######################################################################
## AMSrip.txt: Save this file as  AMSrip.txt  to use it,             #
# stay in the                                                        #
## same directory, get into Maple (by typing: maple <Enter> )        #
## and then type:  read `AMSrip.txt` <Enter>                         #
## Then follow the instructions given there                          #
##                                                                   #
## Written by Doron Zeilberger, Rutgers University ,                 #
##  DoronZeil at gmail dot com                                       # 
######################################################################


print(`First Written: Sept. 2022: tested for Maple 2020 `):
print(`Version  : Sept. 2022:  `):
print():
print(`This is AMSrip.txt, A Maple package`):
print(`accompanying the  article: `):
print(`The Average AMS fellow who died before Aug. 2022 lived 83.36 years, published 98.53 papers, and was cited 2473.23 times`):
print(`by Livia A. Stone and Doron Zeilberger, published in the Personal Journal of Shalosh B. Ekhad and Doron Zeilberger`):
print():
print(`The most current version is available on WWW at:`):
print(` http://sites.math.rutgers.edu/~zeilberg/tokhniot/AMSrip .`):
print(`Please report all bugs to: DoronZeil at gmail dot com .`):
print():
print(`For general help, and a list of the MAIN functions,`):
print(` type "ezra();". For specific help type "ezra(procedure_name);" `):
print(`For a list of the supporting functions type: ezra1();`):
print():
 



ezra1:=proc()
if args=NULL then

print(`The SUPPORTING procedures are`):
print(` AgeGF, CitGF, CorMat, JointGF, PubGF, Sort1, Stat `):

else
ezra(args):

fi:


end:

ezra:=proc()
if args=NULL then

print(` AMSrip.txt: A Maple package for  studying the longevity of deceased AMS Fellows, who died by Aug. 2022`):

print(`The MAIN procedures are`):
print(` DS, Paper, PaperA, PaperC, PaperP, StatA, StatC, StatP `):

elif nargs=1 and args[1]=DS then
print(`DS(): The list of length 146 containing all the date in the form [LastName, FirstName,YearOfBirth,YearOfDeath]. Try: `):
print(`DS(); `):

elif nargs=1 and args[1]=AgeGF then
print(`AgeGF(S,t): Given a data set S finds the Age generating function.`):
print(`Try: AgeGF(DS(),t);`):


elif nargs=1 and args[1]=CitGF then
print(`CitGF(S,t): Given a data set S finds the Number of Citations  generating function.`):
print(`Try: CitGF(DS(),t);`):

elif nargs=1 and args[1]=CorMat then
print(`CorMat(F,var): Given a genearting function in a list of variables var, finds the correlation matrix. Try:`):
print(`CorMat((1+2*x)*(1+y)*(1+z),[x,y,z]);`):

elif nargs=1 and args[1]=JointGF then
print(`JointGF(S,a,p,c): Given a data set S finds the multi-variate generating function according to a^age*p^(number of publication)*c^(Number of citations)`):
print(`Try: JointGF(DS(),a,p,c);`):

elif nargs=1 and args[1]=Paper then
print(`Paper(S), publishes a paper about the  ages at death, number of publications, and number of citations of dead AMS fellows. Try:`):
print(`Paper(DS()):`):

elif nargs=1 and args[1]=PaperA then
print(`PaperA(S), publishes a paper about the ages alone, with data set S. Try:`):
print(`PaperA(DS()):`):


elif nargs=1 and args[1]=PaperC then
print(`PaperC(S), publishes a paper about the  number of citations, with data set S. Try:`):
print(`PaperC(DS()):`):


elif nargs=1 and args[1]=PaperP then
print(`PaperP(S), publishes a paper about the  number of publications with data set S. Try:`):
print(`PaperP(DS()):`):

elif nargs=1 and args[1]=Sort1 then
print(`Sort1(L,k): Given a list of lists L, sorts it according to the k-th component. Try:`):
print(`Sort1([[1,4],[2,7],[3,1]]);`):

elif nargs=1 and args[1]=Stat then
print(`Stat(f,t,K): Given a generating function for a r.v. finds the statistical information: ave, s.d, and scaled moments about the mean up to K. Try:`):
print(`Stat((1+t)^10000,t,4);`):

