diff --git a/engine-proto/ConstructionViewer.jl b/engine-proto/ConstructionViewer.jl
deleted file mode 100644
index 7cb0450..0000000
--- a/engine-proto/ConstructionViewer.jl
+++ /dev/null
@@ -1,203 +0,0 @@
-module Viewer
-
-using Blink
-using Colors
-using Printf
-
-export ConstructionViewer, display!, opentools!, closetools!
-
-# === Blink utilities ===
-
-append_to_head!(w, type, content) = @js w begin
-  @var element = document.createElement($type)
-  element.appendChild(document.createTextNode($content))
-  document.head.appendChild(element)
-end
-
-style!(w, stylesheet) = append_to_head!(w, "style", stylesheet)
-
-script!(w, code) = append_to_head!(w, "script", code)
-
-# === construction viewer ===
-
-mutable struct ConstructionViewer
-  win::Window
-  
-  function ConstructionViewer()
-    # create window and open developer console
-    win = Window(Blink.Dict(:width => 620, :height => 830))
-    
-    # set stylesheet
-    style!(win, """
-      body {
-        background-color: #ccc;
-      }
-      
-      /* the maximum dimensions keep Ganja from blowing up the canvas */
-      #view {
-        display: block;
-        width: 600px;
-        height: 600px;
-        margin-top: 10px;
-        margin-left: 10px;
-        border-radius: 10px;
-        background-color: #f0f0f0;
-      }
-      
-      #control-panel {
-        width: 600px;
-        height: 200px;
-        box-sizing: border-box;
-        padding: 5px 10px 5px 10px;
-        margin-top: 10px;
-        margin-left: 10px;
-        overflow-y: scroll;
-        border-radius: 10px;
-        background-color: #f0f0f0;
-      }
-      
-      #control-panel > div {
-        margin-top: 5px;
-        padding: 4px;
-        border-radius: 5px;
-        border: solid;
-        font-family: monospace;
-      }
-    """)
-    
-    # load Ganja.js
-    loadjs!(win, "https://unpkg.com/ganja.js")
-    
-    # create global functions and variables
-    script!(win, """
-      // create algebra
-      var CGA3 = Algebra(4, 1);
-      
-      // initialize element list and palette
-      var elements = [];
-      var palette = [];
-      
-      // declare handles for the view and its options
-      var view;
-      var viewOpt;
-      
-      // declare handles for the controls
-      var controlPanel;
-      var visToggles;
-      
-      // create scene function
-      function scene() {
-        commands = [];
-        for (let n = 0; n < elements.length; ++n) {
-          if (visToggles[n].checked) {
-            commands.push(palette[n], elements[n]);
-          }
-        }
-        return commands;
-      }
-      
-      function updateView() {
-        requestAnimationFrame(view.update.bind(view, scene));
-      }
-    """)
-    
-    @js win begin
-      # create view
-      viewOpt = Dict(
-        :conformal => true,
-        :gl => true,
-        :devicePixelRatio => window.devicePixelRatio
-      )
-      view = CGA3.graph(scene, viewOpt)
-      view.setAttribute(:id, "view")
-      view.removeAttribute(:style)
-      document.body.replaceChildren(view)
-      
-      # create control panel
-      controlPanel = document.createElement(:div)
-      controlPanel.setAttribute(:id, "control-panel")
-      document.body.appendChild(controlPanel)
-    end
-    
-    new(win)
-  end
-end
-
-function display!(viewer::ConstructionViewer, elements::Matrix)
-  # load elements
-  elements_full = [
-    [0; elt; fill(0, 26)]
-    for elt in eachcol(elements)
-  ]
-  @js viewer.win elements = $elements_full.map((elt) -> @new CGA3(elt))
-  
-  # generate palette. this is Gadfly's `default_discrete_colors` palette,
-  # available under the MIT license
-  palette = distinguishable_colors(
-    length(elements_full),
-    [LCHab(70, 60, 240)],
-    transform = c -> deuteranopic(c, 0.5),
-    lchoices = Float64[65, 70, 75, 80],
-    cchoices = Float64[0, 50, 60, 70],
