Added better isprimepower method; put DJB algorithms to the side

Author: jakewilliami

src/CodingTheory.jl

@@ -6,7 +6,8 @@
 
 module CodingTheory
 
-using Primes: isprime, primes
+using Nemo: isprime, factor, fmpz
+# using Primes: isprime, primes
 using LinearAlgebra: I
 using FLoops: @floop, ThreadedEx
 using Polynomials, StaticArrays
@@ -41,12 +42,15 @@ export FinitePolynomial, list_polys, multiplication_table, list_span, islinear,
         isirreducible, normal_form!, normal_form, equivalent_code!, equivalent_code,
         generator!, generator, parity_check, syndrome, isincode
 
+# Powers
+export isprimepower, isperfectpower
+
 # Levenshtein
 export levenshtein, levenshtein!
 
 include("abstract_types.jl")
 include("rref.jl")
-include("messages.jl") # implicitly exports distance.jl and primes.jl
+include("messages.jl") # implicitly exports distance.jl and powers.jl
 include("bounds.jl")
 include("algebra.jl")
 include("levenshtein.jl")

src/messages.jl

@@ -5,7 +5,7 @@
     =#
 
 include("distance.jl")
-include("primes.jl")
+include("powers.jl")
 
 """
 ```julia

src/powers.jl

@@ -0,0 +1,48 @@
+function __isprime(n)
+	return isprime(fmpz(n))
+end
+
+function __factors(n)
+	return n == 0 ? [] : factor(fmpz(n))
+end
+# function __factors(n)
+# 	first(i) for i in Primes.factor(n)
+# end
+
+function primedivisors(n)
+    n == 0 && return []
+    __isprime(n) && return [fmpz(n)]
+    f = __factors(n)
+    return sort!([p for (p, e) ∈ f])
+end
+
+function ω(n)
+	nprimedivisors = 0
+	if n == 0
+		nprimedivisors = 0
+	elseif __isprime(n)
+		nprimedivisors = 1
+    else
+        nprimedivisors = length(__factors(n))
+	end
+
+	return fmpz(nprimedivisors)
+
+    # # original definition:
+	# return fmpz(length(primedivisors(n)))
+end
+
+function Ω(n)
+    n == fmpz(0) && return 0
+    __isprime(n) && return fmpz(1)
+	
+    return sum(e for (__, e) ∈ __factors(n))
+end
+
+function isperfectpower(n)
+	return ω(n) == 1 && Ω(n) != 1
+end
+
+function isprimepower(n)
+    return ω(n) == 1
+end

test/primepowers.jl src/wip/primepowers.jltest/primepowers.jl renamed to src/wip/primepowers.jl

@@ -1,3 +1,5 @@
+### TAKE TWO
+
 using Primes: primes, factor, isprime
 
 ### Helpers

src/primes.jl src/wip/primes.jlsrc/primes.jl renamed to src/wip/primes.jl

@@ -4,6 +4,55 @@
     "${BASH_SOURCE[0]}" "$@"
     =#
 
+# TAKE ONE
+
+using Nemo, Primes
+
+function _isprime(n)
+	return Nemo.isprime(Nemo.fmpz(n))
+end
+
+function _factors(n)
+	return n == 0 ? [] : Nemo.factor(Nemo.fmpz(n))
+end
+# function _factors(n)
+# 	first(i) for i in Primes.factor(n)
+# end
+
+function primedivisors(n)
+    n == 0 && return []
+    _isprime(n) && return [Nemo.fmpz(n)]
+    f = _factors(n)
+    return sort!([p for (p, e) ∈ f])
+end
+
+function ω(n)
+	nprimedivisors = 0
+	if n == 0
+		nprimedivisors = 0
+	end
+	if _isprime(n)
+		nprimedivisors = length(Nemo.fmpz(n))
+	end
+
+	return length(_factors(n))
+
+	# return fmpz(length(primedivisors(n)))
+end
+
+function Ω(n)
+    n == fmpz(0) && return 0
+    _isprime(n) && return fmpz(1)
+	
+    return sum(e for (_, e) ∈ _factors(n))
+end
+
+function isperfectpower(n)
+	return ω(n) == 1 && Ω(n) != 1
+end
+
+#---------------------------
+
 #=
 You find the smallest pair (a, n) (small with respect to n) such that a^n is your target number. Then you need to check if a is prime.
 =#