求外接圆的半径

zuijianqiugen

数学星空 发表于 2014-4-20 12:05
To mathe : 对于两个椭圆内接和外切四边形的结论能给出分析和求解过程吗？

对于两个相似椭圆的内接和外 ...

（1）看了帖子“椭圆内接N边形的最大面积 ”，内容真丰富。
（2）只要解决了“椭圆的偏心准圆”问题，通过“扩缩变换”就能解决任意两个椭圆存在切接四边形的条件。
（3）目前本人正在学习“偏心准圆的矩阵变换“。

zuijianqiugen

mathe 发表于 2014-4-20 11:11
把本题中关于两条二次圆锥曲线一般情况整理了一下，放在了http://bbs.emath.ac.cn/forum.php?mod=redirect& ...

内容不错，是得好好学习。

zuijianqiugen

mathe 发表于 2014-4-20 11:59
比如题目中四边形换成三角形，我们同样先考虑单位圆里面一个椭圆${x^2}/{a^2}+{y^2}/{b^2}=1$,考虑这个椭圆 ...

若有问题，还少不用了麻烦你。

zuijianqiugen

mathe 发表于 2014-4-20 11:59
比如题目中四边形换成三角形，我们同样先考虑单位圆里面一个椭圆${x^2}/{a^2}+{y^2}/{b^2}=1$,考虑这个椭圆 ...

第三行：√(r₃/r₁)+√(r₃/r₁)=1是怎么来的？

mathe

zuijianqiugen 发表于 2014-4-20 17:53
第三行：√(r/r)+√(r/r)=1是怎么来的？

标准情况（就是一个单位圆，一个${x^2}/{a^2}+{y^2}/{b^2}=1$我们已经得出条件为$a+b=1$)
而17#的结论是对于一般情况，我们总可以变换为标准情况，其中$a=\sqrt({r_3}/{r_1}),b=\sqrt({r_3}/{r_2})$,所以就有此结论

mathe

链接 http://bbs.emath.ac.cn/forum.php ... 4789&fromuid=20 中结论对于本题也非常有用，
其中将外曲线固定为xy=1,那么如果内曲线方程变化为$(x-a)(x-b)=(1-a)(1-b)$，
那么经计算以后，对应的特征方程为$(x-1)(x-1+a)(x-1+b)=0$
也就是说，那里可以得出，如果固定外曲线，里面有三条内曲线，对应特征值分别为$(1,1-a,1-b),(1,1-at,1-bt),(1,1-as,1-bs)$
如果s,t满足条件
$[s^2,s,1][(a^2b^2,-2ab,1),(-2ab,-2ab+4a+4b-2,-2),(1,-2,1)][(t^2),(t),(1)]=0$
那么它们之间有如链接中复合变换关系，利用这个关系是应该可以推算出k边形的情况

zuijianqiugen

mathe 发表于 2014-4-20 20:00
链接 http://bbs.emath.ac.cn/forum.php?mod=redirect&goto=findpost&ptid=2888&pid=34789&fromuid=20 中结 ...

看来你是一个射影几何专家，不知这些几何理论是你自己的独特研究？还是学习欧美的？

mathe

由此我们可以计算复合变换，设$t_1=1,t_2={4(a-1)(b-1)}/{(ab-1)^2}$而且$t_{n+1}={(t_n-1)^2}/{(abt_n-1)^2t_{n-1}}$然后利用$t_n=0$就可以得出n变形情况特征值的约束方程

数学星空

t[1] = 1,

t[2] = (4*(a-1))*(b-1)/(a*b-1)^2,

t[3] = (a^2*b^2-6*a*b+4*a+4*b-3)^2/(3*a^2*b^2-4*a^2*b-4*a*b^2+6*a*b-1)^2,

t[4] = (16*(b-1))*(a-1)*(a*b-2*a+1)^2*(a*b-2*b+1)^2*(a*b-1)^2/(a^4*b^4-20*a^3*b^3+32*a^3*b^2+32*a^2*b^3-16*a^3*b-58*a^2*b^2-16*a*b^3+32*a^2*b+32*a*b^2-20*a*b+1)^2,

t[5] =(a^6*b^6-50*a^5*b^5+140*a^5*b^4+140*a^4*b^5-160*a^5*b^3-445*a^4*b^4-160*a^3*b^5+64*a^5*b^2+560*a^4*b^3+560*a^3*b^4+64*a^2*b^5-240*a^4*b^2-780*a^3*b^3-
240*a^2*b^4+360*a^3*b^2+360*a^2*b^3-105*a^2*b^2-80*a^2*b-80*a*b^2+16*a^2+94*a*b+16*b^2-20*a-20*b+5)^2/(5*a^6*b^6-20*a^6*b^5-20*a^5*b^6+16*a^6*b^4+94*a^5*b^5+16*a^4*b^6-80*a^5*b^4-80*a^4*b^5-105*a^4*b^4+360*a^4*b^3+360*a^3*b^4-240*a^4*b^2-780*a^3*b^3-240*a^2*b^4+
64*a^4*b+560*a^3*b^2+560*a^2*b^3+64*a*b^4-160*a^3*b-445*a^2*b^2-160*a*b^3+140*a^2*b+140*a*b^2-50*a*b+1)^2,

t[6] = (4*(b-1))*(a-1)*(a^2*b^2-6*a*b+4*a+4*b-3)^2*(3*a^2*b^2-4*a^2*b-4*a*b^2+6*a*b-1)^2*(a^2*b^2-4*a*b^2+6*a*b-4*a+1)^2*(a^2*b^2-4*a^2*b+6*a*b-4*b+1)^2/((a*b-1)^2*(a^8*b^8-104*a^7*b^7+448*a^7*b^6+448*a^6*b^7-864*a^7*b^5-2276*a^6*b^6-864*a^5*b^7+768*a^7*b^4+5056*a^6*b^5+5056*a^5*b^6+768*a^4*b^7-256*a^7*b^3-5248*a^6*b^4-
13016*a^5*b^5-5248*a^4*b^6-256*a^3*b^7+2304*a^6*b^3+16000*a^5*b^4+16000*a^4*b^5+2304*a^3*b^6-256*a^6*b^2-9280*a^5*b^3-22970*a^4*b^4-9280*a^3*b^5-256*a^2*b^6+
2304*a^5*b^2+16000*a^4*b^3+16000*a^3*b^4+2304*a^2*b^5-256*a^5*b-5248*a^4*b^2-13016*a^3*b^3-5248*a^2*b^4-256*a*b^5+768*a^4*b+5056*a^3*b^2+5056*a^2*b^3+
768*a*b^4-864*a^3*b-2276*a^2*b^2-864*a*b^3+448*a^2*b+448*a*b^2-104*a*b+1)^2)

t[7]=(a^12*b^12-196*a^11*b^11+1176*a^11*b^10+1176*a^10*b^11-3360*a^11*b^9-8022*a^10*b^10-3360*a^9*b^11+4928*a^11*b^8+25200*a^10*b^9+25200*a^9*b^10+4928*a^8*b^11-3584*a^11*b^7-39536*a^10*b^8-86660*a^9*b^9-39536*a^8*b^10-3584*a^7*b^11+1024*a^11*b^6+30208*a^10*b^7+145240*a^9*b^8+145240*a^8*b^9+30208*a^7*b^10+1024*a^6*b^11-8960*a^10*b^6-116480*a^9*b^7-230713*a^8*b^8-116480*a^7*b^9-8960*a^6*b^10+35840*a^9*b^6+108864*a^8*b^7+108864*a^7*b^8+35840*a^6*b^9+111552*a^8*b^6+265272*a^7*b^7+111552*a^6*b^8-164864*a^8*b^5-739536*a^7*b^6-739536*a^6*b^7-164864*a^5*b^8+89600*a^8*b^4+765632*a^7*b^5+1463980*a^6*b^6+765632*a^5*b^7+89600*a^4*b^8-28672*a^8*b^3-434560*a^7*b^4-1490272*a^6*b^5-1490272*a^5*b^6-434560*a^4*b^7-28672*a^3*b^8+4096*a^8*b^2+144896*a^7*b^3+890720*a^6*b^4+1582104*a^5*b^5+890720*a^4*b^6+144896*a^3*b^7+4096*a^2*b^8-21504*a^7*b^2-311808*a^6*b^3-1005200*a^5*b^4-1005200*a^4*b^5-311808*a^3*b^6-21504*a^2*b^7+48384*a^6*b^2+372736*a^5*b^3+683935*a^4*b^4+372736*a^3*b^5+48384*a^2*b^6-60928*a^5*b^2-271040*a^4*b^3-271040*a^3*b^4-60928*a^2*b^5+47040*a^4*b^2+113932*a^3*b^3+47040*a^2*b^4-19656*a^3*b^2-19656*a^2*b^3-672*a^3*b+1610*a^2*b^2-672*a*b^3+64*a^3+1136*a^2*b+1136*a*b^2+64*b^3-112*a^2-532*a*b-112*b^2+56*a+56*b-7)^2/(7*a^12*b^12-56*a^12*b^11-56*a^11*b^12+112*a^12*b^10+532*a^11*b^11+112*a^10*b^12-64*a^12*b^9-1136*a^11*b^10-1136*a^10*b^11-64*a^9*b^12+672*a^11*b^9-1610*a^10*b^10+672*a^9*b^11+19656*a^10*b^9+19656*a^9*b^10-47040*a^10*b^8-113932*a^9*b^9-47040*a^8*b^10+60928*a^10*b^7+271040*a^9*b^8+271040*a^8*b^9+60928*a^7*b^10-48384*a^10*b^6-372736*a^9*b^7-683935*a^8*b^8-372736*a^7*b^9-48384*a^6*b^10+21504*a^10*b^5+311808*a^9*b^6+1005200*a^8*b^7+1005200*a^7*b^8+311808*a^6*b^9+21504*a^5*b^10-4096*a^10*b^4-144896*a^9*b^5-890720*a^8*b^6-1582104*a^7*b^7-890720*a^6*b^8-144896*a^5*b^9-4096*a^4*b^10+28672*a^9*b^4+434560*a^8*b^5+1490272*a^7*b^6+1490272*a^6*b^7+434560*a^5*b^8+28672*a^4*b^9-89600*a^8*b^4-765632*a^7*b^5-1463980*a^6*b^6-765632*a^5*b^7-89600*a^4*b^8+164864*a^7*b^4+739536*a^6*b^5+739536*a^5*b^6+164864*a^4*b^7-111552*a^6*b^4-265272*a^5*b^5-111552*a^4*b^6-35840*a^6*b^3-108864*a^5*b^4-108864*a^4*b^5-35840*a^3*b^6+8960*a^6*b^2+116480*a^5*b^3+230713*a^4*b^4+116480*a^3*b^5+8960*a^2*b^6-1024*a^6*b-30208*a^5*b^2-145240*a^4*b^3-145240*a^3*b^4-30208*a^2*b^5-1024*a*b^6+3584*a^5*b+39536*a^4*b^2+86660*a^3*b^3+39536*a^2*b^4+3584*a*b^5-4928*a^4*b-25200*a^3*b^2-25200*a^2*b^3-4928*a*b^4+3360*a^3*b+8022*a^2*b^2+3360*a*b^3-1176*a^2*b-1176*a*b^2+196*a*b-1)^2

t[8]=(64*(a-1))*(b-1)*(a*b-2*b+1)^2*(a*b-1)^2*(a*b-2*a+1)^2*(a^4*b^4-8*a^4*b^3+8*a^4*b^2+20*a^3*b^3-24*a^3*b^2-32*a^2*b^3+54*a^2*b^2+16*a*b^3-24*a^2*b-32*a*b^2+8*a^2+20*a*b-8*a+1)^2*(a^4*b^4-20*a^3*b^3+32*a^3*b^2+32*a^2*b^3-16*a^3*b-58*a^2*b^2-16*a*b^3+32*a^2*b+32*a*b^2-20*a*b+1)^2*(a^4*b^4-8*a^3*b^4+20*a^3*b^3+8*a^2*b^4-32*a^3*b^2-24*a^2*b^3+16*a^3*b+54*a^2*b^2-32*a^2*b-24*a*b^2+20*a*b+8*b^2-8*b+1)^2/(a^16*b^16-336*a^15*b^15+2688*a^15*b^14+2688*a^14*b^15-10560*a^15*b^13-24456*a^14*b^14-10560*a^13*b^15+22528*a^15*b^12+105600*a^14*b^13+105600*a^13*b^14+22528*a^12*b^15-26624*a^15*b^11-240896*a^14*b^12-498160*a^13*b^13-240896*a^12*b^14-26624*a^11*b^15+16384*a^15*b^10+299008*a^14*b^11+1212160*a^13*b^12+1212160*a^12*b^13+299008*a^11*b^14+16384*a^10*b^15-4096*a^15*b^9-190976*a^14*b^10-1577600*a^13*b^11-2859236*a^12*b^12-1577600*a^11*b^13-190976*a^10*b^14-4096*a^9*b^15+49152*a^14*b^9+1044480*a^13*b^10+2750208*a^12*b^11+2750208*a^11*b^12+1044480*a^10*b^13+49152*a^9*b^14-276480*a^13*b^9+968448*a^12*b^10+3136944*a^11*b^11+968448*a^10*b^12-276480*a^9*b^13-5154816*a^12*b^9-20678784*a^11*b^10-20678784*a^10*b^11-5154816*a^9*b^12+5990400*a^12*b^8+38714688*a^11*b^9+68067144*a^10*b^10+38714688*a^9*b^11+5990400*a^8*b^12-4128768*a^12*b^7-41840640*a^11*b^8-118173312*a^10*b^9-118173312*a^9*b^10-41840640*a^8*b^11-4128768*a^7*b^12+1900544*a^12*b^6+29958144*a^11*b^7+130475520*a^10*b^8+208436624*a^9*b^9+130475520*a^8*b^10+29958144*a^7*b^11+1900544*a^6*b^12-524288*a^12*b^5-14286848*a^11*b^6-97501184*a^10*b^7-240084480*a^9*b^8-240084480*a^8*b^9-97501184*a^7*b^10-14286848*a^6*b^11-524288*a^5*b^12+65536*a^12*b^4+4071424*a^11*b^5+48366592*a^10*b^6+188153088*a^9*b^7+290931270*a^8*b^8+188153088*a^7*b^9+48366592*a^6*b^10+4071424*a^5*b^11+65536*a^4*b^12-524288*a^11*b^4-14286848*a^10*b^5-97501184*a^9*b^6-240084480*a^8*b^7-240084480*a^7*b^8-97501184*a^6*b^9-14286848*a^5*b^10-524288*a^4*b^11+1900544*a^10*b^4+29958144*a^9*b^5+130475520*a^8*b^6+208436624*a^7*b^7+130475520*a^6*b^8+29958144*a^5*b^9+1900544*a^4*b^10-4128768*a^9*b^4-41840640*a^8*b^5-118173312*a^7*b^6-118173312*a^6*b^7-41840640*a^5*b^8-4128768*a^4*b^9+5990400*a^8*b^4+38714688*a^7*b^5+68067144*a^6*b^6+38714688*a^5*b^7+5990400*a^4*b^8-5154816*a^7*b^4-20678784*a^6*b^5-20678784*a^5*b^6-5154816*a^4*b^7-276480*a^7*b^3+968448*a^6*b^4+3136944*a^5*b^5+968448*a^4*b^6-276480*a^3*b^7+49152*a^7*b^2+1044480*a^6*b^3+2750208*a^5*b^4+2750208*a^4*b^5+1044480*a^3*b^6+49152*a^2*b^7-4096*a^7*b-190976*a^6*b^2-1577600*a^5*b^3-2859236*a^4*b^4-1577600*a^3*b^5-190976*a^2*b^6-4096*a*b^7+16384*a^6*b+299008*a^5*b^2+1212160*a^4*b^3+1212160*a^3*b^4+299008*a^2*b^5+16384*a*b^6-26624*a^5*b-240896*a^4*b^2-498160*a^3*b^3-240896*a^2*b^4-26624*a*b^5+22528*a^4*b+105600*a^3*b^2+105600*a^2*b^3+22528*a*b^4-10560*a^3*b-24456*a^2*b^2-10560*a*b^3+2688*a^2*b+2688*a*b^2-336*a*b+1)^2

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数学星空

为了便于mathe 给出更多更精彩的分析，根据楼上的结果易得到特征方程

\(n=2\)时  

\(4(a-1)(b-1)=0\)  


\(n=3\)时
\((a^2b^2-6ab+4a+4b-3)^2=0\)

\(n=4\)时  
\(16(b-1)(a-1)(ab-2a+1)^2(ab-2b+1)^2(ab-1)^2＝0\)

\(n=5\)时
\((a^6b^6-50a^5b^5+140a^5b^4+140a^4b^5-160a^5b^3-445a^4b^4-160a^3b^5+64a^5b^2+560a^4b^3+560a^3b^4+64a^2b^5-240a^4b^2-780a^3b^3-240a^2b^4+360a^3b^2+360a^2b^3-105a^2b^2-80a^2b-80ab^2+16a^2+94ab+16b^2-20a-20b+5)^2=0\)

\(n=6\)时   
\(4(b-1)(a-1)(a^2b^2-6ab+4a+4b-3)^2(3a^2b^2-4a^2b-4ab^2+6ab-1)^2(a^2b^2-4ab^2+6ab-4a+1)^2(a^2b^2-4a^2b+6ab-4b+1)^2=0\)

\(n=7\)时
\((a^{12}b^{12}-196a^{11}b^{11}+1176a^{11}b^{10}+1176a^{10}b^{11}-3360a^{11}b^9-8022a^{10}b^{10}-3360a^9b^{11}+4928a^{11}b^8+25200a^{10}b^9+25200a^9b^{10}+4928a^8b^{11}-3584a^{11}b^7-39536a^{10}b^8-86660a^9b^9-39536a^8b^{10}-3584a^7b^{11}+1024a^{11}b^6+30208a^{10}b^7+145240a^9b^8+145240a^8b^9+30208a^7b^{10}+1024a^6b^{11}-8960a^{10}b^6-116480a^9b^7-230713a^8b^8-116480a^7b^9-8960a^6b^{10}+35840a^9b^6+108864a^8b^7+108864a^7b^8+35840a^6b^9+111552a^8b^6+265272a^7b^7+111552a^6b^8-164864a^8b^5-739536a^7b^6-739536a^6b^7-164864a^5b^8+89600a^8b^4+765632a^7b^5+1463980a^6b^6+765632a^5b^7+89600a^4b^8-28672a^8b^3-434560a^7b^4-1490272a^6b^5-1490272a^5b^6-434560a^4b^7-28672a^3b^8+4096a^8b^2+144896a^7b^3+890720a^6b^4+1582104a^5b^5+890720a^4b^6+144896a^3b^7+4096a^2b^8-21504a^7b^2-311808a^6b^3-1005200a^5b^4-1005200a^4b^5-311808a^3b^6-21504a^2b^7+48384a^6b^2+372736a^5b^3+683935a^4b^4+372736a^3b^5+48384a^2b^6-60928a^5b^2-271040a^4b^3-271040a^3b^4-60928a^2b^5+47040a^4b^2+113932a^3b^3+47040a^2b^4-19656a^3b^2-19656a^2b^3-672a^3b+1610a^2b^2-672ab^3+64a^3+1136a^2b+1136ab^2+64b^3-112a^2-532ab-112b^2+56a+56b-7)^2=0\)
  
\(n=8\)时
\(64(a-1)(b-1)(ab-2b+1)^2(ab-1)^2(ab-2a+1)^2(a^4b^4-8a^4b^3+8a^4b^2+20a^3b^3-24a^3b^2-32a^2b^3+54a^2b^2+16ab^3-24a^2b-32ab^2+8a^2+20ab-8a+1)^2(a^4b^4-20a^3b^3+32a^3b^2+32a^2b^3-16a^3b-58a^2b^2-16ab^3+32a^2b+32ab^2-20ab+1)^2(a^4b^4-8a^3b^4+20a^3b^3+8a^2b^4-32a^3b^2-24a^2b^3+16a^3b+54a^2b^2-32a^2b-24ab^2+20ab+8b^2-8b+1)^2=0\)

\(n=9\) 时
\((a^2b^2-6ab+4a+4b-3)^2(a^{18}b^{18}-534a^{17}b^{17}+5540a^{17}b^{16}+5540a^{16}b^{17}-28512a^{17}b^{15}-67947a^{16}b^{16}-28512a^{15}b^{17}+82368a^{17}b^{14}+401280a^{16}b^{15}+401280a^{15}b^{16}+82368a^{14}b^{17}-139776a^{17}b^{13}-1323296a^{16}b^{14}-2709904a^{15}b^{15}-1323296a^{14}b^{16}-139776a^{13}b^{17}+138240a^{17}b^{12}+2621952a^{16}b^{13}+10236000a^{15}b^{14}+10236000a^{14}b^{15}+2621952a^{13}b^{16}+138240a^{12}b^{17}-73728a^{17}b^{11}-3234816a^{16}b^{12}-23825376a^{15}b^{13}-43633260a^{14}b^{14}-23825376a^{13}b^{15}-3234816a^{12}b^{16}-73728a^{11}b^{17}+16384a^{17}b^{10}+2523136a^{16}b^{11}+36575168a^{15}b^{12}+114679040a^{14}b^{13}+114679040a^{13}b^{14}+36575168a^{12}b^{15}+2523136a^{11}b^{16}+16384a^{10}b^{17}-1253376a^{16}b^{10}-39191040a^{15}b^{11}-201315744a^{14}b^{12}-334576872a^{13}b^{13}-201315744a^{12}b^{14}-39191040a^{11}b^{15}-1253376a^{10}b^{16}+393216a^{16}b^9+30723072a^{15}b^{10}+250295808a^{14}b^{11}+649247088a^{13}b^{12}+649247088a^{12}b^{13}+250295808a^{11}b^{14}+30723072a^{10}b^{15}+393216a^9b^{16}-65536a^{16}b^8-17899520a^{15}b^9-228034560a^{14}b^{10}-890780128a^{13}b^{11}-1374888172a^{12}b^{12}-890780128a^{11}b^{13}-228034560a^{10}b^{14}-17899520a^9b^{15}-65536a^8b^{16}+7421952a^{15}b^8+151633920a^{14}b^9+889296576a^{13}b^{10}+2045645952a^{12}b^{11}+2045645952a^{11}b^{12}+889296576a^{10}b^{13}+151633920a^9b^{14}+7421952a^8b^{15}-1966080a^{15}b^7-69918720a^{14}b^8-639452160a^{13}b^9-2198557344a^{12}b^{10}-3276437232a^{11}b^{11}-2198557344a^{10}b^{12}-639452160a^9b^{13}-69918720a^8b^{14}-1966080a^7b^{15}+262144a^{15}b^6+20054016a^{14}b^7+314292224a^{13}b^8+1685263360a^{12}b^9+3766379936a^{11}b^{10}+3766379936a^{10}b^{11}+1685263360a^9b^{12}+314292224a^8b^{13}+20054016a^7b^{14}+262144a^6b^{15}-2752512a^{14}b^6-94789632a^{13}b^7-874137600a^{12}b^8-3063034464a^{11}b^9-4601643954a^{10}b^{10}-3063034464a^9b^{11}-874137600a^8b^{12}-94789632a^7b^{13}-2752512a^6b^{14}+13418496a^{13}b^6+275595264a^{12}b^7+1671042240a^{11}b^8+3935370240a^{10}b^9+3935370240a^9b^{10}+1671042240a^8b^{11}+275595264a^7b^{12}+13418496a^6b^{13}-40312832a^{12}b^6-549262336a^{11}b^7-2217363232a^{10}b^8-3461258500a^9b^9-2217363232a^8b^{10}-549262336a^7b^{11}-40312832a^6b^{12}+82704384a^{11}b^6+720792576a^{10}b^7+1898573400a^9b^8+1898573400a^8b^9+720792576a^7b^{10}+82704384a^6b^{11}+172032a^{11}b^5-82747392a^{10}b^6-481365024a^9b^7-816791082a^8b^8-481365024a^7b^9-82747392a^6b^{10}+172032a^5b^{11}-16384a^{11}b^4-16760832a^{10}b^5-76418752a^9b^6-125153152a^8b^7-125153152a^7b^8-76418752a^6b^9-16760832a^5b^{10}-16384a^4b^{11}+4546560a^{10}b^4+89433600a^9b^5+370474656a^8b^6+574721808a^7b^7+370474656a^6b^8+89433600a^5b^9+4546560a^4b^{10}-786432a^{10}b^3-25482240a^9b^4-210040320a^8b^5-546899808a^7b^6-546899808a^6b^7-210040320a^5b^8-25482240a^4b^9-786432a^3b^{10}+65536a^{10}b^2+4587520a^9b^3+62325760a^8b^4+279571040a^7b^5+451992548a^6b^6+279571040a^5b^7+62325760a^4b^8+4587520a^3b^9+65536a^2b^{10}-393216a^9b^2-11649024a^8b^3-86670528a^7b^4-231141120a^6b^5-231141120a^5b^6-86670528a^4b^7-11649024a^3b^8-393216a^2b^9+1032192a^8b^2+16897536a^7b^3+75396384a^6b^4+123071256a^5b^5+75396384a^4b^6+16897536a^3b^7+1032192a^2b^8-1557504a^7b^2-15450624a^6b^3-42642320a^5b^4-42642320a^4b^5-15450624a^3b^6-1557504a^2b^7+1492992a^6b^2+9276768a^5b^3+15840900a^4b^4+9276768a^3b^5+1492992a^2b^6-948672a^5b^2-3699840a^4b^3-3699840a^3b^4-948672a^2b^5+404768a^4b^2+930928a^3b^3+404768a^2b^4-106656a^3b^2-106656a^2b^3-1056a^3b+9273a^2b^2-1056ab^3+64a^3+1536a^2b+1536ab^2+64b^3-96a^2-534ab-96b^2+36a+36b-3)^2=0\)

\(n=10\)时
\(4(a^6b^6-12a^6b^5+16a^6b^4+50a^5b^5-80a^5b^4-140a^4b^5+335a^4b^4+160a^3b^5-264a^4b^3-464a^3b^4-64a^2b^5+208a^4b^2+508a^3b^3+208a^2b^4-64a^4b-464a^3b^2-264a^2b^3+160a^3b+335a^2b^2-140a^2b-80ab^2+50ab+16b^2-12b+1)^2(5a^6b^6-20a^6b^5-20a^5b^6+16a^6b^4+94a^5b^5+16a^4b^6-80a^5b^4-80a^4b^5-105a^4b^4+360a^4b^3+360a^3b^4-240a^4b^2-780a^3b^3-240a^2b^4+64a^4b+560a^3b^2+560a^2b^3+64ab^4-160a^3b-445a^2b^2-160ab^3+140a^2b+140ab^2-50ab+1)^2(a^6b^6-50a^5b^5+140a^5b^4+140a^4b^5-160a^5b^3-445a^4b^4-160a^3b^5+64a^5b^2+560a^4b^3+560a^3b^4+64a^2b^5-240a^4b^2-780a^3b^3-240a^2b^4+360a^3b^2+360a^2b^3-105a^2b^2-80a^2b-80ab^2+16a^2+94ab+16b^2-20a-20b+5)^2(a^6b^6-12a^5b^6+50a^5b^5+16a^4b^6-140a^5b^4-80a^4b^5+160a^5b^3+335a^4b^4-64a^5b^2-464a^4b^3-264a^3b^4+208a^4b^2+508a^3b^3+208a^2b^4-264a^3b^2-464a^2b^3-64ab^4+335a^2b^2+160ab^3-80a^2b-140ab^2+16a^2+50ab-12a+1)^2(a-1)(b-1)=0\)