mathmlben
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Visualization for goldstandard
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text/mathml
<math
xmlns="http://www.w3.org/1998/Math/MathML">
<semantics>
<mrow>
<mrow>
<mo>(</mo>
<mfrac>
<mi>a</mi>
<mi>p</mi>
</mfrac>
<mo>)</mo>
</mrow>
<mo>=</mo>
<mrow>
<mo>{</mo>
<mtable displaystyle="false" columnalign="left left">
<mtr>
<mtd>
<mn>1</mn>
</mtd>
<mtd>
<mtext> if </mtext>
<mi>a</mi>
<mtext> is a quadratic residue modulo </mtext>
<mi>p</mi>
<mtext> and </mtext>
<mi>a</mi>
<mo>¬</mo>
<mo>≡</mo>
<mn>0</mn>
<mrow>
<mo lspace="mediummathspace">(</mo>
<mo rspace="thinmathspace">mod</mo>
<mi>p</mi>
<mo rspace="mediummathspace">)</mo>
</mrow>
<mo>,</mo>
<mtext>\</mtext>
<mo>-</mo>
<mn>1</mn>
</mtd>
<mtd>
<mtext> if </mtext>
<mi>a</mi>
<mtext> is a quadratic non-residue modulo </mtext>
<mi>p</mi>
<mo>,</mo>
<mtext>\</mtext>
<mn>0</mn>
</mtd>
<mtd>
<mtext> if </mtext>
<mi>a</mi>
<mo>≡</mo>
<mn>0</mn>
<mrow>
<mo lspace="mediummathspace">(</mo>
<mo rspace="thinmathspace">mod</mo>
<mi>p</mi>
<mo rspace="mediummathspace">)</mo>
</mrow>
<mo>.</mo>
</mtd>
</mtr>
</mtable>
</mrow>
</mrow>
<annotation encoding="TeX">\left(\frac{a}{p}\right) = \begin{cases} 1 & \text{ if } a \text{ is a quadratic residue modulo } p \text{ and } a \not\equiv 0\pmod{p}, \ -1 & \text{ if } a \text{ is a quadratic non-residue modulo } p, \ 0 & \text{ if } a \equiv 0 \pmod{p}. \end{cases}</annotation>
</semantics>
</math>