elif nargs=1 and args[1]=StatA then
print(`StatA(S,K): Given a data set finds the average, s.d., and all the scaled moments up to the K-th only about the age. Try:`):
print(`StatA(DS(),4);`):


elif nargs=1 and args[1]=StatC then
print(`StatC(S,K): Given a data set finds the average, s.d., and all the scaled moments up to the K-th only about the number of citations. Try:`):
print(`StatC(DS(),4);`):

elif nargs=1 and args[1]=StatP then
print(`StatP(S,K): Given a data set finds the average, s.d., and all the scaled moments up to the K-th only about the number of publications. Try:`):
print(`StatP(DS(),4);`):


elif nargs=1 and args[1]=PubGF then
print(`PubGF(S,t): Given a data set S finds the Number of Publication generating function.`):
print(`Try: PubGF(DS(),t);`):

else
 print(`There is no such thing as`, args):

fi:


end:


#[Last,First,Birth,Death, Pub, Cite]

#[Zeilberger, Doron, 1950,0,229,2987]

DS:=proc():
[
[Abhyankar, Shreeram,1930,2012,190,2111],
[Adler, Roy, 1931,2016,47,1231],
[Apostol, TomM, 1923,2016,87,2886],
[Appel, KennethI, 1932, 2013,31,873],
[Armentrout, Steve, 1930, 2020,37,145],
[Askey, Richard, 1933, 2019,163,4802],
[Atiyah, SirMichael, 1929, 2019,269, 12281],
[Babbitt, Donald, 1936, 2020, 31,161],
[Bade, William, 1924, 2012,35,426],
[Baker, Alan, 1939, 2018,65,1596],
[Barrett, LidaK, 1927,2021,5,2],
[Baumslag, Gilbert, 1933, 2014,166,1937],
[Benkart, Georgia, 1949, 2022,133,1692],
[Berlekamp, Elwyn, 1940, 2019,70,1550],
[Bishop, RichardL, 1931, 2019,49,1173],
[Blattner, RobertJ, 1931, 2015,23,336],
[Boardman, JMichael, 1938, 2021,26,781],
[Borwein, JonathanMichael, 1951, 2016,453, 9810],
[Bousfield, Aldridge, 1941, 2020,48,2563],
[Browder, FelixE, 1927, 2016,200,4743],
[Brown, EdgarH, 1926, 2021,58,586],
[Burkholder, DonaldL, 1927, 2013,57,2165],
[Bushnell,  ColinJ, 1947, 2021,77,1624],
[Cantor, David, 1935, 2012,45,451],
[Chandrasekharan, Komaravolu, 1920, 2017,75,778],
[Cheney, ElliottWardJr, 1929, 2016,105,1642],
[Chernoff, Paul, 1942, 2017,42,658],
[Chernov, Nikolai, 1956, 2014,111,1859],
[Cochran, TimD, 1955, 2014,57,1265],
[Cohen, FrederickR, 1946, 2022,136,1781],
[Cohn, Harvey, 1923, 2014,118,664],
[Comfort, WWistar, 1933, 2016,153,1746],
[Conner,  PierreEJr, 1932, 2018,71,1118],
[Copeland, ArthurHerbert, 1926, 2019, 19,41],
[Craig, Walter, 1953, 2019,84,2084],
[CroninScanlon, Jane, 1922, 2018,66,206],
[Demyanov, VladimirF, 1938, 2014,183,1309],
[doCarmo, ManfredoP, 1928, 2018,110,3685],
[Douglas, JimJr, 1927, 2016,180,5937],
[Douglas, RonaldG, 1938, 2018,168,3732],
[Dudley, RichardM, 1938, 2020,138,2776],
[Duren, Peter, 1935, 2020,126,4490],
[Dynkin, EugeneB, 1924, 2014,222,2851],
[Earle, CliffordJohnJr, 1935, 2017,84,1507],
[Edwards, HaroldM, 1936, 2020,46,542],
[Effros, EdwardG, 1935, 2019,82,3484],
[Ellis, Robert, 1926, 2013,41,978],
[Fadell, Edward, 1926, 2018,59,1065],
[Feferman, Solomon, 1928, 2016,29,1146],
[Fife, Paul, 1930, 2014,118,3509],
[Fraser, DonaldAS, 1925, 2020,182,400],
[Getoor, RonaldK, 1929, 2017,106,1850],
[Gitler, Samuel, 1933, 2014,67,560],
[Golomb, Solomon, 1932, 2016,146,1497],
[Goss, David, 1952, 2017,46,882],
[Graham, Ronald, 1935, 2020,363,7500],
[Gross, KennethI, 1938, 2017,34,181],
[Gruber, PeterM, 1941, 2017,107,1867],
[Grunbaum, Branko, 1929, 2018,271,3814],
[Hajnal, András, 1931, 2016,164,2116],
[Halberstam, Heini, 1926, 2014,81,1086],
[Heins, MauriceH, 1915, 2015,93,401],
[Hempel, John, 1935, 2022,31,1211],
[Hörmander, Lars, 1931, 2012,159,15121],
[Howard, Louis, 1929, 2015,42,275],
[Igusa, Junichi, 1924, 2013,89,1610],
[Jones, VaughanFR, 1952, 2020,117,3924],
[Jonsson, Bjarni, 1920, 2016,90,1632],
[Kadison, RichardV, 1925, 2018,105,3633],
[Kahane, Jean-Pierre, 1926, 2017,288,2639],
[Kalman, Rudolf, 1930, 2016,66,1826],
[Katok, Anatole, 1944, 2018,122,6030],
[Keller, JosephB, 1923, 2016,321,3655],
[Kesten, Harry, 1931, 2016,193,4772],
[Kister, JamesM, 1930, 2018,19,142],
[Kostant, Bertram, 1928, 2017,114,4367],
[Kuku, AderemiOluyomi, 1941, 2022,39,121],
[Kunze, Ray, 1928, 2014,46,452],
[Lacampagne, CaroleB, 1933, 2021,11,12],
[Lanford, OscarEIII, 1940, 2013,50,734],
#[Levy, Paul, 1941, 2016,],
[Liggett, ThomasM, 1944, 2020,106,3918],
[Lorch, Lee, 1915, 2014,86,272],
[Luxemburg, Wilhelmus, 1929, 2018,111,1107],
[Mahowald, Mark, 1931, 2013,164,1281],
[Majda, AndrewJ, 1949, 2021,323,11987],
[Mardešic, Sibe, 1927, 2016,159,1130],
[Mattuck, ArthurP, 1930, 2021,17,152],
[McLaughlin, JoyceR, 1939, 2017,61,914],
[Michael, ErnestA, 1925, 2013,102,2845],
[Mitchell, StephenA, 1951,  2017, 39,366],
[Miura, RobertM, 1938, 2018,49,1370],
[Moore, JohnC, 1923, 2016,37,1254],
[Morawetz, CathleenSynge, 1923, 2017,82,1295],
[Namioka, Isaac, 1928, 2019,57,1183],
[Nash, JohnFJr, 1928, 2015,29,3185],
[Nelson, Edward, 1932, 2014,64,2035],
[Neveu, JacquesJeanPierre, 1932, 2016,74,1172],
[Nevins, Thomas, 1972, 2020,24,173],
[Nijenhuis, Albert, 1926, 2015,61,1054],
[Nirenberg, Louis, 1925, 2020,175,17621],
[Noll, Walter, 1925, 2017,59,1601],
[Odell, Edward, 1947, 2013,92,1337],
[Osborn, Howard, 1928, 2019,36,52],
[Phelps, RobertR, 1926, 2013,71,2519],
[Pless, Vera, 1931, 2020,101,2248],
[Pollack, Richard, 1935, 2018,81,1658],
[Rankin, SamuelMIII, 1945, 2020,25,145],
[Roe, John, 1959, 2018,48,2116],
[Rosenblatt, Murray, 1926, 2019,178,2128],
[Rubin, Herman, 1926, 2018,99,498],
[Rudin, MaryEllen, 1924, 2013,87,791],
[Sally,  PaulJJr, 1933, 2013,37,281],
[Schafer, RichardD, 1918, 2014,46,712],
[Seeley, RobertT, 1932, 2016,53,1510],
[Sell, GeorgeR, 1937, 2015,132,4068],
[Seshadri, ConjeeveramSrirangachari, 1932, 2020,69,1726],
[Shapiro, VictorL, 1924, 2013,99,239],
[Shapley, LloydStowell, 1923, 2016,70,4107],
[Shepp, Lawrence, 1936, 2013,175,2137],
[Sibner, LesleyM, 1934, 2013,29,157],
[Sims, CharlesC, 1937, 2017,33,503],
[Singer, IsadoreM, 1924, 2021,96,5215],
[Sion, Maurice, 1927, 2018,39,525],
[Smoller, JoelA, 1935, 2017,181,4096],
[Steen, LynnArthur, 1941, 2015,18,341],
[Stein, EliasM, 1931, 2018,237,27492],
[Stone, CharlesJ, 1936, 2019,79,2604],
[Strichartz, Robert, 1943, 2021,189,4633],
[Tate, JohnT, 1925, 2019,95,5626],
[Thomas, Robin, 1962, 2020,122,2898],
[Tierney, Myles, 1937, 2017,23,428],
[Traub, JosephF, 1932, 2015,78,1509],
[Varadarajan, VeeravalliS, 1937, 2019,149,2336],
[Vasquez, AlphonseT, 1938, 2021,27,133],
[Veech, WilliamA, 1938, 2016,66,1891],
[Walling, LynneH, 1958, 2021,40,101],
[Walter, JohnH, 1927, 2021,27,214],
[Weinberger, Hans, 1928, 2017,115,6664],
[Weiss, Guido, 1928, 2021,114,8722],
[Wente, Henry, 1936, 2020,34,526],
[Widom, Harold, 1932, 2021,167,4066],
[Wilkerson,ClarenceWJr, 1944, 2019,47,749],
[Willems, JanC, 1939, 2013,186,2677],
[Zelevinsky, AndreiV, 1953, 2013,113,8482],
[Zucker, StevenM, 1949, 2019,55,756]
]:
end:



#Sort1(L,k): Given a list of lists L, sorts it according to the k-th component. Try:
#Sort1([[1,4],[2,7],[3,1]]);
Sort1:=proc(L,k) local L1,gu,gu1,T,i,L2,L3:
L1:=sort([seq(L[i][k],i=1..nops(L))]):
gu:=convert(L1,set):

for gu1 in gu do
 T[gu1]:={}:
od:

for i from 1 to nops(L) do
 T[L[i][k]]:= T[L[i][k]] union {i}:
od:

gu:=sort(convert(gu,list)):

L2:=[seq(op(T[gu[i]]),i=1..nops(gu))]:

L3:=[seq(L[L2[i]],i=1..nops(L2))]:
[seq(L3[nops(L3)+1-i],i=1..nops(L3))]:


end:

#AgeGF(S,t): Given a data set S finds the Age generating function.
#Try: AgeGF(DS(),t);
AgeGF:=proc(S,t) local i:
add(t^(S[i][4]-S[i][3]),i=1..nops(S)):
end:


#CitGF(S,t): Given a data set S finds the Number of Publications  generating function.
#Try: PubGF(DS(),t);
CitGF:=proc(S,t) local i:
add(t^(S[i][6]),i=1..nops(S)):
end:


#PubGF(S,t): Given a data set S finds the Number of Publications  generating function.
#Try: PubGF(DS(),t);
PubGF:=proc(S,t) local i:
add(t^(S[i][5]),i=1..nops(S)):
end:



#StatA(S,K): Given a data set finds the average, s.d., and all the scaled moments up to the K-th of the age. Try:
#StatA(DS(),4);
StatA:=proc(S,K) local t: Stat(AgeGF(S,t),t,K): end:



#StatC(S,K): Given a data set finds the average, s.d., and all the scaled moments up to the K-th of the number of citations. Try:
#StatC(DS(),4);
StatC:=proc(S,K) local t: Stat(CitGF(S,t),t,K): end:

#StatP(S,K): Given a data set finds the average, s.d., and all the scaled moments up to the K-th of the number of publications. Try:
#StatP(DS(),4);
StatP:=proc(S,K) local t: Stat(PubGF(S,t),t,K): end:



