e
suivi des autres decales de une position.

(En plus, je ne vois pas bien le rapport entre islower et l'aleatoire...)
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Re: Module TI-Python: exploration module random + comparaiso

Message non lude critor » 02 Déc 2018, 22:56

Je ne suis pas contre le fait d'inclure KhiCAS et la HP Prime, si les fonctions sont bien présentes sous le même nom avec le même comportement puisqu'il s'agit ici de Python.

Mais voilà, à part tester les fonctions une par une, je ne sais pas comment faire.

Mine de rien, cette série d'articles me sert à construire les tests et outils qui pourront resservir dans un éventuel QCC 2019 qui évaluerait mieux le Python que le QCC 2018. Et effectivement il me faudra bien trouver une solution d'ici-là pour la HP Prime, lui mettre zéro ne serait pas juste.
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Re: Module TI-Python: exploration module random + comparaiso

Message non lude parisse » 03 Déc 2018, 17:35

Il n'y a effectivement pas d'autres methodes que de tester puisque le code source n'a rien a voir. En principe, seule la compatibilite peut poser problemes, le noyau de calcul fonctionne.

Je rajoute dans KhiCAS les synonymes en loi prefixe+variate a la Python pour les commandes Xcas en rand+loi suffixe: expovariate=randexp, normalvariate=randnorm.

Certaines generateurs aleatoires de Xcas n'ont pas d'equivalents dans random mais sont interessants pour le lycee, par exemple randbinomial, randgeometric et randpoisson, d'autres plus tard (randchisquare, randfisher, randmultinomial, randstudentd).

Il y a aussi les commandes randmatrix et randvector (et randpoly) pour generer une matrice ou un vecteur (ou un polynome unitaire) selon une loi, par exemple L=randvector(100,binomial,10,.4) genere une liste de 100 entiers distribues selon la loi binomiale de parametres n=10 et p=0.4, on peut ensuite passer la liste a histogram(L) pour la representer. Ce qui permet de faire facilement de la simulation.
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Re: Module TI-Python: exploration module random + comparaiso

Message non lude Adriweb » 05 Déc 2018, 05:57

N'y aurait-il pas un moyen d'avoir une sorte d'instrospection sur les commandes definies/disponibles ? Ainsi il serait possible de programmatiquement recuperer la liste des fonction, et critor pourrait adapter son script pour avoir ceci de maniere automatique pour chaque version
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Re: Module TI-Python: exploration module random + comparaiso

Message non lude parisse » 05 Déc 2018, 10:05

Pas besoin de script pour ca, il suffit de parcourir la liste des environ 700 commandes reconnues dans le fichier static_lexer.h (voir listing en fin de message), il y a quelques commandes en plus qui sont codees en dur dans le source du lexer (fichier input_lexer.ll, le source est dans l'archive https://www-fourier.ujf-grenoble.fr/~parisse/casio/khicas.tgz).

C'est une liste globale, il n'y a pas de modules dans KhiCAS. Mais la commande d'import d'un module Python donne lieu a des assignations de variables pour compatibilite:
* pour matplotlib np:=numpy:;xlim(a,b):=gl_x=a..b:;ylim(a,b):=gl_y=a..b:;scatter:=scatterplot:;bar:=bar_plot:;
* pour numpy mat:=matrix:;arange:=range:;resize:=redim:;shape:=dim:;conjugate:=conj:;full:=matrix:;eye:=identity:;ones(n,c):=matrix(n,c,1):; astype:=convert:;float64:=float:;asarray:=array:;astype:=convert:;reshape(m,n,c):=matrix(n,c,flatten(m));
* pour cmaths: phase:=arg:;j:=i:;J:=i:;rect(r,theta):=r*exp(i*theta):;
* pour maths: log2(x):=logb(x,2):;gamma:=Gamma:;fabs:=abs:;function modf(x) local y; y:=floor(x); return x-y,y; ffunction:;radians(x):=x/180*pi:;degrees(x):=x/pi*180"

Pour random, comme il y a peu d'entrees (7 pour microrandom, un peu plus pour random), on peut aussi ouvrir le catalogue alphabetique avec shift-catalog et regarder si l'entree de la commande existe.
Code: Tout sélectionner
// -*- mode:text -*-
#ifdef RELEASE
{"Kronecker",0,0,9,13},
{"Heaviside",0,0,9,13},
#endif
{"a2q",0,0,9,13},
{"abcuv",0,0,9,13},
{"about",0,0,9,13},
{"abs",0,0,9,13},
{"acos",0,0,9,13},
{"acos2asin",0,0,9,13},
{"acos2atan",0,0,9,13},
{"acosh",0,0,9,13},
{"acot",0,0,9,13},
{"acsc",0,0,9,13},
{"add",0| 1,0,9,13},
{"add_autosimplify",0,0,9,13},
{"additionally",0| 1,0,9,13},
{"adjoint_matrix",0,0,9,13},
{"alg",0,0,9,13},
{"algsubs",0,0,9,13},
{"algvar",0,0,9,13},
{"alog10",0,0,9,13},
{"and",0| 1,0,33,13},
{"andsto",0 | 1,0,9,13},
{"ans",0,0,9,13},
{"append",0,0,9,13},
{"apply",0,0,9,13},
{"approx",0,0,9,13},
{"arclen",0,0,9,13},
{"arg",0,0,9,13},
{"array_sto",0| 1,0,9,13},
{"asc",0,0,9,13},
{"asec",0,0,9,13},
{"asin",0,0,9,13},
{"asin2acos",0,0,9,13},
{"asin2atan",0,0,9,13},
{"asinh",0,0,9,13},
{"assert",0,0,72,13},
{"assume",0| 1,0,9,13},
{"atan",0,0,9,13},
{"atan2",0,0,9,13},
{"atan2acos",0,0,9,13},
{"atan2asin",0,0,9,13},
{"atanh",0,0,9,13},
{"atrig2ln",0,0,9,13},
{"augment",0,0,9,13},
{"autosimplify",0,0,9,13},
{"avance",0,0,89,13},
{"baisse_crayon",0,0,89,13},
{"barplot",0,0,9,13},
{"basis",0,0,9,13},
{"bernoulli",0,0,9,13},
{"betad",0,0,9,13},
{"betad_cdf",0,0,9,13},
{"betad_icdf",0,0,9,13},
{"bin",0,0,9,13},
{"binomial",0,0,9,13},
{"binomial_cdf",0,0,9,13},
{"binomial_icdf",0,0,9,13},
{"bitand",0,0,9,13},
{"bitnot",0,0,9,13},
{"bitor",0,0,9,13},
{"bitxor",0,0,9,13},
{"blockmatrix",0,0,9,13},
{"border",0,0,9,13},
{"bounded_function",0,0,9,13},
{"break",0,0,63,13},
{"breakpoint",0| 1,0,9,13},
{"cache_tortue",0,0,89,13},
{"camembert",0,0,9,13},
{"canonical_form",0,0,9,13},
{"cap",0,0,89,13},
{"cas_setup",0,0,9,13},
{"cat",0,0,9,13},
{"cauchyd",0,0,9,13},
{"cauchyd_cdf",0,0,9,13},
{"cauchyd_icdf",0,0,9,13},
{"ceil",0,0,9,13},
{"ceiling",0,0,9,13},
{"cercle",0| 1,0,9,13},
{"cfactor",0,0,9,13},
{"cfsolve",0,0,9,13},
{"changebase",0,0,9,13},
{"char",0,0,9,13},
{"charpoly",0,0,9,13},
{"chinrem",0,0,9,13},
{"chisquared",0,0,9,13},
{"chisquared_cdf",0,0,9,13},
{"chisquared_icdf",0,0,9,13},
{"choice",0,0,9,13},
{"cholesky",0,0,9,13},
{"chr",0,0,9,13},
{"chrem",0,0,9,13},
{"circle",0| 1,0,9,13},
