fix: some rendering bugs with negative values

src/lib-v2/canvas/index.ts

@@ -38,6 +38,8 @@ export function drawSemiplane(
         p2 = b / a2
     }
 
+    console.log('a1', a1, 'a2', a2)
+
     const normalize = Math.sqrt(a1 ** 2 + a2 ** 2) / gradientSize
 
     const gradient = g.createLinearGradient(p1, p2, p1 - a1 / normalize, p2 - a2 / normalize)
@@ -62,15 +64,33 @@ export function drawSemiplane(
         }
     } else {
         if (a2 > 0) {
-            g.moveTo(-MAX_LINE_SIZE, (b - a1 * -MAX_LINE_SIZE) / a2)
-            g.lineTo(-MAX_LINE_SIZE, MAX_LINE_SIZE)
-            g.lineTo(-MAX_LINE_SIZE, -MAX_LINE_SIZE)
-            g.lineTo(MAX_LINE_SIZE, (b - a1 * MAX_LINE_SIZE) / a2)
+            if (a1 >= 0) {
+                g.moveTo(-MAX_LINE_SIZE, (b - a1 * -MAX_LINE_SIZE) / a2)
+                g.lineTo(-MAX_LINE_SIZE, MAX_LINE_SIZE)
+                g.lineTo(-MAX_LINE_SIZE, -MAX_LINE_SIZE)
+                g.lineTo(MAX_LINE_SIZE, (b - a1 * MAX_LINE_SIZE) / a2)
+            } else {
+                g.moveTo(-MAX_LINE_SIZE, (b - a1 * -MAX_LINE_SIZE) / a2)
+                g.lineTo(-MAX_LINE_SIZE, -MAX_LINE_SIZE)
+                g.lineTo(MAX_LINE_SIZE, -MAX_LINE_SIZE)
+                g.lineTo(MAX_LINE_SIZE, (b - a1 * MAX_LINE_SIZE) / a2)
+            }
         } else {
-            g.moveTo(MAX_LINE_SIZE, (b - a1 * MAX_LINE_SIZE) / a2)
-            g.lineTo(MAX_LINE_SIZE, -MAX_LINE_SIZE)
-            g.lineTo(MAX_LINE_SIZE, MAX_LINE_SIZE)
-            g.lineTo(-MAX_LINE_SIZE, (b - a1 * -MAX_LINE_SIZE) / a2)
+            // g.moveTo(MAX_LINE_SIZE, (b - a1 * MAX_LINE_SIZE) / a2)
+            // g.lineTo(MAX_LINE_SIZE, -MAX_LINE_SIZE)
+            // g.lineTo(MAX_LINE_SIZE, MAX_LINE_SIZE)
+            // g.lineTo(-MAX_LINE_SIZE, (b - a1 * -MAX_LINE_SIZE) / a2)
+            if (a1 >= 0) {
+                g.moveTo(-MAX_LINE_SIZE, (b - a1 * -MAX_LINE_SIZE) / a2)
+                g.lineTo(-MAX_LINE_SIZE, -MAX_LINE_SIZE)
+                g.lineTo(-MAX_LINE_SIZE, MAX_LINE_SIZE)
+                g.lineTo(MAX_LINE_SIZE, (b - a1 * MAX_LINE_SIZE) / a2)
+            } else {
+                g.moveTo(-MAX_LINE_SIZE, (b - a1 * -MAX_LINE_SIZE) / a2)
+                g.lineTo(-MAX_LINE_SIZE, MAX_LINE_SIZE)
+                g.lineTo(MAX_LINE_SIZE, MAX_LINE_SIZE)
+                g.lineTo(MAX_LINE_SIZE, (b - a1 * MAX_LINE_SIZE) / a2)
+            }
         }
     }
     g.fill()

src/lib-v2/latex.ts

@@ -26,4 +26,5 @@ export const rowVectorToLatex = (vector: Vector<Rational>) =>
               .join(' & ')} \\end{bmatrix}`
         : ''
 
-export const indexSetToLatex = (indices: number[]) => `\\{${indices.map(i => (i + 1).toString()).join(', ')}\\}`
+export const indexSetToLatex = (indices: number[]) =>
+    indices.length > 0 ? `\\{${indices.map(i => (i + 1).toString()).join(', ')}\\}` : '\\varnothing'

src/lib-v2/ro/primal-simplex.ts

@@ -179,14 +179,16 @@ export function computePrimalSimplexSteps(input: ProblemInput): ProblemOutput {
                     content: `N = \\{1, \\dots, ${A.rows}\\} \\setminus B = ${indexSetToLatex(N)}`,
                 })
 
-                comments.push({
-                    type: 'formula',
-                    content: [
-                        `A_N \\xi`,
-                        `${matrixToLatex(A_N)} ${vectorToLatex(xi)}`,
-                        `${vectorToLatex(A_N__xi)}`,
-                    ].join(' = '),
-                })
+                if (N.length > 0) {
+                    comments.push({
+                        type: 'formula',
+                        content: [
+                            `A_N \\xi`,
+                            `${matrixToLatex(A_N)} ${vectorToLatex(xi)}`,
+                            `${vectorToLatex(A_N__xi)}`,
+                        ].join(' = '),
+                    })
+                }
 
                 if (!A_N__xi.getData().every(x => x.leq(RationalField.zero))) {
                     const [k, lambda] = N.filter(i => A_N__xi.at(A_N.forwardRowIndices[i]).gt(RationalField.zero))