Solution 4 to problem h
Expressions |
Parameters |
Inequalities |
Relevance |
Back to problem h
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
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
6*b12 *kap
r737=0
r738
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
2*b12 *kap
r739=0
r740
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
2*b12 *kap
r741=0
r742
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
6*b12 *kap
r743=0
r744=0
r745=0
r746=0
r747=0
r748=0
r749
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
2*b12 *kap
r750=0
r751
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
b12 *kap
r752=0
r753
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
2*b12 *kap
r754=0
r755=0
r756=0
r757=0
r758
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
2*b12 *kap
r759=0
r760
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
2*b12 *kap
r761=0
r762=0
r763
2 2 2 2
a11 *r7391 - a11 *r7448 - a11*b12*r7682 + 2*b12 *kap*r7229 - b12 *kap*r7391
=-----------------------------------------------------------------------------
2 2
6*b12 *kap
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r764=--------------------------------------------------------------
2 2
2*b12 *kap
r765=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r766=--------------------------------------------------------------
2 2
b12 *kap
r767=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r768=--------------------------------------------------------------
2 2
2*b12 *kap
r769=0
r770=0
r771=0
r772=0
r773=0
r774=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r775=--------------------------------------------------------------
2 2
b12 *kap
r776=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r777=--------------------------------------------------------------
2 2
b12 *kap
r778=0
r779=0
r780=0
r781=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r782=--------------------------------------------------------------
2 2
2*b12 *kap
r783=0
r784=0
r7391 + r796
r785=--------------
2
r786=0
r7391 + 2*r796
r787=----------------
2
r788=0
r796
r789=------
2
r790=0
r791=0
r792=0
r793=0
r7391 + 2*r796
r794=----------------
2
r795=0
r797=0
r798=0
r796
r799=------
2
r7242 + 3*r7403 - r7685
r7100=-------------------------
3
r7101=0
r7102=r7403
r7103=0
r7104=0
r7105=0
r7106=0
r7107=r7403
r7108=0
r7109=0
2*r7115 + r7407
r7110=-----------------
2
r7111=0
r7113=0
r7114=0
r7117=0
r7118=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
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7149=--------------------------------------------------------------
2 2
2*b12 *kap
r7150=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7151=--------------------------------------------------------------
2 2
b12 *kap
r7152=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7153=--------------------------------------------------------------
2 2
2*b12 *kap
a11*r7391 - a11*r7448 - b12*r7682
r7154=-----------------------------------
2*b12*kap
r7155=0
a11*r7391 - a11*r7448 - b12*r7682
r7156=-----------------------------------
b12*kap
r7157=0
a11*r7391 - a11*r7448 - b12*r7682
r7158=-----------------------------------
2*b12*kap
r7159=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7160=--------------------------------------------------------------
2 2
b12 *kap
r7161=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7162=--------------------------------------------------------------
2 2
b12 *kap
a11*r7391 - a11*r7448 - b12*r7682
r7163=-----------------------------------
b12*kap
r7164=0
a11*r7391 - a11*r7448 - b12*r7682
