查看“︁0Yψ vs 拓展HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影分析”︁的源代码

上篇：[[0Yψ vs HPrSSψ vs 强LPrSS投影 vs 弱LPrSS投影 分析]]

== 分析1：(0)(1,1,1,1)~(0)(1,1,1,1)(2,1) ==
{| class="wikitable" style="white-space: nowrap;"
|+
!0Yψ
!强LPrSS投影
!拓展HPrSSψ
!弱LPrSS投影
!弱LPrSS向上投影
!BMS
|-
|<math>\psi(\Omega_3)</math>
|<math>\psi(a)</math>
|<math>\psi(\Omega_\omega)</math>
|<math>\psi(\sigma^\omega a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega))</math>
|(0)(1,1,1,1)
|-
|<math>\psi(\Omega_3+\Omega)</math>
|<math>\psi(a+\Omega)</math>
|<math>\psi(\Omega_\omega+\Omega)</math>
|<math>\psi(\sigma^\omega a+\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega)</math>
|(0)(1,1,1,1)(1,1)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_3))</math>
|<math>\psi(a+\psi_1(\Omega_3))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_3))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\Omega_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\Omega_3))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(a+\psi_1(\Omega_4))</math>
|<math>\psi(\Omega_\omega+\psi_1(\psi_3(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\Omega_4))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\Omega_4))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,1)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\Omega_6)))</math>
|<math>\psi(a+\psi_1(\psi_a(a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_4))</math>
|<math>\psi(\sigma^\omega a+\psi_1(a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(a))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_1(\psi_3(\psi_6(\Omega_{10}))))</math>
|<math>\psi(a+\psi_1(\psi_a(\psi_{\sigma a}(\sigma a_2))))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_5))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(1,1)(2,2,1)(3,3,2)(4,4,3)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4))</math>
|<math>\psi(a+\psi_1(a))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4+\Omega_2))</math>
|<math>\psi(a+\psi_1(a+\Omega_2))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\Omega_2))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a+\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)+\Omega_2))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)(2,2)
|-
|<math>\psi(\Omega_3+\psi_1(\Omega_4+\psi_2(\Omega_5)))</math>
|<math>\psi(a+\psi_1(a+\psi_2(a)))</math>
|<math>\psi(\Omega_\omega+\psi_1(\Omega_\omega+\psi_2(\Omega_\omega)))</math>
|<math>\psi(\sigma^\omega a+\psi_1(\sigma^\omega a+\psi_2(\sigma^\omega a)))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_1(\psi_S(\sigma S\times\omega)+\psi_2(\psi_S(\sigma S\times\omega))))</math>
|(0)(1,1,1,1)(1,1)(2,2,1,1)(2,2)(3,3,1,1)
|-
|<math>\psi(\Omega_3+\Omega_2)</math>
|<math>\psi(a+\Omega_2)</math>
|<math>\psi(\Omega_\omega+\Omega_2)</math>
|<math>\psi(\sigma^\omega a+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_2)</math>
|(0)(1,1,1,1)(1,1,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4))</math>
|<math>\psi(a+\Omega_3)</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4))</math>
|<math>\psi(\sigma^\omega a+\Omega_3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_3)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4\omega))</math>
|<math>\psi(a+\Omega_\omega)</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4\omega))</math>
|<math>\psi(\sigma^\omega a+\Omega_\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\Omega_\omega)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(a+\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4\Omega_3))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+1}a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+1}a))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_4^2))</math>
|<math>\psi(a+\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_4^2))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+1}^2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+1}^2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_4(\Omega_5)))</math>
|<math>\psi(a+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_4(\Omega_5)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\varepsilon_{\Omega_{a+1}+1}))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_4(\Omega_6)))</math>
|<math>\psi(a+\psi_a(\Omega_{a+2}))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_4(\Omega_6)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\Omega_{a+2}))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\Omega_{a+2}))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,1)(3,3,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_5))</math>
|<math>\psi(a+\psi_a(a_2))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_5))</math>
|<math>\psi(\sigma^\omega a+\psi_a(a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(a_2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_5(\Omega_8)))</math>
|<math>\psi(a+\psi_a(a_3))</math>
|<math>\psi(\Omega_\omega+\psi_2(\psi_5(\Omega_8)))</math>
|<math>\psi(\sigma^\omega a+\psi_a(a_3))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(a_3))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\psi_5(\Omega_9)))</math>
|<math>\psi(a+\psi_a(\psi_{\sigma a}(\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_6))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times3)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6))</math>
|<math>\psi(a+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\Omega_5))</math>
|<math>\psi(a+\psi_a(\sigma a+a_2))</math>
|<math>\psi(\Omega_\omega+\Omega_3)</math>
|<math>\psi(\sigma^\omega a+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+a)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_8)))</math>
