{
"cells": [
{
"cell_type": "raw",
"id": "2990f581",
"metadata": {},
"source": [
"---\n",
"title: \"First functions\"\n",
"author: \"Jeremy Howard\"\n",
"date: \"2022-07-05\"\n",
"categories: [Dyalog, APL, Glyphs]\n",
"---"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "84e8fa35",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→─────────────────────────────────────┐\n",
"│Was ON -style=max -trains=tree -fns=on│\n",
"└──────────────────────────────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"]box on -style=max -trains=tree -fns=on"
]
},
{
"cell_type": "markdown",
"id": "2dbbce67",
"metadata": {},
"source": [
"## Boolean"
]
},
{
"cell_type": "markdown",
"id": "71f403e7",
"metadata": {},
"source": [
"### `=` (Equal sign)"
]
},
{
"cell_type": "markdown",
"id": "2df02fe7",
"metadata": {},
"source": [
"#### dyadic `=` (Equal to)"
]
},
{
"cell_type": "markdown",
"id": "22de5339-feeb-4050-8fd2-c49604d38546",
"metadata": {},
"source": [
"`=` is equal and returns a boolean (true/false). 1 means true, 0 means false."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f9a1f4c0",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"1\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 = 1"
]
},
{
"cell_type": "markdown",
"id": "2dbd9b1e-f7dd-43ef-9198-42210c33f7f6",
"metadata": {},
"source": [
"`=` works elementwise and will broadcast as needed."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e494be50",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──┐\n",
"│1 0│\n",
"└~──┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 = 1 2"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d31b5778",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──┐\n",
"│1 1│\n",
"└~──┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 = 1 1"
]
},
{
"cell_type": "markdown",
"id": "2fbb3372-ec47-45a7-9c0f-0c5264207eaf",
"metadata": {},
"source": [
"We can also compare characters"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8d9ff9d7",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────┐\n",
"│0 1 0 1 0 1│\n",
"└~──────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"'Banana' = 'aaaaaa'"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0077e614",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────┐\n",
"│0 1 0 1 0 1│\n",
"└~──────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"'Banana' = 'a'"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "aa551f28",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────────────────────────────────┐\n",
"│ ┌→──────────┐ ┌→────────┐ ┌→────────┐ │\n",
"│ │0 1 0 1 0 1│ │0 0 0 0 0│ │0 1 0 0 0│ │\n",
"│ └~──────────┘ └~────────┘ └~────────┘ │\n",
"└∊──────────────────────────────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"'Banana' 'Apple' 'Candy' = 'a'"
]
},
{
"cell_type": "markdown",
"id": "12b33beb",
"metadata": {},
"source": [
"### `≠` (Not equal)"
]
},
{
"cell_type": "markdown",
"id": "3b0b6323",
"metadata": {},
"source": [
"#### monadic `≠` (Unique Mask)"
]
},
{
"cell_type": "markdown",
"id": "5a19caf7-f061-44da-99c0-7495223a1812",
"metadata": {},
"source": [
"Monadic `≠` returns 1 on the first occurrence of an item in an array."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0d283400",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────────┐\n",
"│1 1 0 0 1 0 1 0│\n",
"└~──────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≠22 10 22 22 21 10 5 10"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1b52166b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────┐\n",
"│1 1 1 0 0 0│\n",
"└~──────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≠ 'Banana'"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "84ed720d",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────────────────────┐\n",
"│1 1 1 0 0 0 0 0 1 0 0│\n",
"└~────────────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≠ 'Mississippi'"
]
},
{
"cell_type": "markdown",
"id": "ec2830de",
"metadata": {},
"source": [
"#### dyadic `≠` (Not Equal To)"
]
},
{
"cell_type": "markdown",
"id": "a062070b-2923-4a0b-b964-df59052f23ed",
"metadata": {},
"source": [
"Dyadic `≠` returns true (1) if elements are not equal, and false (0) if elements are equal. "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "21b37853",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│1 0 1│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 ≠ 4 2 ¯1"
]
},
{
"cell_type": "markdown",
"id": "5e01edbc-b54f-458b-a3ac-2b6ad344ae54",
"metadata": {},
"source": [
"The number 7 and the character 7 are not equal."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7b1f2164",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"1\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"7 ≠ '7'"
]
},
{
"cell_type": "markdown",
"id": "2d5dfcd5",
"metadata": {},
"source": [
"### `<` (Less than sign)"
]
},
{
"cell_type": "markdown",
"id": "4277bc63",
"metadata": {},
"source": [
"#### dyadic `<` (Less than)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b3c6be5e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│1 0 0│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 < 4 2 ¯1"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "61f6c499",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│1 0 0│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 < 2"
]
},
{
"cell_type": "markdown",
"id": "3bd3a0ea",
"metadata": {},
"source": [
"### `>` (Greater than sign)"
]
},
{
"cell_type": "markdown",
"id": "b487022a",
"metadata": {},
"source": [
"#### dyadic `>` (Greater than)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ed7bc01e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│0 0 1│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 > 4 2 ¯1"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b68ae705",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│0 0 1│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 > 2"
]
},
{
"cell_type": "markdown",
"id": "903c506f",
"metadata": {},
"source": [
"### `≤` (Less than or equal to sign)"
]
},
{
"cell_type": "markdown",
"id": "21b33cbf",
"metadata": {},
"source": [
"#### dyadic `≤` (Less than or equal to)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "985c9324",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│1 1 0│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 ≤ 4 2 ¯1"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ebb03a6a",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│1 1 0│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 ≤ 2"
]
},
{
"cell_type": "markdown",
"id": "b9409575",
"metadata": {},
"source": [
"### `≥` (Greater than or equal to sign)"
]
},
{
"cell_type": "markdown",
"id": "8dbc6595",
"metadata": {},
"source": [
"#### dyadic `≥` (Greater than or equal to)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c2db65ca",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│0 1 1│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 ≥ 4 2 ¯1"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3c4673b1",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│0 1 1│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 2 3 ≥ 2"
]
},
{
"cell_type": "markdown",
"id": "af629c33",
"metadata": {},
"source": [
"### `≡` (Equal underbar)"
]
},
{
"cell_type": "markdown",
"id": "04409fab",
"metadata": {},
"source": [
"#### monadic `≡` (Depth)"
]
},
{
"cell_type": "markdown",
"id": "9d6a0db6-2820-4e30-a53e-65e6010d8324",
"metadata": {},
"source": [
"Depth shows how nested an array is. A simple scalar is an array with no nesting."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "fcb156fe",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"0\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≡ 7"
]
},
{
"cell_type": "markdown",
"id": "3b3f7079-1edd-4d36-8142-f2fad11bf1db",
"metadata": {},
"source": [
"An array of simple scalars has depth 1."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "53200fb6",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"1\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≡ 'abc'"
]
},
{
"cell_type": "markdown",
"id": "a9b106d5-a182-44fc-b3d9-c660344bc186",
"metadata": {},
"source": [
"An array that is an array of simple arrays has depth 2."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "35407dd6",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────────────┐\n",
"│ ┌→──┐ ┌→──┐ │\n",
"│ │1 2│ │3 4│ │\n",
"│ └~──┘ └~──┘ │\n",
"└∊────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(1 2)(3 4)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f64d2e8e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"2\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≡ (1 2)(3 4)"
]
},
{
"cell_type": "markdown",
"id": "36ec6b8f-882d-483f-a42b-1b2c6f35b559",
"metadata": {},
"source": [
"If the depth is not consistent, then it returns the max depth as a negative number."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0650e6e6",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────────────────────────┐\n",
"│ ┌→──┐ ┌→──┐ ┌→────────┐ │\n",
"│ │1 2│ │3 4│ │ ┌→──┐ │ │\n",
"│ └~──┘ └~──┘ │ 5 │6 7│ │ │\n",
"│ │ └~──┘ │ │\n",
"│ └∊────────┘ │\n",
