Distinguish unique oscillators

As of this commit only p20, p21 and p690 have been converted this way

fixedoscs

@@ -21,8 +21,8 @@
 16 xp16_0c2w3vz33032988 21
 17 xp17_32acy1ca23zy27rszwo8a6y16a8o 36
 18 xp18_66625ak8zy177xcc0cczy1g8mwiozx91gp 43
-20 xp20_35426ow37bkicz65123 30
-21 xp21_5b8b94gszw6520gw6a8ozx332f7zy2121 40
+20 xp20_0jhe8gxg8gz122dl56o8ghzy1123cjc32ac 48
+21 xp21_y68e13zy0o4ogw315b8oz0gx11z121y6252zc88gy04eiczw32qbzw321 60
 22 xp22_178cwggg2y2oo4kozy235433y28111w62sg 36
 23 xp23_y1ggy3o8bdzc82u074wo84s8x31560u28czx11y0hi21y411zy5ddx696zgg0s4y1owsi1isx4s0ggz10230f9y3ogjn45303201zyc65 122
 24 xp24_2hqz037133zssszx777 24
@@ -125,4 +125,3 @@
 496 xp496_ccy04ajaeweaja4y0cczz66y04apaeweapa4y066zzy2oo0o8i22zy368wov 69
 504 xp504_ym356zy364koyh696y6g0s4zyjc871ye11zzy12552yg2bq4y4o8zca6y3oggyp113y3ca6zy823ys8kk8zzy4ggyegs26zy24701y6cicyh354czymcko 111
 512 xp512_yr33y166z0ggy033y16426ye33y0ccz011w66yuggz66yz56zzzy2mqyz66zygckgk2a21ya66woozy133y0ccye6426y1cczy566y1cc 100
-690 xp690_0ooy9vtvzyc757zok4sxs4kozzzz033y133 40

lcm

@@ -0,0 +1,3 @@
+20 xp20_35426ow37bkicz65123 30
+21 xp21_5b8b94gszw6520gw6a8ozx332f7zy2121 40
+690 xp690_0ooy9vtvzyc757zok4sxs4kozzzz033y133 40

skopje.py

@@ -1,30 +1,42 @@
 from constructs import *
-fixed = {}
 
-def skop(p):
-    """Return a list of pairs (Pattern, minimum population) representing
-    the smallest known oscillators of the specified period."""
-    if not fixed:
-        with open("fixedoscs", 'r') as f:
+def read_oscfiles(*fns):
+    """Read oscillators and their minimum populations from provided files
+    and return a dictionary."""
+    res = {}
+    for fn in fns:
+        with open(fn, 'r') as f:
             for l in f:
                 period, apgcode, mpop = l.split()
                 period = int(period)
-                fixed[period] = fixed.get(period, tuple()) + ((lt.pattern(apgcode), int(mpop)),)
-    cands = list(fixed.get(p, []))
-    cands.append(rectifier_loop(p))
-    cands.append(mold_rectifier_loop(p))
-    cands.append(p4_bumper_loop(p))
-    cands.append(p8_loop(p))
-    cands.append(snark_loop(p))
-    cands.append(p6_bumper_loop(p))
-    cands.append(pd_shuttle(p))
-    cands.append(p6thumb_shuttle(p))
-    cands.append(p14_shuttle(p))
-    cands.append(twinbees_shuttle(p))
+                res[period] = res.get(period, tuple()) + ((lt.pattern(apgcode), int(mpop)),)
+    return res
 
+def skop(p, unique=False):
+    """Return a list of pairs (Pattern, minimum population) representing
+    the smallest known oscillators of the specified period. Setting unique=True
+    excludes LCM and adjustable (to infinitely many periods trivially) oscillators."""
+    if not unique:
+        fixed = read_oscfiles("fixedoscs", "lcm")
+        cands = list(fixed.get(p, []))
+        cands.append(rectifier_loop(p))
+        cands.append(mold_rectifier_loop(p))
+        cands.append(p4_bumper_loop(p))
+        cands.append(p8_loop(p))
+        cands.append(snark_loop(p))
+        cands.append(p6_bumper_loop(p))
+        cands.append(pd_shuttle(p))
+        cands.append(p6thumb_shuttle(p))
+        cands.append(p14_shuttle(p))
+        cands.append(twinbees_shuttle(p))
+    else:
+        fixed = read_oscfiles("fixedoscs")
+        cands = list(fixed.get(p, []))
     cands = list(filter(bool, cands))
     if not cands:
         return []
     cands = [pair if pair[1] else (pair[0], minpop(pair[0])) for (i, pair) in enumerate(cands)]
     mp = min(pair[1] for pair in cands)
     return list(filter(lambda pair: pair[1] == mp, cands))
+
+skuop = lambda p: skop(p, True)