Some examples for the Atop case of ⍤

contents/rank.ipynb

@@ -964,7 +964,7 @@
  "source": [
  "## Atop\n",
  "\n",
- "As we mentioned above, from version 18 of Dyalog, `⍤` can also be _Atop_ if given a right operand function instead of array. We'll see more of different kinds of _Atop_ later, but for now it's a functional composition rule, stating that (for the dyadic case),\n",
+ "As we mentioned above, from version 18 of Dyalog, `⍤` can also be _Atop_ if given a right operand function instead of array. We'll see more of different kinds of _Atop_ later in the [tacit](./tacit.ipynb) chapter, but for now it's a functional composition rule, stating that (for the dyadic case),\n",
  "```apl\n",
  "X f⍤g Y → f X g Y\n",
  "```\n",
@@ -977,7 +977,86 @@
  "X f⍤g Y → f X g Y\n",
  "```\n",
  "\n",
- "As the monadic _Atop_ is equivalent for `∘` and `⍤`, it's worth using `⍤` for both monadic and dyadic atops for consistency."
+ "Another way to think about it is that in the dyadic case, the difference between `∘` and `⍤` is which operand function (`f` or `g`) gets the left argument. In the monadic case, _Atop_ is equivalent for `∘` and `⍤`, so it's worth using `⍤` for both monadic and dyadic atops for consistency. \n",
+ "\n",
+ "Here is a simple example of a dyadic _Atop_,"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 1,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<span style=\"white-space:pre; font-family: monospace\">¯5 ¯7 ¯9\n",
+ "</span>"
+ ]
+ },
+ "execution_count": 1,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "1 2 3 -⍤+ 4 5 6 ⍝ Negate the sum of two vectors"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "which, following the `X f⍤g Y → f X g Y` rule, is the same as"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 2,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<span style=\"white-space:pre; font-family: monospace\">¯5 ¯7 ¯9\n",
+ "</span>"
+ ]
+ },
+ "execution_count": 2,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "-1 2 3+4 5 6 ⍝ Negate the sum of two vectors"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "or, as a tacit formulation (which we'll cover in more detail later),"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": 3,
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/html": [
+ "<span style=\"white-space:pre; font-family: monospace\">¯5 ¯7 ¯9\n",
+ "</span>"
+ ]
+ },
+ "execution_count": 3,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "1 2 3 (-+) 4 5 6 ⍝ Negate the sum of two vectors"
  ]
  },
  {