"└∊────────────────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(1 2)(3 4) (5 (6 7))"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ede6ebf7",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"¯3\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≡ (1 2)(3 4) (5 (6 7))"
]
},
{
"cell_type": "markdown",
"id": "d5e95d1d",
"metadata": {},
"source": [
"#### dyadic `≡` (Match)"
]
},
{
"cell_type": "markdown",
"id": "0819ac30-7d8f-446a-b4b9-e6113514cf1e",
"metadata": {},
"source": [
"Match does a comparison to see if 2 objects are equal. It is similar to `=`, but it works on entire objects rather than elementwise. In other words it is equal with a wider scope."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "8f55c331",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"1\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 ≡ 1"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ee929e76",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"0\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 ≡ 0"
]
},
{
"cell_type": "markdown",
"id": "1f48a33b-e717-47d3-a6f8-3395c759759e",
"metadata": {},
"source": [
"`≡` works on whole objects and **not** elementwise with broadcasting."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1419197c",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"0\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 ≡ 1 1"
]
},
{
"cell_type": "markdown",
"id": "284ae899",
"metadata": {},
"source": [
"### `≢` (Equal Underbar Slash)"
]
},
{
"cell_type": "markdown",
"id": "f6f859db",
"metadata": {},
"source": [
"#### monadic `≢` (Tally)"
]
},
{
"cell_type": "markdown",
"id": "026eab0b-68de-46c8-874e-f07035768242",
"metadata": {},
"source": [
"Tally counts the major cells in an array. This means it gives the length of the leading axis. For a vector, or rank 1 array, this is the same as it's shape but as a scalar."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "10011239",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"3\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≢ 1 2 3"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6f6449ea",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→┐\n",
"│3│\n",
"└~┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⍴ 1 2 3"
]
},
{
"cell_type": "markdown",
"id": "9adbc6a0-e791-46df-83ef-dcf6787d0ed4",
"metadata": {},
"source": [
"If there are multiple dimensions, Tally returns the number of major cells, which is the size of the first dimension"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7d2d2315",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"2\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≢ 2 3 ⍴ ⍳6"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b5c6f177-ce42-4718-8c3d-710febac94c2",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"3\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"≢ 3 2 ⍴ ⍳6"
]
},
{
"cell_type": "markdown",
"id": "63bf5a7c",
"metadata": {},
"source": [
"#### dyadic `≢` (Not match)"
]
},
{
"cell_type": "markdown",
"id": "b22c9e10-a63b-48c0-b811-96f416e76289",
"metadata": {},
"source": [
"Not match does a comparison to see if 2 objects are not equal. It is similar to `≠`, but it works on entire objects rather than elementwise. In other words, it is equal with a wider scope."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "762603e0",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"0\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 ≢ 1"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "87ebb14d",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"1\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 ≢ 0"
]
},
{
"cell_type": "markdown",
"id": "0846d742-8ba9-4a7e-b141-bc8cad0171c6",
"metadata": {},
"source": [
"``≢`` works on whole objects and **not** elementwise with broadcasting."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9f3fb7c0",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"1\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 ≢ 1 1"
]
},
{
"cell_type": "markdown",
"id": "fa5c0d84",
"metadata": {},
"source": [
"### `∨` (Logical or)"
]
},
{
"cell_type": "markdown",
"id": "42407b65",
"metadata": {},
"source": [
"#### dyadic `∨` (Greatest Common Divisor (Or))"
]
},
{
"cell_type": "markdown",
"id": "37035211-ea5a-424d-8e3f-cd1735dab5a8",
"metadata": {},
"source": [
"Standard `or` operator when applied to booleans."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "439d7541",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────┐\n",
"│0 1 1 1│\n",
