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"<pre class='cython code score-17 '> __pyx_t_3 = <span class='pyx_c_api'>__Pyx_PyInt_From_long</span>((__pyx_v_lent + 1));<span class='error_goto'> if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 35, __pyx_L1_error)</span>\n",
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"</pre><pre class=\"cython line score-0\"> <span class=\"\">36</span>: <span class=\"k\">else</span><span class=\"p\">:</span></pre>\n",
"<pre class=\"cython line score-17\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">37</span>: <span class=\"n\">count</span><span class=\"p\">[(</span><span class=\"n\">lent</span><span class=\"o\">+</span><span class=\"mf\">1</span><span class=\"p\">,</span><span class=\"n\">t</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">])]</span><span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
"<pre class='cython code score-17 '> /*else*/ {\n",
" __pyx_t_11 = <span class='pyx_c_api'>__Pyx_PyInt_From_long</span>((__pyx_v_lent + 1));<span class='error_goto'> if (unlikely(!__pyx_t_11)) __PYX_ERR(0, 37, __pyx_L1_error)</span>\n",
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" __pyx_L11:;\n",
"</pre><pre class=\"cython line score-0\"> <span class=\"\">38</span>: </pre>\n",
"<pre class=\"cython line score-0\"> <span class=\"\">39</span>: <span class=\"c\">#recursive call</span></pre>\n",
"<pre class=\"cython line score-0\"> <span class=\"\">40</span>: <span class=\"k\">cdef</span> <span class=\"kt\">unsigned</span> <span class=\"kt\">long</span> <span class=\"kt\">long</span> <span class=\"nf\">r</span></pre>\n",
"<pre class=\"cython line score-0\"> <span class=\"\">41</span>: <span class=\"c\">#print(l)</span></pre>\n",
"<pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">42</span>: <span class=\"k\">if</span> <span class=\"n\">l</span><span class=\"o\">!=</span><span class=\"mf\">0</span><span class=\"p\">:</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_8 = ((__pyx_v_l != 0) != 0);\n",
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"</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">43</span>: <span class=\"n\">r</span><span class=\"o\">=</span><span class=\"mf\">0</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_v_r = 0;\n",
"</pre><pre class=\"cython line score-0\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">44</span>: <span class=\"k\">for</span> <span class=\"n\">k</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"o\">+</span><span class=\"mf\">1</span><span class=\"p\">,</span><span class=\"n\">nn1</span><span class=\"p\">):</span></pre>\n",
"<pre class='cython code score-0 '> __pyx_t_12 = __pyx_v_nn1;\n",
" __pyx_t_14 = __pyx_t_12;\n",
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" __pyx_v_k = __pyx_t_15;\n",
"</pre><pre class=\"cython line score-0\"> <span class=\"\">45</span>: <span class=\"c\">#print("Process(t,k,l-1,tuples,nn1)")</span></pre>\n",
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"<pre class='cython code score-1 '> __pyx_t_3 = __pyx_f_46_cython_magic_a771caaea75b905f51e41df3c6438720_ProcessRT(__pyx_v_t, __pyx_v_k, (__pyx_v_l - 1), __pyx_v_nn1, 0);<span class='error_goto'> if (unlikely(!__pyx_t_3)) __PYX_ERR(0, 47, __pyx_L1_error)</span>\n",
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" __pyx_t_3 = 0;\n",
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"<pre class='cython code score-43 '> if (likely(<span class='py_c_api'>PyList_CheckExact</span>(__pyx_v_ucount)) || <span class='py_c_api'>PyTuple_CheckExact</span>(__pyx_v_ucount)) {\n",
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" for (;;) {\n",