{"clear",0,0,9,13},
{"clearscreen",0,0,9,13},
{"coeff",0,0,9,13},
{"coeffs",0,0,9,13},
{"col",0,0,9,13},
{"coldim",0,0,9,13},
{"collect",0,0,9,13},
{"colnorm",0,0,9,13},
{"color",0,0,9,13},
{"comDenom",0,0,9,13},
{"comb",0,0,9,13},
{"combine",0,0,9,13},
{"comment",0,0,9,13},
{"companion",0,0,9,13},
{"compare",0,0,9,13},
{"complex",0,0,9,13},
{"concat",0,0,9,13},
{"cond",0,0,9,13},
{"conj",0,0,9,13},
{"cont",0| 1,0,9,13},
{"contains",0,0,9,13},
{"content",0,0,9,13},
{"convert",0,0,9,13},
{"coordinates",0,0,9,13},
{"copy",0,0,9,13},
{"copysign",0,0,9,13},
{"correlation",0,0,9,13},
{"cos",0,0,9,13},
{"cos2sintan",0,0,9,13},
{"cosh",0,0,9,13},
{"count",0,0,9,13},
{"count_eq",0,0,9,13},
{"count_inf",0,0,9,13},
{"count_sup",0,0,9,13},
{"covariance",0,0,9,13},
{"cpartfrac",0,0,9,13},
{"crayon",0,0,89,13},
{"cross",0,0,9,13},
{"crossproduct",0,0,9,13},
{"csolve",0| 1,0,9,13},
{"curl",0| 1,0,9,13},
{"curve",0,0,9,13},
{"cyclotomic",0,0,9,13},
{"cylinder",0,0,9,13},
{"czeros",0,0,9,13},
{"debug",0| 1,0,9,13},
{"debug_infolevel",0,0,5,13},
{"decrement",0| 1,0,9,13},
{"degree",0,0,9,13},
{"del",0,0,89,13},
{"delcols",0,0,9,13},
{"delrows",0,0,9,13},
{"denom",0,0,9,13},
{"deriver",0,0,9,13},
{"desolve",0| 1,0,9,13},
{"dessine_tortue",0,0,89,13},
{"det",0,0,9,13},
{"dfc",0,0,9,13},
{"dfc2f",0,0,9,13},
{"diag",0,0,9,13},
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{"dim",0,0,9,13},
{"display",0,0,9,13},
{"disque",0,0,89,13},
{"disque_centre",0,0,89,13},
{"div",0,0,22,13},
{"divcrement",0| 1,0,9,13},
{"divergence",0| 1,0,9,13},
{"divis",0,0,9,13},
{"divisors",0,0,9,13},
{"divmod",0,0,9,13},
{"divpc",0,0,9,13},
{"domain",0,0,9,13},
{"dot",0,0,9,13},
{"draw_arc",0,0,9,13},
{"draw_circle",0,0,9,13},
{"draw_line",0,0,9,13},
{"draw_pixel",0,0,9,13},
{"draw_polygon",0,0,9,13},
{"draw_rectangle",0,0,9,13},
{"draw_string",0,0,9,13},
{"droite",0,0,9,13},
{"dtype",0,0,9,13},
{"e2r",0,0,9,13},
{"ecris",0,0,89,13},
{"efface",0,0,89,13},
{"egcd",0,0,9,13},
{"egv",0,0,9,13},
{"egvl",0,0,9,13},
{"eigenvals",0,0,9,13},
{"eigenvalues",0,0,9,13},
{"eigenvectors",0,0,9,13},
{"eigenvects",0,0,9,13},
{"eliminate",0,0,9,13},
{"epsilon2zero",0| 1,0,9,13},
{"equal2diff",0,0,9,13},
{"equal2list",0,0,9,13},
{"equation",0,0,9,13},
{"erf",0,0,9,13},
{"erfc",0,0,9,13},
{"erfs",0,0,9,13},
{"euler",0,0,9,13},
{"euler_mac_laurin",0,0,9,13},
{"eval",0| 1,0,9,13},
{"eval_level",0,0,9,13},
{"evalb",0| 1,0,9,13},
{"evalc",0,0,9,13},
{"evalf",0,0,9,13},
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{"even",0,0,9,13},
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{"exp2pow",0,0,9,13},
{"exp2trig",0,0,9,13},
{"expexpand",0,0,9,13},
{"expln2trig",0,0,9,13},
{"expm1",0,0,9,13},
{"exponential_regression",0,0,9,13},
{"exponential_regression_plot",0,0,9,13},
{"exponentiald",0,0,9,13},
{"exponentiald_cdf",0,0,9,13},
{"exponentiald_icdf",0,0,9,13},
{"expovariate",0,0,9,13},
{"expr",0,0,9,13},
{"extend",0,0,9,13},
{"f2nd",0,0,9,13},
{"fMax",0,0,9,13},
{"fMin",0,0,9,13},
{"factor",0,0,9,13},
{"factor_xn",0,0,9,13},
{"factorial",0,0,9,13},
{"factors",0,0,9,13},
{"fclose",0| 1,0,9,13},
{"fcoeff",0,0,9,13},
{"fft",0,0,9,13},
{"fft_mult_size",0,0,9,13},
{"filter",0,0,9,13},
{"find",0,0,9,13},
{"findhelp",0| 1,0,9,13},
{"fisher",0,0,9,13},
{"fisher_cdf",0,0,9,13},
{"fisher_icdf",0,0,9,13},
{"fisherd",0,0,9,13},
{"fisherd_cdf",0,0,9,13},
{"fisherd_icdf",0,0,9,13},
{"flatten",0,0,9,13},
{"flatten1",0,0,9,13},
{"float",0,0,9,13},
{"float2rational",0,0,9,13},
{"floor",0,0,9,13},
{"fmod",0,0,9,13},
{"fopen",0,0,9,13},
{"format",0,0,9,13},
{"fourier_an",0,0,9,13},
{"fourier_bn",0,0,9,13},
{"fourier_cn",0,0,9,13},
{"fprint",0,0,9,13},
{"frac",0,0,9,13},
{"fracmod",0,0,9,13},
{"frobenius_norm",0,0,9,13},
{"froot",0,0,9,13},
{"fsolve",0| 1,0,9,13},
{"function_diff",0,0,9,13},
{"fxnd",0,0,9,13},
{"galoisconj",0,0,9,13},
{"gammad",0,0,9,13},
{"gammad_cdf",0,0,9,13},
{"gammad_icdf",0,0,9,13},
{"gauss",0,0,9,13},
{"gaussquad",0,0,9,13},
{"gbasis",0,0,9,13},
{"gcd",0,0,9,13},
{"genpoly",0,0,9,13},
{"geometric",0,0,9,13},
{"geometric_cdf",0,0,9,13},
{"geometric_icdf",0,0,9,13},
{"getDenom",0,0,9,13},
{"getKey",0,0,9,13},
{"getNum",0,0,9,13},
{"goto",0,0,89,13},
{"grad",0| 1,0,9,13},
{"gramschmidt",0,0,9,13},
{"greduce",0,0,9,13},
{"hadamard",0,0,9,13},
{"halftan",0,0,9,13},
{"halftan_hyp2exp",0,0,9,13},
{"halt",0| 1,0,9,13},
{"has",0,0,9,13},
{"heapify",0,0,9,13},
{"heappop",0,0,9,13},
{"heappush",0,0,9,13},
{"help",0,0,9,13},
{"hermite",0,0,9,13},
{"hessenberg",0,0,9,13},
{"hessian",0| 1,0,9,13},
{"hex",0,0,9,13},
{"hilbert",0,0,9,13},
{"histogram",0,0,9,13},
{"hold",0| 1,0,9,13},
{"horner",0,0,9,13},
{"hyp2exp",0,0,9,13},
{"iabcuv",0,0,9,13},
{"ibasis",0,0,9,13},
{"ibpdv",0,0,9,13},
{"ibpu",0,0,9,13},
{"ichinrem",0,0,9,13},
{"ichrem",0,0,9,13},
{"icontent",0,0,9,13},
{"id",0,0,9,13},
{"idivis",0,0,9,13},
{"idn",0,0,9,13},
{"iegcd",0,0,9,13},
{"ifactor",0,0,9,13},
{"ifactors",0,0,9,13},
{"ifft",0,0,9,13},
{"igamma_exp",0,0,9,13},
{"igcd",0,0,9,13},
{"ilaplace",0,0,9,13},
{"im",0,0,9,13},
{"imag",0,0,9,13},
{"image",0,0,9,13},
{"in_ideal",0,0,9,13},
{"increment",0| 1,0,9,13},
{"indets",0,0,9,13},
{"index",0,0,9,13},
{"inferieur_strict_sort",0,0,9,13},
{"input",0| 1,0,9,13},
{"insert",0,0,9,13},
{"int",0,0,9,13},
{"integer_format",0,0,9,13},
{"integrate",0| 1,0,9,13},
{"interp",0,0,9,13},
{"inv",0,0,9,13},
{"inverse",0,0,9,13},
{"invlaplace",0,0,9,13},
#ifdef RELEASE
{"invztrans",0,0,9,13},
#endif
{"iquo",0,0,9,13},
{"iquorem",0,0,9,13},
{"iquosto",0 | 1,0,9,13},
{"iratrecon",0,0,9,13},
{"irem",0,0,9,13},
{"iremsto",0 | 1,0,9,13},
{"is_prime",0,0,9,13},
{"is_pseudoprime",0,0,9,13},
{"isfinite",0,0,9,13},
{"isinf",0,0,9,13},
{"isnan",0,0,9,13},
{"isprime",0,0,9,13},
{"ithprime",0,0,9,13},
{"jacobi_symbol",0,0,9,13},
{"join",0,0,9,13},
{"jordan",0,0,9,13},
{"ker",0,0,9,13},
{"kernel",0,0,9,13},
{"kill",0,0,9,13},
{"l1norm",0,0,9,13},
{"l2norm",0,0,9,13},
{"label",0,0,72,13},
{"lagrange",0,0,9,13},
{"laguerre",0,0,9,13},
{"laplace",0,0,9,13},
{"laplacian",0| 1,0,9,13},
{"lcm",0,0,9,13},
{"lcoeff",0,0,9,13},
{"ldegree",0,0,9,13},
{"left",0,0,9,13},
{"legend",0| 1,0,9,13},
{"legendre",0,0,9,13},
{"legendre_symbol",0,0,9,13},
{"len",0,0,9,13},
{"length",0,0,9,13},
{"leve_crayon",0,0,89,13},
{"lgamma",0,0,9,13},
{"lgcd",0,0,9,13},
{"lhs",0,0,9,13},
{"limit",0| 1,0,9,13},
{"limite",0,0,9,13},
{"lin",0,0,9,13},
{"line",0| 1,0,9,13},
{"linear_regression",0,0,9,13},
{"linear_regression_plot",0,0,9,13},
{"linetan",0,0,9,13},
{"linfnorm",0,0,9,13},
{"linsolve",0| 1,0,9,13},
{"linspace",0,0,9,13},
{"list2mat",0,0,9,13},
{"lll",0,0,9,13},
{"ln",0,0,9,13},
{"lname",0,0,9,13},
{"lncollect",0,0,9,13},
{"lnexpand",0,0,9,13},
{"log10",0,0,9,13},
{"logarithmic_regression",0,0,9,13},
{"logarithmic_regression_plot",0,0,9,13},
{"logb",0,0,9,13},
{"lower",0,0,9,13},
{"lu",0,0,9,13},
{"lvar",0,0,9,13},
{"makelist",0,0,9,13},
{"makemat",0,0,9,13},
{"makemod",0,0,9,13},
{"makesuite",0,0,9,13},
{"makevector",0,0,9,13},
{"map",0,0,9,13},
{"mat2list",0,0,9,13},
{"matpow",0,0,9,13},
{"matrix",0,0,9,13},
{"matrix_norm",0,0,9,13},
{"max",0,0,9,13},
{"max_algext",0,0,9,13},
{"maxnorm",0,0,9,13},
{"mean",0,0,9,13},
{"member",0| 1,0,9,13},
{"mid",0,0,9,13},
{"min",0,0,9,13},
{"mods",0,0,9,13},
{"montre_tortue",0,0,89,13},
{"mult_c_conjugate",0| 1,0,9,13},
{"mult_conjugate",0,0,9,13},
{"multcrement",0| 1,0,9,13},
{"multinomial",0,0,9,13},
{"multiply",0,0,9,13},
{"ncols",0,0,9,13},
{"negbinomial",0,0,9,13},
{"negbinomial_cdf",0,0,9,13},
{"negbinomial_icdf",0,0,9,13},
{"newton",0,0,9,13},
{"nextprime",0,0,9,13},
{"nop",0,0,9,13},
{"nops",0,0,9,13},
{"norm",0,0,9,13},
{"normal",0,0,9,13},
{"normald",0,0,9,13},
{"normald_cdf",0,0,9,13},
{"normald_icdf",0,0,9,13},
{"normalize",0,0,9,13},
{"normalvariate",0,0,9,13},
{"nprimes",0,0,9,13},
{"nrows",0,0,9,13},
{"numer",0,0,9,13},
{"oct",0,0,9,13},
{"odd",0,0,9,13},
{"odesolve",0,0,9,13},
{"op",0,0,9,13},
{"or",0| 1,0,33,13},
{"ord",0,0,9,13},
{"order_size",0,0,9,13},
{"orsto",0 | 1,0,9,13},
{"ou",0| 1,0,33,13},
{"part",0,0,9,13},
{"partfrac",0,0,9,13},
{"pas_de_cote",0,0,89,13},
{"pcar",0,0,9,13},
{"pcoeff",0,0,9,13},
{"periodic",0,0,9,13},
{"peval",0,0,9,13},
{"piecewise",0| 1,0,9,13},
{"plot",0| 1,0,9,13},
#ifdef RELEASE
{"plotarea",0,0,9,13},
#endif
{"plotcontour",0,0,9,13},
{"plotfield",0,0,9,13},
{"plotfunc",0| 1,0,9,13},
{"plotlist",0,0,9,13},
{"plotode",0,0,9,13},
{"plotparam",0| 1,0,9,13},
{"plotpolar",0| 1,0,9,13},
{"plotseq",0,0,9,13},
{"pmin",0,0,9,13},
{"point",0,0,9,13},
{"poisson",0,0,9,13},
{"poisson_cdf",0,0,9,13},
{"poisson_icdf",0,0,9,13},
{"polar2rectangular",0,0,9,13},
{"polar_complex",0,0,9,13},
{"poly2symb",0,0,9,13},
{"polygamma",0,0,9,13},
{"polygon",0,0,9,13},
{"polygone_rempli",0,0,89,13},
{"polygonplot",0,0,9,13},
{"polygonscatterplot",0,0,9,13},
{"polynomial_regression",0,0,9,13},
{"polynomial_regression_plot",0,0,9,13},
{"pop",0,0,9,13},
{"position",0,0,89,13},
{"potential",0| 1,0,9,13},
{"pow2exp",0,0,9,13},
{"power_regression",0,0,9,13},
{"power_regression_plot",0,0,9,13},
{"powermod",0,0,9,13},
{"powexpand",0,0,9,13},
{"powmod",0,0,9,13},
{"prepend",0,0,9,13},
{"preval",0,0,9,13},
{"prevprime",0,0,9,13},
{"primpart",0,0,9,13},
{"print",0| 1,0,9,13},
{"printf",0,0,9,13},
{"printpow",0,0,9,13},
{"product",0| 1,0,9,13},
{"prog_eval_level",0,0,9,13},
{"proot",0,0,9,13},
{"propfrac",0,0,9,13},
{"ptayl",0,0,9,13},
{"purge",0,0,9,13},
{"python",0,0,9,13},
{"python_compat",0,0,9,13},
{"python_list",0,0,9,13},
{"q2a",0,0,9,13},
{"qr",0,0,9,13},
{"quo",0,0,9,13},
{"quorem",0,0,9,13},
{"quote",0| 1,0,9,13},
{"r2e",0,0,9,13},
{"rand",0,0,9,13},
{"randbinomial",0,0,9,13},
{"randchisquare",0,0,9,13},
{"randchisquared",0,0,9,13},
{"randexp",0,0,9,13},
{"randfisherd",0,0,9,13},
{"randgeometric",0,0,9,13},
{"randint",0,0,9,13},
{"randmatrix",0,0,9,13},
{"randmultinomial",0,0,9,13},
{"randnormald",0,0,9,13},
{"random",0,0,9,13},
{"randpoisson",0,0,9,13},
{"randpoly",0,0,9,13},
{"randrange",0,0,9,13},
{"randstudentd",0,0,9,13},
{"randvector",0,0,9,13},
{"range",0,0,9,13},
{"rank",0,0,9,13},
{"ranm",0,0,9,13},
{"ranv",0,0,9,13},
{"rassembler_trigo",0,0,9,13},
{"rat_jordan",0,0,9,13},
{"ratnormal",0,0,9,13},
{"re",0,0,9,13},
{"read",0,0,72,13},
{"real",0,0,9,13},
{"realproot",0,0,9,13},
{"rectangle_plein",0,0,89,13},
{"rectangular2polar",0,0,9,13},
{"rectangular2spherical",0,0,9,13},
{"recule",0,0,89,13},
{"regroup",0,0,9,13},
{"rem",0,0,9,13},
{"remove",0,0,9,13},
{"reorder",0,0,9,13},
{"repete",0,0,89,13},
#ifdef RELEASE
{"residue",0,0,9,13},
#endif
{"resultant",0,0,9,13},
{"reverse",0,0,9,13},
{"reverse_rsolve",0,0,9,13},
{"revert",0,0,9,13},
{"revlist",0,0,9,13},
{"rgb",0,0,9,13},
{"rhs",0,0,9,13},
{"right",0,0,9,13},
{"rm_a_z",0,0,9,13},
{"rm_all_vars",0,0,9,13},
{"rmbreakpoint",0| 1,0,9,13},
{"rmwatch",0| 1,0,9,13},
{"rond",0,0,89,13},
{"rootof",0,0,9,13},
{"roots",0,0,9,13},
{"rotate",0,0,9,13},
{"rotatesto",0| 1,0,9,13},
{"round",0,0,9,13},
{"row",0,0,9,13},
{"rowdim",0,0,9,13},
{"rownorm",0,0,9,13},
{"rpn",0,0,9,13},
{"rref",0,0,9,13},
{"rsolve",0| 1,0,9,13},
{"sample",0,0,9,13},
{"saute",0,0,89,13},
{"scatterplot",0,0,9,13},
{"sec",0,0,9,13},
{"segment",0,0,9,13},
{"select",0,0,9,13},
{"semi_augment",0,0,9,13},
{"seq",0| 1,0,9,13},
{"series",0,0,9,13},
{"set_pixel",0,0,9,13},
{"shift",0,0,9,13},
{"shift_phase",0,0,9,13},
{"shiftsto",0| 1,0,9,13},
{"shuffle",0,0,9,13},
{"sign",0,0,9,13},
{"signe",0,0,89,13},
{"simp2",0,0,9,13},
{"simplify",0,0,9,13},
{"sin",0,0,9,13},
{"sin2costan",0,0,9,13},
{"sincos",0,0,9,13},
{"sinh",0,0,9,13},
{"size",0,0,9,13},
{"sizes",0,0,9,13},
{"smod",0,0,9,13},
{"snedecord",0,0,9,13},
{"snedecord_cdf",0,0,9,13},
{"snedecord_icdf",0,0,9,13},
{"solve",0| 1,0,9,13},
{"sommet",0,0,9,13},
{"sort",0,0,9,13},