"└~──────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"0 1 0 1 ∨ 0 0 1 1 ⍝ Truth table for *or*"
]
},
{
"cell_type": "markdown",
"id": "ceae61c8-16d3-4c50-83f6-655f20aaeaad",
"metadata": {},
"source": [
"5 is the largest number that divides 15 and 35 cleanly (meaning no remainder). Therefore, 5 is the greatest common divisor of 15 and 35."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "47abd9d1",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────┐\n",
"│5 1 2 7│\n",
"└~──────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"15 1 2 7 ∨ 35 1 4 0 ⍝ GCD"
]
},
{
"cell_type": "markdown",
"id": "fc3e5b03",
"metadata": {},
"source": [
"### `⍱` (Logical NOR)"
]
},
{
"cell_type": "markdown",
"id": "47ff8cd5",
"metadata": {},
"source": [
"#### dyadic `⍱` (Nor)"
]
},
{
"cell_type": "markdown",
"id": "f067a891-a383-4794-9e2e-731f6d750c69",
"metadata": {},
"source": [
"For more details on logical nor, [see this page](https://en.wikipedia.org/wiki/Logical_NOR#Truth_table)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "dc80c88d",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────┐\n",
"│1 0 0 0│\n",
"└~──────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
" 0 1 0 1 ⍱ 0 0 1 1 ⍝ Truth table for *nor*"
]
},
{
"cell_type": "markdown",
"id": "27932e1b",
"metadata": {},
"source": [
"### `∧` (Logical AND)"
]
},
{
"cell_type": "markdown",
"id": "31a3b8b5",
"metadata": {},
"source": [
"#### dyadic `∧` (Lowest Common Multiple (And))"
]
},
{
"cell_type": "markdown",
"id": "65f4a4d0-59ed-4e72-914e-c2ef482d8291",
"metadata": {},
"source": [
"Standard `and` operator when applied to booleans."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ac4309ef",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────┐\n",
"│0 0 0 1│\n",
"└~──────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"0 1 0 1 ∧ 0 0 1 1 ⍝ Truth table for *and*"
]
},
{
"cell_type": "markdown",
"id": "71b974e9-6f78-4e29-937f-ffb31a62af74",
"metadata": {},
"source": [
"105 is the smallest multiple of both 15 and 35, therefore 105 is the lowest common multiple of 15 and 35."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "fbfaebf4",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────────┐\n",
"│105 1 4 0│\n",
"└~────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"15 1 2 7 ∧ 35 1 4 0 ⍝ LCM"
]
},
{
"cell_type": "markdown",
"id": "04987504-6a54-4e01-b38f-3e69b99c1abe",
"metadata": {},
"source": [
"### `~` (Logical NOT)"
]
},
{
"cell_type": "markdown",
"id": "09ab7565-f35c-4072-ab77-3e1cd58e17ee",
"metadata": {},
"source": [
"#### monadic `~` (Not)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b0abb3ae",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──┐\n",
"│1 0│\n",
"└~──┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"~ 0 1 ⍝ Truth table for *not*"
]
},
{
"cell_type": "markdown",
"id": "190b5d68-57b5-4f04-a21e-3864fe8d8122",
"metadata": {},
"source": [
"#### dyadic `~` (Without;Excluding)"
]
},
{
"cell_type": "markdown",
"id": "d41d8180-bfaa-46f2-808e-d451673f4e5f",
"metadata": {},
"source": [
"Gives the elements from the left argument that are not in the right."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f6b788cd",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──┐\n",
"│3 4│\n",
"└~──┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"3 1 4 1 5 ~ 5 1"
]
},
{
"cell_type": "markdown",
"id": "82641989-2b43-4e01-a3d1-0489c417cae5",
"metadata": {},
"source": [
"Also works on the character vectors"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "bfdf7e89",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────┐\n",
"│ ┌→─┐ ┌→─┐ │\n",
"│ │aa│ │cc│ │\n",
"│ └──┘ └──┘ │\n",
"└∊──────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"'aa' 'bb' 'cc' 'bb' ~ 'bb' 'xx'"
]
},
{
"cell_type": "markdown",
"id": "51a97128-c2ee-499a-a5e7-2f2e84897496",
"metadata": {},
"source": [
"Also works on nested arrays"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9085478e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→┐\n",
"│3│\n",
"└~┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(1 2) 3 ~ ⊂1 2"
]
},
{
"cell_type": "markdown",
"id": "5f8cab64",
"metadata": {},
"source": [
"### `⍲` (Logical NAND)"
]
},
{
"cell_type": "markdown",
"id": "8b59feac",
"metadata": {},
"source": [
"#### dyadic `⍲` (Nand)"
]
},
{
"cell_type": "markdown",
"id": "abf07f68-d2d1-4784-b9f3-2fce4665a498",
"metadata": {},
"source": [
"Nand is \"Not and\""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "0ee272ec",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────┐\n",
"│1 1 1 0│\n",
