with(combinat):
read "RSDataset.m":

#Proc to pull a random SYT P from dataset Q
RandP:=proc():
local i, j:
i:=rand(1..n)():
j:=rand(1..nops(Q[i]))():
Q[i][j][2][1];
end proc:

#Proc to pull a random SYT Q from dataset Q
RandQ:=proc():
local i, j:
i:=rand(1..n)():
j:=rand(1..nops(Q[i]))():
Q[i][j][2][2];
end proc:

#Proc to pull a random SYT P from dataset Q with n=n
RandPn:=proc(n):
local j:
j:=rand(1..nops(Q[n]))():
Q[n][j][2][1];
end proc:

#Proc to pull a random SYT Q from dataset Q with n=n
RandQn:=proc(n):
local j:
j:=rand(1..nops(Q[n]))():
Q[n][j][2][2];
end proc:

#Proc to find the sum of rows and return as a vector
RowSum:=proc(SYT):
local L, i, n:
n:=nops(SYT):
L:=Array(1..n):
for i from 1 to n do
L[i]:=convert(SYT[i],`+`):
end do;
convert(L, list);
end proc:

#Proc to find the sum of cols and return as a vector
ColSum:=proc(SYT):
local L, i, n, s, j, m:
n:=nops(SYT[1]):
m:=nops(SYT):
L:=Array(1..n):
for j from 1 to n do
s:=0:
for i from 1 to m do
if j <= nops(SYT[i]) then
s:=s + SYT[i][j];
end if;
end do;
L[j]:=s:
end do;
convert(L, list);
end proc:

#Finds Index of value x in SYT [row,col]
FindSYTdex:=proc(SYT,x):
local i, j:
for i from 1 to nops(SYT) do
for j from 1 to nops(SYT[i]) do
if SYT[i][j]=x then return([i,j]); end if;
end do; end do; end proc: