docs:Better examples.

Author: antononcube

docs/Basic-usage.ipynb

@@ -23,7 +23,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 32,
    "id": "9d5fa8a4",
    "metadata": {},
    "outputs": [],
@@ -52,7 +52,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 33,
    "id": "77a819d7",
    "metadata": {},
    "outputs": [
@@ -62,7 +62,7 @@
        "[\"Root\",[\"Add\",[\"Add\",[\"Multiply\",4,[\"Power\",\"x\",2]],[\"Multiply\",12,\"x\"]],9],2]"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -81,7 +81,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 34,
    "id": "9807bee7",
    "metadata": {},
    "outputs": [
@@ -91,7 +91,7 @@
        "<table border=\"1\"><thead><tr><th>expr</th><th>Cortex-JS</th><th>LaTeX::Grammar</th></tr></thead><tbody><tr><td align=left>4 x^2 + 12 x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Power&quot;,&quot;4 x&quot;,2],&quot;12 x&quot;],9]</td></tr><tr><td align=left>4 \\times x^2 + 12 \\times x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9]</td></tr><tr><td align=left>4 * x^2 + 12 * x + 9</td><td align=left>$[&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]</td><td align=left>[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9]</td></tr><tr><td align=left>\\sqrt{4 * x^2 + 12 * x + 9}</td><td align=left>$[&quot;Sqrt&quot;, [&quot;Add&quot;, [&quot;Multiply&quot;, 4, [&quot;Power&quot;, &quot;x&quot;, 2]], [&quot;Multiply&quot;, 12, &quot;x&quot;], 9]]</td><td align=left>[&quot;Root&quot;,[&quot;Add&quot;,[&quot;Add&quot;,[&quot;Multiply&quot;,4,[&quot;Power&quot;,&quot;x&quot;,2]],[&quot;Multiply&quot;,12,&quot;x&quot;]],9],2]</td></tr></tbody></table>"
       ]
      },
-     "execution_count": 3,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -120,7 +120,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 35,
    "id": "20cb12fa",
    "metadata": {},
    "outputs": [
@@ -130,7 +130,7 @@
        "-1"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 35,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -143,7 +143,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 36,
    "id": "2904bf39",
    "metadata": {},
    "outputs": [
@@ -153,7 +153,7 @@
        "a^2+b^2+2ab"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 36,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -175,7 +175,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 37,
    "id": "71b73b96",
    "metadata": {},
    "outputs": [
@@ -185,7 +185,7 @@
        "2x^2+3x^2+x+5 = 5x^2+x+5"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 37,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -205,27 +205,27 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 42,
    "id": "779d56cf",
    "metadata": {},
    "outputs": [
     {
      "data": {
       "text/markdown": [
        "$$\n",
-       "\\sqrt{3x^2 + 2x^2 + x + 5}\n",
+       "\\sqrt{5x^2+x+5}\n",
        "$$"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 42,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
     "#%markdown\n",
     "'\\sqrt{3x^2 + 2x^2 + x + 5}'\n",
-    "==> to-latex()\n",
+    "==> parse-latex()\n",
     "==> simplify()\n",
     "==> to-latex()\n",
     "==> { $_.subst(/ '\\text{\\text{' (.*) '}}' $ /, {$0.Str}) }()\n",
@@ -252,13 +252,24 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 44,
    "id": "6662e6ef",
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "6"
+      ]
+     },
+     "execution_count": 44,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
-    "$ce.evaluate($ce.parse('f(x) := 2x'));\n",
-    "$ce.evaluate($ce.parse('f(3)'));"
+    "evaluate(parse-latex('f(x) := 2x'));\n",
+    "evaluate(parse-latex('f(3)'));"
    ]
   }
  ],