r7165=-----------------------------------
b12*kap
r7166=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7167=--------------------------------------------------------------
2 2
2*b12 *kap
a11*r7391 - a11*r7448 - b12*r7682
r7168=-----------------------------------
2*b12*kap
r7169=0
r7170=r7391
r7171=0
r7172=r7391
r7173=0
2*a11*r7614 - 2*a11*r7685 + b12*r7288
r7174=---------------------------------------
b12*kap
r7175=0
2*a11*r7614 - 2*a11*r7685 + b12*r7288
r7176=---------------------------------------
b12*kap
r7177=0
r7178=0
r7179=r7391
r7180=0
2*a11*r7614 - 2*a11*r7685 + b12*r7288
r7181=---------------------------------------
b12*kap
r7182=0
r7183=0
r7184=0
r7185=r7242 + r7403 - r7685
r7186=0
r7187=r7403
r7188= - r7395
r7189=0
- 2*r7395 - r7457
r7190=--------------------
2
r7191=0
r7192=r7403
- 2*r7395 - r7457
r7193=--------------------
2
r7194=0
r7195=r7407
r7196=0
r7198=0
r7199=0
r7200=0
r7201=r7412
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
2*r7229 - r7391
r7225=-----------------
2
r7226=0
4*r7229 - r7391
r7227=-----------------
2
r7228=0
r7230=0
2*a11*r7614 - 2*a11*r7685 + b12*r7288
r7231=---------------------------------------
b12*kap
r7232=0
2*a11*r7614 - 2*a11*r7685 + b12*r7288
r7233=---------------------------------------
b12*kap
4*r7229 - r7391 - r7448
r7234=-------------------------
2
r7235=0
4*r7229 - r7448
r7236=-----------------
2
r7237=0
2*a11*r7614 - 2*a11*r7685 + b12*r7288
r7238=---------------------------------------
b12*kap
2*r7229 - r7448
r7239=-----------------
2
r7240=r7685
r7241=0
r7243=0
r7244=0
r7245=r7457
r7246=0
r7247=r7614
r7248=0
r7249=0
2*a11*r7395 + b12*kap*r7391 + 2*b12*kap*r796
r7250=----------------------------------------------
2*b12
r7251=0
2*a11*r7395 + a11*r7457 + 2*b12*kap*r796 + b12*r7407
r7252=------------------------------------------------------
2*b12
r7253=0
r7254= - r7462
2*a11*r7395 + a11*r7457 + 2*b12*kap*r796 + b12*r7407 - b12*r7464
r7255=------------------------------------------------------------------
2*b12
a11*r7462 + b12*kap*r7403
r7256=---------------------------
b12
r7257=0
r7258=0
a11*r7411 + b12*kap*r7115
r7259=---------------------------
b12
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
r7277=0
r7242 + 2*r7685
r7278=-----------------
3
r7279= - r7682
r7280=0
r7457 - 2*r7682
r7281=-----------------
2
r7282=0
r7283=r7614
r7457 + r7617 - 2*r7682
r7284=-------------------------
3
r7285=0
- a11*r7457 + b12*kap*r7391
r7286=------------------------------
b12
r7287=0
r7289=0
r7290=0
r7291=0
a11*r7462 + b12*kap*r7403
r7292=---------------------------
b12
- 2*a11*r7407 + 2*a11*r7464 - 2*b12*kap*r7395 - b12*kap*r7457
r7293=----------------------------------------------------------------
2*b12
r7294=0
r7295=0
r7296=0
r7297=0
r7298=0
r7299=0
r7300=0
r7301=0
r7302=0
r7303=0
r7304=0
a11*r7682 + 2*b12*kap*r7229 - b12*kap*r7391
r7305=---------------------------------------------
2*b12
r7306=0
- a11*r7457 + a11*r7682 + 2*b12*kap*r7229
r7307=--------------------------------------------
2*b12
r7308=0
r7309=r7288
r7310
- 2*a11*r7457 - 2*a11*r7617 - a11*r7682 + 2*b12*kap*r7229 - b12*kap*r7448
=----------------------------------------------------------------------------
2*b12
- a11*r7288 + b12*kap*r7685
r7311=------------------------------
2*b12
r7312=0
r7313=0
2 2
r7314=(a11 *r7407 - a11 *r7464 + 2*a11*b12*kap*r7395 + a11*b12*kap*r7457
2 2 2
+ b12 *kap *r796)/(2*b12 )
r7315=0
r7316=0
r7317=0
r7318=0
r7319=0
r7320=0
r7321=0
- a11*r7288 + b12*kap*r7685
r7322=------------------------------
2*b12
2 2 2