"└~──────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
" 0 1 0 1 ⍲ 0 0 1 1 ⍝ Truth table for *nand*"
]
},
{
"cell_type": "markdown",
"id": "327836f3-8acd-474d-a594-2fa525763bc6",
"metadata": {},
"source": [
"We could use and (`^`) apply not (`~`) afterward to get the same result. As you can see it truly is \"Not and\""
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "113f86fa-9645-4c8e-b559-6b5cf7c822f8",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────┐\n",
"│1 1 1 0│\n",
"└~──────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"~ 0 1 0 1 ∧ 0 0 1 1 ⍝ Truth table for *nand*"
]
},
{
"cell_type": "markdown",
"id": "ebf0e3e4",
"metadata": {},
"source": [
"### `/` (Slash)"
]
},
{
"cell_type": "markdown",
"id": "81223d6f",
"metadata": {},
"source": [
"#### monadic `/` (Replicate)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1e6ccb42",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────────┐\n",
"│1 1 0 0 1 0 1 0│\n",
"└~──────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"v←22 10 22 22 21 10 5 10\n",
"≠v"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "ed0370b6",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→─────────┐\n",
"│22 10 21 5│\n",
"└~─────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(≠v)/v"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "4a7aa794",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→───────────┐\n",
"│BBBannnannna│\n",
"└────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"3 1 3 1 3 1 / 'Banana'"
]
},
{
"cell_type": "markdown",
"id": "95f0d135",
"metadata": {},
"source": [
"## Min, max, index, concat"
]
},
{
"cell_type": "markdown",
"id": "c184a076",
"metadata": {},
"source": [
"### `⍳` (iota)"
]
},
{
"cell_type": "markdown",
"id": "8485edff",
"metadata": {},
"source": [
"#### monadic `⍳` (index generator)"
]
},
{
"cell_type": "markdown",
"id": "6581d1bf-551f-42b5-a027-b080d72d4629",
"metadata": {},
"source": [
"Creates index locations for array with specified shape."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "69cc99e0",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────┐\n",
"│1 2 3 4│\n",
"└~──────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⍳4"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "155302ac",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────────────┐\n",
"↓ ┌→──┐ ┌→──┐ ┌→──┐ │\n",
"│ │1 1│ │1 2│ │1 3│ │\n",
"│ └~──┘ └~──┘ └~──┘ │\n",
"│ ┌→──┐ ┌→──┐ ┌→──┐ │\n",
"│ │2 1│ │2 2│ │2 3│ │\n",
"│ └~──┘ └~──┘ └~──┘ │\n",
"└∊──────────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⍳2 3"
]
},
{
"cell_type": "markdown",
"id": "841c9175-1100-41ed-8a7c-ec4bb7783504",
"metadata": {},
"source": [
"`⍳` is often used with `⍴` to create arrays "
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "73e93a04",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"↓1 2 3│\n",
"│4 5 6│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"2 3 ⍴ ⍳6"
]
},
{
"cell_type": "markdown",
"id": "22e8cdfd-5251-432f-b0a6-716bd803085d",
"metadata": {},
"source": [
"To generate an array with various patterns you can combine with other functions."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1744f807",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────────────┐\n",
"│3 5 7 9 11 13│\n",
"└~────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1+2×⍳6"
]
},
{
"cell_type": "markdown",
"id": "f92ecb85-02b0-46fe-9812-d4ed90ed9498",
"metadata": {},
"source": [
"Array of shape 0 is nan empty vector and the index locations of a shape 0 array is and empty vector."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "3fd77f85",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌⊖┐\n",
"│0│\n",
"└~┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⍳0"
]
},
{
"cell_type": "markdown",
"id": "51f01e92",
"metadata": {},
"source": [
"#### dyadic `⍳` (index of)"
]
},
{
"cell_type": "markdown",
"id": "24713038-4260-48c3-aa7a-e79815cec6e8",
"metadata": {},
"source": [
"Provides the index locations for where `⍵` (right argument) is in `⍺` (left argument)"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "db34fc0c",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"2\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"1 3 6 5 4 ⍳ 3"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1604dc20",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────────┐\n",
"│1 3 10 11│\n",
"└~────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"'ABCDABCDEF' ⍳ 'ACFG'"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e6a697da",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──┐\n",
