二次元上のユークリッド幾何の問題 その２４

ジュニア算数オリンピック・算数オリンピックにおけるユークリッド幾何学の問題の解答の自動化を模索している。まず三角形定理ループを回し、回答できなかったら1ステップの作図を試していって、それらで回答できるか探る。それでも駄目だったら2ステップ、3ステップと増やしていく。作業手順は今はこれを参考にする。
　

算数オリンピック13年度トライアル問題　問題10

『図の四角形ABCDで、点E、F、G、H、MはAE : EB = AF : FD = 2 : 5、BG : GH : HC = 3 : 2 : 2、CM = DMを満たす辺上の点です。いま、EG、FH上にそれぞれEP = PG、FQ = QHとなる点P、Qをとるとき、PQ = BMを求めなさい。

』

昨日の続きで、今日はクラスタに直線の点も入れて同じ作業をする。

名付けられていない交点は、上からR、Sと名付ける。今回は、最初から全体をクラスタとして登録する。

graph := [
    A : [
        [[F, D], []],
        [[E, B], []]
    ]
    ,
    B : [
        [[E, A], []],
        [[S, R, M], []],
        [[G, H, C], []]
    ]
    ,
    C : [
        [[B, G, H], []],
        [[D, M], []]
    ]
    ,
    D : [
        [[A, F], []],
        [[M, C], []]
    ]
    ,
    E : [
        [[A], [B]],
        [[P, S, G], []]
    ]
    ,
    F : [
        [[A], [D]],
        [[Q, R, H], []]
    ]
    ,
    G : [
        [[B], [H, C]],
        [[E, P, S], []]
    ]
    ,
    H : [
        [[B, G], [C]],
        [[F, Q, R], []]
    ]
    ,
    M : [
        [[D], [C]],
        [[B, S, R], []]
    ]
    ,
    P : [
        [[E], [S, G]],
        [[Q], []]
    ]
    ,
    Q : [
        [[P], []],
        [[F], [R, H]]
    ]
    ,
    R : [
        [[F, Q], [H]],
        [[B, S], [M]]
    ]
    ,
    S : [
        [[E, P], [G]],
        [[B], [R, M]]
    ]
];

parallel_lines_lst := [
];

triangle_lst := [
];

cluster_lst := [
    [[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
];

always {
    BE * 2 == AE * 5;
    DF * 2 == AF * 5;
    BG * 2 == GH * 3;
    BG * 2 == CH * 3;
    GH == CH;
    CM == DM;
    EP == PG;
    FQ == HQ;
}

今回はここからスタート。
で、graphを見て、辺の和と、180度の角の和を登録する。
平行線リストを見て、平行線による角のイコールも登録する。
三角形も登録する。graphを見て、点と繋がっている点と点が繋がっていたら、三角形。

graph := [
    A : [
        [[F, D], []],
        [[E, B], []]
    ]
    ,
    B : [
        [[E, A], []],
        [[S, R, M], []],
        [[G, H, C], []]
    ]
    ,
    C : [
        [[B, G, H], []],
        [[D, M], []]
    ]
    ,
    D : [
        [[A, F], []],
        [[M, C], []]
    ]
    ,
    E : [
        [[A], [B]],
        [[P, S, G], []]
    ]
    ,
    F : [
        [[A], [D]],
        [[Q, R, H], []]
    ]
    ,
    G : [
        [[B], [H, C]],
        [[E, P, S], []]
    ]
    ,
    H : [
        [[B, G], [C]],
        [[F, Q, R], []]
    ]
    ,
    M : [
        [[D], [C]],
        [[B, S, R], []]
    ]
    ,
    P : [
        [[E], [S, G]],
        [[Q], []]
    ]
    ,
    Q : [
        [[P], []],
        [[F], [R, H]]
    ]
    ,
    R : [
        [[F, Q], [H]],
        [[B, S], [M]]
    ]
    ,
    S : [
        [[E, P], [G]],
        [[B], [R, M]]
    ]
];

parallel_lines_lst := [
];

triangle_lst := [
    △BES : [EBS, BE, BEP, ES, BSE, BS],
    △BEG : [EBS, BE, BEP, EG, BGE, BG],
    △BGS : [GBS, BG, BGE, GS, BSE, BS],
    △BHR : [GBS, BH, BHF, HR, BRH, BR],
    △BCM : [GBS, BC, BCD, CM, BMC, BM]
];

cluster_lst := [
    [[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
];

always {
    BE * 2 == AE * 5;
    DF * 2 == AF * 5;
    BG * 2 == GH * 3;
    BG * 2 == CH * 3;
    GH == CH;
    CM == DM;
    EP == PG;
    FQ == HQ;

    AE + BE == AB;
    AF + DF == AD;
    BG + GH == BH;
    BG + CG == BC;
    BH + CH == BC;
    GH + CH == CG;
    DM + CM == CD;
    EP + PS == ES;
    EP + GP == EG;
    FQ + QR == FR;
    FQ + HQ == FH;
    FR + HR == FH;
    QR + HR == QH;
    BR + MR == BM;
    RS + MR == MS;
    ES + GS == EG;
    PS + GS == GP;
    BS + RS == BR;
    BS + MS == BM;
    AEP_p + BEP_p == AEB_h;
    AFQ_p + DFQ_p == AFD_h;
    BGE_p + EGH_p == BGH_h;
    BHF_p + CHF_p == BHC_h;
    BMD_p + BMC_p == CMD_h;
    EPQ_p + QPS_p == EPS_h;
    FQP_p + PQR_p == FQR_h;
    BRF_p + BRH_p == FRH_h;
    FRM_p + HRM_p == FRH_h;
    BRF_p + FRM_p == BRM_h;
    BRH_p + HRM_p == BRM_h;
    BSE_p + BSG_p == ESG_h;
    ESR_p + GSR_p == ESG_h;
    BSE_p + ESR_p == BSR_h;
    BSG_p + GSR_p == BSR_h;
}

昨日と同じように、クラスタからクラスタを弾き出す。思考過程を晒す。今回は点だけに着目して、graphでクラスタ内でクラスタ以外の方法で繋がっているものを探していった。

[[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
BM
EG
FH

[[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
BM
　[[B, G, H, C, M], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, BM]
　[[A, E, B, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BM, BMD_p, DM, ADM_p, DF, AFD_h, AF]]

[[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
EG
　[[A, E, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EG, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
　[[E, B, G], [BEP_p, BE, EBG_p, BG, BGE_p, EG]]

[[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
FH
　[[H, C, M, D, F], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FH]]
　[[A, E, B, G, H, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, FH, AFQ_p AF]]

いや、本当は、交点の判定を先にするべきなのだろうな。

[A, E, B, G, H, C, M, D, F]
BM
EG
FH

[E, B, G, H, M, F]

BMには、B側にEG、M側にFH
EGとFHにBMと一つずつ

B : [
　[[S, R, M], ],
]

M : [
　[[B, S, R], ]
]

R : [
　[[B, S], [M]]
]

S : [
　[[B], [R, M]]
]

E : [
　[[P, S, G], ]
]

G : [
　[[E, P, S], ]
]

S : [
　[[E, P], [G]],
]

F : [
　[[Q, R, H], ]
]

H : [
　[[F, Q, R], ]
]

R : [
　[[F, Q], [H]],
]

PとS、QとRの位置関係はどう考えよう。
分からないのではないか？そうすると、どうしよう。

前者のPとSのケースについて考えてみる。

E : [
　[[P, S, G], ]
]

G : [
　[[E, P, S], ]
]

S : [
　[[E, P], [G]],
]

P : [
　[[E], [S, G]],
]

んー、こう考えてみるか？

E : [
　[[P, S, G], ]
]

G : [
　[[E, P, S], ]
]

S : [
　[[E], [G]],
]

P : [
　[[E], [G]],
]

修正前だと、E→P→S→G、あるいはG→S→P→Eが可能。修正後だと、E→S→、の後がGにおいてはE・P・Sなので続かない。そういう場合は無視すべきか？
あるいは、

E : [
　[[P, S, G], , ]
]

G : [
　[[E, P, S], , ]
]

S : [
　[[E], [P], [G]],
]

P : [
　[[E], [S], [G]],
]

一方から見て位置関係がどちらか分からないということは、もう一方からも分からないということではないか。
いやどうだろう、これは昔考えた「位置の制約」に近いのではないか。

EG ~ @{E < G, P, S}
EG ~ @{E, P, S < G}
EG ~ @{E < P < G}
EG ~ @{E < S < G}

だっけか？忘れたけど。

そういうものが確定しないと交点を認めないというスタンスでは、この問題のクラスタを取得し切ることはできない。1番目と2番目と3番目（位置の制約）について、2番目と3番目は本質的に同じだとして、1番目を試して駄目だったら、2番目を試すことにしよう。というか3番目は、できればこれ以上話をややこしくしたくない。

まあでもこれは、初期段階ならこの判断はいらないし、作図段階なら、更に少し作図して三角関数で素直に判定した方が良いのかもしれない。分からないなら本当にどちらか分からない状態なわけで、そんな状態でそういう機能で交点を考えるのに何の旨味があるのかというか。

一晩開けて思うのだけど、1番目と2番目は、大は小を兼ねるというか、2番目の真ん中を消せば1番目になるから、とりあえず2番目にしてみようかな。
そもそも交点を作らないというのが元々だったんだけど、そうするとクラスタEAFRSを考えることができなくなる。そういう順番が関わるみたいなのは、できれば避けたい。失敗し次第、その交点を作らない方針に戻すとして、だからとりあえず2番目で行こう。

まあ、今回は、そもそも作図で無く初期のセットアップだから、やり直さずこのまま続けるが。

BMの間は、B、S、R、M。BS, BSR_h, RS, BRM_h, MR。

[[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]]
[[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]]

EGの間は、E、P、S、G。EP, EPS_h, PS, ESG_h, GS。

[[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
[[E, B, G, S, P], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]]

FHの間は、F、Q、R、H。FQ, FQR_h, QR, FRH_h, HR

[[H, C, M, D, F, Q, R], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]]
[[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]]

graph := [
    A : [
        [[F, D], [], []],
        [[E, B], [], []]
    ]
    ,
    B : [
        [[E, A], [], []],
        [[S, R, M], [], []],
        [[G, H, C], [], []]
    ]
    ,
    C : [
        [[B, G, H], [], []],
        [[D, M], [], []]
    ]
    ,
    D : [
        [[A, F], [], []],
        [[M, C], [], []]
    ]
    ,
    E : [
        [[A], [], [B]],
        [[P, S, G], [], []]
    ]
    ,
    F : [
        [[A], [], [D]],
        [[Q, R, H], [], []]
    ]
    ,
    G : [
        [[B], [], [H, C]],
        [[E, P, S], [], []]
    ]
    ,
    H : [
        [[B, G], [], [C]],
        [[F, Q, R], [], []]
    ]
    ,
    M : [
        [[D], [], [C]],
        [[B, S, R], [], []]
    ]
    ,
    P : [
        [[E], [], [S, G]],
        [[Q], [], []]
    ]
    ,
    Q : [
        [[P], [], []],
        [[F], [], [R, H]]
    ]
    ,
    R : [
        [[F, Q], [], [H]],
        [[B, S], [], [M]]
    ]
    ,
    S : [
        [[E, P], [], [G]],
        [[B], [], [R, M]]
    ]
];

parallel_lines_lst := [
];

triangle_lst := [
    △BES : [EBS, BE, BEP, ES, BSE, BS],
    △BEG : [EBS, BE, BEP, EG, BGE, BG],
    △BGS : [GBS, BG, BGE, GS, BSE, BS],
    △BHR : [GBS, BH, BHF, HR, BRH, BR],
    △BCM : [GBS, BC, BCD, CM, BMC, BM]
];

cluster_lst := [
    [[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
    [[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]],
    [[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, G, S, P], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]],
    [[H, C, M, D, F, Q, R], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
    [[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]]
];

always {
    BE * 2 == AE * 5;
    DF * 2 == AF * 5;
    BG * 2 == GH * 3;
    BG * 2 == CH * 3;
    GH == CH;
    CM == DM;
    EP == PG;
    FQ == HQ;

    AE + BE == AB;
    AF + DF == AD;
    BG + GH == BH;
    BG + CG == BC;
    BH + CH == BC;
    GH + CH == CG;
    DM + CM == CD;
    EP + PS == ES;
    EP + GP == EG;
    FQ + QR == FR;
    FQ + HQ == FH;
    FR + HR == FH;
    QR + HR == QH;
    BR + MR == BM;
    RS + MR == MS;
    ES + GS == EG;
    PS + GS == GP;
    BS + RS == BR;
    BS + MS == BM;
    AEP_p + BEP_p == AEB_h;
    AFQ_p + DFQ_p == AFD_h;
    BGE_p + EGH_p == BGH_h;
    BHF_p + CHF_p == BHC_h;
    BMD_p + BMC_p == CMD_h;
    EPQ_p + QPS_p == EPS_h;
    FQP_p + PQR_p == FQR_h;
    BRF_p + BRH_p == FRH_h;
    FRM_p + HRM_p == FRH_h;
    BRF_p + FRM_p == BRM_h;
    BRH_p + HRM_p == BRM_h;
    BSE_p + BSG_p == ESG_h;
    ESR_p + GSR_p == ESG_h;
    BSE_p + ESR_p == BSR_h;
    BSG_p + GSR_p == BSR_h;
}

いろいろ考察したんで、一旦表示した。続きをする。

[[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]]
GS
HR

[[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]]
GS

[[B, G, S], [GBS_p, BG, BGE_p, GS, BSG_p, BS]]
[[G, H, C, M, R, S], [EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, GSR_p, GS]]

[[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]]
HR

[[B, G, H, R, S], [GBS_p, BG, BGH_h, GH, BHF_p, RH, BRH_p, RS, BSR_h, BS]]
[[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]]

[[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]]
ES
FR

[[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]]
ES

[[A, E, S, R, M, D, F], [EAF_p, AE, AEP_p, ES, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]]
[[E, B, S], [BEP_p, BE, EBS_p, BS, BSE_p, ES]]

ES。E, P, S。EP, EPS_h, PS

[[A, E, S, R, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]]
[[E, B, S], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_h, EP]]

[[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]]
FR

[[A, E, B, S, R, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, FR, AFQ_p, AF]]
[[R, M, D, F], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FR]]

FR。F、Q、R。FQ, FQR_h, QR。

[[A, E, B, S, R, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, QR, FQR_h, FR, AFQ_p, AF]]
[[R, M, D, F], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR]]

[[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
MS
FH

[[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
MS

[[A, E, P, S, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, MS, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
[[S, G, H, C, M], [GSR_p, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MS]],

MS。M、R、S。MR, BRM_h, RS

[[A, E, P, S, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
[[S, G, H, C, M], [GSR_p, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS]],

[[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
FH

[[A, E, P, S, G, H, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, FH, AFQ_p, AF]],
[[H, C, M, D, F], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FH]],

FH。F、Q、R、H。FQ, FQR_h, QR, FRH_h, HR。

[[A, E, P, S, G, H, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
[[H, C, M, D, F], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],

[[E, B, G, S, P], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]]
BS

[[E, B, S, P], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_h, EP]]
[[B, G, S], [GBS_p, BG, BGE_p, GS, BSG_p, BS]]

[[H, C, M, D, F, Q, R], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
MR

[[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]],
[[M, D, F, Q, R], [BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRM_p, MR]],

[[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]]
EG
BR

[[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]]
EG

[[A, E, G, H, R, Q, F], [EAF_p, AE, AEP_p, EG, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]]
[[E, B, G], [BEP_p, BE, EBG_p, BG, BGE_p, EG]]

EG。E, P, S, G。EP, EPS_h, PS, ESG_h, GS。

[[A, E, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]]
[[E, B, G], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]]

[[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]]
BR

[[A, E, B, R, Q, F], [EAF_p, AE, AEB_h, BE, EBS_p, BR, BRF_p, QR, FQR_h, FQ, AFQ_p AF]]
[[B, G, H, R], [GBS_p, BG, BGH_h, GH, BHF_p, HR, BRH_p, BR]]

graph := [
    A : [
        [[F, D], [], []],
        [[E, B], [], []]
    ]
    ,
    B : [
        [[E, A], [], []],
        [[S, R, M], [], []],
        [[G, H, C], [], []]
    ]
    ,
    C : [
        [[B, G, H], [], []],
        [[D, M], [], []]
    ]
    ,
    D : [
        [[A, F], [], []],
        [[M, C], [], []]
    ]
    ,
    E : [
        [[A], [], [B]],
        [[P, S, G], [], []]
    ]
    ,
    F : [
        [[A], [], [D]],
        [[Q, R, H], [], []]
    ]
    ,
    G : [
        [[B], [], [H, C]],
        [[E, P, S], [], []]
    ]
    ,
    H : [
        [[B, G], [], [C]],
        [[F, Q, R], [], []]
    ]
    ,
    M : [
        [[D], [], [C]],
        [[B, S, R], [], []]
    ]
    ,
    P : [
        [[E], [], [S, G]],
        [[Q], [], []]
    ]
    ,
    Q : [
        [[P], [], []],
        [[F], [], [R, H]]
    ]
    ,
    R : [
        [[F, Q], [], [H]],
        [[B, S], [], [M]]
    ]
    ,
    S : [
        [[E, P], [], [G]],
        [[B], [], [R, M]]
    ]
];

parallel_lines_lst := [
];

triangle_lst := [
    △BES : [EBS, BE, BEP, ES, BSE, BS],
    △BEG : [EBS, BE, BEP, EG, BGE, BG],
    △BGS : [GBS, BG, BGE, GS, BSE, BS],
    △BHR : [GBS, BH, BHF, HR, BRH, BR],
    △BCM : [GBS, BC, BCD, CM, BMC, BM]
];

cluster_lst := [
    [[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],

    [[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]],
    [[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, G, S, P], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]],
    [[H, C, M, D, F, Q, R], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
    [[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]],

    [[B, G, S], [GBS_p, BG, BGE_p, GS, BSG_p, BS]],
    [[G, H, C, M, R, S], [EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, GSR_p, GS]],
    [[B, G, H, R, S], [GBS_p, BG, BGH_h, GH, BHF_p, RH, BRH_p, RS, BSR_h, BS]],
    [[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]],
    [[A, E, S, R, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, S], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_h, EP]],
    [[A, E, B, S, R, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, QR, FQR_h, FR, AFQ_p, AF]],
    [[R, M, D, F], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR]]
    [[A, E, P, S, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[S, G, H, C, M], [GSR_p, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS]],
    [[A, E, P, S, G, H, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
    [[H, C, M, D, F], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
    [[E, B, S, P], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_h, EP]],
    [[M, D, F, Q, R], [BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRM_p, MR]],
    [[A, E, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
    [[E, B, G], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]],
    [[A, E, B, R, Q, F], [EAF_p, AE, AEB_h, BE, EBS_p, BR, BRF_p, QR, FQR_h, FQ, AFQ_p AF]],
    [[B, G, H, R], [GBS_p, BG, BGH_h, GH, BHF_p, HR, BRH_p, BR]]
];

always {
    BE * 2 == AE * 5;
    DF * 2 == AF * 5;
    BG * 2 == GH * 3;
    BG * 2 == CH * 3;
    GH == CH;
    CM == DM;
    EP == PG;
    FQ == HQ;

    AE + BE == AB;
    AF + DF == AD;
    BG + GH == BH;
    BG + CG == BC;
    BH + CH == BC;
    GH + CH == CG;
    DM + CM == CD;
    EP + PS == ES;
    EP + GP == EG;
    FQ + QR == FR;
    FQ + HQ == FH;
    FR + HR == FH;
    QR + HR == QH;
    BR + MR == BM;
    RS + MR == MS;
    ES + GS == EG;
    PS + GS == GP;
    BS + RS == BR;
    BS + MS == BM;
    AEP_p + BEP_p == AEB_h;
    AFQ_p + DFQ_p == AFD_h;
    BGE_p + EGH_p == BGH_h;
    BHF_p + CHF_p == BHC_h;
    BMD_p + BMC_p == CMD_h;
    EPQ_p + QPS_p == EPS_h;
    FQP_p + PQR_p == FQR_h;
    BRF_p + BRH_p == FRH_h;
    FRM_p + HRM_p == FRH_h;
    BRF_p + FRM_p == BRM_h;
    BRH_p + HRM_p == BRM_h;
    BSE_p + BSG_p == ESG_h;
    ESR_p + GSR_p == ESG_h;
    BSE_p + ESR_p == BSR_h;
    BSG_p + GSR_p == BSR_h;
}

えー、続き。該当するものだけ表示することにする。

[[G, H, C, M, R, S], [EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, GSR_p, GS]],
HR

[[G, H, R, S], [EGH_p, GH, BHF_p, HR, BHR_p, RS, GSR_p, GS]],
[[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]],

[[A, E, S, R, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
FR

[[A, E, S, R, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, FR, AFQ_p, AF]],
[[R, M, D, F], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FR],

FR。F, Q, R。FQ, FQR_p, QR

[[A, E, S, R, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, QR, FQR_p, FQ, AFQ_p, AF]],
[[R, M, D, F], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_p, QR],

[[A, E, B, S, R, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, QR, FQR_h, FR, AFQ_p, AF]],
ES

[[A, E, S, R, F], [EAF_p, AE, AEP_p, ES, ESR_p, RS, BRF_p, QR, FQR_h, FR, AFQ_p, AF]],
[[E, B, S], [BEP_p, BE, EBS_p, BS, BSE_p, ES]],

ES。E, P, S。EP, EPS_p, PS

[[A, E, S, R, F], [EAF_p, AE, AEP_p, EP, EPS_p, PS, ESR_p, RS, BRF_p, QR, FQR_h, FR, AFQ_p, AF]],
[[E, B, S], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_p, EP]],

[[A, E, P, S, R, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
FR

[[A, E, P, S, R, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, FR, AFQ_p, AF]],
[[R, M, D, F], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFR_p, FR]],

FR。FQ, FQR_p, QR

[[A, E, P, S, R, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, QR, FQR_p, FQ, AFQ_p, AF]],
[[R, M, D, F], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFR_p, FQ, FQR_p, QR]],

[[S, G, H, C, M, R], [GSR_p, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS]],
HR

[[S, G, H, R], [GSR_p, GS, EGH_p, GH, BHF_p, HR, BRH_p, RS]],
[[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]],

[[A, E, P, S, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
PQ
RS

[[A, E, P, S, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
PQ

[[A, E, P, Q, F], [EAF_p, AE, AEP_p, EP, EPQ_p, PQ, FQP_p, FQ, AFQ_p, AF]],
[[P, S, G, H, R, Q], [QPS_p, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, PQR_p, PQ]],

[[A, E, P, S, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
RS

[[A, E, P, S, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, QR, FQR_h, FQ, AFQ_p, AF]],
[[S, G, H, R], [GSR_p, GS, EGH_p, GH, BHF_p, HR, BRH_p, RS]],

[[H, C, M, D, F, Q, R], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
MR

[[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]],
[[M, D, F, Q, R], [BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRM_p, MR]],

[[A, E, P, S, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
PQ
RS

[[A, E, P, S, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
PQ

[[A, E, P, Q, F], [EAF_p, AE, AEP_p, EP, EPQ_p, PQ, FQP_p, FQ, AFQ_p, AF]],
[[P, S, G, H, R, Q], [QPS_p, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, PQR_p, PQ]],

[[A, E, P, S, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
RS

[[A, E, P, S, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, QR, FQR_h, FQ, AFQ_p, AF]],
[[S, G, H, R], [GSR_p, GS, EGH_p, GH, BHF_p, HR, BRH_p, RS]],

[[A, E, B, R, Q, F], [EAF_p, AE, AEB_h, BE, EBS_p, BR, BRF_p, QR, FQR_h, FQ, AFQ_p AF]],

↑、今回はこういうミスが多かった、ほとんど書かずに直したが。[A, E, B, G, H, R, Q, F]の時に、BRの間にSがある。それが抜けているという単純ミスだ。早く自動化してえ、できないんだっけか？

BR。B, S, R。BS, BSR_h, RS。

[[A, E, B, S, R, Q, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, QR, FQR_h, FQ, AFQ_p AF]],

[[A, E, B, S, R, Q, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, QR, FQR_h, FQ, AFQ_p AF]],
ES

[[A, E, S, R, Q, F], [EAF_p, AE, AEP_p, ES, ESR_p, RS, BRF_p, QR, FQR_h, FQ, AFQ_p AF]],
[[E, B, S], [BEP_p, BE, EBS_p, BS, BSE_p, ES]],

[[B, G, H, R], [GBS_p, BG, BGH_h, GH, BHF_p, HR, BRH_p, BR]]

同じくSが抜けている。ただしRBなので注意。

[[B, G, H, R, S], [GBS_p, BG, BGH_h, GH, BHF_p, HR, BRH_p, RS, BSR_h, BS]]

[[B, G, H, R, S], [GBS_p, BG, BGH_h, GH, BHF_p, HR, BRH_p, RS, BSR_h, BS]]
GS

[[B, G, S], [GBS_p, BG, BGE_p, GS, BSG_p, BS]]
[[G, H, R, S], [EGH_p, GH, BHF_p, HR, BRH_p, RS, GSR_p, GS]]

graph := [
    A : [
        [[F, D], [], []],
        [[E, B], [], []]
    ]
    ,
    B : [
        [[E, A], [], []],
        [[S, R, M], [], []],
        [[G, H, C], [], []]
    ]
    ,
    C : [
        [[B, G, H], [], []],
        [[D, M], [], []]
    ]
    ,
    D : [
        [[A, F], [], []],
        [[M, C], [], []]
    ]
    ,
    E : [
        [[A], [], [B]],
        [[P, S, G], [], []]
    ]
    ,
    F : [
        [[A], [], [D]],
        [[Q, R, H], [], []]
    ]
    ,
    G : [
        [[B], [], [H, C]],
        [[E, P, S], [], []]
    ]
    ,
    H : [
        [[B, G], [], [C]],
        [[F, Q, R], [], []]
    ]
    ,
    M : [
        [[D], [], [C]],
        [[B, S, R], [], []]
    ]
    ,
    P : [
        [[E], [], [S, G]],
        [[Q], [], []]
    ]
    ,
    Q : [
        [[P], [], []],
        [[F], [], [R, H]]
    ]
    ,
    R : [
        [[F, Q], [], [H]],
        [[B, S], [], [M]]
    ]
    ,
    S : [
        [[E, P], [], [G]],
        [[B], [], [R, M]]
    ]
];

parallel_lines_lst := [
];

triangle_lst := [
    △BES : [EBS, BE, BEP, ES, BSE, BS],
    △BEG : [EBS, BE, BEP, EG, BGE, BG],
    △BGS : [GBS, BG, BGE, GS, BSE, BS],
    △BHR : [GBS, BH, BHF, HR, BRH, BR],
    △BCM : [GBS, BC, BCD, CM, BMC, BM]
];

cluster_lst := [
    [[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],

    [[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]],
    [[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, G, S, P], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]],
    [[H, C, M, D, F, Q, R], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
    [[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]],

    [[B, G, S], [GBS_p, BG, BGE_p, GS, BSG_p, BS]],
    [[G, H, C, M, R, S], [EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, GSR_p, GS]],
    [[B, G, H, R, S], [GBS_p, BG, BGH_h, GH, BHF_p, RH, BRH_p, RS, BSR_h, BS]],
    [[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]],
    [[A, E, S, R, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, S], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_h, EP]],
    [[A, E, B, S, R, Q, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, QR, FQR_h, FR, AFQ_p, AF]],
    [[R, M, D, F], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR]]
    [[A, E, P, S, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[S, G, H, C, M], [GSR_p, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS]],
    [[A, E, P, S, G, H, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
    [[H, C, M, D, F], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
    [[E, B, S, P], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_h, EP]],
    [[M, D, F, Q, R], [BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRM_p, MR]],
    [[A, E, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],
    [[E, B, G], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]],
    [[B, G, H, R], [GBS_p, BG, BGH_h, GH, BHF_p, HR, BRH_p, BR]]

    [[G, H, R, S], [EGH_p, GH, BHF_p, HR, BHR_p, RS, GSR_p, GS]],
    [[R, M, D, F, Q], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_p, QR],
    [[A, E, P, Q, F], [EAF_p, AE, AEP_p, EP, EPQ_p, PQ, FQP_p, FQ, AFQ_p, AF]],
    [[P, S, G, H, R, Q], [QPS_p, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, PQR_p, PQ]],
    [[A, E, P, S, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, QR, FQR_h, FQ, AFQ_p, AF]],
];

always {
    BE * 2 == AE * 5;
    DF * 2 == AF * 5;
    BG * 2 == GH * 3;
    BG * 2 == CH * 3;
    GH == CH;
    CM == DM;
    EP == PG;
    FQ == HQ;

    AE + BE == AB;
    AF + DF == AD;
    BG + GH == BH;
    BG + CG == BC;
    BH + CH == BC;
    GH + CH == CG;
    DM + CM == CD;
    EP + PS == ES;
    EP + GP == EG;
    FQ + QR == FR;
    FQ + HQ == FH;
    FR + HR == FH;
    QR + HR == QH;
    BR + MR == BM;
    RS + MR == MS;
    ES + GS == EG;
    PS + GS == GP;
    BS + RS == BR;
    BS + MS == BM;
    AEP_p + BEP_p == AEB_h;
    AFQ_p + DFQ_p == AFD_h;
    BGE_p + EGH_p == BGH_h;
    BHF_p + CHF_p == BHC_h;
    BMD_p + BMC_p == CMD_h;
    EPQ_p + QPS_p == EPS_h;
    FQP_p + PQR_p == FQR_h;
    BRF_p + BRH_p == FRH_h;
    FRM_p + HRM_p == FRH_h;
    BRF_p + FRM_p == BRM_h;
    BRH_p + HRM_p == BRM_h;
    BSE_p + BSG_p == ESG_h;
    ESR_p + GSR_p == ESG_h;
    BSE_p + ESR_p == BSR_h;
    BSG_p + GSR_p == BSR_h;
}

いろいろ消えた。被ってたんで。

では続き。

[[P, S, G, H, R, Q], [QPS_p, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, PQR_p, PQ]],
RS

[[P, S, R, Q], [QPS_p, PS, ESR_p, RS, BRF_p, QR, PQR_p, PQ]],
[[S, G, H, R], [GSR_p, GS, EGH_p, GH, BHF_p, HR, BRH_p, RS]],

[[A, E, P, S, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, QR, FQR_h, FQ, AFQ_p, AF]],
PQ

[A, E, P, Q, F], [EAF_p, AE, AEP_p, EP, EPQ_p, PQ, FQP, FQ, AFQ_p, AF]],
[P, S, R, Q], [QPS_p, PS, ESR_p, RS, BRF_p, QR, PQR_p, PQ]],

graph := [
    A : [
        [[F, D], [], []],
        [[E, B], [], []]
    ]
    ,
    B : [
        [[E, A], [], []],
        [[S, R, M], [], []],
        [[G, H, C], [], []]
    ]
    ,
    C : [
        [[B, G, H], [], []],
        [[D, M], [], []]
    ]
    ,
    D : [
        [[A, F], [], []],
        [[M, C], [], []]
    ]
    ,
    E : [
        [[A], [], [B]],
        [[P, S, G], [], []]
    ]
    ,
    F : [
        [[A], [], [D]],
        [[Q, R, H], [], []]
    ]
    ,
    G : [
        [[B], [], [H, C]],
        [[E, P, S], [], []]
    ]
    ,
    H : [
        [[B, G], [], [C]],
        [[F, Q, R], [], []]
    ]
    ,
    M : [
        [[D], [], [C]],
        [[B, S, R], [], []]
    ]
    ,
    P : [
        [[E], [], [S, G]],
        [[Q], [], []]
    ]
    ,
    Q : [
        [[P], [], []],
        [[F], [], [R, H]]
    ]
    ,
    R : [
        [[F, Q], [], [H]],
        [[B, S], [], [M]]
    ]
    ,
    S : [
        [[E, P], [], [G]],
        [[B], [], [R, M]]
    ]
];

parallel_lines_lst := [
];

triangle_lst := [
    △BES : [EBS, BE, BEP, ES, BSE, BS],
    △BEG : [EBS, BE, BEP, EG, BGE, BG],
    △BGS : [GBS, BG, BGE, GS, BSE, BS],
    △BHR : [GBS, BH, BHF, HR, BRH, BR],
    △BCM : [GBS, BC, BCD, CM, BMC, BM]
];

cluster_lst := [
    [[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],

    [[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]],
    [[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, G, S, P], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]],
    [[H, C, M, D, F, Q, R], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
    [[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]],

    [[B, G, S], [GBS_p, BG, BGE_p, GS, BSG_p, BS]],
    [[G, H, C, M, R, S], [EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, GSR_p, GS]],
    [[B, G, H, R, S], [GBS_p, BG, BGH_h, GH, BHF_p, RH, BRH_p, RS, BSR_h, BS]],
    [[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]],
    [[A, E, P, S, R, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, S, P], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_h, EP]],
    [[A, E, B, S, R, Q, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, QR, FQR_h, FR, AFQ_p, AF]],
    [[R, M, D, F, Q], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR]]
    [[A, E, P, S, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],

    [[G, H, R, S], [EGH_p, GH, BHF_p, HR, BHR_p, RS, GSR_p, GS]],
    [[A, E, P, Q, F], [EAF_p, AE, AEP_p, EP, EPQ_p, PQ, FQP_p, FQ, AFQ_p, AF]],
    [[P, S, G, H, R, Q], [QPS_p, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, PQR_p, PQ]],
    [[A, E, P, S, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, QR, FQR_h, FQ, AFQ_p, AF]],

    [[P, S, R, Q], [QPS_p, PS, ESR_p, RS, BRF_p, QR, PQR_p, PQ]],
    [[S, G, H, R], [GSR_p, GS, EGH_p, GH, BHF_p, HR, BRH_p, RS]],
    [[A, E, P, Q, F], [EAF_p, AE, AEP_p, EP, EPQ_p, PQ, FQP, FQ, AFQ_p, AF]],
];

always {
    BE * 2 == AE * 5;
    DF * 2 == AF * 5;
    BG * 2 == GH * 3;
    BG * 2 == CH * 3;
    GH == CH;
    CM == DM;
    EP == PG;
    FQ == HQ;

    AE + BE == AB;
    AF + DF == AD;
    BG + GH == BH;
    BG + CG == BC;
    BH + CH == BC;
    GH + CH == CG;
    DM + CM == CD;
    EP + PS == ES;
    EP + GP == EG;
    FQ + QR == FR;
    FQ + HQ == FH;
    FR + HR == FH;
    QR + HR == QH;
    BR + MR == BM;
    RS + MR == MS;
    ES + GS == EG;
    PS + GS == GP;
    BS + RS == BR;
    BS + MS == BM;
    AEP_p + BEP_p == AEB_h;
    AFQ_p + DFQ_p == AFD_h;
    BGE_p + EGH_p == BGH_h;
    BHF_p + CHF_p == BHC_h;
    BMD_p + BMC_p == CMD_h;
    EPQ_p + QPS_p == EPS_h;
    FQP_p + PQR_p == FQR_h;
    BRF_p + BRH_p == FRH_h;
    FRM_p + HRM_p == FRH_h;
    BRF_p + FRM_p == BRM_h;
    BRH_p + HRM_p == BRM_h;
    BSE_p + BSG_p == ESG_h;
    ESR_p + GSR_p == ESG_h;
    BSE_p + ESR_p == BSR_h;
    BSG_p + GSR_p == BSR_h;
}

目視で確認して、だいぶインチキというか削ったが、まあ単純ミスだろうし、良しとしよう。
って、角の和を登録するのを忘れていたか。

[[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]]
BM

とか、こういう段階で、クラスタのBかMの角がハーフで無くポジティブの時に、角の和を登録する。
今回はBがポジティブで、EBM（適当）とMBGが、足したらEBG_pになると登録する。

EBS_p + GBS_p == MBG_p、という具合。

他は無かった。いやあるんだが、まあそういうことだ。

graph := [
    A : [
        [[F, D], [], []],
        [[E, B], [], []]
    ]
    ,
    B : [
        [[E, A], [], []],
        [[S, R, M], [], []],
        [[G, H, C], [], []]
    ]
    ,
    C : [
        [[B, G, H], [], []],
        [[D, M], [], []]
    ]
    ,
    D : [
        [[A, F], [], []],
        [[M, C], [], []]
    ]
    ,
    E : [
        [[A], [], [B]],
        [[P, S, G], [], []]
    ]
    ,
    F : [
        [[A], [], [D]],
        [[Q, R, H], [], []]
    ]
    ,
    G : [
        [[B], [], [H, C]],
        [[E, P, S], [], []]
    ]
    ,
    H : [
        [[B, G], [], [C]],
        [[F, Q, R], [], []]
    ]
    ,
    M : [
        [[D], [], [C]],
        [[B, S, R], [], []]
    ]
    ,
    P : [
        [[E], [], [S, G]],
        [[Q], [], []]
    ]
    ,
    Q : [
        [[P], [], []],
        [[F], [], [R, H]]
    ]
    ,
    R : [
        [[F, Q], [], [H]],
        [[B, S], [], [M]]
    ]
    ,
    S : [
        [[E, P], [], [G]],
        [[B], [], [R, M]]
    ]
];

parallel_lines_lst := [
];

triangle_lst := [
    △BES : [EBS, BE, BEP, ES, BSE, BS],
    △BEG : [EBS, BE, BEP, EG, BGE, BG],
    △BGS : [GBS, BG, BGE, GS, BSE, BS],
    △BHR : [GBS, BH, BHF, HR, BRH, BR],
    △BCM : [GBS, BC, BCD, CM, BMC, BM]
];

cluster_lst := [
    [[A, E, B, G, H, C, M, D, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],

    [[B, G, H, C, M, R, S], [GBS_p, BG, BGH_h, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, BSR_h, BS]],
    [[A, E, B, S, R, M, D, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[A, E, P, S, G, H, C, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHC_h, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, G, S, P], [BEP_p, BE, EBG_p, BG, BGE_p, GS, ESG_h, PS, EPS_h, EP]],
    [[H, C, M, D, F, Q, R], [CHF_p, CH, BCD_p, CM, CMD_h, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR, FRH_h, HR]],
    [[A, E, B, G, H, R, Q, F], [EAF_p, AE, AEB_h, BE, EBG_p, BG, BGH_h, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p AF]],

    [[B, G, S], [GBS_p, BG, BGE_p, GS, BSG_p, BS]],
    [[G, H, C, M, R, S], [EGH_p, GH, BHC_h, CH, BCD_p, CM, BMC_p, MR, BRM_h, RS, GSR_p, GS]],
    [[B, G, H, R, S], [GBS_p, BG, BGH_h, GH, BHF_p, RH, BRH_p, RS, BSR_h, BS]],
    [[H, C, M, R], [CHF_p, CH, BCD_p, CM, BMC_p, MR, HRM_p, HR]],
    [[A, E, P, S, R, M, D, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRM_h, MR, BMD_p, DM, ADM_p, DF, AFD_h, AF]],
    [[E, B, S, P], [BEP_p, BE, EBS_p, BS, BSE_p, PS, EPS_h, EP]],
    [[A, E, B, S, R, Q, F], [EAF_p, AE, AEB_h, BE, EBS_p, BS, BSR_h, RS, BRF_p, QR, FQR_h, FR, AFQ_p, AF]],
    [[R, M, D, F, Q], [FRM_p, MR, BMD_p, DM, ADM_p, DF, DFQ_p, FQ, FQR_h, QR]]
    [[A, E, P, S, G, H, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, FQR_h, FQ, AFQ_p, AF]],

    [[G, H, R, S], [EGH_p, GH, BHF_p, HR, BHR_p, RS, GSR_p, GS]],
    [[A, E, P, Q, F], [EAF_p, AE, AEP_p, EP, EPQ_p, PQ, FQP_p, FQ, AFQ_p, AF]],
    [[P, S, G, H, R, Q], [QPS_p, PS, ESG_h, GS, EGH_p, GH, BHF_p, HR, FRH_h, QR, PQR_p, PQ]],
    [[A, E, P, S, R, Q, F], [EAF_p, AE, AEP_p, EP, EPS_h, PS, ESR_p, RS, BRF_p, QR, FQR_h, FQ, AFQ_p, AF]],

    [[P, S, R, Q], [QPS_p, PS, ESR_p, RS, BRF_p, QR, PQR_p, PQ]],
    [[S, G, H, R], [GSR_p, GS, EGH_p, GH, BHF_p, HR, BRH_p, RS]],
    [[A, E, P, Q, F], [EAF_p, AE, AEP_p, EP, EPQ_p, PQ, FQP, FQ, AFQ_p, AF]],
];

always {
    BE * 2 == AE * 5;
    DF * 2 == AF * 5;
    BG * 2 == GH * 3;
    BG * 2 == CH * 3;
    GH == CH;
    CM == DM;
    EP == PG;
    FQ == HQ;

    AE + BE == AB;
    AF + DF == AD;
    BG + GH == BH;
    BG + CG == BC;
    BH + CH == BC;
    GH + CH == CG;
    DM + CM == CD;
    EP + PS == ES;
    EP + GP == EG;
    FQ + QR == FR;
    FQ + HQ == FH;
    FR + HR == FH;
    QR + HR == QH;
    BR + MR == BM;
    RS + MR == MS;
    ES + GS == EG;
    PS + GS == GP;
    BS + RS == BR;
    BS + MS == BM;
    AEP_p + BEP_p == AEB_h;
    AFQ_p + DFQ_p == AFD_h;
    BGE_p + EGH_p == BGH_h;
    BHF_p + CHF_p == BHC_h;
    BMD_p + BMC_p == CMD_h;
    EPQ_p + QPS_p == EPS_h;
    FQP_p + PQR_p == FQR_h;
    BRF_p + BRH_p == FRH_h;
    FRM_p + HRM_p == FRH_h;
    BRF_p + FRM_p == BRM_h;
    BRH_p + HRM_p == BRM_h;
    BSE_p + BSG_p == ESG_h;
    ESR_p + GSR_p == ESG_h;
    BSE_p + ESR_p == BSR_h;
    BSG_p + GSR_p == BSR_h;

    EBS_p + GBS_p == MBG_p;
}

これでセットアップは終わりだろう。長かった。

いや、誤解を生みそうだけど、今回のは終わりってことね。おそらくまだ続く。