formula fix

docs/chapters/canonical/content.en-GB.md

@@ -248,6 +248,18 @@ First, let's just do that translation step as a "preprocessing" operation so we
     \cdot
     \left (  x_4 - \frac{x_2 \cdot y_4}{y_2} / x_3-\frac{x_2 \cdot y_3}{y_2} \right )
   \end{matrix}
+\right ) = \left (
+  \begin{matrix}
+   x_{43}
+\\
+\\
+    \frac{y_4}{y_2}
+    +
+    x_{43}
+    \left ( 1 - \frac{y_3}{y_2} \right )
+  \end{matrix}
+\right ),\textit{ where } x_{43} = \left (
+  x_4 - \frac{x_2 \cdot y_4}{y_2} \middle / x_3-\frac{x_2 \cdot y_3}{y_2}
 \right )
 \]
 
@@ -256,16 +268,17 @@ Suddenly things look a lot simpler: the mapped x is fairly straight forward to c
 \[
 ... = \left (
   \begin{matrix}
-   \left ( x_4 - x_2 \cdot y_{42} \right ) / \left (  x_3- x_2 \cdot y_{32}  \right )
+   x_{43}
 \\
 \\
     y_{42}
     +
+    x_{43}
     \left ( 1 - y_{32} \right )
-    \cdot
-    x
   \end{matrix}
-\right ),\textit{ where } y_{32} = \frac{y_3}{y_2},\textit{ and } \ y_{42} = \frac{y_4}{y_2}
+\right ), \textit{ where } x_{43} = \left (
+  \frac{x_4 - x_2 \cdot y_{42}}{x_3 - x_2 \cdot y_{32}}
+\right ), \textit{ } y_{42} = \frac{y_4}{y_2}, \textit{ and } y_{32} = \frac{y_3}{y_2}
 \]
 
 That's kind of super-simple to write out in code, I think you'll agree. Coding math tends to be easier than the formulae initially make it look!

docs/index.html

@@ -4000,8 +4000,8 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/63ccae0ebe0ca70dc2afb507ab32e4bd.svg"
-                width="187px"
-                height="36px"
+                width="180px"
+                height="37px"
                 loading="lazy"
               />
             </li>
@@ -4014,8 +4014,8 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/add5f7fb210a306fe9ff933113f6fb91.svg"
-                width="241px"
-                height="37px"
+                width="231px"
+                height="39px"
                 loading="lazy"
               />
             </li>
@@ -4027,7 +4027,7 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/4230e959138d8400e04abf316360009a.svg"
-                width="159px"
+                width="153px"
                 height="37px"
                 loading="lazy"
               />
@@ -4156,7 +4156,7 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/10025fdab2b3fd20f5d389cbe7e3e3ce.svg"
-            width="208px"
+            width="195px"
             height="53px"
             loading="lazy"
           />
@@ -4168,8 +4168,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/20684d22b3ddc52fd6abde8ce56608a9.svg"
-            width="135px"
-            height="65px"
+            width="133px"
+            height="67px"
             loading="lazy"
           />
           <p>
@@ -4189,8 +4189,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/8cbef24b8c3b26f9daf2f89d27d36e95.svg"
-            width="136px"
-            height="67px"
+            width="137px"
+            height="71px"
             loading="lazy"
           />
           <p>
@@ -4210,7 +4210,7 @@ function getCubicRoots(pa, pb, pc, pd) {
             class="LaTeX SVG"
             src="./images/chapters/canonical/0430e8c7f7d4ec80e6527f96f3d56e5c.svg"
             width="140px"
-            height="63px"
+            height="65px"
             loading="lazy"
           />
           <p>
@@ -4242,8 +4242,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           </p>
           <img
             class="LaTeX SVG"
-            src="./images/chapters/canonical/16fad73cbbbd2202b08ebef05b1579c5.svg"
-            width="317px"
+            src="./images/chapters/canonical/13c09950363c33627fd3a20343f2f6ce.svg"
+            width="775px"
             height="67px"
             loading="lazy"
           />
@@ -4256,9 +4256,9 @@ function getCubicRoots(pa, pb, pc, pd) {
           </p>
           <img
             class="LaTeX SVG"
-            src="./images/chapters/canonical/5af3d1772ee07e634d04259a02f7201f.svg"
-            width="483px"
-            height="56px"
+            src="./images/chapters/canonical/ddee51855ef3a9ee7660c395b0a041c7.svg"
+            width="563px"
+            height="55px"
             loading="lazy"
           />
           <p>