#Stat(F,t,K): Given a generating function F of t, for a r.v. finds the statistical information. Try:
#Stat((1_t)^10000,4);
Stat:=proc(F,t,K) local gu,mu,sd,k,f:
f:=evalf(F/subs(t=1,F)):
mu:=subs(t=1,diff(f,t)):
gu:=[mu]:
f:=f/t^mu:
f:=t*diff(t*diff(f,t),t):
sd:=sqrt(subs(t=1,f)):
gu:=[op(gu),sd]:
for k from 3 to K do
 f:=t*diff(f,t):
gu:=[op(gu),subs(t=1,f)/sd^k]:
od:

gu:


end:


#PaperA(S), publishes a paper about the ages alone with data set S. Try:
#PaperA(DS()):
PaperA:=proc(S) local mu,k,f,t,i,lu,i1,T,j:
print(`Statistical Analysis of Longevity of Fellows of the American Mathematical Sociecty who Died Before Aug. 2022`):
print(``):
print(`By Shalosh B. Ekhad, Livia A. Stone, and Doron Zeilberger `):
print(``):



print(nops(S), `AMS Fellows died between its inauguration in 2013 and Aug. 2022.`):
print(``):
print(`In this paper we statistically analyze their age at death. `):
print(``):
mu:=StatA(S,10):
print(``):
print(`The average age at death of an AMS Fellow who died before Aug. 2022 is `, mu[1]):
print(``):
print(`The standard deviation is`, mu[2] ):
print(``):
print(`The skewness is`, mu[3] ):
print(``):
print(`The kurtosis is`, mu[4] ):
print(``):
for k from 5 to 10 do
print(`The scaled`, k, `moment is`, mu[k]):
od:

f:=sort(AgeGF(S,t)):
print(``):
print(`The age generating function, with the variable t is`):
print(``):
print(f):
print(``):
print(``):
print(`and in Maple notation `):
print(``):
lprint(f):
print(``):

for i from 0 to degree(f,t) while add(coeff(f,t,i1),i1=0..i)<subs(t=1,f)/2 do od:
print(``):
print(`The median age is`, i+0.5):
print(``):
#print(add(coeff(f,t,i1),i1=0..i)):

for i from ldegree(f,t) to degree(f,t) do
T[i]:={}:
od:

for j from 1 to nops(S) do
lu:=S[j][4]-S[j][3]:
T[lu]:=T[lu] union {j}:
od:

[seq([i,T[i]],i=ldegree(f,t)..degree(f,t))]:

print(`The youngest age was`, ldegree(f,t)):
print(``):
print(`The oldest age was`, degree(f,t)):
print(``):
print(`Here are all the dead fellows listed, in decreasing order, by their age at death, followed by their number of publications and number of citations (in MathSciNet)  `):
print(``):
for i from degree(f,t) by -1 to ldegree(f,t) do
if T[i]<>{} then
print(`There were`, nops(T[i]), `fellows who died at the age of`, i):
print(``):
for i1 in T[i] do
 print(cat(S[i1][2], ` `, S[i1][1],` `,   `( `,S[i1][3], "-", S[i1][4], `)`, ` `, S[i1][5], `;`, S[i1][6]  )):
od:
print(``):
fi:
od:


end:




#PaperP(S), publishes a paper about the publications alone with data set S. Try:
#PaperP(DS()):
PaperP:=proc(S) local mu,t,f,i,i1,k,L:
print(`Statistical Analysis of Number of Publications of Fellows of the American Mathematical Sociecty who Died Before Aug. 2022`):
print(``):
print(`By Shalosh B. Ekhad, Livia A. Stone, and Doron Zeilberger `):
print(``):



print(nops(S), `AMS Fellows died between its inauguration in 2013 and Aug. 2022.`):
print(``):
print(`In this paper we statistically analyze their number of publications listed at MathSciNet, viewed Sept. 2022 `):
print(``):
mu:=StatP(S,10):
print(``):
print(`The average number of publications is `, mu[1]):
print(``):
print(`The standard deviation is`, mu[2] ):
print(``):
print(`The skewness is`, mu[3] ):
print(``):
print(`The kurtosis is`, mu[4] ):
print(``):
for k from 5 to 10 do
print(`The scaled`, k, `moment is`, mu[k]):
od:

f:=sort(PubGF(S,t)):
print(``):
print(`The Number of Publication generating function, with the variable t is`):
print(``):
print(f):
print(``):
print(``):
print(`and in Maple notation `):
print(``):
lprint(f):
print(``):

for i from 0 to degree(f,t) while add(coeff(f,t,i1),i1=0..i)<subs(t=1,f)/2 do od:
print(``):
print(`The median number of publications is`, i):
print(``):

