Editing Knot polynomial (section)

==Examples==
{| class="wikitable"
|-
! [[Alexander–Briggs notation]] !! [[Alexander polynomial]] <math>\Delta(t)</math> !!  [[Alexander polynomial#Alexander.E2.80.93Conway polynomial|Conway polynomial]] <math>\nabla(z) </math> !! [[Jones polynomial]]  <math>V(q)</math> !! [[HOMFLY polynomial]] <math>H(a,z)</math>
|-
|<math>0_1</math> ([[Unknot]])|| <math>1</math> || <math>1</math> || <math>1</math> || <math>1</math>
|-
|<math>3_1</math> ([[Trefoil knot|Trefoil Knot]])|| <math>t - 1 + t^{-1}</math> || <math>z^2 + 1</math> || <math>q^{-1} + q^{-3} - q^{-4}</math> || <math>-a^{4}+a^{2}z^{2}+2a^{2}</math>
|-
| <math>4_1</math> ([[Figure-eight knot (mathematics)|Figure-eight Knot]]) || <math>-t + 3 - t^{-1}</math> || <math>-z^2+1</math> || <math>q^2 - q + 1 - q^{-1} + q^{-2}</math> || <math>a^{2}+a^{-2}-z^{2}-1</math>
|-
| <math>5_1</math> ([[Cinquefoil knot|Cinquefoil Knot]]) || <math>t^2 - t + 1 - t^{-1} + t^{-2}</math> || <math>z^4 + 3z^2 + 1</math> || <math>q^{-2} + q^{-4} - q^{-5} + q^{-6} - q^{-7}</math> || <math>-a^{6}z^{2}-2a^{6}+a^{4}z^{4}+4a^{4}z^{2}+3a^{4}</math>
|-
| <math>3_1 \# 3_1</math> ([[Granny knot (mathematics)|Granny Knot]]) || <math>\left(t - 1 + t^{-1}\right)^2</math> || <math>\left(z^2 + 1\right)^2</math> || <math>\left(q^{-1} + q^{-3} - q^{-4}\right)^2</math> || <math>\left(-a^{4}+a^{2}z^{2}+2a^{2}\right)^2</math>
|-
| <math>3_1 \# 3^*_1</math> ([[Square knot (mathematics)|Square Knot]]) || <math>\left(t - 1 + t^{-1}\right)^2</math> || <math>\left(z^2 + 1\right)^2</math> || <math>\left(q^{-1} + q^{-3} - q^{-4}\right)\left(q + q^{3} - q^{4}\right)</math> || <math>\left(-a^{4}+a^{2}z^{2}+2a^{2}\right) \times</math> <br/> <math>\left(-a^{-4}+a^{-2}z^{-2}+2a^{-2}\right)</math>
|}

[[Alexander–Briggs notation]] organizes knots by their crossing number.

[[Alexander polynomial]]s and [[Alexander polynomial#Alexander.E2.80.93Conway polynomial|Conway polynomial]]s can ''not'' recognize the difference of left-trefoil knot and right-trefoil knot.
<gallery widths="60px" heights="60px" align="center">
Image:Trefoil knot left.svg|The left-trefoil knot.
Image:TrefoilKnot_01.svg|The right-trefoil knot.
</gallery>
So we have the same situation as the granny knot and square knot since the [[Knot theory#Adding knots|addition]] of knots in <math>\mathbb{R}^3</math> is the product of knots in [[Knot theory#Knot polynomials|knot polynomials]].