Solution 6 to problem h
Remaining equations |
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem h
Equations
The following unsolved equations remain:
2 2 2
0=a23 + a33 + b12 *kap
Expressions
The solution is given through the following expressions:
r70=0
r71=0
r72=0
r73=0
r74=0
r75=0
r76=0
r77=0
r78=0
r79=0
r710=0
r711=0
r712=0
r713=0
r714=0
r715=0
r716=0
r717=0
r718=0
r719=0
r720=0
r721=0
r722=0
r723=0
r724=0
r725=0
r726=0
r727=0
r728=0
r729=0
r730=0
r731=0
r732=0
r733=0
r734=0
r735=0
r736=0
r737=0
r738=0
r739=0
r740=0
r741=0
r742=0
r743=0
r744=0
r745=0
r746=0
r747=0
r748=0
r749=0
r750=0
r751=0
r752=0
r753=0
r754=0
r755=0
r756=0
r757=0
r758=0
r759=0
r760=0
r761=0
r762=0
r763=0
1
---*b12*r7445
2
r764=---------------
a23
r765=0
b12*r7445
r766=-----------
a23
r767=0
1
---*b12*r7445
2
r768=---------------
a23
r769=0
r770=0
r771=0
r772=0
r773=0
r774=0
b12*r7445
r775=-----------
a23
r776=0
b12*r7445
r777=-----------
a23
r778=0
r779=0
r780=0
r781=0
1
---*b12*r7445
2
r782=---------------
a23
r783=0
r784=0
r785=0
r786=0
r787=0
r788=0
r789=0
r790= - r7445
r791=0
r792= - r7445
r793=0
r794=0
r795=0
r796=0
r797= - r7445
r798=0
r799=0
2 2 2
- a23 *r7445 - a33 *r7445 - b12 *kap*r7445
r7100=---------------------------------------------
a23*b12
r7101=0
r7102=0
r7103=0
r7104=0
r7105=0
r7106=0
r7107=0
r7108=0
r7109=0
r7110=0
r7111=0
r7112=0
r7113= - kap*r7445
r7114=0
r7115=0
2 2 2 2 1 2 2
---*a23 *kap*r7445 + ---*a33 *kap*r7445 - ----*b12 *kap *r7445
5 5 10
r7116=----------------------------------------------------------------
a23*b12
r7117=0
r7118=0
r7119=0
r7120=0
r7121=0
r7122=0
r7123=0
r7124=0
r7125=0
r7126=0
r7127=0
r7128=0
r7129=0
r7130=0
r7131=0
r7132=0
r7133=0
r7134=0
r7135=0
r7136=0
r7137=0
r7138=0
r7139=0
r7140=0
r7141=0
r7142=0
r7143=0
r7144=0
r7145=0
r7146=0
r7147=0
r7148=0
1
---*b12*r7445
2
r7149=---------------
a23
r7150=0
b12*r7445
r7151=-----------
a23
r7152=0
1
---*b12*r7445
2
r7153=---------------
a23
r7154=0
r7155=0
r7156=0
r7157=0
r7158=0
r7159=0
b12*r7445
r7160=-----------
a23
r7161=0
b12*r7445
r7162=-----------
a23
r7163=0
r7164=0
r7165=0
r7166=0
1
---*b12*r7445
2
r7167=---------------
a23
r7168=0
r7169=0
r7170=0
r7171=0
r7172=0
r7173=0
a33*r7445
r7174=-----------
a23
r7175= - r7445
a33*r7445
r7176=-----------
a23
r7177= - r7445
r7178=0
r7179=0
r7180=0
a33*r7445
r7181=-----------
a23
r7182= - r7445
r7183=0
r7184=0
2 2 2
- 3*a23 *r7445 - 3*a33 *r7445 - 3*b12 *kap*r7445
r7185=---------------------------------------------------
a23*b12
r7186=0
r7187=0
r7188=0
r7189=0
r7190=0
r7191=0
r7192=0
r7193=0
r7194=0
r7195=0
r7196=0
a33*kap*r7445
r7197=---------------
a23
r7198= - kap*r7445
r7199=0
r7200=0
2 2 2 2 1 2 2
---*a23 *kap*r7445 + ---*a33 *kap*r7445 - ----*b12 *kap *r7445
5 5 10
r7201=----------------------------------------------------------------
a23*b12
r7202=0
r7203=0
r7204=0
r7205=0
r7206=0
r7207=0
r7208=0
r7209=0
r7210=0
r7211=0
r7212=0
r7213=0
r7214=0
r7215=0
r7216=0
r7217=0
r7218=0
r7219=0
r7220=0
r7221=0
r7222=0
r7223=0
r7224=0
r7225=0
r7226=0
r7227=0
r7228=0
r7229=0
r7230=0
a33*r7445
r7231=-----------
a23
r7232=0
a33*r7445
r7233=-----------
a23
r7234=0
r7235=0
r7236=0
r7237=0
a33*r7445
r7238=-----------
a23
r7239=0
r7240=0
r7241=0
2 2 2
- 2*a23 *r7445 - 2*a33 *r7445 - 2*b12 *kap*r7445
r7242=---------------------------------------------------
a23*b12
r7243=0
r7244=0
r7245=0
r7246=0
r7247=0
r7248=0
r7249=0
r7250=0
r7251=0
r7252=0
r7253= - kap*r7445
a33*kap*r7445
r7254=---------------
a23
r7255=0
2 2
a23 *kap*r7445 + a33 *kap*r7445
r7256=---------------------------------
a23*b12
r7257=0
r7258=0
r7259=0
r7260=0
r7261=0
r7262=0
r7263=0
r7264=0
r7265=0
r7266=0
r7267=0
r7268=0
r7269=0
r7270=0
r7271=0
r7272=0
r7273=0
r7274=0
r7275=0
r7276=0
r7277=0
r7278=0
r7279=0
r7280=0
r7281=0
r7282=0
r7283=0
r7284=0
r7285=0
r7286=0
r7287=0
a33*kap*r7445
r7288=---------------
a23
r7289= - kap*r7445
r7290=0
r7291=0
2 2
a23 *kap*r7445 + a33 *kap*r7445
r7292=---------------------------------
a23*b12
r7293=0
r7294=0
r7295=0
r7296=0
r7297=0
r7298=0
r7299=0
r7300=0
r7301=0
r7302=0
r7303=0
r7304=0
r7305=0
r7306=0
r7307=0
r7308=0
a33*kap*r7445
r7309=---------------
a23
r7310=0
1 2
- ---*b12*kap *r7445
2
r7311=-----------------------
a23
r7312=0
r7313=0
r7314=0
r7315=0
r7316=0
r7317=0
r7318=0
r7319=0
r7320=0
r7321=0
1 2
- ---*b12*kap *r7445
2
r7322=-----------------------
a23
r7323=0
r7324=0
r7325=0
r7326=0
r7327=0
r7328=0
r7329=0
r7330=0
r7331=0
r7332=0
r7333=0
r7334=0
r7335=0
r7336=0
r7337=0
r7338=0
r7339=0
r7340=0
r7341=0
r7342=0
r7343=0
r7344=0
r7345=0
r7346=0
r7347=0
r7348=0
r7349=0
r7350=0
r7351=0
r7352=0
r7353=0
r7354=0
r7355=0
r7356=0
r7357=0
r7358=0
r7359=0
r7360=0
r7361=0
r7362=0
r7363=0
1
---*b12*r7445
2
r7364=---------------
a23
r7365=0
b12*r7445
r7366=-----------
a23
r7367=0
1
---*b12*r7445
2
r7368=---------------
a23
r7369=0
r7370=0
r7371=0
r7372=0
b12*r7445
r7373=-----------
a23
r7374=0
b12*r7445
r7375=-----------
a23
r7376=0
r7377=0
1
---*b12*r7445
2
r7378=---------------
a23
r7379=r7445
- a33*r7445
r7380=--------------
a23
r7381=r7445
- a33*r7445
r7382=--------------
a23
r7383=0
r7384=0
r7385=0
r7386=0
r7387=0
r7388=0
- a33*r7445
r7389=--------------
a23
r7390= - r7445
r7391=0
r7392=0
r7393= - r7445
r7394=0
r7395=0
r7396=0
r7397=0
2 2 2
- 3*a23 *r7445 - 3*a33 *r7445 - 3*b12 *kap*r7445
r7398=---------------------------------------------------
a23*b12
r7399=0
r7400=0
r7401=0
r7402=0
r7403=0
r7404=kap*r7445
- a33*kap*r7445
r7405=------------------
a23
r7406=0
r7407=0
r7408=0
r7409= - kap*r7445
r7410=0
r7411=0
2 2 2 2 1 2 2
---*a23 *kap*r7445 + ---*a33 *kap*r7445 - ----*b12 *kap *r7445
5 5 10
r7412=----------------------------------------------------------------
a23*b12
r7413=0
r7414=0
r7415=0
r7416=0
r7417=0
r7418=0
r7419=0
r7420=0
r7421=0
r7422=0
r7423=0
r7424=0
r7425=0
r7426=0
r7427=0
r7428=0
r7429=0
r7430=0
r7431=0
r7432=0
r7433=0
r7434=0
r7435=0
r7436=r7445
- a33*r7445
r7437=--------------
a23
r7438=r7445
- a33*r7445
r7439=--------------
a23
r7440=0
r7441=0
r7442=0
r7443=0
a33*r7445
r7444=-----------
a23
r7446=0
r7447=0
r7448=0
a33*r7445
r7449=-----------
a23
r7450=0
r7451=0
r7452=0
r7453=0
r7454=0
r7455=0
r7456=0
r7457=0
r7458=0
r7459=0
r7460=0
r7461=kap*r7445
- a33*kap*r7445
r7462=------------------
a23
r7463=0
r7464=0
a33*kap*r7445
r7465=---------------
a23
r7466=0
r7467=0
r7468=0
r7469=0
r7470=0
r7471=0
r7472=0
r7473=0
r7474=0
r7475=0
r7476=0
r7477=0
r7478=0
r7479=0
r7480=0
r7481=0
r7482=0
r7483=0
r7484=0
r7485=0
r7486=0
r7487=0
r7488=0
r7489=0
r7490=0
r7491=0
r7492=0
r7493=0
r7494=0
r7495=kap*r7445
- a33*kap*r7445
r7496=------------------
a23
r7497=0
r7498=0
r7499=0
r7500= - kap*r7445
r7501=0
r7502=0
2 2
a23 *kap*r7445 + a33 *kap*r7445
r7503=---------------------------------
a23*b12
r7504=0
r7505=0
r7506=0
r7507=0
r7508=0
r7509=0
r7510=0
r7511=0
r7512=0
r7513=0
r7514=0
r7515=0
r7516=kap*r7445
- a33*kap*r7445
r7517=------------------
a23
r7518=0
r7519=0
a33*kap*r7445
r7520=---------------
a23
r7521=0
r7522=0
r7523=0
r7524=0
r7525=0
r7526=0
r7527=0
r7528=0
r7529=0
r7530=0
r7531=0
r7532=0
1 2
- ---*b12*kap *r7445
2
r7533=-----------------------
a23
r7534=0
r7535=0
r7536=0
r7537=0
r7538=0
r7539=0
r7540=0
r7541=0
r7542=0
r7543=0
r7544=0
r7545=0
r7546=0
r7547=0
r7548=0
r7549=0
r7550=0
r7551=0
r7552=0
r7553=0
r7554=0
r7555=0
r7556=0
r7557=0
r7558=0
r7559=0
r7560=0
r7561=0
r7562=0
r7563=0
r7564=0
r7565=0
r7566=r7445
- a33*r7445
r7567=--------------
a23
r7568=r7445
- a33*r7445
r7569=--------------
a23
r7570=0
r7571=0
r7572=0
r7573=r7445
- a33*r7445
r7574=--------------
a23
r7575=0
r7576=0
r7577=0
r7578=0
r7579=0
r7580=0
r7581=0
r7582=0
2 2 2
- 2*a23 *r7445 - 2*a33 *r7445 - 2*b12 *kap*r7445
r7583=---------------------------------------------------
a23*b12
r7584=0
r7585=0
r7586=0
r7587=0
r7588=0
r7589=0
- a33*kap*r7445
r7590=------------------
a23
r7591=0
2 2
a23 *kap*r7445 + a33 *kap*r7445
r7592=---------------------------------
a23*b12
r7593=0
r7594=0
r7595=0
r7596=0
r7597=0
r7598=0
r7599=0
r7600=0
r7601=0
r7602=0
r7603=0
r7604=0
r7605=0
r7606=0
r7607=0
r7608=0
r7609=0
r7610=0
r7611=0
r7612=0
r7613=0
r7614=0
r7615=0
r7616=0
r7617=0
r7618=0
r7619=0
r7620=0
r7621=0
r7622=0
r7623=0
a33*kap*r7445
r7624=---------------
a23
r7625= - kap*r7445
r7626=0
r7627=0
2
- b12*kap *r7445
r7628=-------------------
a23
r7629=0
r7630=0
r7631=0
r7632=0
r7633=0
r7634=0
r7635=0
r7636=0
r7637=0
r7638=0
r7639=0
r7640=0
r7641=0
r7642=0
r7643=0
r7644=kap*r7445
r7645=0
r7646=0
2
- b12*kap *r7445
r7647=-------------------
a23
r7648=0
r7649=0
r7650=0
r7651=0
r7652=0
r7653=0
r7654=0
r7655=0
r7656=0
r7657=0
2
- b12*kap *r7445
r7658=-------------------
a23
r7659=0
r7660=0
r7661=0
r7662=0
r7663=0
r7664=0
r7665=0
r7666=0
r7667=0
r7668=0
r7669=0
r7670=0
r7671=0
r7672=0
r7673=0
r7674=0
r7675=0
r7676=0
r7677=0
r7678=0
r7679=0
r7680=0
r7681=0
r7682=0
r7683=0
r7684=0
r7685=0
r7686=0
r7687=0
r7688=0
r7689=0
r7690=0
r7691=kap*r7445
- a33*kap*r7445
r7692=------------------
a23
r7693=0
r7694=0
r7695=0
2 2 2
- 8*a23 *r7445 - 8*a33 *r7445 - 9*b12 *kap*r7445
r7696=---------------------------------------------------
2
b12
r7697=0
r7698=0
2
- b12*kap *r7445
r7699=-------------------
a23
r7700=0
r7701=0
r7702=0
r7703=0
r7704=0
r7705=0
r7706=0
r7707=0
r7708=0
r7709=0
r7710=0
r7711=0
r7712=kap*r7445
- a33*kap*r7445
r7713=------------------
a23
r7714=0
r7715=0
a33*kap*r7445
r7716=---------------
a23
r7717=0
r7718=0
r7719=0
r7720=0
r7721=0
r7722=0
r7723=0
r7724=0
r7725=0
r7726=0
r7727=0
r7728=0
2
- b12*kap *r7445
r7729=-------------------
a23
r7730=0
r7731=0
r7732=0
r7733=0
r7734=0
r7735=0
r7736=0
r7737=0
r7738=0
r7739=0
r7740=0
r7741=0
r7742=0
r7743=0
r7744=0
r7745=0
r7746=0
r7747=0
r7748=0
r7749=kap*r7445
- a33*kap*r7445
r7750=------------------
a23
r7751=0
1 2
- ---*b12*kap *r7445
2
r7752=-----------------------
a23
r7753=0
r7754=0
r7755=0
r7756=0
r7757=0
r7758=0
r7759=0
r7760=0
r7761=0
r7762=0
1 2
- ---*b12*kap *r7445
2
r7763=-----------------------
a23
r7764=0
r7765=0
r7766=0
r7767=0
r7768=0
r7769=0
r7770=0
r7771=0
r7772=0
r7773=0
r7774=0
r7775=0
r7776=0
r7777=0
r7778=0
1 2
- ---*b12*kap *r7445