L:=Sort1(DS(),5):

print(`Here is the list of all`, nops(L), `dead AMS fellows in decreasing order of their number of publications. It lists the year of birth, year of death, number of publications, and number of citations `):
print(``):
for i1 from 1 to nops(L) do
 print(cat(i1, `. `,` `,L[i1][2], ` `, L[i1][1],` `,   `( `,L[i1][3], "-", L[i1][4], `)`, ` `, L[i1][5], `;`, L[i1][6]  )):
od:

end:





#PaperC(S), publishes a paper about the number of citationt alone with data set S. Try:
#PaperC(DS()):
PaperC:=proc(S) local mu,t,f,i,i1,k,L:
print(`Statistical Analysis of The  Number of Citations of  Fellows of the American Mathematical Sociecty who Died Before Aug. 2022`):
print(``):
print(`By Shalosh B. Ekhad, Livia A. Stone, and Doron Zeilberger `):
print(``):



print(nops(S), `AMS Fellows died between its inauguration in 2013 and Aug. 2022.`):
print(``):
print(`In this paper we statistically analyze their number of citations listed at MathSciNet, viewed Sept. 2022 `):
print(``):
mu:=StatC(S,10):
print(``):
print(`The average number of citations is `, mu[1]):
print(``):
print(`The standard deviation is`, mu[2] ):
print(``):
print(`The skewness is`, mu[3] ):
print(``):
print(`The kurtosis is`, mu[4] ):
print(``):
for k from 5 to 10 do
print(`The scaled`, k, `moment is`, mu[k]):
od:

f:=sort(CitGF(S,t)):
print(``):
print(`The Number of Citations generating function, with the variable t is`):
print(``):
print(f):
print(``):
print(`and in Maple notation `):
print(``):
lprint(f):
print(``):

print(``):
for i from 0 to degree(f,t) while add(coeff(f,t,i1),i1=0..i)<subs(t=1,f)/2 do od:
print(``):
print(`The median number of publications is`, i):
print(``):

L:=Sort1(DS(),6):

print(`Here is the list of all`, nops(L), `dead AMS fellows in decreasing order of their number of citations. It lists the year of birth, year of death, number of publications, and number of citations `):
print(``):
for i1 from 1 to nops(L) do
 print(cat(i1, `. `,` `,L[i1][2], ` `, L[i1][1],` `,   `( `,L[i1][3], "-", L[i1][4], `)`, ` `, L[i1][5], `;`, L[i1][6]  )):
od:

end:





#JointGF(S,a,p,c): Given a data set S finds the multi-variate generating function according to a^age*p^(number of publication)*c^(Number of citations)
#Try: JointGF(DS(),a,p,c);
JointGF:=proc(S,a,p,c) local i:
add(a^(S[i][4]-S[i][3])*p^S[i][5]*c^S[i][6],i=1..nops(S)):
end:

#CorMat(F,var): Given a genearting function in a list of variables var, finds the correlation matrix. Try:
#CorMat((1+2*x)*(1+y)*(1+z),[x,y,z]);
CorMat:=proc(F,var) local f, i,mu,i1,sd1,C,j:
f:=F/subs({seq(var[i]=1,i=1..nops(var))},F):

for i from 1 to nops(var) do
mu[i]:=diff(f,var[i]):
mu[i]:=subs({seq(var[i1]=1,i1=1..nops(var))},mu[i]):
od:

f:=f/mul(var[i]^mu[i],i=1..nops(var)):

for i from 1 to nops(var) do

sd1[i]:=diff(var[i]*diff(f,var[i]),var[i]):
sd1[i]:=sqrt(evalf(subs({seq(var[i1]=1,i1=1..nops(var))},sd1[i]))):
od:

[seq(sd1[i],i=1..nops(var))]:

for i from 1 to nops(var) do
for j from 1 to nops(var) do
 if i=j then
   C[i,j]:=1:
 else
 
