#Caroline Cote and Guy Adami
#Experimental Mathematics Spring 2026
#Project 2 .txt file

read AsyRec.txt
read DZools.txt

print(`Multiple help functions are available:`):
print(`For the functions using DZtools type "Help()" or "Help1()"`):
print(`For the functions using AsyRec type "ezra()" or "ezra1()"`):
print(`For other project specific helps type "HelpProj()"`):

HelpProj:=proc() 
print(`For a list of all sequences we tested, type "HelpSeq()"`):
print(`To check if a sequence corresponds to a current OEIS number type "HelpOEIS(x)"`):
print('To check if we determined an Asymptotic Relation type "HelpAsy(x)"`):
end:




a:= {[1,0],[0,1]}:
b:= {[1,0],[0,1],[1,1]}:
c:= {[2,0],[0,2],[1,1]}:
d:= {[1,0],[0,1],[2,1],[1,2]}:
e:= {[2,1],[1,2]}:
f:= {[1,0],[0,1],[2,1],[1,2],[2,2]}:
g:= {[1,0,0],[0,1,0],[0,0,1]}:
h:= {[1,1,0],[1,0,1],[0,1,1]}:
i:= {[1,0,0],[0,1,0],[0,0,1],[1,1,0],[1,0,1],[0,1,1]}:
j:= {[1,0,0],[0,1,0],[0,0,1],[1,1,1]}:
k:= {[1,1,0],[1,0,1],[0,1,1],[1,1,1]}:
l:= {[1,0,0],[0,1,0],[0,0,1],[2,0,0],[0,2,0],[0,0,2]}:
m:= {[1,0,0],[0,1,0],[0,0,1],[2,1,0],[2,0,1],[1,2,0],[1,0,2],[0,2,1],[0,1,2]}:
n:= {[1,0,0],[0,1,0],[0,0,1],[2,1,1],[1,2,1],[1,1,2]}:
o:= {[1,1,0],[1,0,1],[0,1,1],[2,1,0],[2,0,1],[1,2,0],[1,0,2],[0,2,1],[0,1,2]}:
p:= {[1,0,0],[0,1,0],[0,0,1],[1,1,0],[1,0,1],[0,1,1],[1,1,1]}:
q:= {[1,0,0],[0,1,0],[0,0,1],[1,1,0],[1,0,1],[0,1,1],[2,0,0],[0,2,0],[0,0,2]}:
r:= {[1,0,0],[0,1,0],[0,0,1],[1,1,0],[1,0,1],[0,1,1],[2,1,0],[2,0,1],[1,2,0],[1,0,2],[0,2,1],[0,1,2]}:
s:= {[1,1,1]}:


HelpSeq:=proc()
print(`a := ` a);
print(`b := ` b);
print(`c := ` c);
print(`d := ` d);
print(`e := ` e);
print(`f := ` f);
print(`g := ` g);
print(`h := ` h);
print(`i := ` i);
print(`j := ` j);
print(`k := ` k);
print(`l := ` l);
print(`m := ` m);
print(`n := ` n);
print(`o := ` o);
print(`p := ` p);
print(`q := ` q);
print(`r := ` r);
print(`s := ` s);
end:


HelpOEIS:=proc(x) local OEIS_1, OEIS_2:
	OEIS_1:=00000:
	OEIS_2:=00000:

	if x = a then
		OEIS_1:= A000984:
		OEIS_2:= A002894:
	elif x=b then
		OEIS_1:=A001850:
		OEIS_2:=A002898:
	elif x=c then
		OEIS_1:=A002426:
		OEIS_2:=Not Available:
	elif x=d then
		OEIS_1:=A137635:
		OEIS_2:=Not Available:
	elif x=e then
		OEIS_1:=A000984:
		OEIS_2:=A002894
	elif x=f then
		OEIS_1:=A026933:
		OEIS_2:=Not Available:
	elif x=g then
		OEIS_1:=A006480:
		OEIS_2:=A002896:
	elif x=h then
		OEIS_1:=A245086:
		OEIS_2:=A002896
	elif x=i then
		OEIS_1:=A268550:
		OEIS_2:=Not Available:
	elif x=j then
		OEIS_1:=A081798:
		OEIS_2:=A002897:
	elif x=k then
		OEIS_1:=A208425:
		OEIS_2:=Not Available:
	elif x=l then
		OEIS_1:= Not Available:
		OEIS_2:=Not Available:
	elif x=m then
		OEIS_1:=Not Available:
		OEIS_2:=Not Available:
	elif x=n then
		OEIS_1:=A361728:
		OEIS_2:=Not Available:
	elif x=o then
		OEIS_1:=Not Available:
		OEIS_2:=Not Available:
	elif x=p then
		OEIS_1:=A126086:
		OEIS_2:=A328735:
	elif x=q then	
		OEIS_1:= Not Available:
		OEIS_2:=Not Available:
	elif x=r then	
		OEIS_1:= Not Available:
		OEIS_2:=Not Available:
	elif x = s then
		OEIS_1:= A000012:
		OEIS_2:=A126869:
	fi:

print(`For sequence ` x):
print(`The corresponding OEIS number for stopping at point [n,...,n] is  ` OEIS_1):
print(`The corresponding OEIS number for going to point  [n,...,n] and returning to the origin is  ` OEIS_2):
end:


HelpAsy:=proc(x) local Asy1, Asy2:
	Asy1 := 1:
	Asy2 := 1:

	if x = a then
		Asy1 := 1:
		Asy2 := 1:
	elif x=b then
		Asy1 := 1:
		Asy2 := 1:
	elif x=c then
		Asy1 := 1:
		Asy2 := 2:
		
	elif x=d then
		Asy1:=1:
		Asy2:=2:
	elif x=e then
		Asy1 := 1:
		Asy2 := 1:
	elif x=f then
		Asy1 := 1:
		Asy2 := 2:
	elif x=g then
		Asy1:=1:
		Asy2:=1:
	elif x=h then
		Asy1:=1:
		Asy2:=1
	elif x=i then
		Asy1:=1:
		Asy2:=2:
	elif x=j then
		Asy1:=1:
		Asy2:=1:
	elif x=k then
		Asy1:=1:
		Asy2:=0:
	elif x=l then
		Asy1:= 1:
		Asy2:=0:
	elif x=m then
		Asy1:=1:
		Asy2:=0:
	elif x=n then
		Asy1:=1:
		Asy2:=0:
	elif x=o then
		Asy1:=1:
		Asy2:=0:
	elif x=p then
		Asy1:=1:
		Asy2:=1:
	elif x=q then	
		Asy1:= 0:
		Asy2:=0:
	elif x=r then	
		Asy1:= 0:
		Asy2:=0:
	elif x = s then
		Asy1:= 1:
		Asy2:=1:
	fi:

	print(`For the sequence stopping at the point [n,...,n]`):	
	if Asy1 = 1 then
		print(`The sequence is already in the OEIS`):
	elif Asy1= 2 then
		print(`An Asymptotic Relation has been found. Please refer to the project writeup`):
	elif Asy1= 0 then
		print(`No Asymptotic Relation has been found`):
	fi:
	print(`For the sequence returning to the origin:`):
	if Asy2 = 1 then
		print(`The sequence is already in the OEIS`):
	elif Asy2= 2 then
		print(`An Asymptotic Relation has been found. Please refer to the project writeup`):
	elif Asy2= 0 then
		print(`No Asymptotic Relation has been found`):
	fi:
end: