SymPy support, and try to solve my LookAt quaternion equation.

.vscode/extensions.json

@@ -10,6 +10,7 @@
 		"brunnerh.insert-unicode",
 		"ms-python.black-formatter",
 		"ms-python.mypy-type-checker",
-		"iliazeus.vscode-ansi"
+		"iliazeus.vscode-ansi",
+		"ms-toolsai.jupyter"
 	]
-}
+}

BUILD.bazel

@@ -255,6 +255,7 @@ py_venv(
         "//project/cultist/gen/testing",
         "//py/hello_world:hello_world_bin",
         "//py/ibazel:ibazel_bin",
+        "//py/ipynb:ipynb_bin",
         "//py/sectxt:sectxt_bin",
     ],
 )

py/ipynb/BUILD.bazel

@@ -0,0 +1,15 @@
+load("//bzl:rules.bzl", "bazel_lint")
+load("//py:rules.bzl", "py_binary")
+
+py_binary(
+    name = "ipynb_bin",
+    srcs = ["__main__.py"],
+    main = "__main__.py",
+    visibility = ["//:__subpackages__"],
+    deps = ["@pip//sympy"],
+)
+
+bazel_lint(
+    name = "bazel_lint",
+    srcs = ["BUILD.bazel"],
+)

py/ipynb/__main__.py

@@ -0,0 +1,42 @@
+from sympy import Quaternion, solve, symbols, Eq
+
+centre = Quaternion(0, *symbols('c_i c_j c_k', real=True))
+
+# vector from centre upward
+up = Quaternion(0, *symbols('u_i u_j u_k', real=True))
+
+forward = Quaternion(0, *symbols('fw_i fw_j fw_k', real=True))
+
+r_w, r_i, r_j, r_k = symbols('r_w r_i r_j r_k', real=True)
+
+rotation = Quaternion(r_w, r_i, r_j, r_k)
+
+look_at = Quaternion(0, *symbols('la_i la_j la_k', real=True))
+
+centre_does_not_rotate = Eq(centre * rotation, centre)
+
+forward_will_look_at = Eq(
+	((centre - forward) * rotation).normalize(),
+	(centre - look_at).normalize()
+)
+
+length_of_forward_unchanged = Eq(
+	(forward-centre).norm(),
+    ((forward * rotation) - centre).norm()
+)
+
+up_will_still_be_up = Eq(
+    (up * rotation),
+	up
+)
+
+solve(
+    [
+		length_of_forward_unchanged,
+		centre_does_not_rotate,
+		forward_will_look_at,
+		up_will_still_be_up
+	], [
+        r_w, r_i, r_j, r_k
+	]
+)