C[i,j]:=evalf(subs({seq(var[i1]=1,i1=1..nops(var))},diff(diff(f,var[i]),var[j]))):
C[i,j]:=C[i,j]/(sd1[i]*sd1[j]):
fi:
od:
od:

[seq([seq(C[i,j],j=1..nops(var))],i=1..nops(var))]:
end:









#PaperA1(S), publishes a paper about the ages alone with data set S. Try:
#PaperA1(DS()):
PaperA1:=proc(S) local mu,k,f,t,i,lu,i1,T,j:
print(`Statistical Analysis of Longevity of Fellows of the American Mathematical Sociecty who Died Before Aug. 2022`):
print(``):

print(nops(S), `AMS Fellows died between its inauguration in 2013 and Aug. 2022.`):
print(``):
print(`In this chapter we statistically analyze their age at death. `):
print(``):
mu:=StatA(S,10):
print(``):
print(`The average age at death of an AMS Fellow who died before Aug. 2022 is `, mu[1]):
print(``):
print(`The standard deviation is`, mu[2] ):
print(``):
print(`The skewness is`, mu[3] ):
print(``):
print(`The kurtosis is`, mu[4] ):
print(``):
for k from 5 to 10 do
print(`The scaled`, k, `moment is`, mu[k]):
od:

f:=sort(AgeGF(S,t)):
print(``):
print(`The age generating function, with the variable t is`):
print(``):
print(f):
print(``):
print(``):
print(`and in Maple notation `):
print(``):
lprint(f):
print(``):

for i from 0 to degree(f,t) while add(coeff(f,t,i1),i1=0..i)<subs(t=1,f)/2 do od:
print(``):
print(`The median age is`, i):
print(``):
#print(add(coeff(f,t,i1),i1=0..i)):

for i from ldegree(f,t) to degree(f,t) do
T[i]:={}:
od:

for j from 1 to nops(S) do
lu:=S[j][4]-S[j][3]:
T[lu]:=T[lu] union {j}:
od:

[seq([i,T[i]],i=ldegree(f,t)..degree(f,t))]:

print(`The youngest age was`, ldegree(f,t)):
print(``):
print(`The oldest age was`, degree(f,t)):
print(``):
print(`Here are all the dead fellows listed, in decreasing order, by their age at death, followed by their number of publications and number of citations (in MathSciNet)  `):
print(``):
for i from degree(f,t) by -1 to ldegree(f,t) do
if T[i]<>{} then
print(`There were`, nops(T[i]), `fellows who died at the age of`, i):
print(``):
for i1 in T[i] do
 print(cat(S[i1][2], ` `, S[i1][1],` `,   `( `,S[i1][3], "-", S[i1][4], `)`, ` `, S[i1][5], `;`, S[i1][6]  )):
od:
print(``):
fi:
od:


end:


#PaperP1(S), publishes a paper about the publications alone with data set S. Try:
#PaperP1(DS()):
PaperP1:=proc(S) local mu,t,f,i,i1,k,L:
print(`Statistical Analysis of Number of Publications of Fellows of the American Mathematical Sociecty who Died Before Aug. 2022`):
print(``):


print(nops(S), `AMS Fellows died between its inauguration in 2013 and Aug. 2022.`):
print(``):
print(`In this chapter we statistically analyze their number of publications listed at MathSciNet, viewed Sept. 2022 `):
print(``):
mu:=StatP(S,10):
print(``):
print(`The average number of publications is `, mu[1]):
print(``):
print(`The standard deviation is`, mu[2] ):
print(``):
print(`The skewness is`, mu[3] ):
print(``):
print(`The kurtosis is`, mu[4] ):
print(``):
for k from 5 to 10 do
print(`The scaled`, k, `moment is`, mu[k]):
od:

f:=sort(PubGF(S,t)):
print(``):
print(`The Number of Publication generating function, with the variable t is`):
print(``):
print(f):
print(``):
print(``):
print(`and in Maple notation `):
print(``):
lprint(f):
print(``):

for i from 0 to degree(f,t) while add(coeff(f,t,i1),i1=0..i)<subs(t=1,f)/2 do od:
print(``):
print(`The median number of publications is`, i):
print(``):

L:=Sort1(DS(),5):

print(`Here is the list of all`, nops(L), `dead AMS fellows in decreasing order of their number of publications. It lists the year of birth, year of death, number of publications, and number of citations `):
print(``):
for i1 from 1 to nops(L) do
 print(cat(i1, `. `,` `,L[i1][2], ` `, L[i1][1],` `,   `( `,L[i1][3], "-", L[i1][4], `)`, ` `, L[i1][5], `;`, L[i1][6]  )):
od:

end:



#PaperC1(S), publishes a paper about the number of citationt alone with data set S. Try:
#PaperC1(DS()):
PaperC1:=proc(S) local mu,t,f,i,i1,k,L:
print(`Statistical Analysis of The  Number of Citations of  Fellows of the American Mathematical Sociecty who Died Before Aug. 2022`):
print(``):



print(nops(S), `AMS Fellows died between its inauguration in 2013 and Aug. 2022.`):
print(``):
print(`In this chapter we statistically analyze their number of citations listed at MathSciNet, viewed Sept. 2022 `):
print(``):
mu:=StatC(S,10):
print(``):
print(`The average number of citations is `, mu[1]):
print(``):
print(`The standard deviation is`, mu[2] ):
print(``):
print(`The skewness is`, mu[3] ):
print(``):
print(`The kurtosis is`, mu[4] ):
print(``):
for k from 5 to 10 do
print(`The scaled`, k, `moment is`, mu[k]):
od:

f:=sort(CitGF(S,t)):
print(``):
print(`The Number of Citations generating function, with the variable t is`):
print(``):
print(f):
print(``):
print(`and in Maple notation `):
print(``):
lprint(f):
print(``):

print(``):
print(`and in Maple notation `):
print(``):
lprint(f):
print(``):

for i from 0 to degree(f,t) while add(coeff(f,t,i1),i1=0..i)<subs(t=1,f)/2 do od:
print(``):
print(`The median number of publications is`, i):
print(``):

L:=Sort1(DS(),6):

print(`Here is the list of all`, nops(L), `dead AMS fellows in decreasing order of their number of citations. It lists the year of birth, year of death, number of publications, and number of citations `):
print(``):
for i1 from 1 to nops(L) do
 print(cat(i1, `. `,` `,L[i1][2], ` `, L[i1][1],` `,   `( `,L[i1][3], "-", L[i1][4], `)`, ` `, L[i1][5], `;`, L[i1][6]  )):
od:

end:

#Paper(S), publishes a paper about the  ages at death, number of publications, and number of citations of dead AMS fellows. Try:
#Paper(DS()):
Paper:=proc(S) local a,c,p,f,M:
print(`Statistical Analysis of Longevity, Number of Publications, and Number of Citations of Fellows of the American Mathematical Sociecty who Died Before Aug. 2022`):
print(``):
print(`By Shalosh B. Ekhad, Livia A. Stone, and Doron Zeilberger `):
print(``):

print(`Chapter I: Analysis of Longevity `):
print(``):
PaperA1(S):
print(``):
print(`-------------------------------------`):
print(``):
print(`Chapter II: Analysis of Number of Publications `):
print(``):
PaperP1(S):
print(``):
print(`-------------------------------------`):
print(``):
print(`Chapter III: Analysis of Number of Citations `):
print(``):
PaperC1(S):
print(`-------------------------------------`):


f:=JointGF(DS(),a,p,c);
M:=CorMat(f,[a,p,c]):

f:=sort(collect(f,a),a):

print(`Chapter IV:  Correlation `):

print(``):
print(`The joint generation function with variables a,p,c for age at death, number of publication, and number of citations is`):
print(``):
print(f):
print(``):
print(`and in Maple notation`):
print(``):
lprint(f):
print(``):
print(``):
print(`The correlation between age at death and number of publication is`, M[1][2] ):
print(``):
print(`The correlation between age at death and number of citations is`, M[1][3] ):
print(``):
print(`The correlation between the number of publications and number of citations is`, M[2][3] ):
print(``):
print(`This ends this article`):
print(``):
print(`May you live a long life, whether or not you are an AMS fellow. `):
print(``):
end: