Create xenotation.dyalog

xenotation.dyalog

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+⍝∇/∆ APL XENOTATION ∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆\∇/∆
+
+⍝ Generate a list of prime factors. ⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝
+Prime←{1↓(~v∊1 1↓v∘.×v)/v←⍳(⍵+1)}
+
+⍝ We need the full decomposition, not just the prime factors.  (Rosetta Code) ⍝
+∇ PrimeFactorDecomposition←{⎕ML ⎕IO←1          ⍝ Prime factors of ⍵.
+    ⍵{                      ⍝ note: ⎕wa>(⍵*÷2)×2*4.
+        ⍵,(⍺÷×/⍵)~1         ⍝ append factor > sqrt(⍵).
+    }∊⍵{                    ⍝ concatenated,
+        (0=(⍵*⍳⌊⍵⍟⍺)|⍺)/⍵   ⍝ powers of each prime factor.
+    }¨⍬{                    ⍝ remove multiples:
+        nxt←⊃⍵              ⍝ next prime, and
+        msk←0≠nxt|⍵         ⍝ ... mask of non-multiples.
+        ∧/1↓msk:⍺,⍵         ⍝ all non multiples - finished.
+        (⍺,nxt)∇ msk/⍵      ⍝ sieve remainder.
+    }⍵{                     ⍝ from,
+        (0=⍵|⍺)/⍵           ⍝ divisors of ⍵ in:
+    }2,(1+2×⍳⌊0.5×⍵*÷2),⍵   ⍝ 2,3 5 .. sqrt(⍵),⍵
+}
+∇
+
+⍝ Find the xenotative form of a number. ⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝⍝
+∇ Xeno←Xenotate n
+  ⍝ Find prime factors of an Arabic-style number.
+  Factors ← PrimeFactorDecomposition n
+  ⍝ Use the prime indices in the generation of the xenotative number.
+  Primes ← Prime 1000
+
+  ⍝ Construct xenotative form of each prime factor.
+  ⍝ This can probably be made more APL-like.
+  Xeno ← ''
+  :For Factor :In Factors
+    :If Factor = 2      ⍝ Add ':'
+      Xeno←Xeno,':'
+    :Else              ⍝ Implex
+      PrimeIndex ← (Factor ⍷ Primes) / ⍳⍴Primes
+      InnerValue ← Xenotate( PrimeIndex )
+      Xeno←Xeno,'(',InnerValue,')'
+    :EndIf
+  :EndFor
+∇