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"<pre class='cython code score-19 '> <span class='pyx_macro_api'>__Pyx_INCREF</span>(__pyx_v_key);\n",
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"<pre class=\"cython line score-0\"> <span class=\"\">56</span>: <span class=\"c\">#print(tuples)</span></pre>\n",
"<pre class=\"cython line score-0\"> <span class=\"\">57</span>: <span class=\"c\">#tuples.append(tuple(t))</span></pre>\n",
"<pre class=\"cython line score-0\"> <span class=\"\">58</span>: </pre>\n",
"<pre class=\"cython line score-0\"> <span class=\"\">59</span>: </pre>\n",
"<pre class=\"cython line score-14\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">60</span>: <span class=\"k\">print</span><span class=\"p\">(</span><span class=\"s\">"Branch process"</span><span class=\"p\">,</span><span class=\"n\">t</span><span class=\"p\">[</span><span class=\"mf\">0</span><span class=\"p\">])</span></pre>\n",
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"<pre class=\"cython line score-5\" onclick=\"(function(s){s.display=s.display==='block'?'none':'block'})(this.nextElementSibling.style)\">+<span class=\"\">66</span>: <span class=\"n\">cont</span><span class=\"o\">=</span><span class=\"p\">[]</span></pre>\n",
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"%%cython --annotate\n",
"from math import log \n",
"\n",
"cpdef ProcessRT(t,int i,int l,int nn1):\n",
" \"\"\"This function recursively extends an input tuple of integers, which represents \n",
" a set of sets (more precisily, a formal context), by adding to it an integer i (a new set).\n",
" The length of a terminal tuple is constrained by l, while nn1 should be passed as 2**n-1. \n",
" The function checks whether the new tuple forms a unique closure system and returns the dictionary of the first elements of\n",
" processed tuples as keys and values 1 for clousre system with T1 propery and 0 otherwise.\"\"\"\n",
" \n",
" count={}\n",
" t=t[:]\n",
" cdef int P\n",
" cdef int lent=len(t)\n",
"\n",
" \n",
" #checking whether the context is reducible\n",
" for j in range(lent-1,-1,-1):\n",
" P=i\n",
" #print(\"t[j],i\",t[j],i,t[j]&i,)\n",
" tji=t[j]&i\n",
" if tji in t[0:j]:\n",
" return count\n",
" \n",
" if tji==t[j]:\n",
" #print(\"t[j],i\",t[j],i,t[j]&i,)\n",
" for h in range(j+1,lent):\n",
" if t[j]&t[h]==t[j]:\n",
" P=P&t[h]\n",
" if P==t[j]: \n",
" return count\n",
" t.append(i)\n",
"\n",
" #checking T1 property\n",
" if Check(t,nn1):\n",
" count[(lent+1,t[0])]=1\n",
" else:\n",
" count[(lent+1,t[0])]=0\n",
"\n",
" #recursive call\n",
" cdef unsigned long long r\n",
" #print(l)\n",
" if l!=0:\n",
" r=0\n",
" for k in range(i+1,nn1):\n",
" #print(\"Process(t,k,l-1,tuples,nn1)\")\n",
" #print(\"t\",t,\"k\",k)\n",
" ucount=ProcessRT(t,k,l-1,nn1)\n",
" for key in ucount:\n",
" if key in count:\n",
" count[key]+=ucount[key]\n",
" else:\n",
" count[key]=ucount[key]\n",
" #if r<0: print(\"r\",r)\n",
" return count\n",
" else: \n",
" #print(tuples)\n",
" #tuples.append(tuple(t))\n",
" \n",
" \n",
" print(\"Branch process\",t[0])\n",
" return count\n",
"\n",
" \n",
"def isClosed(t,g):\n",
" \"\"\"Checks whether g is closed in t.\"\"\"\n",
" cont=[]\n",
" for h in t:\n",
" if g&h==g:\n",
" cont.append(h)\n",
" if len(cont)>0:\n",
" res=cont[0]\n",
" for h in cont:\n",
" res=h&res\n",
" return res==g\n",
" else:\n",
" return g==0\n",
"\n",
" \n",
"def Check(t,nn1):\n",
" \"\"\"Checks whether T1 is fulfilled for t.\"\"\"\n",
" n=int(log(nn1+1,2))\n",
" members=[0]\n",
" members.extend([2**i for i in range(n)])\n",
" for m in members:\n",
" if not isClosed(t,m):\n",
" return False\n",
" return True"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def merge(r):\n",
" \"\"\"This is a value collector for the resulting list of dictionaries\n",
" \"\"\"\n",
" merged={}\n",
" for dic in r:\n",
" for key in dic:\n",
" if key in merged:\n",
" merged[key]+=dic[key]\n",
" else:\n",
" merged[key]=dic[key]\n",
" return merged"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 2. Counting A334254 for n=6."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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{(2, 53): 0, (3, 53): 0}, {(2, 53): 0}, {(2, 54): 0, (3, 54): 0, (4, 54): 0, (5, 54): 0, (6, 54): 0}, {(2, 54): 0, (3, 54): 0, (4, 54): 0}, {(2, 54): 0, (3, 54): 0, (4, 54): 0, (5, 54): 0}, {(2, 54): 0, (3, 54): 0, (4, 54): 0, (5, 54): 0}, {(2, 54): 0, (3, 54): 0, (4, 54): 0}, {(2, 54): 0, (3, 54): 0}, {(2, 54): 0, (3, 54): 0}, {(2, 54): 0}, {(2, 55): 0, (3, 55): 0, (4, 55): 0}, {(2, 55): 0, (3, 55): 0, (4, 55): 0, (5, 55): 0}, {(2, 55): 0, (3, 55): 0, (4, 55): 0, (5, 55): 0}, {(2, 55): 0, (3, 55): 0, (4, 55): 0}, {(2, 55): 0, (3, 55): 0}, {(2, 55): 0, (3, 55): 0}, {(2, 55): 0}, {(2, 56): 0, (3, 56): 0}, {(2, 56): 0, (3, 56): 0}, {(2, 56): 0, (3, 56): 0}, {(2, 56): 0, (3, 56): 0}, {(2, 56): 0, (3, 56): 0}, {(2, 56): 0}, {(2, 57): 0, (3, 57): 0, (4, 57): 0}, {(2, 57): 0, (3, 57): 0, (4, 57): 0}, {(2, 57): 0, (3, 57): 0}, {(2, 57): 0, (3, 57): 0}, {(2, 57): 0}, {(2, 58): 0, (3, 58): 0, (4, 58): 0}, {(2, 58): 0, (3, 58): 0}, {(2, 58): 0, (3, 58): 0}, {(2, 58): 0}, {(2, 59): 0, (3, 59): 0}, {(2, 59): 0, (3, 59): 0}, {(2, 59): 0}, {(2, 60): 0}, {(2, 60): 0}, {(2, 61): 0}]\n",
"66960965307\n",
"CPU times: user 9min 14s, sys: 8min 19s, total: 17min 33s\n",
"Wall time: 4d 6h 37min 41s\n"
]
}
],
"source": [
"%%time\n",
"\n",
"\n",
"\n",
"from multiprocess import Pool\n",
"from multiprocess import cpu_count\n",
"\n",
"\n",
"n=6\n",
"\n",
"#computing A334254 for n=6 by levels\n",
"if __name__ == \"__main__\":\n",
" pool = Pool(cpu_count())\n",
" \n",
" nn1=2**n-1\n",
"\n",
" lt=[]\n",
" lk=[]\n",
"\n",
" count={}\n",
"\n",
" \n",
" for t in range(nn1):\n",
" \n",
" for i in range(t+1,nn1):\n",
" lt.append([t])\n",
" lk.append(i)\n",
" \n",
" ln_2=[nn1-1]* len(lt)\n",
" lnn1=[nn1]* len(lt)\n",
" \n",
" \n",
" \n",
" print(list(zip(lt,lk,ln_2,lnn1)))\n",
"\n",
" \n",
" #parallel execution of ProcessRT function\n",
" res6 = pool.starmap_async(ProcessRT, zip(lt,lk,ln_2,lnn1))\n",
" print(res6.get())# print the list of resulting dictionaries\n",
" print(sum(merge(res6.get()).values()))#print the number of closure systems w.r.t. T1\n",
" pool.close() # 'TERM'\n",
" pool.join() # 'KILL'"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"#saving the result to A334254_6.pickle file with pickle\n",
"import pickle\n",
"pikd = open(\"A334254_6.pickle\", \"wb\")\n",
"pickle.dump(res6.get(), pikd)\n",
"pikd.close()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
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" {(2, 18): 0,\n",
" (3, 18): 0,\n",
" (4, 18): 0,\n",
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" (6, 18): 0,\n",
" (7, 18): 0,\n",
" (8, 18): 0},\n",
" {(2, 18): 0, (3, 18): 0, (4, 18): 0, (5, 18): 0, (6, 18): 0, (7, 18): 0},\n",
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" ...]"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"res6.get()"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"66960965307"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum(merge(res6.get()).values())# the computed value A334254 for n=6"
]
},
{
"cell_type": "markdown",
"metadata": {
"scrolled": true
},
"source": [
"# 3. Checking A334254 for n=3, 4, 5."
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
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14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 3, (6, 14): 82, (7, 14): 264, (8, 14): 190, (9, 14): 21}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0, (6, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0, (6, 14): 0, (7, 14): 0, (8, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0, (6, 14): 0, (7, 14): 0, (8, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0, (6, 14): 0, (7, 14): 0, (8, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0, (6, 14): 0, (7, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0, (6, 14): 0, (7, 14): 0, (8, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0, (6, 14): 0, (7, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0, (6, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0, (5, 14): 0}, {(2, 14): 0, (3, 14): 0, (4, 14): 0}, {(2, 14): 0, (3, 14): 0}, {(2, 14): 0, (3, 14): 0}, {(2, 14): 0}, {(2, 15): 0, (3, 15): 0, (4, 15): 0, (5, 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16): 0, (3, 16): 0, (4, 16): 0, (5, 16): 0}, {(2, 16): 0, (3, 16): 0, (4, 16): 0, (5, 16): 0}, {(2, 16): 0, (3, 16): 0, (4, 16): 0}, {(2, 16): 0, (3, 16): 0, (4, 16): 0}, {(2, 16): 0, (3, 16): 0, (4, 16): 0, (5, 16): 0}, {(2, 16): 0, (3, 16): 0, (4, 16): 0, (5, 16): 0}, {(2, 16): 0, (3, 16): 0, (4, 16): 0}, {(2, 16): 0, (3, 16): 0}, {(2, 16): 0, (3, 16): 0}, {(2, 16): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0, (5, 17): 0, (6, 17): 0, (7, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0, (5, 17): 0, (6, 17): 0, (7, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0, (5, 17): 0, (6, 17): 0, (7, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0, (5, 17): 0, (6, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0, (5, 17): 0, (6, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0, (5, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0, (5, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0, (5, 17): 0}, {(2, 17): 0, (3, 17): 0, (4, 17): 0}, {(2, 17): 0, (3, 17): 0}, {(2, 17): 0, (3, 17): 0}, {(2, 17): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0, (5, 18): 0, (6, 18): 0, (7, 18): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0, (5, 18): 0, (6, 18): 0, (7, 18): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0, (5, 18): 0, (6, 18): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0, (5, 18): 0, (6, 18): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0, (5, 18): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0, (5, 18): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0, (5, 18): 0}, {(2, 18): 0, (3, 18): 0, (4, 18): 0}, {(2, 18): 0, (3, 18): 0}, {(2, 18): 0, (3, 18): 0}, {(2, 18): 0}, {(2, 19): 0, (3, 19): 0, (4, 19): 0, (5, 19): 0, (6, 19): 0}, {(2, 19): 0, (3, 19): 0, (4, 19): 0, (5, 19): 0, (6, 19): 0, (7, 19): 0}, {(2, 19): 0, (3, 19): 0, (4, 19): 0, (5, 19): 0, (6, 19): 0, (7, 19): 0}, {(2, 19): 0, (3, 19): 0, (4, 19): 0, (5, 19): 0, (6, 19): 0}, {(2, 19): 0, (3, 19): 0, (4, 19): 0}, {(2, 19): 0, (3, 19): 0, (4, 19): 0, (5, 19): 0}, {(2, 19): 0, (3, 19): 0, (4, 19): 0, (5, 19): 0}, {(2, 19): 0, (3, 19): 0, (4, 19): 0}, {(2, 19): 0, (3, 19): 0}, {(2, 19): 0, (3, 19): 0}, {(2, 19): 0}, {(2, 20): 0, (3, 20): 0, (4, 20): 0, (5, 20): 0, (6, 20): 0}, {(2, 20): 0, (3, 20): 0, (4, 20): 0, (5, 20): 0, (6, 20): 0}, {(2, 20): 0, (3, 20): 0, (4, 20): 0, (5, 20): 0}, {(2, 20): 0, (3, 20): 0, (4, 20): 0}, {(2, 20): 0, (3, 20): 0, (4, 20): 0, (5, 20): 0}, {(2, 20): 0, (3, 20): 0, (4, 20): 0, (5, 20): 0}, {(2, 20): 0, (3, 20): 0, (4, 20): 0}, {(2, 20): 0, (3, 20): 0}, {(2, 20): 0, (3, 20): 0}, {(2, 20): 0}, {(2, 21): 0, (3, 21): 0, (4, 21): 0, (5, 21): 0, (6, 21): 0, (7, 21): 0}, {(2, 21): 0, (3, 21): 0, (4, 21): 0, (5, 21): 0, (6, 21): 0}, {(2, 21): 0, (3, 21): 0, (4, 21): 0}, {(2, 21): 0, (3, 21): 0, (4, 21): 0, (5, 21): 0}, {(2, 21): 0, (3, 21): 0, (4, 21): 0, (5, 21): 0}, {(2, 21): 0, (3, 21): 0, (4, 21): 0}, {(2, 21): 0, (3, 21): 0}, {(2, 21): 0, (3, 21): 0}, {(2, 21): 0}, {(2, 22): 0, (3, 22): 0, (4, 22): 0, (5, 22): 0, (6, 22): 0}, {(2, 22): 0, (3, 22): 0, (4, 22): 0}, {(2, 22): 0, (3, 22): 0, (4, 22): 0, (5, 22): 0}, {(2, 22): 0, (3, 22): 0, (4, 22): 0, (5, 22): 0}, {(2, 22): 0, (3, 22): 0, (4, 22): 0}, {(2, 22): 0, (3, 22): 0}, {(2, 22): 0, (3, 22): 0}, {(2, 22): 0}, {(2, 23): 0, (3, 23): 0, (4, 23): 0}, {(2, 23): 0, (3, 23): 0, (4, 23): 0, (5, 23): 0}, {(2, 23): 0, (3, 23): 0, (4, 23): 0, (5, 23): 0}, {(2, 23): 0, (3, 23): 0, (4, 23): 0}, {(2, 23): 0, (3, 23): 0}, {(2, 23): 0, (3, 23): 0}, {(2, 23): 0}, {(2, 24): 0, (3, 24): 0}, {(2, 24): 0, (3, 24): 0}, {(2, 24): 0, (3, 24): 0}, {(2, 24): 0, (3, 24): 0}, {(2, 24): 0, (3, 24): 0}, {(2, 24): 0}, {(2, 25): 0, (3, 25): 0, (4, 25): 0}, {(2, 25): 0, (3, 25): 0, (4, 25): 0}, {(2, 25): 0, (3, 25): 0}, {(2, 25): 0, (3, 25): 0}, {(2, 25): 0}, {(2, 26): 0, (3, 26): 0, (4, 26): 0}, {(2, 26): 0, (3, 26): 0}, {(2, 26): 0, (3, 26): 0}, {(2, 26): 0}, {(2, 27): 0, (3, 27): 0}, {(2, 27): 0, (3, 27): 0}, {(2, 27): 0}, {(2, 28): 0}, {(2, 28): 0}, {(2, 29): 0}]\n",
"702525\n",
"CPU times: user 59.3 ms, sys: 42.8 ms, total: 102 ms\n",
"Wall time: 4.26 s\n"
]
}
],
"source": [
"%%time\n",
"\n",
"\n",
"\n",
"from multiprocess import Pool\n",
"from multiprocess import cpu_count\n",
"\n",
"\n",
"n=5\n",
"\n",
"#computing A334254 for n=5 by levels\n",
"if __name__ == \"__main__\":\n",
" pool = Pool(cpu_count())\n",
" \n",
" nn1=2**n-1\n",
"\n",
" lt=[]\n",
" lk=[]\n",
"\n",
" count={}\n",
"\n",
" \n",
" for t in range(nn1):\n",
" \n",
" for i in range(t+1,nn1):\n",
" lt.append([t])\n",
" lk.append(i)\n",
" \n",
" ln_2=[nn1-1]* len(lt)\n",
" lnn1=[nn1]* len(lt)\n",
" \n",
" \n",
" \n",
" print(list(zip(lt,lk,ln_2,lnn1)))\n",
"\n",
" \n",
" #parallel execution of ProcessRT function\n",
" res5 = pool.starmap_async(ProcessRT, zip(lt,lk,ln_2,lnn1))\n",
" print(res5.get())# print the list of resulting dictionaries\n",
" print(sum(merge(res5.get()).values()))#print the number of closure systems w.r.t. T1\n",
"\n",
" pool.close() # 'TERM'\n",
" pool.join() # 'KILL'"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"702525"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum(merge(res5.get()).values())# the computed value A334254 for n=5"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[([0], 1, 14, 15), ([0], 2, 14, 15), ([0], 3, 14, 15), ([0], 4, 14, 15), ([0], 5, 14, 15), ([0], 6, 14, 15), ([0], 7, 14, 15), ([0], 8, 14, 15), ([0], 9, 14, 15), ([0], 10, 14, 15), ([0], 11, 14, 15), ([0], 12, 14, 15), ([0], 13, 14, 15), ([0], 14, 14, 15), ([1], 2, 14, 15), ([1], 3, 14, 15), ([1], 4, 14, 15), ([1], 5, 14, 15), ([1], 6, 14, 15), ([1], 7, 14, 15), ([1], 8, 14, 15), ([1], 9, 14, 15), ([1], 10, 14, 15), ([1], 11, 14, 15), ([1], 12, 14, 15), ([1], 13, 14, 15), ([1], 14, 14, 15), ([2], 3, 14, 15), ([2], 4, 14, 15), ([2], 5, 14, 15), ([2], 6, 14, 15), ([2], 7, 14, 15), ([2], 8, 14, 15), ([2], 9, 14, 15), ([2], 10, 14, 15), ([2], 11, 14, 15), ([2], 12, 14, 15), ([2], 13, 14, 15), ([2], 14, 14, 15), ([3], 4, 14, 15), ([3], 5, 14, 15), ([3], 6, 14, 15), ([3], 7, 14, 15), ([3], 8, 14, 15), ([3], 9, 14, 15), ([3], 10, 14, 15), ([3], 11, 14, 15), ([3], 12, 14, 15), ([3], 13, 14, 15), ([3], 14, 14, 15), ([4], 5, 14, 15), ([4], 6, 14, 15), ([4], 7, 14, 15), ([4], 8, 14, 15), ([4], 9, 14, 15), ([4], 10, 14, 15), ([4], 11, 14, 15), ([4], 12, 14, 15), ([4], 13, 14, 15), ([4], 14, 14, 15), ([5], 6, 14, 15), ([5], 7, 14, 15), ([5], 8, 14, 15), ([5], 9, 14, 15), ([5], 10, 14, 15), ([5], 11, 14, 15), ([5], 12, 14, 15), ([5], 13, 14, 15), ([5], 14, 14, 15), ([6], 7, 14, 15), ([6], 8, 14, 15), ([6], 9, 14, 15), ([6], 10, 14, 15), ([6], 11, 14, 15), ([6], 12, 14, 15), ([6], 13, 14, 15), ([6], 14, 14, 15), ([7], 8, 14, 15), ([7], 9, 14, 15), ([7], 10, 14, 15), ([7], 11, 14, 15), ([7], 12, 14, 15), ([7], 13, 14, 15), ([7], 14, 14, 15), ([8], 9, 14, 15), ([8], 10, 14, 15), ([8], 11, 14, 15), ([8], 12, 14, 15), ([8], 13, 14, 15), ([8], 14, 14, 15), ([9], 10, 14, 15), ([9], 11, 14, 15), ([9], 12, 14, 15), ([9], 13, 14, 15), ([9], 14, 14, 15), ([10], 11, 14, 15), ([10], 12, 14, 15), ([10], 13, 14, 15), ([10], 14, 14, 15), ([11], 12, 14, 15), ([11], 13, 14, 15), ([11], 14, 14, 15), ([12], 13, 14, 15), ([12], 14, 14, 15), ([13], 14, 14, 15)]\n",
"[{(2, 0): 0, (3, 0): 0, (4, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0, (5, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0, (5, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0, (5, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0, (5, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0, (5, 0): 0}, {(2, 0): 0, (3, 0): 0, (4, 0): 0}, {(2, 0): 0, (3, 0): 0}, {(2, 0): 0, (3, 0): 0}, {(2, 0): 0}, {(2, 1): 0, (3, 1): 0, (4, 1): 1, (5, 1): 25, (6, 1): 67, (7, 1): 12}, {(2, 1): 0, (3, 1): 0, (4, 1): 0, (5, 1): 8, (6, 1): 21, (7, 1): 5}, {(2, 1): 0, (3, 1): 0, (4, 1): 0, (5, 1): 5, (6, 1): 13, (7, 1): 1}, {(2, 1): 0, (3, 1): 0, (4, 1): 0, (5, 1): 4, (6, 1): 8}, {(2, 1): 0, (3, 1): 0, (4, 1): 3, (5, 1): 15, (6, 1): 8}, {(2, 1): 0, (3, 1): 0, (4, 1): 1, (5, 1): 5}, {(2, 1): 0, (3, 1): 0, (4, 1): 0}, {(2, 1): 0, (3, 1): 0, (4, 1): 0, (5, 1): 0}, {(2, 1): 0, (3, 1): 0, (4, 1): 0, (5, 1): 0}, {(2, 1): 0, (3, 1): 0, (4, 1): 0}, {(2, 1): 0, (3, 1): 0}, {(2, 1): 0, (3, 1): 0}, {(2, 1): 0}, {(2, 2): 0, (3, 2): 0, (4, 2): 0, (5, 2): 8, (6, 2): 21, (7, 2): 5}, {(2, 2): 0, (3, 2): 0, (4, 2): 0, (5, 2): 5, (6, 2): 13, (7, 2): 1}, {(2, 2): 0, (3, 2): 0, (4, 2): 3, (5, 2): 18, (6, 2): 14}, {(2, 2): 0, (3, 2): 0, (4, 2): 0, (5, 2): 1, (6, 2): 2}, {(2, 2): 0, (3, 2): 0, (4, 2): 1, (5, 2): 5}, {(2, 2): 0, (3, 2): 0, (4, 2): 0}, {(2, 2): 0, (3, 2): 0, (4, 2): 0, (5, 2): 0}, {(2, 2): 0, (3, 2): 0, (4, 2): 0, (5, 2): 0}, {(2, 2): 0, (3, 2): 0, (4, 2): 0}, {(2, 2): 0, (3, 2): 0}, {(2, 2): 0, (3, 2): 0}, {(2, 2): 0}, {(2, 3): 0, (3, 3): 0, (4, 3): 3, (5, 3): 21, (6, 3): 20}, {(2, 3): 0, (3, 3): 0, (4, 3): 4, (5, 3): 31, (6, 3): 44, (7, 3): 8}, {(2, 3): 0, (3, 3): 0, (4, 3): 3, (5, 3): 18, (6, 3): 12, (7, 3): 1}, {(2, 3): 0, (3, 3): 0, (4, 3): 0, (5, 3): 6, (6, 3): 3}, {(2, 3): 0, (3, 3): 0, (4, 3): 0}, {(2, 3): 0, (3, 3): 0, (4, 3): 0, (5, 3): 0}, {(2, 3): 0, (3, 3): 0, (4, 3): 0, (5, 3): 0}, {(2, 3): 0, (3, 3): 0, (4, 3): 0}, {(2, 3): 0, (3, 3): 0}, {(2, 3): 0, (3, 3): 0}, {(2, 3): 0}, {(2, 4): 0, (3, 4): 0, (4, 4): 0, (5, 4): 1, (6, 4): 2}, {(2, 4): 0, (3, 4): 0, (4, 4): 0, (5, 4): 1, (6, 4): 2}, {(2, 4): 0, (3, 4): 0, (4, 4): 1, (5, 4): 5}, {(2, 4): 0, (3, 4): 0, (4, 4): 0}, {(2, 4): 0, (3, 4): 0, (4, 4): 0, (5, 4): 0}, {(2, 4): 0, (3, 4): 0, (4, 4): 0, (5, 4): 0}, {(2, 4): 0, (3, 4): 0, (4, 4): 0}, {(2, 4): 0, (3, 4): 0}, {(2, 4): 0, (3, 4): 0}, {(2, 4): 0}, {(2, 5): 0, (3, 5): 0, (4, 5): 3, (5, 5): 18, (6, 5): 12, (7, 5): 1}, {(2, 5): 0, (3, 5): 0, (4, 5): 0, (5, 5): 6, (6, 5): 3}, {(2, 5): 0, (3, 5): 0, (4, 5): 0}, {(2, 5): 0, (3, 5): 0, (4, 5): 0, (5, 5): 0}, {(2, 5): 0, (3, 5): 0, (4, 5): 0, (5, 5): 0}, {(2, 5): 0, (3, 5): 0, (4, 5): 0}, {(2, 5): 0, (3, 5): 0}, {(2, 5): 0, (3, 5): 0}, {(2, 5): 0}, {(2, 6): 0, (3, 6): 0, (4, 6): 0, (5, 6): 6, (6, 6): 3}, {(2, 6): 0, (3, 6): 0, (4, 6): 0}, {(2, 6): 0, (3, 6): 0, (4, 6): 0, (5, 6): 0}, {(2, 6): 0, (3, 6): 0, (4, 6): 0, (5, 6): 0}, {(2, 6): 0, (3, 6): 0, (4, 6): 0}, {(2, 6): 0, (3, 6): 0}, {(2, 6): 0, (3, 6): 0}, {(2, 6): 0}, {(2, 7): 0, (3, 7): 0, (4, 7): 0}, {(2, 7): 0, (3, 7): 0, (4, 7): 1, (5, 7): 5}, {(2, 7): 0, (3, 7): 0, (4, 7): 0, (5, 7): 1}, {(2, 7): 0, (3, 7): 0, (4, 7): 1}, {(2, 7): 0, (3, 7): 0}, {(2, 7): 0, (3, 7): 0}, {(2, 7): 0}, {(2, 8): 0, (3, 8): 0}, {(2, 8): 0, (3, 8): 0}, {(2, 8): 0, (3, 8): 0}, {(2, 8): 0, (3, 8): 0}, {(2, 8): 0, (3, 8): 0}, {(2, 8): 0}, {(2, 9): 0, (3, 9): 0, (4, 9): 0}, {(2, 9): 0, (3, 9): 0, (4, 9): 0}, {(2, 9): 0, (3, 9): 0}, {(2, 9): 0, (3, 9): 0}, {(2, 9): 0}, {(2, 10): 0, (3, 10): 0, (4, 10): 0}, {(2, 10): 0, (3, 10): 0}, {(2, 10): 0, (3, 10): 0}, {(2, 10): 0}, {(2, 11): 0, (3, 11): 0}, {(2, 11): 0, (3, 11): 0}, {(2, 11): 0}, {(2, 12): 0}, {(2, 12): 0}, {(2, 13): 0}]\n",
"545\n",
"CPU times: user 31 ms, sys: 43.9 ms, total: 75 ms\n",
"Wall time: 86 ms\n"
]
}
],
"source": [
"%%time\n",
"\n",
"\n",
"\n",
"from multiprocess import Pool\n",
"from multiprocess import cpu_count\n",
"\n",
"\n",
"n=4\n",
"\n",
"#computing A334254 for n=4 by levels\n",
"if __name__ == \"__main__\":\n",
" pool = Pool(cpu_count())\n",
" \n",
" nn1=2**n-1\n",
"\n",
" lt=[]\n",
" lk=[]\n",
"\n",
" count={}\n",
"\n",
" \n",
" for t in range(nn1):\n",
" \n",
" for i in range(t+1,nn1):\n",
" lt.append([t])\n",
" lk.append(i)\n",
" \n",
" ln_2=[nn1-1]* len(lt)\n",
" lnn1=[nn1]* len(lt)\n",
" \n",
" \n",
" \n",
" print(list(zip(lt,lk,ln_2,lnn1)))\n",
"\n",
" \n",
" #parallel execution of ProcessRT function\n",
" res4 = pool.starmap_async(ProcessRT, zip(lt,lk,ln_2,lnn1))\n",
" print(res4.get())# print the list of resulting dictionaries\n",
" print(sum(merge(res4.get()).values()))#print the number of closure systems w.r.t. T1\n",
"\n",
" pool.close() # 'TERM'\n",
" pool.join() # 'KILL'"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"545"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum(merge(res4.get()).values())# the computed value A334254 for n=4"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[([0], 1, 6, 7), ([0], 2, 6, 7), ([0], 3, 6, 7), ([0], 4, 6, 7), ([0], 5, 6, 7), ([0], 6, 6, 7), ([1], 2, 6, 7), ([1], 3, 6, 7), ([1], 4, 6, 7), ([1], 5, 6, 7), ([1], 6, 6, 7), ([2], 3, 6, 7), ([2], 4, 6, 7), ([2], 5, 6, 7), ([2], 6, 6, 7), ([3], 4, 6, 7), ([3], 5, 6, 7), ([3], 6, 6, 7), ([4], 5, 6, 7), ([4], 6, 6, 7), ([5], 6, 6, 7)]\n",
"[{(2, 0): 0, (3, 0): 0}, {(2, 0): 0, (3, 0): 0}, {(2, 0): 0, (3, 0): 0}, {(2, 0): 0, (3, 0): 0}, {(2, 0): 0, (3, 0): 0}, {(2, 0): 0}, {(2, 1): 0, (3, 1): 1, (4, 1): 4}, {(2, 1): 0, (3, 1): 0, (4, 1): 1}, {(2, 1): 0, (3, 1): 0}, {(2, 1): 0, (3, 1): 0}, {(2, 1): 0}, {(2, 2): 0, (3, 2): 0, (4, 2): 1}, {(2, 2): 0, (3, 2): 0}, {(2, 2): 0, (3, 2): 0}, {(2, 2): 0}, {(2, 3): 0, (3, 3): 0}, {(2, 3): 0, (3, 3): 1}, {(2, 3): 0}, {(2, 4): 0}, {(2, 4): 0}, {(2, 5): 0}]\n",
"8\n",
"CPU times: user 21 ms, sys: 32 ms, total: 53.1 ms\n",
"Wall time: 57 ms\n"
]
}
],
"source": [
"%%time\n",
"\n",
"\n",
"\n",
"from multiprocess import Pool\n",
"from multiprocess import cpu_count\n",
"\n",
"\n",
"n=3\n",
"\n",
"#computing A334254 for n=3 by levels\n",
"if __name__ == \"__main__\":\n",
" pool = Pool(cpu_count())\n",
" \n",
" nn1=2**n-1\n",
"\n",
" lt=[]\n",
" lk=[]\n",
"\n",
" count={}\n",
"\n",
" \n",
" for t in range(nn1):\n",
" \n",
" for i in range(t+1,nn1):\n",
" lt.append([t])\n",
" lk.append(i)\n",
" \n",
" ln_2=[nn1-1]* len(lt)\n",
" lnn1=[nn1]* len(lt)\n",
" \n",
" \n",
" \n",
" print(list(zip(lt,lk,ln_2,lnn1)))\n",
"\n",
" \n",
" #parallel execution of ProcessRT function\n",
" res3 = pool.starmap_async(ProcessRT, zip(lt,lk,ln_2,lnn1))\n",
" print(res3.get())# print the list of resulting dictionaries\n",
" print(sum(merge(res3.get()).values()))#print the number of closure systems w.r.t. T1\n",
"\n",
" pool.close() # 'TERM'\n",
" pool.join() # 'KILL'"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"8"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"sum(merge(res3.get()).values())# the computed value A334254 for n=3"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
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"language_info": {
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"file_extension": ".py",
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