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| 1 | +--- |
| 2 | +date: 2026-02-20T17:00:00.000Z |
| 3 | +category: uncategorized |
| 4 | +title: MathML Rendering Test |
| 5 | +layout: blog-post |
| 6 | +author: Joyee Cheung |
| 7 | +--- |
| 8 | + |
| 9 | +Testing block and inline MathML rendering. Geometric series, finite and infinite: |
| 10 | + |
| 11 | +<math display="block"> |
| 12 | + <mtable columnalign="left"> |
| 13 | + <mtr> |
| 14 | + <mtd> |
| 15 | + <msub><mi>S</mi><mi>n</mi></msub> |
| 16 | + <mo>=</mo> |
| 17 | + <munderover> |
| 18 | + <mo>∑</mo> |
| 19 | + <mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow> |
| 20 | + <mrow><mi>n</mi><mo>-</mo><mn>1</mn></mrow> |
| 21 | + </munderover> |
| 22 | + <msup><mi>r</mi><mi>k</mi></msup> |
| 23 | + <mo>=</mo> |
| 24 | + <mfrac> |
| 25 | + <mrow><mn>1</mn><mo>-</mo><msup><mi>r</mi><mi>n</mi></msup></mrow> |
| 26 | + <mrow><mn>1</mn><mo>-</mo><mi>r</mi></mrow> |
| 27 | + </mfrac> |
| 28 | + <mo>,</mo> |
| 29 | + <mspace width="0.5em"/> |
| 30 | + <mi>r</mi> |
| 31 | + <mo>≠</mo> |
| 32 | + <mn>1</mn> |
| 33 | + </mtd> |
| 34 | + </mtr> |
| 35 | + <mtr> |
| 36 | + <mtd> |
| 37 | + <msub><mi>S</mi><mo>∞</mo></msub> |
| 38 | + <mo>=</mo> |
| 39 | + <munder> |
| 40 | + <mo>∑</mo> |
| 41 | + <mrow><mi>k</mi><mo>=</mo><mn>0</mn></mrow> |
| 42 | + </munder> |
| 43 | + <msup><mi>r</mi><mi>k</mi></msup> |
| 44 | + <mo>=</mo> |
| 45 | + <mfrac> |
| 46 | + <mn>1</mn> |
| 47 | + <mrow><mn>1</mn><mo>-</mo><mi>r</mi></mrow> |
| 48 | + </mfrac> |
| 49 | + <mo>,</mo> |
| 50 | + <mspace width="0.5em"/> |
| 51 | + <mo stretchy="false">|</mo><mi>r</mi><mo stretchy="false">|</mo> |
| 52 | + <mo><</mo> |
| 53 | + <mn>1</mn> |
| 54 | + </mtd> |
| 55 | + </mtr> |
| 56 | + </mtable> |
| 57 | +</math> |
| 58 | + |
| 59 | +RMSE, where <math><msubsup><mi>e</mi><mi>i</mi><mn>2</mn></msubsup><mo>=</mo><msup><mrow><mo>(</mo><msub><mi>y</mi><mi>i</mi></msub><mo>-</mo><msub><mover><mi>y</mi><mo>^</mo></mover><mi>i</mi></msub><mo>)</mo></mrow><mn>2</mn></msup></math> and capacity grows as <math><msup><mn>2</mn><mrow><mi>N</mi><mo>-</mo><mn>1</mn></mrow></msup></math>: |
| 60 | + |
| 61 | +<math display="block"> |
| 62 | + <mtable columnalign="left"> |
| 63 | + <mtr> |
| 64 | + <mtd> |
| 65 | + <mtext>RMSE</mtext> |
| 66 | + <mo>=</mo> |
| 67 | + <msqrt> |
| 68 | + <mfrac> |
| 69 | + <mn>1</mn> |
| 70 | + <mi>N</mi> |
| 71 | + </mfrac> |
| 72 | + <munder> |
| 73 | + <mo>∑</mo> |
| 74 | + <mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow> |
| 75 | + </munder> |
| 76 | + <msup> |
| 77 | + <mrow> |
| 78 | + <mo>(</mo> |
| 79 | + <msub><mi>y</mi><mi>i</mi></msub> |
| 80 | + <mo>-</mo> |
| 81 | + <msub><mover><mi>y</mi><mo>^</mo></mover><mi>i</mi></msub> |
| 82 | + <mo>)</mo> |
| 83 | + </mrow> |
| 84 | + <mn>2</mn> |
| 85 | + </msup> |
| 86 | + </msqrt> |
| 87 | + </mtd> |
| 88 | + </mtr> |
| 89 | + <mtr> |
| 90 | + <mtd> |
| 91 | + <mtext>NRMSE</mtext> |
| 92 | + <mo>=</mo> |
| 93 | + <mn>100</mn> |
| 94 | + <mo>⋅</mo> |
| 95 | + <msqrt> |
| 96 | + <mfrac> |
| 97 | + <mn>1</mn> |
| 98 | + <msup><mi>N</mi><mn>2</mn></msup> |
| 99 | + </mfrac> |
| 100 | + <munder> |
| 101 | + <mo>∑</mo> |
| 102 | + <mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow> |
| 103 | + </munder> |
| 104 | + <msup> |
| 105 | + <mrow> |
| 106 | + <mo>(</mo> |
| 107 | + <mfrac> |
| 108 | + <mrow><msub><mi>c</mi><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>-</mo><mtext>expected</mtext></mrow> |
| 109 | + <mtext>expected</mtext> |
| 110 | + </mfrac> |
| 111 | + <mo>)</mo> |
| 112 | + </mrow> |
| 113 | + <mn>2</mn> |
| 114 | + </msup> |
| 115 | + </msqrt> |
| 116 | + </mtd> |
| 117 | + </mtr> |
| 118 | + </mtable> |
| 119 | +</math> |
| 120 | + |
| 121 | +Some inline bitwise stuff: |
| 122 | + |
| 123 | +- <math><mi>a</mi><mo>⊕</mo><mi>b</mi><mo>⊕</mo><mi>b</mi><mo>=</mo><mi>a</mi></math> |
| 124 | +- <math><mi>x</mi><mspace width="0.3em"/><mo>&</mo><mspace width="0.3em"/><mo stretchy="false">(</mo><msup><mn>2</mn><mi>k</mi></msup><mo>-</mo><mn>1</mn><mo stretchy="false">)</mo><mo>≡</mo><mi>x</mi><mspace width="0.5em"/><mo>(</mo><mtext>mod</mtext><mspace width="0.3em"/><msup><mn>2</mn><mi>k</mi></msup><mo>)</mo></math> |
| 125 | +- <math><mo>-</mo><mi>x</mi><mo>=</mo><mo>¬</mo><mi>x</mi><mo>+</mo><mn>1</mn></math> |
| 126 | +- <math><mi>x</mi><mo><<</mo><mi>k</mi><mo>=</mo><mi>x</mi><mo>⋅</mo><msup><mn>2</mn><mi>k</mi></msup></math> |
| 127 | +- <math><mi>x</mi><mo>>></mo><mi>k</mi><mo>=</mo><mo>⌊</mo><mi>x</mi><mo>/</mo><msup><mn>2</mn><mi>k</mi></msup><mo>⌋</mo></math> |
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