2
r7779=-----------------------
a23
r7780=0
r7781=0
r7782=0
r7783=0
r7784=0
r7785=0
r7786=0
r7787=0
r7788=0
r7789=0
r7790=0
r7791=0
a22= - a33
a13=0
a11= - a33
Parameters
Apart from the condition that they must not vanish to give
a non-trivial solution and a non-singular solution with
non-vanishing denominators, the following parameters are free:
r7445, a33, a23, b12
Inequalities
In the following not identically vanishing expressions are shown.
Any auxiliary variables g00?? are used to express that at least
one of their coefficients must not vanish, e.g. g0019*p4 + g0020*p3
means that either p4 or p3 or both are non-vanishing.
{r7445,b12,a23,a33}
Relevance for the application:
Modulo the following equation:
2 2 2
0=a23 + a33 + b12 *kap
the system of equations related to the Hamiltonian HAM:
2 2 2
HAM= - u1 *a33 + u1*v2*b12 - u2 *a33 + 2*u2*u3*a23 - u2*v1*b12 + u3 *a33
has apart from the Hamiltonian and Casimirs only the following first integral:
5 3 2 4 3 2 4 2 3 2
FI= - 5*u1 *u3*v1*b12 *kap - 5*u1 *u2*u3*v2*b12 *kap - 5*u1 *u3 *v3*b12 *kap
4 2 4 2
- 10*u1 *u3*v1*v2*a33*b12 *kap + 10*u1 *u3*v1*v3*a23*b12 *kap
3 2 3 2 3 2 2
- 10*u1 *u2 *u3*v1*b12 *kap + 10*u1 *u2*u3*v1 *a33*b12 *kap
3 2 2 3 2
- 10*u1 *u2*u3*v2 *a33*b12 *kap + 10*u1 *u2*u3*v2*v3*a23*b12 *kap
3 3 3 2
- 10*u1 *u3 *v1*b12 *kap
3 2 2 3 2 2
+ u1 *u3 *v1 *( - 80*a23 - 80*a23*a33 - 90*a23*b12 *kap)
3 2 2 3 2 2 2
- 10*u1 *u3 *v2*v3*a33*b12 *kap + 10*u1 *u3 *v3 *a23*b12 *kap
2 3 3 2 2 2 2 3 2
- 10*u1 *u2 *u3*v2*b12 *kap - 10*u1 *u2 *u3 *v3*b12 *kap
2 2 2 2 3 3 2
+ 10*u1 *u2 *u3*v1*v3*a23*b12 *kap - 10*u1 *u2*u3 *v2*b12 *kap
2 2 2 2 2 2
- 10*u1 *u2*u3 *v1*v2*a23*b12 *kap + 10*u1 *u2*u3 *v1*v3*a33*b12 *kap
2 4 2 2
+ u1 *u3 *v3*(10*a23 *b12*kap + 10*a33 *b12*kap)
2 3 2
- 10*u1 *u3 *v1*v2*a33*b12 *kap
2 2 2 2 2 3
+ u1 *u3 *v1 *v3*( - 20*a23 *b12 - 20*a33 *b12 - 20*b12 *kap)
2 3 2 2 3 2
- 10*u1 *u3*v1 *v2*a33*b12 + 10*u1 *u3*v1 *v3*a23*b12
2 3 2 2 2 2
- 10*u1 *u3*v1*v2 *a33*b12 + 10*u1 *u3*v1*v2 *v3*a23*b12
2 2 2 2 3 2
- 10*u1 *u3*v1*v2*v3 *a33*b12 + 10*u1 *u3*v1*v3 *a23*b12
4 3 2 3 2 2
- 5*u1*u2 *u3*v1*b12 *kap + 10*u1*u2 *u3*v1 *a33*b12 *kap
3 2 2 3 2
- 10*u1*u2 *u3*v2 *a33*b12 *kap + 10*u1*u2 *u3*v2*v3*a23*b12 *kap
2 3 2 2
+ u1*u2 *u3 *v1*(10*a23 *b12*kap + 10*a33 *b12*kap)
2 2 2 2 2 2 2
- 10*u1*u2 *u3 *v1 *a23*b12 *kap - 10*u1*u2 *u3 *v2*v3*a33*b12 *kap
2 2 2 2 3 2 2
+ 10*u1*u2 *u3 *v3 *a23*b12 *kap + 10*u1*u2*u3 *v1 *a33*b12 *kap
3 2 2 3 2
- 10*u1*u2*u3 *v2 *a33*b12 *kap + 10*u1*u2*u3 *v2*v3*a23*b12 *kap
4 2 2 2
+ 10*u1*u2*u3*v1 *a33*b12 + 10*u1*u2*u3*v1 *v2*v3*a23*b12
2 2 2 4 2
+ 10*u1*u2*u3*v1 *v3 *a33*b12 - 10*u1*u2*u3*v2 *a33*b12
3 2 2 2 2
+ 10*u1*u2*u3*v2 *v3*a23*b12 - 10*u1*u2*u3*v2 *v3 *a33*b12
3 2
+ 10*u1*u2*u3*v2*v3 *a23*b12
5 2 2 3 2
+ u1*u3 *v1*(4*a23 *b12*kap + 4*a33 *b12*kap - b12 *kap )
4 2 2 4 2
- 10*u1*u3 *v1 *a23*b12 *kap - 10*u1*u3 *v2*v3*a33*b12 *kap
4 2 2
+ 10*u1*u3 *v3 *a23*b12 *kap
3 2 2 2 3
+ u1*u3 *v1*v3 *( - 30*a23 *b12 - 30*a33 *b12 - 30*b12 *kap)
2 4 2 2 2 2 2
- 10*u1*u3 *v1 *a23*b12 - 10*u1*u3 *v1 *v2 *a23*b12
2 2 2 2 3 2
- 10*u1*u3 *v1 *v2*v3*a33*b12 - 10*u1*u3 *v2 *v3*a33*b12
2 2 2 2 2 3 2
+ 10*u1*u3 *v2 *v3 *a23*b12 - 10*u1*u3 *v2*v3 *a33*b12
2 4 2 5 3 3 2 3
+ 10*u1*u3 *v3 *a23*b12 + 5*u1*u3*v1 *b12 + 10*u1*u3*v1 *v2 *b12
3 2 3 4 3 2 2 3
+ 10*u1*u3*v1 *v3 *b12 + 5*u1*u3*v1*v2 *b12 + 10*u1*u3*v1*v2 *v3 *b12
4 3 5 3 2 4 2 3 2
+ 5*u1*u3*v1*v3 *b12 - 5*u2 *u3*v2*b12 *kap - 5*u2 *u3 *v3*b12 *kap
4 2
+ 10*u2 *u3*v1*v2*a33*b12 *kap
3 3 2 2
+ u2 *u3 *v2*(10*a23 *b12*kap + 10*a33 *b12*kap)
3 2 2 3 2 2
- 10*u2 *u3 *v1*v2*a23*b12 *kap + 10*u2 *u3 *v1*v3*a33*b12 *kap
2 4 2 2
+ u2 *u3 *v3*(10*a23 *b12*kap + 10*a33 *b12*kap)
2 3 2 2 3 2
+ 10*u2 *u3 *v1*v2*a33*b12 *kap - 10*u2 *u3 *v1*v3*a23*b12 *kap
2 2 2 2 2 3
+ u2 *u3 *v2 *v3*( - 20*a23 *b12 - 20*a33 *b12 - 20*b12 *kap)
2 3 2 2 3 2
+ 10*u2 *u3*v1 *v2*a33*b12 + 10*u2 *u3*v1*v2 *a33*b12
2 2 2
+ 10*u2 *u3*v1*v2*v3 *a33*b12
5 2 2 3 2
+ u2*u3 *v2*(4*a23 *b12*kap + 4*a33 *b12*kap - b12 *kap )
4 2 4 2
- 10*u2*u3 *v1*v2*a23*b12 *kap + 10*u2*u3 *v1*v3*a33*b12 *kap
3 2 2 2 3
+ u2*u3 *v2*v3 *( - 30*a23 *b12 - 30*a33 *b12 - 30*b12 *kap)
2 3 2 2 3 2
- 10*u2*u3 *v1 *v2*a23*b12 + 10*u2*u3 *v1 *v3*a33*b12
2 3 2 2 2 2
- 10*u2*u3 *v1*v2 *a23*b12 + 10*u2*u3 *v1*v2 *v3*a33*b12
2 2 2 2 3 2
- 10*u2*u3 *v1*v2*v3 *a23*b12 + 10*u2*u3 *v1*v3 *a33*b12
4 3 2 3 3 2 2 3
+ 5*u2*u3*v1 *v2*b12 + 10*u2*u3*v1 *v2 *b12 + 10*u2*u3*v1 *v2*v3 *b12
5 3 3 2 3 4 3
+ 5*u2*u3*v2 *b12 + 10*u2*u3*v2 *v3 *b12 + 5*u2*u3*v2*v3 *b12
6 2 2 3 2
+ u3 *v3*(4*a23 *b12*kap + 4*a33 *b12*kap - b12 *kap )
5 2
- 10*u3 *v1*v3*a23*b12 *kap
4 3 2 2 3
+ u3 *v3 *( - 10*a23 *b12 - 10*a33 *b12 - 10*b12 *kap)
3 3 2 3 2 2
- 10*u3 *v1 *v3*a23*b12 - 10*u3 *v1*v2 *v3*a23*b12
3 3 2 2 4 3 2 2 2 3
- 10*u3 *v1*v3 *a23*b12 + 5*u3 *v1 *v3*b12 + 10*u3 *v1 *v2 *v3*b12
2 2 3 3 2 4 3 2 2 3 3
+ 10*u3 *v1 *v3 *b12 + 5*u3 *v2 *v3*b12 + 10*u3 *v2 *v3 *b12
2 5 3
+ 5*u3 *v3 *b12
4 4 5 4
= - u3*((((5*u2 + u3 )*(u2*v2 + u3*v3) + 5*u1 *v1 + 5*(u2*v2 + u3*v3)*u1
2 2 3 2 2 2
+ 10*(u2 + u3 )*u1 *v1 + 10*(u2 *v2 + u2*u3*v3 + u3 *v2)*u1 *u2
4 4 2
+ (5*u2 + u3 )*u1*v1)*kap + 5*(2
*((2*u1*v1 + 3*u3*v3)*u1*v1 + (2*u2*v2 + u3*v3)*(u2*v2 + u3*v3))
2 2 2 2 3
*kap*u3*v3 - (u2*v2 + u3*v3 + u1*v1)*(v1 + v2 + v3 ) ))*b12 - 2
2 2 2 2 2
*(5*((((u1 *v3 - u2*u3*v2 - u3 *v3)*(u1 + u2 + u3 )*v1
2 2 3
+ (u2*v2*v3 - 9*u3*v1 + u3*v3 )*u1
2 2
- ((v1 + v3)*(v1 - v3)*u3 - u2*v2*v3)*(u2 + u3 )*u1)*kap
2 2 2
+ (u1*v1 + u2*v2 + u3*v3)*(u1*v3 - u3*v1)*(v1 + v2 + v3 ))
2 2 3 2
*b12 - 8*a33 *u1 *u3*v1 )*a23 + ((
2 2 2
(5*u2 + 2*u3 )*(u2*v2 + u3*v3) + 5*u1 *u3*v3
2 2
+ (5*u2 + 2*u3 )*u1*v1)*kap*u3 - 5
*((2*u1*v1 + 3*u3*v3)*u1*v1 + (2*u2*v2 + u3*v3)*(u2*v2 + u3*v3))
2 2
*v3)*(a23 + a33 )*b12*u3 - 5*(
2 2 2 2 2 2
(kap*u1 + kap*u2 + kap*u3 + v1 + v2 + v3 )
2
*(u1*v1 + u2*v2 + u3*v3)*(u1*v2 - u2*v1)*a33*b12
3 3 2
+ 8*a23 *u1 *u3*v1 )))
{HAM,FI} = 0
And again in machine readable form:
HAM= - u1**2*a33 + u1*v2*b12 - u2**2*a33 + 2*u2*u3*a23 - u2*v1*b12 + u3**2*a33$
FI= - 5*u1**5*u3*v1*b12**3*kap**2 - 5*u1**4*u2*u3*v2*b12**3*kap**2 - 5*u1**4*u3
**2*v3*b12**3*kap**2 - 10*u1**4*u3*v1*v2*a33*b12**2*kap + 10*u1**4*u3*v1*v3*a23*
b12**2*kap - 10*u1**3*u2**2*u3*v1*b12**3*kap**2 + 10*u1**3*u2*u3*v1**2*a33*b12**
2*kap - 10*u1**3*u2*u3*v2**2*a33*b12**2*kap + 10*u1**3*u2*u3*v2*v3*a23*b12**2*
kap - 10*u1**3*u3**3*v1*b12**3*kap**2 + u1**3*u3**2*v1**2*( - 80*a23**3 - 80*a23
*a33**2 - 90*a23*b12**2*kap) - 10*u1**3*u3**2*v2*v3*a33*b12**2*kap + 10*u1**3*u3
**2*v3**2*a23*b12**2*kap - 10*u1**2*u2**3*u3*v2*b12**3*kap**2 - 10*u1**2*u2**2*
u3**2*v3*b12**3*kap**2 + 10*u1**2*u2**2*u3*v1*v3*a23*b12**2*kap - 10*u1**2*u2*u3
**3*v2*b12**3*kap**2 - 10*u1**2*u2*u3**2*v1*v2*a23*b12**2*kap + 10*u1**2*u2*u3**
2*v1*v3*a33*b12**2*kap + u1**2*u3**4*v3*(10*a23**2*b12*kap + 10*a33**2*b12*kap)
- 10*u1**2*u3**3*v1*v2*a33*b12**2*kap + u1**2*u3**2*v1**2*v3*( - 20*a23**2*b12 -
20*a33**2*b12 - 20*b12**3*kap) - 10*u1**2*u3*v1**3*v2*a33*b12**2 + 10*u1**2*u3*
v1**3*v3*a23*b12**2 - 10*u1**2*u3*v1*v2**3*a33*b12**2 + 10*u1**2*u3*v1*v2**2*v3*
a23*b12**2 - 10*u1**2*u3*v1*v2*v3**2*a33*b12**2 + 10*u1**2*u3*v1*v3**3*a23*b12**
2 - 5*u1*u2**4*u3*v1*b12**3*kap**2 + 10*u1*u2**3*u3*v1**2*a33*b12**2*kap - 10*u1
*u2**3*u3*v2**2*a33*b12**2*kap + 10*u1*u2**3*u3*v2*v3*a23*b12**2*kap + u1*u2**2*
u3**3*v1*(10*a23**2*b12*kap + 10*a33**2*b12*kap) - 10*u1*u2**2*u3**2*v1**2*a23*
b12**2*kap - 10*u1*u2**2*u3**2*v2*v3*a33*b12**2*kap + 10*u1*u2**2*u3**2*v3**2*
a23*b12**2*kap + 10*u1*u2*u3**3*v1**2*a33*b12**2*kap - 10*u1*u2*u3**3*v2**2*a33*
b12**2*kap + 10*u1*u2*u3**3*v2*v3*a23*b12**2*kap + 10*u1*u2*u3*v1**4*a33*b12**2
+ 10*u1*u2*u3*v1**2*v2*v3*a23*b12**2 + 10*u1*u2*u3*v1**2*v3**2*a33*b12**2 - 10*
u1*u2*u3*v2**4*a33*b12**2 + 10*u1*u2*u3*v2**3*v3*a23*b12**2 - 10*u1*u2*u3*v2**2*
v3**2*a33*b12**2 + 10*u1*u2*u3*v2*v3**3*a23*b12**2 + u1*u3**5*v1*(4*a23**2*b12*
kap + 4*a33**2*b12*kap - b12**3*kap**2) - 10*u1*u3**4*v1**2*a23*b12**2*kap - 10*
u1*u3**4*v2*v3*a33*b12**2*kap + 10*u1*u3**4*v3**2*a23*b12**2*kap + u1*u3**3*v1*
v3**2*( - 30*a23**2*b12 - 30*a33**2*b12 - 30*b12**3*kap) - 10*u1*u3**2*v1**4*a23
*b12**2 - 10*u1*u3**2*v1**2*v2**2*a23*b12**2 - 10*u1*u3**2*v1**2*v2*v3*a33*b12**
2 - 10*u1*u3**2*v2**3*v3*a33*b12**2 + 10*u1*u3**2*v2**2*v3**2*a23*b12**2 - 10*u1
*u3**2*v2*v3**3*a33*b12**2 + 10*u1*u3**2*v3**4*a23*b12**2 + 5*u1*u3*v1**5*b12**3
+ 10*u1*u3*v1**3*v2**2*b12**3 + 10*u1*u3*v1**3*v3**2*b12**3 + 5*u1*u3*v1*v2**4*
b12**3 + 10*u1*u3*v1*v2**2*v3**2*b12**3 + 5*u1*u3*v1*v3**4*b12**3 - 5*u2**5*u3*
v2*b12**3*kap**2 - 5*u2**4*u3**2*v3*b12**3*kap**2 + 10*u2**4*u3*v1*v2*a33*b12**2
*kap + u2**3*u3**3*v2*(10*a23**2*b12*kap + 10*a33**2*b12*kap) - 10*u2**3*u3**2*
v1*v2*a23*b12**2*kap + 10*u2**3*u3**2*v1*v3*a33*b12**2*kap + u2**2*u3**4*v3*(10*
a23**2*b12*kap + 10*a33**2*b12*kap) + 10*u2**2*u3**3*v1*v2*a33*b12**2*kap - 10*
u2**2*u3**3*v1*v3*a23*b12**2*kap + u2**2*u3**2*v2**2*v3*( - 20*a23**2*b12 - 20*
a33**2*b12 - 20*b12**3*kap) + 10*u2**2*u3*v1**3*v2*a33*b12**2 + 10*u2**2*u3*v1*
v2**3*a33*b12**2 + 10*u2**2*u3*v1*v2*v3**2*a33*b12**2 + u2*u3**5*v2*(4*a23**2*
b12*kap + 4*a33**2*b12*kap - b12**3*kap**2) - 10*u2*u3**4*v1*v2*a23*b12**2*kap +
10*u2*u3**4*v1*v3*a33*b12**2*kap + u2*u3**3*v2*v3**2*( - 30*a23**2*b12 - 30*a33
**2*b12 - 30*b12**3*kap) - 10*u2*u3**2*v1**3*v2*a23*b12**2 + 10*u2*u3**2*v1**3*
v3*a33*b12**2 - 10*u2*u3**2*v1*v2**3*a23*b12**2 + 10*u2*u3**2*v1*v2**2*v3*a33*
b12**2 - 10*u2*u3**2*v1*v2*v3**2*a23*b12**2 + 10*u2*u3**2*v1*v3**3*a33*b12**2 +
5*u2*u3*v1**4*v2*b12**3 + 10*u2*u3*v1**2*v2**3*b12**3 + 10*u2*u3*v1**2*v2*v3**2*
b12**3 + 5*u2*u3*v2**5*b12**3 + 10*u2*u3*v2**3*v3**2*b12**3 + 5*u2*u3*v2*v3**4*
b12**3 + u3**6*v3*(4*a23**2*b12*kap + 4*a33**2*b12*kap - b12**3*kap**2) - 10*u3
**5*v1*v3*a23*b12**2*kap + u3**4*v3**3*( - 10*a23**2*b12 - 10*a33**2*b12 - 10*
b12**3*kap) - 10*u3**3*v1**3*v3*a23*b12**2 - 10*u3**3*v1*v2**2*v3*a23*b12**2 -
10*u3**3*v1*v3**3*a23*b12**2 + 5*u3**2*v1**4*v3*b12**3 + 10*u3**2*v1**2*v2**2*v3
*b12**3 + 10*u3**2*v1**2*v3**3*b12**3 + 5*u3**2*v2**4*v3*b12**3 + 10*u3**2*v2**2
*v3**3*b12**3 + 5*u3**2*v3**5*b12**3$