{"sorta",0,0,9,13},
{"sortd",0,0,9,13},
{"sorted",0,0,9,13},
{"sphere",0,0,9,13},
{"spherical2rectangular",0,0,9,13},
{"split",0,0,9,13},
{"sq",0,0,9,13},
{"sqrfree",0,0,9,13},
{"sqrt",0,0,9,13},
{"srand",0,0,72,13},
{"sst",0| 1,0,9,13},
{"sst_in",0| 1,0,9,13},
{"stddev",0,0,9,13},
{"sto",0,0,9,13},
{"str",0,0,9,13},
{"string",0,0,9,13},
{"strip",0,0,9,13},
{"studentd",0,0,9,13},
{"studentd_cdf",0,0,9,13},
{"studentd_icdf",0,0,9,13},
{"sturm",0,0,9,13},
{"sturmab",0,0,9,13},
{"sturmseq",0,0,9,13},
{"subst",0,0,9,13},
{"substituer",0,0,9,13},
{"subtype",0,0,9,13},
{"sum",0| 1,0,9,13},
{"suppress",0,0,9,13},
{"surd",0,0,9,13},
{"svd",0,0,9,13},
{"sylvester",0,0,9,13},
{"symb2poly",0,0,9,13},
{"table",0,0,9,13},
{"tabvar",0,0,9,13},
{"tan",0,0,9,13},
{"tan2cossin2",0,0,9,13},
{"tan2sincos",0,0,9,13},
{"tan2sincos2",0,0,9,13},
{"tanh",0,0,9,13},
{"taux_accroissement",0,0,9,13},
{"taylor",0,0,9,13},
{"tchebyshev1",0,0,9,13},
{"tchebyshev2",0,0,9,13},
{"tcoeff",0,0,9,13},
{"tcollect",0,0,9,13},
{"tcollectsin",0,0,9,13},
{"texpand",0,0,9,13},
{"throw",0,0,72,13},
{"time",0| 1,0,9,13},
{"tlin",0,0,9,13},
{"total_degree",0,0,9,13},
{"tourne_droite",0,0,89,13},
{"tourne_gauche",0,0,89,13},
{"trace",0,0,9,13},
{"tran",0,0,9,13},
{"triangle_plein",0,0,89,13},
{"trig2exp",0,0,9,13},
{"trigcos",0,0,9,13},
{"trigexpand",0,0,9,13},
{"trigsimplify",0,0,9,13},
{"trigsin",0,0,9,13},
{"trigtan",0,0,9,13},
{"trn",0,0,9,13},
{"trunc",0,0,9,13},
{"truncate",0,0,9,13},
{"tsimplify",0,0,9,13},
{"type",0,0,9,13},
{"unapply",0| 1,0,9,13},
{"uniform",0,0,9,13},
{"uniform_cdf",0,0,9,13},
{"uniform_icdf",0,0,9,13},
{"uniformd",0,0,9,13},
{"uniformd_cdf",0,0,9,13},
{"uniformd_icdf",0,0,9,13},
{"unquote",0,0,9,13},
{"upper",0,0,9,13},
{"valuation",0,0,9,13},
{"vandermonde",0,0,9,13},
{"variance",0,0,9,13},
{"vector",0,0,9,13},
{"vers",0,0,89,13},
{"version",0,0,9,13},
{"vpotential",0| 1,0,9,13},
{"warn_equal_in_prog",0,0,9,13},
{"watch",0| 1,0,9,13},
{"weibulld",0,0,9,13},
{"weibulld_cdf",0,0,9,13},
{"weibulld_icdf",0,0,9,13},
{"when",0| 1,0,9,13},
{"with_sqrt",0,0,9,13},
{"write",0| 1,0,9,13},
{"wz_certificate",0,0,9,13},
{"xcas",0,0,9,13},
{"xcas_mode",0,0,9,13},
{"xorsto",0| 1,0,9,13},
{"zeros",0| 1,0,9,13},
{"zip",0,0,9,13},
#ifdef RELEASE
{"ztrans",0,0,9,13},
#endif

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