#OK to post homework
#AJ Bu, January 22, 2024, Assignment 2

##############  PROBLEM 3 ############## 
#MyIfactor(n): that inputs a positive integer and 
#outputs a list of its prime factors (with repetition), in weakly increasing order. 
#For example, MyIfactor(100) 
#outputs [2,2,5,5]

MyIfactor:=proc(n) local L,p,n1::
	if n=1 then
		RETURN([]):
	fi:

	if isprime(n)=true then
		RETURN([n]):
	fi:
	
	L:=[]:
	p:=2:
	n1:=n:

	while isprime(n1)=false do
		while type(n1/p,integer)=false do
			p:=nextprime(p): 
		od:
		L:=[op(L),p]:
		n1:=n1/p:
	od:
	L:=[op(L),n1]:
end:

#This homemade procedure was slightly slower than Maple's ifactor procedure for some
#of the values I tested.


#time(MyIfactor(9239193239134))
#                               0.
#time(ifactor(9239193239134))
#                               0.
#time(MyIfactor(n))
#                             0.015
#time(ifactor(n))
#                               0.
#n:=rand(10^16..10^17)()
#                     n := 46650214228473823
#time(MyIfactor(n))
#                               0.
#time(ifactor(n))
#                               0.
#n:=rand(10^16..10^17)()
#                     n := 79920570985588261
#time(MyIfactor(n))
#                             0.734
#time(ifactor(n))
#                               0.
#n:=rand(10^16..10^17)()
#                     n := 90830494221539044
#time(MyIfactor(n))
#                             0.015
#time(ifactor(n))
#                               0.
#time(ifactor(n))
#                               0.
#n:=rand(10^16..10^17)()
#                     n := 82883713678695162
#time(MyIfactor(n))
#                               0.
#time(ifactor(n))
#                               0.
#n:=rand(10^16..10^17)()
#                     n := 35144326511170833
#time(MyIfactor(n))
#                             0.015
#time(ifactor(n))
#                               0.