-    hchoices = range(0, stop=330, length=24)
-  )
-  palette_packed = [RGB24(c).color for c in palette]
-  @js viewer.win palette = $palette_packed
-  
-  # create visibility toggles
-  @js viewer.win begin
-    controlPanel.replaceChildren()
-    visToggles = []
-  end
-  for (elt, c) in zip(eachcol(elements), palette)
-    vec_str = join(map(t -> @sprintf("%.3f", t), elt), ", ")
-    color_str = "#$(hex(c))"
-    style_str = "background-color: $color_str; border-color: $color_str;"
-    @js viewer.win begin
-      @var toggle = document.createElement(:div)
-      toggle.setAttribute(:style, $style_str)
-      toggle.checked = true
-      toggle.addEventListener(
-        "click",
-        () -> begin
-          toggle.checked = !toggle.checked
-          toggle.style.backgroundColor = toggle.checked ? $color_str : "inherit";
-          updateView()
-        end
-      )
-      toggle.appendChild(document.createTextNode($vec_str))
-      visToggles.push(toggle);
-      controlPanel.appendChild(toggle);
-    end
-  end
-  
-  # update view
-  @js viewer.win updateView()
-end
-
-function opentools!(viewer::ConstructionViewer)
-  size(viewer.win, 1240, 830)
-  opentools(viewer.win)
-end
-
-function closetools!(viewer::ConstructionViewer)
-  closetools(viewer.win)
-  size(viewer.win, 620, 830)
-end
-
-end
-
-# ~~~ sandbox setup ~~~
-
-# in the default view, e4 + e5 is the point at infinity
-elements = sqrt(0.5) * BigFloat[
-  1  1 -1 -1  0;
-  1 -1  1 -1  0;
-  1 -1 -1  1  0;
-  0  0  0  0 -sqrt(6);
-  1  1  1  1  2
-]
-
-# show construction
-viewer = Viewer.ConstructionViewer()
-Viewer.display!(viewer, elements)
\ No newline at end of file
diff --git a/engine-proto/ganja-test/ganja-test.html b/engine-proto/ganja-test/ganja-test.html
deleted file mode 100644
index d6efc90..0000000
--- a/engine-proto/ganja-test/ganja-test.html
+++ /dev/null
@@ -1,76 +0,0 @@
-<!DOCTYPE html>
-<html>
-<head>
-  <style>
-    body {
-      background-color: #ffe0f0;
-    }
-    
-    /* needed to keep Ganja canvas from blowing up */
-    canvas {
-      min-width: 600px;
-      max-width: 600px;
-      min-height: 600px;
-      max-height: 600px;
-    }
-  </style>
-  <script src="https://unpkg.com/ganja.js"></script>
-</head>
-<body>
-  <p><button onclick="flip()">Flip</button></p>
-  <script>
-  // in the default view, e4 + e5 is the point at infinity
-  let CGA3 = Algebra(4, 1);
-  let elements = [
-    CGA3.inline(() => Math.sqrt(0.5)*( 1e1 + 1e2 + 1e3 + 1e5))(),
-    CGA3.inline(() => Math.sqrt(0.5)*( 1e1 - 1e2 - 1e3 + 1e5))(),
-    CGA3.inline(() => Math.sqrt(0.5)*(-1e1 + 1e2 - 1e3 + 1e5))(),
-    CGA3.inline(() => Math.sqrt(0.5)*(-1e1 - 1e2 + 1e3 + 1e5))(),
-    CGA3.inline(() => -Math.sqrt(3)*1e4 + Math.sqrt(2)*1e5)()
-  ];
-  
-  // set up palette
-  var colorIndex;
-  var palette = [0xff00b0, 0x00ffb0, 0x00b0ff, 0x8040ff, 0xc0c0c0];
-  function nextColor() {
-    colorIndex = (colorIndex + 1) % palette.length;
-    return palette[colorIndex];
-  }
-  function resetColorCycle() {
-    colorIndex = palette.length - 1;
-  }
-  resetColorCycle();
-  
-  // create scene function
-  function scene() {
-    commands = [];
-    resetColorCycle();
-    elements.forEach((elt) => commands.push(nextColor(), elt));
-    return commands;
-  }
-  
-  // initialize graph
-  let graph = CGA3.graph(
-    scene,
-    {
-      conformal: true, gl: true, grid: true
-    }
-  )
-  document.body.appendChild(graph);
-  
-  function flip() {
-    let last = elements.length - 1;
-    for (let n = 0; n < last; ++n) {
-      // reflect
-      elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
-      
-      // de-noise
-      for (let k = 6; k < elements[n].length; ++k) {
-        elements[n][k] = 0;
-      }
-    }
-    requestAnimationFrame(graph.update.bind(graph, scene));
-  }
-  </script>
-</body>
-</html>
