Update group_by documentation

Author: hoijnet

src/app/docs/group-query-results/page.md

@@ -19,10 +19,12 @@ If we need to group variables according to some criteria, we can create an aggre
 
 A group by is composed of a _focus_, a _template_, and a _group_ together with a query.
 
-We will demonstrate this with the following query:
+### Single Variable Template (Flat Array)
+
+When grouping a single variable, the template produces a **flat array** of values:
 
 ```javascript
-let v = Vars("person", "label", "eyes", "group");
+let v = Vars("person", "label", "eyes", "group", "member");
 limit(1)
 .group_by(
   "eyes",
@@ -35,7 +37,7 @@ limit(1)
 
 The first argument, here `"eyes"` refers to the eyes variable, and is the variable around which to form the group, the _focus_.
 
-The second `["label"]` is the _template_, which refers to the variable `"label"`. The template will be those things grouped under the first variable.
+The second `["label"]` is the _template_, which refers to the variable `"label"`. Since the template contains only one variable, the results will be collected as a **flat array**.
 
 The third variable `v.group`, is the _group_ variable, which will include groups of templates for each set of solutions which shares a _focus_.
 
@@ -48,48 +50,133 @@ This raw query output will be:
         "@value": "black"
     },
     "group": [
-        [{
+        {
             "@type": "xsd:string",
             "@value": "Greedo"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "Nien Nunb"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "Gasgano"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "Kit Fisto"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "Plo Koon"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "Lama Su"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "Taun We"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "Shaak Ti"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "Tion Medon"
-        }],
-        [{
+        },
+        {
             "@type": "xsd:string",
             "@value": "BB8"
-        }]
+        }
+    ],
+    "label": null,
+    "person": null
+}
+```
+
+Notice how each result is a flat array of values, not nested arrays. To make this into individual solutions, use the `member` operator: `member(v.member, v.group)`, which will expand the `group` array into individual elements in the v.member variable.
+
+### Multiple Variable Template (Array of Tuples)
+
+When grouping multiple variables, the template produces an **array of tuples**:
+
+```javascript
+let v = Vars("person", "label", "eyes", "group");
+limit(1)
+.group_by(
+  "eyes",
+  ["label", "eyes"],
+  v.group,
+  and(triple(v.person, "rdf:type", "@schema:People"),
+      triple(v.person, "label", v.label),
+      triple(v.person, "eye_color", v.eyes)))
+```
+
+Now the template `["label", "eyes"]` includes two variables, so each result will be a tuple (array) containing both values:
+
+```json
+{
+    "eyes": {
+        "@type": "xsd:string",
+        "@value": "black"
+    },
+    "group": [
+        [
+            {
+                "@type": "xsd:string",
+                "@value": "Greedo"
+            },
+            {
+                "@type": "xsd:string",
+                "@value": "black"
+            }
+        ],
+        [
+            {
+                "@type": "xsd:string",
+                "@value": "Nien Nunb"
+            },
+            {
+                "@type": "xsd:string",
+                "@value": "black"
+            }
+        ],
+        [
+            {
+                "@type": "xsd:string",
+                "@value": "Gasgano"
+            },
+            {
+                "@type": "xsd:string",
+                "@value": "black"
+            }
+        ],
+        [
+            {
+                "@type": "xsd:string",
+                "@value": "Kit Fisto"
+            },
+            {
+                "@type": "xsd:string",
+                "@value": "black"
+            }
+        ],
+        [
+            {
+                "@type": "xsd:string",
+                "@value": "Plo Koon"
+            },
+            {
+                "@type": "xsd:string",
+                "@value": "black"
+            }
+        ]
     ],
     "label": null,
     "person": null
 }
-```
+```
+
+Each element in the `group` array is now a tuple `[label, eyes]` containing both values.