|<math>\psi(a+\psi_a(\sigma a+a_3))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_6))</math>
|<math>\psi(\sigma^\omega a+a_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+a_2)</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,2)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_9)))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_7))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma a}(\sigma a_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_S(\sigma S\times2+S_2))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10})))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a)))</math>
|<math>\psi(\Omega_\omega+\psi_3(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_{\psi_S(\sigma S\times3)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10}+\Omega_9)))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a+\sigma a_2)))</math>
|<math>\psi(\Omega_\omega+\Omega_4)</math>
|<math>\psi(\sigma^\omega a+\sigma a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_S(\sigma S\times3))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)(3,3,3)
|-
|<math>\psi(\Omega_3+\psi_2(\Omega_6+\psi_5(\Omega_{10}+\psi_9(\Omega_{15}))))</math>
|<math>\psi(a+\psi_a(\sigma a+\psi_{\sigma a}(\sigma^2a+\psi_{\sigma^2a}(\sigma^3a))))</math>
|<math>\psi(\Omega_\omega+\psi_4(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a+\psi_{\sigma^2a}(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)+\psi_{\psi_S(\sigma S\times4)}(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2)(3,3,3,1)(3,3,3)(4,4,4,1)
|-
|<math>\psi(\Omega_32)</math>
|<math>\psi(a2)</math>
|<math>\psi(\Omega_\omega2)</math>
|<math>\psi(\sigma^\omega a2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2)</math>
|(0)(1,1,1,1)(1,1,1,1)
|-
|<math>\psi(\Omega_32+\Omega_2)</math>
|<math>\psi(a2+\Omega_2)</math>
|<math>\psi(\Omega_\omega2+\Omega_2)</math>
|<math>\psi(\sigma^\omega a2+\Omega_2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\Omega_2)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_6))</math>
|<math>\psi(a2+\psi_a(\sigma a))</math>
|<math>\psi(\Omega_\omega2+\psi_2(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a2+\psi_a(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\psi_a(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_62))</math>
|<math>\psi(a2+\psi_a(\sigma a2))</math>
|<math>\psi(\Omega_\omega2+\psi_2(\Omega_\omega2))</math>
|<math>\psi(\sigma^\omega a2+\psi_a(\sigma^\omega a2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+\psi_a(\psi_S(\sigma S\times\omega)\times2))</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2,1)
|-
|<math>\psi(\Omega_32+\psi_2(\Omega_62+\Omega_5))</math>
|<math>\psi(a2+\psi_a(\sigma a2+a_2))</math>
|<math>\psi(\Omega_\omega2+\Omega_3)</math>
|<math>\psi(\sigma^\omega a2+a)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times2+a)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1)(2,2,2,1)(2,2,2,1)(2,2,2)
|-
|<math>\psi(\Omega_33)</math>
|<math>\psi(a3)</math>
|<math>\psi(\Omega_\omega3)</math>
|<math>\psi(\sigma^\omega a3)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times3)</math>
|(0)(1,1,1,1)(1,1,1,1)(1,1,1,1)
|-
|<math>\psi(\Omega_3\omega)</math>
|<math>\psi(a\omega)</math>
|<math>\psi(\Omega_\omega\omega)</math>
|<math>\psi(\sigma^\omega a\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega)</math>
|(0)(1,1,1,1)(2)
|-
|<math>\psi(\Omega_3\times(\omega+1))</math>
|<math>\psi(a\times(\omega+1))</math>
|<math>\psi(\Omega_\omega\times(\omega+1))</math>
|<math>\psi(\sigma^\omega a\times(\omega+1))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times(\omega+1))</math>
|(0)(1,1,1,1)(2)(1,1,1,1)
|-
|<math>\psi(\Omega_3\times\omega2)</math>
|<math>\psi(a\times\omega2)</math>
|<math>\psi(\Omega_\omega\times\omega2)</math>
|<math>\psi(\sigma^\omega a\times\omega2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega2)</math>
|(0)(1,1,1,1)(2)(1,1,1,1)(2)
|-
|<math>\psi(\Omega_3\times\omega^2)</math>
|<math>\psi(a\times\omega^2)</math>
|<math>\psi(\Omega_\omega\times\omega^2)</math>
|<math>\psi(\sigma^\omega a\times\omega^2)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega^2)</math>
|(0)(1,1,1,1)(2)(2)
|-
|<math>\psi(\Omega_3\times\omega^\omega)</math>
|<math>\psi(a\times\omega^\omega)</math>
|<math>\psi(\Omega_\omega\times\omega^\omega)</math>
|<math>\psi(\sigma^\omega a\times\omega^\omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\omega^\omega)</math>
|(0)(1,1,1,1)(2)(3)
|-
|<math>\psi(\Omega_3\times\varepsilon_0)</math>
|<math>\psi(a\times\varepsilon_0)</math>
|<math>\psi(\Omega_\omega\times\varepsilon_0)</math>
|<math>\psi(\sigma^\omega a\times\varepsilon_0)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\varepsilon_0)</math>
|(0)(1,1,1,1)(2)(3,1)
|-
|<math>\psi(\Omega_3\times\psi(\Omega_2))</math>
|<math>\psi(a\times\psi(\Omega_2))</math>
|<math>\psi(\Omega_\omega\times\psi(\Omega_2))</math>
|<math>\psi(\sigma^\omega a\times\psi(\Omega_2))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi(\Omega_2))</math>
|(0)(1,1,1,1)(2)(3,1,1)
|-
|<math>\psi(\Omega_3\times\psi(\Omega_3))</math>
|<math>\psi(a\times\psi(a))</math>
|<math>\psi(\Omega_\omega\times\psi(\Omega_\omega))</math>
|<math>\psi(\sigma^\omega a\times\psi(\sigma^\omega a))</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\psi(\psi_S(\sigma S\times\omega)))</math>
|(0)(1,1,1,1)(2)(3,1,1,1)
|-
|<math>\psi(\Omega_3\Omega)</math>
|<math>\psi(a\Omega)</math>
|<math>\psi(\Omega_\omega\Omega)</math>
|<math>\psi(\sigma^\omega a\Omega)</math>
|<math>\psi(\psi_S(\sigma S\times\omega)\times\Omega)</math>
|(0)(1,1,1,1)(2,1)
|}