diff --git a/engine-proto/ganja-test/ganja-test.jl b/engine-proto/ganja-test/ganja-test.jl
deleted file mode 100644
index 6c55061..0000000
--- a/engine-proto/ganja-test/ganja-test.jl
+++ /dev/null
@@ -1,127 +0,0 @@
-using Blink
-using Colors
-
-# === utilities ===
-
-append_to_head!(w, type, content) = @js w begin
-  @var element = document.createElement($type)
-  element.appendChild(document.createTextNode($content))
-  document.head.appendChild(element)
-end
-
-style!(w, stylesheet) = append_to_head!(w, "style", stylesheet)
-
-script!(w, code) = append_to_head!(w, "script", code)
-
-function add_element!(vec)
-  # add element
-  full_vec = [0; vec; fill(0, 26)]
-  n = @js win elements.push(@new CGA3($full_vec))
-  
-  # generate palette. this is Gadfly's `default_discrete_colors` palette,
-  # available under the MIT license
-  palette = distinguishable_colors(
-    n,
-    [LCHab(70, 60, 240)],
-    transform = c -> deuteranopic(c, 0.5),
-    lchoices = Float64[65, 70, 75, 80],
-    cchoices = Float64[0, 50, 60, 70],
-    hchoices = range(0, stop=330, length=24)
-  )
-  palette_packed = [RGB24(c).color for c in palette]
-  @js win palette = $palette_packed
-end
-
-# === build page ===
-
-# create window and open developer console
-win = Window()
-opentools(win)
-
-# set stylesheet
-style!(win, """
-  body {
-    background-color: #ffe0f0;
-  }
-
-  /* needed to keep Ganja canvas from blowing up */
-  canvas {
-    min-width: 600px;
-    max-width: 600px;
-    min-height: 600px;
-    max-height: 600px;
-  }
-""")
-
-# load Ganja.js
-loadjs!(win, "https://unpkg.com/ganja.js")
-
-# create global functions and variables
-script!(win, """
-  // create algebra
-  var CGA3 = Algebra(4, 1);
-  
-  // initialize element list and palette
-  var elements = [];
-  var palette = [];
-  
-  // declare visualization handle
-  var graph;
-  
-  // create scene function
-  function scene() {
-    commands = [];
-    for (let n = 0; n < elements.length; ++n) {
-      commands.push(palette[n], elements[n]);
-    }
-    return commands;
-  }
-  
-  function flip() {
-    let last = elements.length - 1;
-    for (let n = 0; n < last; ++n) {
-      // reflect
-      elements[n] = CGA3.Mul(CGA3.Mul(elements[last], elements[n]), elements[last]);
-      
-      // de-noise
-      for (let k = 6; k < elements[n].length; ++k) {
-        elements[n][k] = 0;
-      }
-    }
-    requestAnimationFrame(graph.update.bind(graph, scene));
-  }
-""")
-
-# set up controls
-body!(win, """
-  <p><button id="flip-button" onclick="flip()">Flip</button></p>
-""", async = false)
-
-# === set up visualization ===
-
-# list elements. in the default view, e4 + e5 is the point at infinity
-elements = sqrt(0.5) * BigFloat[
-  1  1 -1 -1  0;
-  1 -1  1 -1  0;
-  1 -1 -1  1  0;
-  0  0  0  0 -sqrt(6);
-  1  1  1  1  2
-]
-
-# load elements
-for vec in eachcol(elements)
-  add_element!(vec)
-end
-
-# initialize visualization
-@js win begin
-  graph = CGA3.graph(
-    scene,
-    Dict(
-      "conformal" => true,
-      "gl" => true,
-      "grid" => true
-    )
-  )
-  document.body.appendChild(graph)
-end
\ No newline at end of file
diff --git a/engine-proto/gram-test/descent-test.jl b/engine-proto/gram-test/descent-test.jl
index 2f20143..9b6fb7a 100644
--- a/engine-proto/gram-test/descent-test.jl
+++ b/engine-proto/gram-test/descent-test.jl
@@ -10,10 +10,10 @@ using PolynomialRoots
 # the difference between the matrices `target` and `attempt`, projected onto the
 # subspace of matrices whose entries vanish at each empty index of `target`
 function proj_diff(target, attempt)
-  J, K, values = findnz(target)
+  I, J, values = findnz(target)
   result = zeros(size(target)...)
-  for (j, k, val) in zip(J, K, values)
-    result[j, k] = val - attempt[j, k]
+  for (i, j, val) in zip(I, J, values)
+    result[i, j] = val - attempt[i, j]
   end
   result
 end
@@ -21,24 +21,24 @@ end
 # === example ===
 
 # the Lorentz form
-Q = diagm([1, 1, 1, 1, -1])
+Q = diagm([-1, 1, 1, 1, 1])
 
 # initialize the partial gram matrix for an arrangement of seven spheres in
 # which spheres 1 through 5 are mutually tangent, and spheres 3 through 7 are
 # also mutually tangent
+I = Int64[]
 J = Int64[]
-K = Int64[]
 values = BigFloat[]
-for j in 1:7
-  for k in 1:7
-    if (j <= 5 && k <= 5) || (j >= 3 && k >= 3)
+for i in 1:7
+  for j in 1:7
+    if (i <= 5 && j <= 5) || (i >= 3 && j >= 3)
+      push!(I, i)
       push!(J, j)
-      push!(K, k)
-      push!(values, j == k ? 1 : -1)
+      push!(values, i == j ? 1 : -1)
     end
   end
 end
-gram = sparse(J, K, values)
+gram = sparse(I, J, values)
 
 # set the independent variable
 #
@@ -54,11 +54,11 @@ gram[1, 6] = gram[6, 1]
 # in this initial guess, the mutual tangency condition is satisfied for spheres
 # 1 through 5
 guess = sqrt(0.5) * BigFloat[
+  1  1  1  1  2        0.2  0.1;
+  0  0  0  0 -sqrt(6)  0.3 -0.2;
   1  1 -1 -1  0       -0.1  0.3;
   1 -1  1 -1  0       -0.5  0.4;
-  1 -1 -1  1  0        0.1 -0.2;
-  0  0  0  0 -sqrt(6)  0.3 -0.2;
-  1  1  1  1  2        0.2  0.1;
+  1 -1 -1  1  0        0.1 -0.2
 ]
 
 # search parameters
@@ -108,11 +108,11 @@ println("\nLoss: ", loss, "\n")
 
 # === algebraic check ===
 
-R, gens = polynomial_ring(AbstractAlgebra.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
+R, gens = polynomial_ring(Generic.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
 x = gens[1]
 t = gens[2:4]
 
-S, u = polynomial_ring(AbstractAlgebra.Rationals{BigInt}(), "u")
+S, u = polynomial_ring(Generic.Rationals{BigInt}(), "u")
 
 M = matrix_space(R, 7, 7)
 gram_symb = M(R[
diff --git a/engine-proto/gram-test/gram-test.jl b/engine-proto/gram-test/gram-test.jl
index 0e88ff4..4b2f859 100644
--- a/engine-proto/gram-test/gram-test.jl
+++ b/engine-proto/gram-test/gram-test.jl
@@ -11,7 +11,7 @@ function printbad(msg)
   println(" ", msg)
 end
 
-F, gens = rational_function_field(AbstractAlgebra.Rationals{BigInt}(), ["a₁", "a₂", "b₁", "b₂", "c₁", "c₂"])
+F, gens = rational_function_field(Generic.Rationals{BigInt}(), ["a₁", "a₂", "b₁", "b₂", "c₁", "c₂"])
 a = gens[1:2]
 b = gens[3:4]
 c = gens[5:6]
diff --git a/engine-proto/gram-test/overlap-test.jl b/engine-proto/gram-test/overlap-test.jl
index e75531a..beeaeca 100644
--- a/engine-proto/gram-test/overlap-test.jl
+++ b/engine-proto/gram-test/overlap-test.jl
@@ -11,7 +11,7 @@ function printbad(msg)
   println(" ", msg)
 end
 
-F, gens = rational_function_field(AbstractAlgebra.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
+F, gens = rational_function_field(Generic.Rationals{BigInt}(), ["x", "t₁", "t₂", "t₃"])
 x = gens[1]
 t = gens[2:4]