Ｐ1（ｘ）＝１，Ｑ1（ｘ）＝１

　　sl(2u)=2sl(u)sl'(u)/(1+sl^4(u))より

　Ｐ2（ｘ）＝２，Ｑ2（ｘ）＝１＋ｘ

Ｑ3(x)=Ｑ1(x)｛Ｑ2^2(x)＋ｘ（１－ｘ）Ｐ2^2(x)｝

＝（１＋ｘ）^2＋４ｘ（１－ｘ）＝１＋６ｘ－３ｘ^2

Ｐ3(x)=２（１－ｘ）Ｐ2(x)Ｑ2(x)Ｑ1(x)－Ｐ1(x)｛Ｑ2^2(x)＋ｘ（１－ｘ）Ｐ2^2(x)｝

＝４（１－ｘ）（１＋ｘ）－｛（１＋ｘ）^2＋４ｘ（１－ｘ）｝

＝４－４ｘ^2－｛１＋６ｘ－３ｘ^2｝

＝３－６ｘ－ｘ^2

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝

Ｑ4(x)=Ｑ2(x)｛Ｑ3^2(x)＋ｘＰ3^2(x)｝

＝（１＋ｘ）｛（１＋６ｘ－３ｘ^2）^2＋ｘ（３－６ｘ－ｘ^2）^2｝

＝（１＋ｘ）｛１＋３６ｘ^2＋９ｘ^4＋１２ｘ－３６ｘ^3－６ｘ^2

＋９ｘ＋３６ｘ^3＋ｘ^5－３６ｘ^2＋１２ｘ^4－６ｘ^3｝

＝（１＋ｘ）｛１＋２１ｘ－６ｘ^2－６ｘ^3＋２１ｘ^4＋ｘ^5｝

＝（１＋ｘ）^2｛１＋２０ｘ－２６ｘ^2＋２０ｘ^3＋ｘ^4｝

Ｐ4(x)=２Ｐ3(x)Ｑ3(x)Ｑ2(x)－Ｐ2(x)｛Ｑ3^2(x)＋ｘＰ3^2(x)｝

＝２（３－６ｘ－ｘ^2）（１＋６ｘ－３ｘ^2）（１＋ｘ）－２（１＋ｘ）｛１＋２０ｘ－２６ｘ^2＋２０ｘ^3＋ｘ^4｝

＝２（１＋ｘ）｛３＋１２ｘ－４６ｘ^2＋１２ｘ^3＋３ｘ^4－１－２０ｘ＋２６ｘ^2－２０ｘ^3－ｘ^4｝

＝２（１＋ｘ）｛２－８ｘ－２０ｘ^2－８ｘ^3＋２ｘ^4｝

＝２（１＋ｘ）^2｛２－１０ｘ－１０ｘ^2＋２ｘ^3）

＝４（１＋ｘ）^3｛１－６ｘ＋ｘ^2）

最大公約数因子で割って

Ｑ4(x)＝｛１＋２０ｘ－２６ｘ^2＋２０ｘ^3＋ｘ^4｝

Ｐ4(x)＝４（１＋ｘ）｛１－６ｘ＋ｘ^2）

＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝＝

Ｑ5(x)＝（１－２ｘ＋５ｘ^2）（１＋５２ｘ－２６ｘ^2－１２ｘ^3＋ｘ^4｝

Ｐ5(x)＝（５－２ｘ＋ｘ^2）（１－１２ｘ－２６ｘ^2＋５２ｘ^3＋ｘ^4｝

係数の表現の対称性がおもしろい．

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