20棵树最优解计算

hujunhua · 发表于 2010-2-8 14:53:20

这样的直线射影图，总是可以找到有理解的。给我一个可行的组合表，我或许能给出有理解来

mathe · 发表于 2010-2-9 10:39:15

这样的直线射影图，总是可以找到有理解的。给我一个可行的组合表，我或许能给出有理解来 hujunhua 发表于 2010-2-8 14:53

自己论坛里面找吧，反例很多很多

sheng_jianguo · 发表于 2010-3-1 14:24:51

请教mathe： 1）是否已找到20棵树22行种法的具体坐标 2）是否有较简单的做法找到20棵树23行的所有种法（按您的分类法）

mathe · 发表于 2010-3-2 15:19:22

23行都已经找到了，找22行当然不在话下。但是我前面已经多次说过，现在限于计算能力，还无法找到所有23行解（也有可能只有两个，但是现在无法确认）

sheng_jianguo · 发表于 2010-3-3 09:06:24

23行都已经找到了，找22行当然不在话下。 mathe 发表于 2010-3-2 15:19

有空的话能否在这里给出一些与已知23行种法无关的20棵树22行种法的具体坐标

mathe · 发表于 2010-3-3 09:19:52

这个没有尝试过，主要意义不大

mathe · 发表于 2019-9-12 16:36:42

@sheng_jianguo 在很早以前要求找出一些和23行无关的22行的结果，这个还是有难度的。
最近重新找了一下，分别各自给出两个20行，21行，22行的结果:

EHIJCGHLFIKLBCIMADJMBGJNDELNBEFOAHKOCJKPFHMPDGOPCDFQAINQACERBDKRABLSEGMSAFGTBHQTIRST
[t equation] -1-2*t-3*t^2-1*t^3
Node[A] 0 , 0 , 1
Node[B] 1 , 0 , 1
Node[C] 1 , 1 , 1
Node[D] 0 , 1 , 1
Node[E] 1 , 1 , 2+1*t
Node[F] 0-1*t , 1 , 1
Node[G] 0-1*t , 1 , 0-2*t-1*t^2
Node[H] 0-1*t^2 , -1-1*t-1*t^2 , 0+1*t
Node[I] -1-1*t-1*t^2 , 0+1*t , -1-1*t-1*t^2
Node[J] 0 , -1 , 0+1*t+1*t^2
Node[K] -1-1*t , 1 , 0-1*t
Node[L] -1 , 0 , -1-1*t
Node[M] 0 , 1 , 0
Node[N] -1-1*t-1*t^2 , 0+1*t , 0+1*t+1*t^2
Node[O] 0-1*t^2 , -1-1*t-1*t^2 , 0
Node[P] 0-1*t , 2+2*t+1*t^2 , 1
Node[Q] 1+2*t+2*t^2 , 1+1*t+1*t^2 , 1+1*t+1*t^2
Node[R] -1 , -1 , -2
Node[S] -1 , 0 , -2-1*t
Node[T] 0-1*t , 1 , 0-3*t-1*t^2
Edge[EHIJ] -2-2*t-1*t^2 , 0+1*t+1*t^2 , 1
Edge[CGHL] -1-1*t , 0+1*t , 1
Edge[FIKL] 1+1*t , 1+1*t+1*t^2 , -1
Edge[BCIM] -1 , 0 , 1
Edge[ADJM] 1 , 0 , 0
Edge[BGJN] -1 , 0+1*t+1*t^2 , 1
Edge[DELN] 1+1*t , 1 , -1
Edge[BEFO] -1 , -1-1*t , 1
Edge[AHKO] 1+1*t+1*t^2 , 0-1*t^2 , 0
Edge[CJKP] -1-1*t , -1 , 2+1*t
Edge[FHMP] 1 , 0 , 0+1*t
Edge[DGOP] -1-2*t-1*t^2 , 0-1*t , 0+1*t
Edge[CDFQ] 0 , -1 , 1
Edge[AINQ] 0-1*t , -1-1*t-1*t^2 , 0
Edge[ACER] 1 , -1 , 0
Edge[BDKR] -1 , -1 , 1
Edge[ABLS] 0 , -1 , 0
Edge[EGMS] -2-1*t , 0 , 1
Edge[AFGT] 1 , 0+1*t , 0
Edge[BHQT] 1+1*t+1*t^2 , 0-1*t-1*t^2 , -1-1*t-1*t^2
Edge[IRST] 2+1*t , 0-1*t , -1

CEFIBFHKBEJLBDGMAIKMADFNCGHNGJKOAHLOCDLPFJMPBIOPAEGQDHIQACJREKNRLMNSBCQSDEOTFRST
[t equation] -20-32*t-20*t^2-4*t^3
Node[A] 0 , 0 , 1
Node[B] 1 , 0 , 1
Node[C] 2+2*t+1*t^2 , 3+3*t+1*t^2 , 4+3*t+1*t^2
Node[D] 1 , 1 , 1
Node[E] -1-2*t-1*t^2 , -3-3*t-1*t^2 , -2-2*t-1*t^2
Node[F] -1 , -1 , -2
Node[G] -1 , 2+1*t , -1
Node[H] 0 , 1 , 1
Node[I] 1+1*t , 2+1*t , 2+1*t
Node[J] -6-6*t-2*t^2 , -4-6*t-2*t^2 , -14-14*t-4*t^2
Node[K] -1-1*t , -2-1*t , -3-2*t
Node[L] 0 , -1-1*t , -2-1*t
Node[M] -1-1*t , -2-1*t , -1-1*t
Node[N] -1 , -1 , -4-1*t
Node[O] 0 , -2-1*t , -1
Node[P] 3+3*t+1*t^2 , 4+4*t+1*t^2 , 5+4*t+1*t^2
Node[Q] 1+2*t+1*t^2 , 3+3*t+1*t^2 , 3+3*t+1*t^2
Node[R] 12+12*t+4*t^2 , 8+12*t+4*t^2 , 32+40*t+12*t^2
Node[S] 27/8+9/2*t+9/4*t^2 , -9/8-9/8*t , -9/8+9/8*t^2
Node[T] 0+2*t+1*t^2 , 2+3*t+1*t^2 , 1+2*t+1*t^2
Edge[CEFI] 2+1*t , 0-1*t , -1
Edge[BFHK] -1 , -1 , 1
Edge[BEJL] 3+3*t+1*t^2 , 1 , -3-3*t-1*t^2
Edge[BDGM] -1 , 0 , 1
Edge[AIKM] -2-1*t , 1+1*t , 0
Edge[ADFN] 1 , -1 , 0
Edge[CGHN] 3+1*t , 1 , -1
Edge[GJKO] 4+2*t , 1 , -2-1*t
Edge[AHLO] 1 , 0 , 0
Edge[CDLP] 1 , -2-1*t , 1+1*t
Edge[FJMP] -3-1*t , 1+1*t , 1
Edge[BIOP] -2-1*t , -1 , 2+1*t
Edge[AEGQ] 3+3*t+1*t^2 , -1-2*t-1*t^2 , 0
Edge[DHIQ] 0 , -1 , 1
Edge[ACJR] 4+6*t+2*t^2 , -6-6*t-2*t^2 , 0
Edge[EKNR] -5-4*t-1*t^2 , 1+3*t+1*t^2 , 1
Edge[LMNS] -3-2*t , 2+3*t+1*t^2 , -1-2*t-1*t^2
Edge[BCQS] -3-3*t-1*t^2 , -2-1*t , 3+3*t+1*t^2
Edge[DEOT] 1+1*t , 1 , -2-1*t
Edge[FRST] -16-16*t-4*t^2 , 8+16*t+4*t^2 , 4

ADGHBCGIBDJKFIKNDELNACMNBFHOCEJOAEFPCHLPDIOPAIJQBEMQABLRGJMRHKQRCDFSEGKSFGLTHMST
[t equation] -1+1*t^2
Node[A] 0 , 0 , 1
Node[B] 1 , 0 , 1
Node[C] 1 , 1 , 1
Node[D] 0 , 1 , 1
Node[E] 1 , 0+1*t , 0+2*t
Node[F] -1 , 0-1*t , 0-1*t
Node[G] 0 , 1 , 0
Node[H] 0 , 1 , 1-1*t
Node[I] 1 , 2-1*t , 1
Node[J] 0+1*t , -1+2*t , -1+3*t
Node[K] 0+1*t , 2-1*t , 2
Node[L] 1 , 0 , 0+1*t
Node[M] 0-1*t , 0-1*t , 1-3*t
Node[N] 1 , 1 , 1+1*t
Node[O] 1 , -1+2*t , -2+3*t
Node[P] -1 , 0-1*t , 1-2*t
Node[Q] 0-1*t , 1-2*t , 4-6*t
Node[R] -1 , 0 , -3+1*t
Node[S] -1 , 0-2*t , 0-2*t
Node[T] -1+1*t , 1-2*t , 1-1*t
Edge[ADGH] 1 , 0 , 0
Edge[BCGI] -1 , 0 , 1
Edge[BDJK] -1 , -1 , 1
Edge[FIKN] 1 , -1 , 1-1*t
Edge[DELN] 0+1*t , 1 , -1
Edge[ACMN] 1 , -1 , 0
Edge[BFHO] -1 , -1+1*t , 1
Edge[CEJO] 0+1*t , 1-2*t , -1+1*t
Edge[AEFP] 0-1*t , 1 , 0
Edge[CHLP] 0+1*t , 1-1*t , -1
Edge[DIOP] -1+1*t , 1 , -1
Edge[AIJQ] 2-1*t , -1 , 0
Edge[BEMQ] 0-1*t , 1-2*t , 0+1*t
Edge[ABLR] 0 , -1 , 0
Edge[GJMR] 1-3*t , 0 , 0+1*t
Edge[HKQR] -3+1*t , -1+1*t , 1
Edge[CDFS] 0 , -1 , 1
Edge[EGKS] 0-2*t , 0 , 1
Edge[FGLT] 0-1*t , 0 , 1
Edge[HMST] 0-2*t , 1-1*t , 0+1*t

ADIJEHILEFGMCDHMABKMEJKNAGHODFLODGKPAFNPBCOPBDEQCGIQCFJRBHNRALQRACESBFISBGJTCKLTMNST
Node[A] 0 , 0 , 1
Node[B] 1 , 0 , 1
Node[C] 1 , 1 , 1
Node[D] 0 , 1 , 1
Node[E] -1 , -1 , -2
Node[F] -1/2 , -1 , -2
Node[G] 1/2 , -1/2 , -1
Node[H] -1/2 , 1/2 , 1/2
Node[I] 0 , 1 , 3/2
Node[J] 0 , 1/2 , 3/2
Node[K] 1/2 , 0 , -1/2
Node[L] -1/4 , -3/4 , -5/4
Node[M] -1 , 0 , 0
Node[N] 1/4 , 1/2 , 5/4
Node[O] 1/2 , -1/2 , 1/2
Node[P] -1/2 , -1 , -1/2
Node[Q] 1/2 , 3/2 , 2
Node[R] -1/4 , -3/4 , -7/4
Node[S] -1 , -1 , -5/2
Node[T] 1/4 , -1/2 , -5/4
Edge[ADIJ] 1 , 0 , 0
Edge[EHIL] 1/2 , 3/2 , -1
Edge[EFGM] 0 , 2 , -1
Edge[CDHM] 0 , -1 , 1
Edge[ABKM] 0 , -1 , 0
Edge[EJKN] -1/4 , 3/4 , -1/4
Edge[AGHO] -1/2 , -1/2 , 0
Edge[DFLO] 1 , 1/2 , -1/2
Edge[DGKP] 1/2 , -1/2 , 1/2
Edge[AFNP] -1 , 1/2 , 0
Edge[BCOP] -1 , 0 , 1
Edge[BDEQ] -1 , -1 , 1
Edge[CGIQ] 1/2 , -3/2 , 1
Edge[CFJR] -1 , 3/2 , -1/2
Edge[BHNR] -1/2 , -1 , 1/2
Edge[ALQR] 3/2 , -1/2 , 0
Edge[ACES] 1 , -1 , 0
Edge[BFIS] -1 , -3/2 , 1
Edge[BGJT] 1/2 , 3/2 , -1/2
Edge[CKLT] -1/2 , 1 , -1/2
Edge[MNST] 0 , -5/2 , 1

ABGHAEJKCGILACDMEFGMHIJMFIKNDHKOBJLODGNPBDFQCEHQAIOQCFJRALNRBEPRBCKSDELSAFPSBMNTCOPTGQRT
Node[A] 0 , 0 , 1
Node[B] 1 , 0 , 1
Node[C] 1 , 1 , 1
Node[D] 1 , 1 , 0
Node[E] 0 , 1 , 1
Node[F] 1 , 2 , -1
Node[G] 1 , 0 , -3
Node[H] -1 , 0 , 0
Node[I] -2 , -1 , 2
Node[J] 0 , -1 , 2
Node[K] 0 , 1 , 0
Node[L] -3 , -2 , 1
Node[M] -1 , -1 , 2
Node[N] -3 , -2 , 3
Node[O] 2 , 1 , 0
Node[P] 1 , 2 , 3
Node[Q] 2 , 1 , 1
Node[R] -3 , -2 , -5
Node[S] 1 , 2 , 1
Node[T] 5 , 2 , -1
Edge[ABGH] 0 , -1 , 0
Edge[AEJK] 1 , 0 , 0
Edge[CGIL] 3 , -4 , 1
Edge[ACDM] 1 , -1 , 0
Edge[EFGM] 3 , -1 , 1
Edge[HIJM] 0 , 2 , 1
Edge[FIKN] 1 , 0 , 1
Edge[DHKO] 0 , 0 , -1
Edge[BJLO] -1 , 2 , 1
Edge[DGNP] 3 , -3 , 1
Edge[BDFQ] -1 , 1 , 1
Edge[CEHQ] 0 , -1 , 1
Edge[AIOQ] 1 , -2 , 0
Edge[CFJR] -3 , 2 , 1
Edge[ALNR] -2 , 3 , 0
Edge[BEPR] -1 , -1 , 1
Edge[BCKS] -1 , 0 , 1
Edge[DELS] 1 , -1 , 1
Edge[AFPS] 2 , -1 , 0
Edge[BMNT] 1 , -3 , -1
Edge[COPT] -1 , 2 , -1
Edge[GQRT] -3 , 7 , -1

ACHIAFJKDGILADEMBFIMHKLMBJLNEINOEHJPCGKPEFGQCDJQABOQBDKRAGNRCFORBCESDFHSALPSBGHTCMNTDOPT
Node[A] 0 , 0 , 1
Node[B] 1 , 0 , 1
Node[C] 1 , 1 , 1
Node[D] 0 , 1 , 1
Node[E] 0 , 1 , 0
Node[F] -1 , -1/2 , 0
Node[G] -1/2 , -1 , 0
Node[H] 1 , 1 , 1/2
Node[I] 1/2 , 1/2 , -1/2
Node[J] -1 , -1/2 , -1/2
Node[K] -1 , -1/2 , -3/2
Node[L] 1/2 , 3/4 , -1/4
Node[M] 0 , 1/2 , -1
Node[N] 1/4 , 1/2 , -1/4
Node[O] -1/2 , 0 , 1/2
Node[P] -1/2 , -3/4 , -1/4
Node[Q] -1 , 0 , 0
Node[R] 1/2 , 1 , 3/2
Node[S] -1 , -3/2 , -1
Node[T] 3/4 , 1 , 1/4
Edge[ACHI] 1 , -1 , 0
Edge[AFJK] -1/2 , 1 , 0
Edge[DGIL] -1 , 1/2 , -1/2
Edge[ADEM] 1 , 0 , 0
Edge[BFIM] 1/2 , -1 , -1/2
Edge[HKLM] 5/4 , -1 , -1/2
Edge[BJLN] 1/2 , -1/2 , -1/2
Edge[EINO] 1/2 , 0 , 1/2
Edge[EHJP] 1/2 , 0 , -1
Edge[CGKP] -1 , 1/2 , 1/2
Edge[EFGQ] 0 , 0 , -1
Edge[CDJQ] 0 , -1 , 1
Edge[ABOQ] 0 , -1 , 0
Edge[BDKR] -1 , -1 , 1
Edge[AGNR] -1 , 1/2 , 0
Edge[CFOR] 1/2 , -1 , 1/2
Edge[BCES] -1 , 0 , 1
Edge[DFHS] -1/2 , 1 , -1
Edge[ALPS] -3/4 , 1/2 , 0
Edge[BGHT] 1 , -1/2 , -1
Edge[CMNT] -3/2 , 1 , 1/2
Edge[DOPT] -1/2 , 1/2 , -1/2

再添加新找到的23行结果
print(BFHICDJKAEGLHJLMDGINAKMNFGKOCIMOEIKPBGMPBCLQFJNQADOQACHRBENRDLPRABJSEHOSCFPSDEFTGHQTIJRTKLST);
solve([+1-2*T_X+1*P_Y*T_X-2*T_X*T_X,+1*P_Y-1*T_X-1*T_X*T_X,+1*P_Y*P_Y+1*T_X-3*P_Y*T_X,+1*N_X-1*P_Y+1*T_X,-1+1*P_X+1*P_Y-1*T_X,-1+1*S_X+1*T_X,-1+1*S_Y-1*T_X,+1*Q_Y+1*T_X,-2+1*A_Y+1*P_Y-1*T_X,+1+1*L_Y-1*P_Y+1*T_X,+3+1*F_Y-1*P_Y+2*T_X,-1+1*N_Y+1*P_Y,-1+1*K_X+1*P_Y,+1*D_X-1*P_Y,-1+1*G_Y+1*P_Y,-1+1*E_X+1*T_X,-1+1*O_X+1*T_X,-1+1*B_Y+1*P_Y-1*T_X,-1+1*R_X,-1+1*A_X,-1+1*D_Y+1*P_Y,+1*G_X-1*T_X,+1*Q_X-1*T_X,-1+1*R_Y,-1+1*T_Y,+1*K_Y-1*P_Y,+1*E_Y-1*P_Y],[P_Y,T_X,N_X,P_X,S_X,S_Y,Q_Y,A_Y,L_Y,F_Y,N_Y,K_X,D_X,G_Y,E_X,O_X,B_Y,R_X,A_X,D_Y,G_X,Q_X,R_Y,T_Y,K_Y,E_Y]);
print("B=(1,B_y,0) C_x=1 C_y=0 F=(1,F_y,0) H=(0,1,0) I=(1,0,0) J_x=0 J_y=1 L_x=0 M_x=0 M_y=0 O_y=0 ");

wreck · 发表于 2019-9-15 04:10:21

请问能能否将对应的图形贴出来下？

mathe · 发表于 2019-9-15 07:22:03

以前的很多数据代码我也没有备份，丢了也就没有了，现在还没弄好作图的部分代码

mathe · 发表于 2019-9-15 07:45:40

wayne在贴子https://bbs.emath.ac.cn/forum.ph ... hlight=%B9%FB%CA%F7 中做过一些23行图谱
他用mathematica做的图，还有源码

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[原创] 20棵树最优解计算