"↓1 2│\n",
"│3 4│\n",
"│5 6│\n",
"└~──┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⎕←mat←3 2 ⍴ ⍳6"
]
},
{
"cell_type": "markdown",
"id": "4a0af1fb-7e47-4b68-8639-2d5e34d75dc2",
"metadata": {},
"source": [
"`⍳` works on major cells, or along the first dimension. The third major cell of mat is `5 6`."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "e7e56d92",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"3\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mat←3 2 ⍴ ⍳6\n",
"mat ⍳ 5 6"
]
},
{
"cell_type": "markdown",
"id": "8dbfe270",
"metadata": {},
"source": [
"### `⍸` (iota underbar)"
]
},
{
"cell_type": "markdown",
"id": "c623312c",
"metadata": {},
"source": [
"#### monadic `⍸` (Where)"
]
},
{
"cell_type": "markdown",
"id": "6eb50df5-420e-456b-aebc-df8bcc377870",
"metadata": {},
"source": [
"When applied to a boolean/binary array, where gives index locations of the true values."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "cd826c58",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│1 4 5│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⍸ 1 0 0 1 1"
]
},
{
"cell_type": "markdown",
"id": "80929a44-9b23-491a-98ef-d530ba1f3490",
"metadata": {},
"source": [
"When applied to a natural number, where repeats the index locations if the number is greater than 1. For example `⍸1 2 3` would give `1 2 2 3 3 3`"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "1b6a928b-705a-48bc-89b9-0f48158568cc",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────┐\n",
"│1 2 2 3 3 3│\n",
"└~──────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⍸1 2 3"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f6dd11af",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────────┐\n",
"│1 1 4 4 5│\n",
"└~────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⍸ 2 0 0 2 1"
]
},
{
"cell_type": "markdown",
"id": "7be22017-4047-404f-a9fa-34c0a589c6ed",
"metadata": {},
"source": [
"When applied to a higher rank array it still provides the index locations of the elements, but index locations have multiple values (in this case row and column)."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a8a4bf88",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"↓0 1 0│\n",
"│1 0 1│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
"┌→──────────────────┐\n",
"│ ┌→──┐ ┌→──┐ ┌→──┐ │\n",
"│ │1 2│ │2 1│ │2 3│ │\n",
"│ └~──┘ └~──┘ └~──┘ │\n",
"└∊──────────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⎕←bmat ← 2 3 ⍴ 0 1 0 1 0 1\n",
"⍸ bmat"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "b3c0b9fa-98a8-4914-973e-57e01081c83b",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"↓0 2 0│\n",
"│2 0 2│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"text/html": [
"┌→────────────────────────────────────┐\n",
"│ ┌→──┐ ┌→──┐ ┌→──┐ ┌→──┐ ┌→──┐ ┌→──┐ │\n",
"│ │1 2│ │1 2│ │2 1│ │2 1│ │2 3│ │2 3│ │\n",
"│ └~──┘ └~──┘ └~──┘ └~──┘ └~──┘ └~──┘ │\n",
"└∊────────────────────────────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⎕←bmat ← 2 3 ⍴ 0 2 0 2 0 2\n",
"⍸ bmat"
]
},
{
"cell_type": "markdown",
"id": "1c86ab76",
"metadata": {},
"source": [
"#### dyadic `⍸` (Interval Index)"
]
},
{
"cell_type": "markdown",
"id": "057b305f-dd6e-4658-9c53-55576cef9585",
"metadata": {},
"source": [
"Interval index creates intervals and returns an array that tells you which interval a value falls in.\n",
"\n",
"If the following example, `⍵` is `2 4 6`. Therefore the following intervals (sometimes called bins) are created.\n",
"\n",
"+ **0th interval:** Less than 2\n",
"+ **1st interval:** 2-4 (excluding 4)\n",
"+ **2nd interval:** 4-6 (excluding 6)\n",
"+ **3rd interval:** Greater than or equal to 6\n",
"\n",
"`⍺` (right argument) is `1 2 3 4 5 6 7` so let's put those into intervals, which the first interval starting at 0.\n",
"\n",
"+ The first value of `⍺` is 1. 1 is Less than 2. Therefore it is in the 0th interval and interval index returns 0.\n",
"+ The second value of `⍺` is 2. 2 is in the 2-4 range. Therefore it is in the 1st interval and interval index returns 1.\n",
"+ The third value of `⍺` is 3. 3 is in the 2-4 range. Therefore it is in the 1st interval and interval index returns 1.\n",
"+ The fourth value of `⍺` is 4. 4 is in the 4-6 range. Therefore it is in the 2nd interval and interval index returns 2.\n",
"\n",
"And so on and so forth."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "c402ce31",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────────────┐\n",
"│0 1 1 2 2 3 3│\n",
"└~────────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"2 4 6 ⍸ 1 2 3 4 5 6 7"
]
},
{
"cell_type": "markdown",
"id": "46aea64b-c2d1-4ce9-ab66-de44e7cf5f52",
"metadata": {},
"source": [
"Interval index works the same way with character vectors.\n",
"\n",
"+ `D` is in the first interval because it is between `A` and `E`.\n",
"+ `Y` is in the last interval (fifth) because it is larger than all values\n",
"+ `A` is in the first interval because it is between `A` and `E`.\n",
"+ `L` is in the third interval because it is between `I` and `O`.\n",
"\n",
"etc."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f66c7d8a",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──────────┐\n",
"│1 5 1 3 4 2│\n",
"└~──────────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"'AEIOU' ⍸ 'DYALOG'"
]
},
{
"cell_type": "markdown",
"id": "88e6e4a7-6538-4372-b752-48c2cfc9dfb1",
"metadata": {},
"source": [
"Interval index works across major cells."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "9c607eb4",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──┐\n",
"↓1 2│\n",
"│3 4│\n",
"│5 6│\n",
"└~──┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⎕←mat←3 2⍴⍳6"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d4e1c0b4",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"1\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mat ⍸ 3 3"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "5af2f8d1",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"2\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mat ⍸ 3 5"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "fc9be234",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──┐\n",
"│1 2│\n",
"└~──┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"mat ⍸ 2 2 ⍴ 3 3 3 5"
]
},
{
"cell_type": "markdown",
"id": "ad28d0b2",
"metadata": {},
"source": [
"### `⌈` (Upstile)"
]
},
{
"cell_type": "markdown",
"id": "3db6d6cb",
"metadata": {},
"source": [
"#### monadic `⌈` (Ceiling)"
]
},
{
"cell_type": "markdown",
"id": "f162a21e-b887-4a58-bb02-9c70e67100fa",
"metadata": {},
"source": [
"Rounds up to nearest whole number."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7223b897",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→───────┐\n",
"│4 ¯3 3 0│\n",
"└~───────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⌈ 3.4 ¯3.4 3 0"
]
},
{
"cell_type": "markdown",
"id": "0717d224",
"metadata": {},
"source": [
"#### dyadic `⌈` (Maximum)"
]
},
{
"cell_type": "markdown",
"id": "e97c8bc5-420c-44a4-850d-1f900c0f48e8",
"metadata": {},
"source": [
"Takes maximum of 2 values"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "785a5a38",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"3\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"3⌈2"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "7a410ee3",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→──┐\n",
"│3 3│\n",
"└~──┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"3 2⌈2 3"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "f9f78ce3",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"6\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"4 ⌈ 6 ⌈ 2"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "04ed6871",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→────┐\n",
"│0 6 2│\n",
"└~────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a ← ¯4 6 2\n",
"0 ⌈ a"
]
},
{
"cell_type": "markdown",
"id": "c9a8d1b5",
"metadata": {},
"source": [
"### `⌊` (Downstile)"
]
},
{
"cell_type": "markdown",
"id": "c054a3e9",
"metadata": {},
"source": [
"#### monadic `⌊` (Floor)"
]
},
{
"cell_type": "markdown",
"id": "8feeafed-2657-4651-b817-95a4e09075a6",
"metadata": {},
"source": [
"Rounds down to nearest whole number"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "aa41f28e",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"┌→───────┐\n",
"│3 ¯4 3 0│\n",
"└~───────┘\n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"⌊ 3.4 ¯3.4 3 0"
]
},
{
"cell_type": "markdown",
"id": "a40dd397",
"metadata": {},
"source": [
"#### dyadic `⌊` (Minimum)"
]
},
{
"cell_type": "markdown",
"id": "524a4b1b-3f65-4a2c-850a-37dd0deed965",
"metadata": {},
"source": [
"Takes minimum of 2 values"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "d9a0b9a6",
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
" \n",
"2.5\n",
" \n",
""
]
},
"execution_count": null,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"4 ⌊ 6 ⌊ 2.5"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Dyalog APL",
"language": "apl",
"name": "dyalog-kernel"
}
},
"nbformat": 4,
"nbformat_minor": 5
}