#M14.txt: Maple code for Lecture 14 of Dynamical Modesl in Biology, Fall 2021 (taught by Dr. Z.)

Help14:=proc(): print(` RevOp(n,k), RevOpTr(n,k) `):end:

#RevOp(n,k): The operation of taking a k-digit number, sorting its digits from large to small, and subtractiong it from the revers. For example
#RevOp(39,2) should give 93-39=54
RevOp:=proc(n,k) local L,L1,L2,i:
if not (type(n,integer) and n>=0 and n<10^k) then
print(`Bad input`):
RETURN(FAIL):
fi:
L:=convert(n,base, 10):
L1:=sort([op(L),0$(k-nops(L))]):
L2:=[seq(L1[k+1-i],i=1..k)]:
add(L1[i]*10^(i-1),i=1..k)-add(L2[i]*10^(i-1),i=1..k):
end:

#RevOpTr(n,k): The trajectory of the dynamical system RevOp(n,k) until it hits the first repetition (and then it keeps cycling for ever)
RevOpTr:=proc(n,k) local L,n1:
if not (type(n,integer) and n>=0 and n<10^k) then
RETURN(FAIL):
fi:

L:=[]:
n1:=n:

while not member(n1,L) do
 L:=[op(L),n1]:
 n1:=RevOp(n1,k):
od:

[op(L),n1]:

end: