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jph00 committed Sep 14, 2024
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"np.array(a)"
]
},
{
"cell_type": "markdown",
"id": "90ad8377",
"metadata": {},
"source": [
"### Example algorithms"
]
},
{
"cell_type": "markdown",
"id": "d0660108",
"metadata": {},
"source": [
"The fibonacci sequence:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "77cc837d",
"metadata": {},
"outputs": [
{
"data": {
"application/javascript": [
"; (_ => {\n",
"\tlet hc = { '<': '&lt;', '&': '&amp;', \"'\": '&apos;', '\"': '&quot;' }, he = x => x.replace(/[<&'\"]/g, c => hc[c]) //html chars and escape fn\n",
"\t\t, tcs = '<-←xx×/\\\\×:-÷*O⍟[-⌹-]⌹OO○77⌈FF⌈ll⌊LL⌊T_⌶II⌶|_⊥TT⊤-|⊣|-⊢=/≠L-≠<=≤<_≤>=≥>_≥==≡=_≡7=≢Z-≢vv∨^^∧^~⍲v~⍱^|↑v|↓((⊂cc⊂(_⊆c_⊆))⊃[|⌷|]⌷A|⍋V|⍒ii⍳i_⍸ee∊e_⍷' +\n",
"\t\t\t'uu∪UU∪nn∩/-⌿\\\\-⍀,-⍪rr⍴pp⍴O|⌽O-⊖O\\\\⍉::¨\"\"¨~:⍨~\"⍨*:⍣*\"⍣oo∘o:⍤o\"⍤O:⍥O\"⍥[\\'⍞\\']⍞[]⎕[:⍠:]⍠[=⌸=]⌸[<⌺>]⌺o_⍎oT⍕o-⍕<>⋄^v⋄on⍝->→aa⍺ww⍵VV∇v-∇--¯0~⍬' +\n",
"\t\t\t'AA∆^-∆A_⍙^=⍙[?⍰?]⍰:V⍢∇\"⍢||∥ox¤)_⊇_)⊇V~⍫\\'\\'`'\n",
"\t\t, lbs = ['←←\\nASSIGN', ' ', '++\\nconjugate\\nplus', '--\\nnegate\\nminus', '××\\ndirection\\ntimes', '÷÷\\nreciprocal\\ndivide', '**\\nexponential\\npower', '⍟⍟\\nnatural logarithm\\nlogarithm',\n",
"\t\t\t'⌹⌹\\nmatrix inverse\\nmatrix divide', '○○\\npi times\\ncircular', '!!\\nfactorial\\nbinomial', '??\\nroll\\ndeal', ' ', '||\\nmagnitude\\nresidue',\n",
"\t\t\t'⌈⌈\\nceiling\\nmaximum', '⌊⌊\\nfloor\\nminimum', '⊥⊥\\ndecode', '⊤⊤\\nencode', '⊣⊣\\nsame\\nleft', '⊢⊢\\nsame\\nright', ' ', '==\\nequal', '≠≠\\nunique mask\\nnot equal',\n",
"\t\t\t'≤≤\\nless than or equal to', '<<\\nless than', '>>\\ngreater than', '≥≥\\ngreater than or equal to', '≡≡\\ndepth\\nmatch', '≢≢\\ntally\\nnot match', ' ', '∨∨\\ngreatest common divisor/or',\n",
"\t\t\t'∧∧\\nlowest common multiple/and', '⍲⍲\\nnand', '⍱⍱\\nnor', ' ', '↑↑\\nmix\\ntake', '↓↓\\nsplit\\ndrop', '⊂⊂\\nenclose\\npartioned enclose', '⊃⊃\\nfirst\\npick', '⊆⊆\\nnest\\npartition', '⌷⌷\\nmaterialise\\nindex', '⍋⍋\\ngrade up\\ngrades up',\n",
"\t\t\t'⍒⍒\\ngrade down\\ngrades down', ' ', '⍳⍳\\nindices\\nindices of', '⍸⍸\\nwhere\\ninterval index', '∊∊\\nenlist\\nmember of', '⍷⍷\\nfind', '∪∪\\nunique\\nunion', '∩∩\\nintersection', '~~\\nnot\\nwithout', ' ',\n",
"\t\t\t'//\\nreplicate\\nReduce', '\\\\\\\\\\n\\expand\\nScan', '⌿⌿\\nreplicate first\\nReduce First', '⍀⍀\\nexpand first\\nScan First', ' ', ',,\\nravel\\ncatenate/laminate',\n",
"\t\t\t'⍪⍪\\ntable\\ncatenate first/laminate', '⍴⍴\\nshape\\nreshape', '⌽⌽\\nreverse\\nrotate', '⊖⊖\\nreverse first\\nrotate first',\n",
"\t\t\t'⍉⍉\\ntranspose\\nreorder axes', ' ', '¨¨\\nEach', '⍨⍨\\nConstant\\nSelf\\nSwap', '⍣⍣\\nRepeat\\nUntil', '..\\nOuter Product (∘.)\\nInner Product',\n",
"\t\t\t'∘∘\\nOUTER PRODUCT (∘.)\\nBind\\nBeside', '⍤⍤\\nRank\\nAtop', '⍥⍥\\nOver', '@@\\nAt', ' ', '⍞⍞\\nSTDIN\\nSTDERR', '⎕⎕\\nEVALUATED STDIN\\nSTDOUT\\nSYSTEM NAME PREFIX', '⍠⍠\\nVariant',\n",
"\t\t\t'⌸⌸\\nIndex Key\\nKey', '⌺⌺\\nStencil', '⌶⌶\\nI-Beam', '⍎⍎\\nexecute', '⍕⍕\\nformat', ' ', '⋄⋄\\nSTATEMENT SEPARATOR', '⍝⍝\\nCOMMENT', '→→\\nABORT\\nBRANCH', '⍵⍵\\nRIGHT ARGUMENT\\nRIGHT OPERAND (⍵⍵)', '⍺⍺\\nLEFT ARGUMENT\\nLEFT OPERAND (⍺⍺)',\n",
"\t\t\t'∇∇\\nrecursion\\nRecursion (∇∇)', '&&\\nSpawn', ' ', '¯¯\\nNEGATIVE', '⍬⍬\\nEMPTY NUMERIC VECTOR', '∆∆\\nIDENTIFIER CHARACTER', '⍙⍙\\nIDENTIFIER CHARACTER']\n",
"\t\t, bqk = ' =1234567890-qwertyuiop\\\\asdfghjk∙l;\\'zxcvbnm,./q[]+!@#$%^&*()_QWERTYUIOP|ASDFGHJKL:\"ZXCVBNM<>?~{}'.replace(/∙/g, '')\n",
"\t\t, bqv = '`÷¨¯<≤=≥>≠∨∧×⋄⍵∊⍴~↑↓⍳○*⊢∙⍺⌈⌊_∇∆∘\\'⎕⍎⍕∙⊂⊃∩∪⊥⊤|⍝⍀⌿⋄←→⌹⌶⍫⍒⍋⌽⍉⊖⍟⍱⍲!⍰W⍷R⍨YU⍸⍥⍣⊣ASDF⍢H⍤⌸⌷≡≢⊆⊇CVB¤∥⍪⍙⍠⌺⍞⍬'.replace(/∙/g, '')\n",
"\t\t, tc = {}, bqc = {} //tab completions and ` completions\n",
"\tfor (let i = 0; i < bqk.length; i++)bqc[bqk[i]] = bqv[i]\n",
"\tfor (let i = 0; i < tcs.length; i += 3)tc[tcs[i] + tcs[i + 1]] = tcs[i + 2]\n",
"\tfor (let i = 0; i < tcs.length; i += 3) { let k = tcs[i + 1] + tcs[i]; tc[k] = tc[k] || tcs[i + 2] }\n",
"\tlet lbh = ''; for (let i = 0; i < lbs.length; i++) {\n",
"\t\tlet ks = []\n",
"\t\tfor (let j = 0; j < tcs.length; j += 3)if (lbs[i][0] === tcs[j + 2]) ks.push('\\n' + tcs[j] + ' ' + tcs[j + 1] + ' <tab>')\n",
"\t\tfor (let j = 0; j < bqk.length; j++)if (lbs[i][0] === bqv[j]) ks.push('\\n` ' + bqk[j])\n",
"\t\tlbh += '<b title=\"' + he(lbs[i].slice(1) + (ks.length ? '\\n' + ks.join('') : '')) + '\">' + lbs[i][0] + '</b>'\n",
"\t}\n",
"\tlet d = document, el = d.createElement('div'); el.innerHTML =\n",
"\t\t`<div class=ngn_lb><span class=ngn_x title=Close>❎</span>${lbh}</div>\n",
" <style>@font-face{font-family:\"DejaVu Sans Mono\";src:local(\"DejaVu Sans Mono\"),url(DejaVuBQNSansMono.ttf)format('ttf');}</style>\n",
" <style>\n",
" .ngn_lb{position:fixed;top:0;left:0;right:0;background-color:#eee;color:#000;cursor:default;z-index:2147483647;\n",
" font-family:\"DejaVu Sans Mono\",monospace;border-bottom:solid #999 1px;padding:2px 2px 0 2px;word-wrap:break-word;}\n",
" .ngn_lb b{cursor:pointer;padding:0 1px;font-weight:normal}\n",
" .ngn_lb b:hover,.ngn_bq .ngn_lb{background-color:#777;color:#fff}\n",
" .ngn_x{float:right;color:#999;cursor:pointer;margin-top:-3px}\n",
" .ngn_x:hover{color:#f00}\n",
" </style>`\n",
"\td.body.appendChild(el)\n",
"\tlet t, ts = [], lb = el.firstChild, bqm = 0 //t:textarea or input, lb:language bar, bqm:backquote mode\n",
"\tlet pd = x => x.preventDefault()\n",
"\tlet ev = (x, t, f, c) => x.addEventListener(t, f, c)\n",
"\tev(lb, 'mousedown', x => {\n",
"\t\tif (x.target.classList.contains('ngn_x')) { lb.hidden = 1; upd(); pd(x); return }\n",
"\t\tif (x.target.nodeName === 'B' && t) {\n",
"\t\t\tlet i = t.selectionStart, j = t.selectionEnd, v = t.value, s = x.target.textContent\n",
"\t\t\tif (i != null && j != null) { t.value = v.slice(0, i) + s + v.slice(j); t.selectionStart = t.selectionEnd = i + 1 }\n",
"\t\t\tpd(x); return\n",
"\t\t}\n",
"\t})\n",
"\tlet fk = x => {\n",
"\t\tlet t = x.target\n",
"\t\tif (bqm) {\n",
"\t\t\tlet i = t.selectionStart, v = t.value, c = bqc[x.key]\n",
"\t\t\tif (x.key === '`') {\n",
"\t\t\t\tt.value = v.slice(0, i) + '```' + v.slice(i)\n",
"\t\t\t\tt.selectionStart = t.selectionEnd = i + 1\n",
"\t\t\t\tbqm = 0\n",
"\t\t\t\td.body.classList.remove('ngn_bq')\n",
"\t\t\t\tpd(x)\n",
"\t\t\t\treturn !1\n",
"\t\t\t}\n",
"\t\t\tif (x.which > 31) { bqm = 0; d.body.classList.remove('ngn_bq') }\n",
"\t\t\tif (c) { t.value = v.slice(0, i) + c + v.slice(i); t.selectionStart = t.selectionEnd = i + 1; pd(x); return !1 }\n",
"\t\t}\n",
"\t\tif (!x.ctrlKey && !x.shiftKey && !x.altKey && !x.metaKey) {\n",
"\t\t\tif (\"`½²^º§ùµ°\".indexOf(x.key) > -1) {\n",
"\t\t\t\tbqm = 1; d.body.classList.add('ngn_bq'); pd(x); // ` or other trigger symbol pressed, wait for next key\n",
"\t\t\t} else if (x.key == \"Tab\") {\n",
"\t\t\t\tlet i = t.selectionStart, v = t.value, c = tc[v.slice(i - 2, i)]\n",
"\t\t\t\tif (c) { t.value = v.slice(0, i - 2) + c + v.slice(i); t.selectionStart = t.selectionEnd = i - 1; pd(x) }\n",
"\t\t\t}\n",
"\t\t}\n",
"\t}\n",
"\tlet ff = x => {\n",
"\t\tlet t0 = x.target, nn = t0.nodeName.toLowerCase()\n",
"\t\tif (nn !== 'textarea' && (nn !== 'input' || t0.type !== 'text' && t0.type !== 'search')) return\n",
"\t\tt = t0; if (!t.ngn) { t.ngn = 1; ts.push(t); ev(t, 'keydown', fk) }\n",
"\t}\n",
"\tlet upd = _ => { d.body.style.marginTop = lb.clientHeight + 'px' }\n",
"\tupd(); ev(window, 'resize', upd)\n",
"\tev(d, 'focus', ff, !0); let ae = d.activeElement; ae && ff({ type: 'focus', target: ae })\n",
"})();\n"
],
"text/plain": [
"<IPython.core.display.Javascript object>"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"[1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597]"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%apl {⍵,+/¯2↑⍵}⍣15⊢1 1"
]
},
{
"cell_type": "markdown",
"id": "4939224a",
"metadata": {},
"source": [
"Explanation:\n",
"\n",
"1. `1 1`: Initial seed (first two Fibonacci numbers)\n",
"2. `{⍵,+/¯2↑⍵}`: Function that appends the sum of the last two elements\n",
"3. `⍣15`: Apply the function 15 times\n",
"4. `⊢`: Identity function, passes the initial argument (1 1) to the iteration"
]
},
{
"cell_type": "markdown",
"id": "c74bb1b9",
"metadata": {},
"source": [
"Prime number sieve:"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c89a63d5",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47]"
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%%apl\n",
"primes ← {⍵×2=+⌿0=⍵∘.|⍵}⍳\n",
"(primes 50)~0"
]
},
{
"cell_type": "markdown",
"id": "eec3f4b3",
"metadata": {},
"source": [
"Explanation:\n",
"\n",
"1. `⍳50` generates integers 1 to 50\n",
"2. `⍵∘.|⍵` creates a 50x50 matrix of divisibility (1 if divisible, 0 if not)\n",
"3. `0=` inverts the matrix (1 for non-divisible)\n",
"4. `+⌿` sums columns, counting non-divisors for each number\n",
"5. `2=` checks if count equals 2 (prime property)\n",
"6. `⍵×` multiplies result with original numbers, keeping primes\n",
"7. `~0` removes zero from the result"
]
},
{
"cell_type": "markdown",
"id": "e61c4ea2",
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