docs/ja-JP/index.html

@@ -3708,8 +3708,8 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/63ccae0ebe0ca70dc2afb507ab32e4bd.svg"
-                width="187px"
-                height="36px"
+                width="180px"
+                height="37px"
                 loading="lazy"
               />
             </li>
@@ -3722,8 +3722,8 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/add5f7fb210a306fe9ff933113f6fb91.svg"
-                width="241px"
-                height="37px"
+                width="231px"
+                height="39px"
                 loading="lazy"
               />
             </li>
@@ -3735,7 +3735,7 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/4230e959138d8400e04abf316360009a.svg"
-                width="159px"
+                width="153px"
                 height="37px"
                 loading="lazy"
               />
@@ -3864,7 +3864,7 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/10025fdab2b3fd20f5d389cbe7e3e3ce.svg"
-            width="208px"
+            width="195px"
             height="53px"
             loading="lazy"
           />
@@ -3876,8 +3876,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/20684d22b3ddc52fd6abde8ce56608a9.svg"
-            width="135px"
-            height="65px"
+            width="133px"
+            height="67px"
             loading="lazy"
           />
           <p>
@@ -3897,8 +3897,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/8cbef24b8c3b26f9daf2f89d27d36e95.svg"
-            width="136px"
-            height="67px"
+            width="137px"
+            height="71px"
             loading="lazy"
           />
           <p>
@@ -3918,7 +3918,7 @@ function getCubicRoots(pa, pb, pc, pd) {
             class="LaTeX SVG"
             src="./images/chapters/canonical/0430e8c7f7d4ec80e6527f96f3d56e5c.svg"
             width="140px"
-            height="63px"
+            height="65px"
             loading="lazy"
           />
           <p>
@@ -3950,8 +3950,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           </p>
           <img
             class="LaTeX SVG"
-            src="./images/chapters/canonical/16fad73cbbbd2202b08ebef05b1579c5.svg"
-            width="317px"
+            src="./images/chapters/canonical/13c09950363c33627fd3a20343f2f6ce.svg"
+            width="775px"
             height="67px"
             loading="lazy"
           />
@@ -3964,9 +3964,9 @@ function getCubicRoots(pa, pb, pc, pd) {
           </p>
           <img
             class="LaTeX SVG"
-            src="./images/chapters/canonical/5af3d1772ee07e634d04259a02f7201f.svg"
-            width="483px"
-            height="56px"
+            src="./images/chapters/canonical/ddee51855ef3a9ee7660c395b0a041c7.svg"
+            width="563px"
+            height="55px"
             loading="lazy"
           />
           <p>

docs/zh-CN/index.html

@@ -3718,8 +3718,8 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/63ccae0ebe0ca70dc2afb507ab32e4bd.svg"
-                width="187px"
-                height="36px"
+                width="180px"
+                height="37px"
                 loading="lazy"
               />
             </li>
@@ -3732,8 +3732,8 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/add5f7fb210a306fe9ff933113f6fb91.svg"
-                width="241px"
-                height="37px"
+                width="231px"
+                height="39px"
                 loading="lazy"
               />
             </li>
@@ -3745,7 +3745,7 @@ function getCubicRoots(pa, pb, pc, pd) {
               <img
                 class="LaTeX SVG"
                 src="./images/chapters/canonical/4230e959138d8400e04abf316360009a.svg"
-                width="159px"
+                width="153px"
                 height="37px"
                 loading="lazy"
               />
@@ -3874,7 +3874,7 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/10025fdab2b3fd20f5d389cbe7e3e3ce.svg"
-            width="208px"
+            width="195px"
             height="53px"
             loading="lazy"
           />
@@ -3886,8 +3886,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/20684d22b3ddc52fd6abde8ce56608a9.svg"
-            width="135px"
-            height="65px"
+            width="133px"
+            height="67px"
             loading="lazy"
           />
           <p>
@@ -3907,8 +3907,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           <img
             class="LaTeX SVG"
             src="./images/chapters/canonical/8cbef24b8c3b26f9daf2f89d27d36e95.svg"
-            width="136px"
-            height="67px"
+            width="137px"
+            height="71px"
             loading="lazy"
           />
           <p>
@@ -3928,7 +3928,7 @@ function getCubicRoots(pa, pb, pc, pd) {
             class="LaTeX SVG"
             src="./images/chapters/canonical/0430e8c7f7d4ec80e6527f96f3d56e5c.svg"
             width="140px"
-            height="63px"
+            height="65px"
             loading="lazy"
           />
           <p>
@@ -3960,8 +3960,8 @@ function getCubicRoots(pa, pb, pc, pd) {
           </p>
           <img
             class="LaTeX SVG"
-            src="./images/chapters/canonical/16fad73cbbbd2202b08ebef05b1579c5.svg"
-            width="317px"
+            src="./images/chapters/canonical/13c09950363c33627fd3a20343f2f6ce.svg"
+            width="775px"
             height="67px"
             loading="lazy"
           />
@@ -3974,9 +3974,9 @@ function getCubicRoots(pa, pb, pc, pd) {
           </p>
           <img
             class="LaTeX SVG"
-            src="./images/chapters/canonical/5af3d1772ee07e634d04259a02f7201f.svg"
-            width="483px"
-            height="56px"
+            src="./images/chapters/canonical/ddee51855ef3a9ee7660c395b0a041c7.svg"
+            width="563px"
+            height="55px"
             loading="lazy"
           />
           <p>