docs: rewrite double pendulum example using vectors

examples/braking_deceleration.ipynb

@@ -1,69 +1,72 @@
-{
- "cells": [
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Solution( t = 1.1176 seconds )\n"
-     ]
-    },
-    {
-     "data": {
-      "text/latex": [
-       "$\\displaystyle \\frac{1397}{1250} \\hspace{1.25em} \\text{s}$"
-      ],
-      "text/plain": [
-       "1.1176 seconds"
-      ]
-     },
-     "execution_count": 1,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "from mathpad import *\n",
-    "\n",
-    "t = \"t\" * seconds  # \"t seconds\"\n",
-    "\n",
-    "velocity = 5 * miles / hour  # \"5 miles/hour\"\n",
-    "\n",
-    "deceleration = 2 * meters / second ** 2  # \"10 meters/second**2\"\n",
-    "\n",
-    "solution = solve(t == velocity / deceleration, t)  # \"Solution(t = 1.1176 seconds)\"\n",
-    "print(solution)\n",
-    "\n",
-    "solution[t]"
-   ]
-  }
- ],
- "metadata": {
-  "interpreter": {
-   "hash": "bec35ff8d3ceac10428ff23ff3d495acaf5c2f0370f6a03008458d4f010ac403"
-  },
-  "kernelspec": {
-   "display_name": "Python 3.9.1 64-bit ('mathpad-tPciuzSw-py3.9': poetry)",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.9.1"
-  },
-  "orig_nbformat": 4
- },
- "nbformat": 4,
- "nbformat_minor": 2
-}
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Solution( t = 1.1176 seconds )\n"
+     ]
+    },
+    {
+     "data": {
+      "text/latex": [
+       "$\\displaystyle \\frac{1397}{1250} \\hspace{1.25em} \\text{s}$"
+      ],
+      "text/plain": [
+       "1.1176 seconds"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "from mathpad import *\n",
+    "\n",
+    "t = \"t\" * seconds  # \"t seconds\"\n",
+    "\n",
+    "velocity = 5 * miles / hour  # \"5 miles/hour\"\n",
+    "\n",
+    "deceleration = 2 * meters / second ** 2  # \"10 meters/second**2\"\n",
+    "\n",
+    "solution = solve(t == velocity / deceleration, t)  # \"Solution(t = 1.1176 seconds)\"\n",
+    "print(solution)\n",
+    "\n",
+    "solution[t]"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3.8.10 ('mathpad-IMbbmyaw-py3.8')",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.8.10"
+  },
+  "orig_nbformat": 4,
+  "vscode": {
+   "interpreter": {
+    "hash": "c68f6f75b9b5074b455bff57bf843aee0a1a4f29736bbb117f262860b9efa145"
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2
+}

mathpad/__init__.py

@@ -11,7 +11,7 @@
 
 from mathpad.functions import piecewise, sqrt
 from mathpad.calculus import diff, integral
-from mathpad.trigonometry import cos, sin, tan, magnitude, hypotenuse
+from mathpad.trigonometry import cos, sin, tan
 from mathpad.vector_space import VectorSpace, R2, R3
 from mathpad.simulate_dynamic_system import simulate_dynamic_system
 

mathpad/trigonometry.py

@@ -14,19 +14,6 @@ def cos(x: Q[Angle]) -> Dimensionless:
 def tan(x: Q[Angle]) -> Dimensionless:
     return Dimensionless(1, sympy.tan(x.val))  # type: ignore
 
-
-def magnitude(*xs: Q[ValT]) -> ValT:
-    "x's are lengths in orthogonal directions. ie (i, j k)"
-    c_2 = 0
-    for x in xs:
-        c_2 += x ** 2
-    return sqrt(c_2)
-
-
-def hypotenuse(a: Q[Length], b: Q[Length]) -> Length:
-    return cartesian_distance(a, b)
-
-
 # TODO: add more trig functions
 
 
@@ -37,7 +24,7 @@ def sine_rule(
     beta: Q[Angle],  # internal angle opposite to side b
 ) -> Equation:
     "Relates lengths of two sides of any triangle the internal angle opposite"
-    return a == b * sin(alpha) / sin(beta)
+    return a == b * sin(alpha) / sin(beta) # type: ignore
 
 
 def cosine_rule(
@@ -46,4 +33,4 @@ def cosine_rule(
     c: Q[Length],  # length of side c
     C: Q[Angle],  # internal angle opposite to side c
 ) -> Equation:
-    return c ** 2 == a ** 2 + b ** 2 - 2 * a * b * cos(C)
+    return c ** 2 == a ** 2 + b ** 2 - 2 * a * b * cos(C) # type: ignore

mathpad/vector.py

@@ -162,8 +162,20 @@ def __neg__(self) -> Self:
         return self.__class__(self.space, -self.val) # type: ignore
 
     def __abs__(self):
-        from mathpad.trigonometry import magnitude
-        return magnitude(*self) # type: ignore
+        """
+        Returns the norm / magnitude of this vector
+
+        Raises:
+            ValueError: if the vector does not have uniform dimensionality (each base_unit in the vector space must be equivalent)
+        """
+        from mathpad.functions import sqrt
+
+        try:
+            norm_squared = sum(val ** 2 for val in self)
+        except SumDimensionsMismatch:
+            raise ValueError("Cannot take the norm of a vector with non-uniform units")
+
+        return sqrt(norm_squared)
 
     def __mul__(self, other: Q[Val]):
         return Vec(
@@ -199,6 +211,7 @@ def __repr__(self) -> str:
 
     # TODO: extend this to higher dimensions and other bases somehow
     # PS: technically cross product is only defined for 3D and 7D, but the concept of orthogonal basis vectors is more general
+    # TODO: should this only be defined for R3?
     def cross(self, other: Self) -> 'Vec':
         """
         Cross product of two vectors.