r7323=(2*a11 *r7457 + 2*a11 *r7617 + 2*a11 *r7682 - a11*b12*kap*r7391
2 2
+ a11*b12*kap*r7448 - b12 *kap*r7682)/(2*b12 )
r7324=0
r7325=0
r7326=0
r7327=0
3 3 3 2
r7328=( - 2*a11 *r7457 - 2*a11 *r7617 - 2*a11 *r7682 + a11 *b12*kap*r7391
2 2 3 2
- a11 *b12*kap*r7448 + 2*a11*b12 *kap*r7682 + 2*b12 *kap *r7229
3 2 3
- b12 *kap *r7391)/(6*b12 )
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
- a11*r7391 + a11*r7448 + b12*r7682
r7359=--------------------------------------
2*b12*kap
r7360=0
- a11*r7391 + a11*r7448 + b12*r7682
r7361=--------------------------------------
b12*kap
r7362=0
- a11*r7391 + a11*r7448 + b12*r7682
r7363=--------------------------------------
2*b12*kap
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7364=--------------------------------------------------------------
2 2
2*b12 *kap
r7365=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7366=--------------------------------------------------------------
2 2
b12 *kap
r7367=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7368=--------------------------------------------------------------
2 2
2*b12 *kap
r7369=0
- a11*r7391 + a11*r7448 + b12*r7682
r7370=--------------------------------------
b12*kap
r7371=0
- a11*r7391 + a11*r7448 + b12*r7682
r7372=--------------------------------------
b12*kap
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7373=--------------------------------------------------------------
2 2
b12 *kap
r7374=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7375=--------------------------------------------------------------
2 2
b12 *kap
r7376=0
2 2 2
2*a11 *r7614 - 2*a11 *r7685 + a11*b12*r7288 + b12 *kap*r7685
r7378=--------------------------------------------------------------
2 2
2*b12 *kap
r7379=0
- 2*a11*r7614 + 2*a11*r7685 - b12*r7288
r7380=------------------------------------------
b12*kap
r7381=0
- 2*a11*r7614 + 2*a11*r7685 - b12*r7288
r7382=------------------------------------------
b12*kap
r7383=0
r7384=r7391
r7385=0
r7386=r7391
r7387=0
r7388=0
- 2*a11*r7614 + 2*a11*r7685 - b12*r7288
r7389=------------------------------------------
b12*kap
r7390=0
r7392=0
r7393=0
r7394=0
r7396=0
2*r7395 + r7457
r7397=-----------------
2
r7398=r7242 + r7403 - r7685
r7399=0
r7401=0
2*r7395 + r7457
r7402=-----------------
2
r7404=0
r7405=r7462
r7406=0
r7408=0
r7409=0
r7410=0
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=0
- 2*a11*r7614 + 2*a11*r7685 - b12*r7288
r7437=------------------------------------------
b12*kap
r7438=0
- 2*a11*r7614 + 2*a11*r7685 - b12*r7288
r7439=------------------------------------------
b12*kap
r7440=0
r7441=r7448
r7442=0
r7443=r7448
2*a11*r7614 - 2*a11*r7685 + b12*r7288
r7444=---------------------------------------
b12*kap
r7445=0
r7446=0
r7447=0
r7450=0
r7451=0
r7452= - r7457
r7453=0
r7454=0
r7455=2*r7242 - 2*r7614
r7456=0
r7458=0
r7459=0
r7460=0
r7461=0
r7463=0
r7465= - r7462
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=r7682
r7487=0
- r7457 + 2*r7682
r7488=--------------------
2
r7489=r7685
r7490=0
r7491=r7242 - 2*r7614 + 2*r7685
r7492=0
r7494=r7614
r7495=0
r7496= - r7288
r7497=0
- a11*r7457 + b12*kap*r7391
r7498=------------------------------
b12
r7499=0
r7500=0
r7501=0
2*a11*r7407 - 2*a11*r7464 + 2*b12*kap*r7395 + b12*kap*r7457
r7502=-------------------------------------------------------------
2*b12
a11*r7462 + b12*kap*r7403
r7503=---------------------------
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=0
r7517= - r7288
r7518=0
a11*r7457 + 2*a11*r7617 + 2*a11*r7682 + b12*kap*r7448
r7519=-------------------------------------------------------
b12
r7520=r7288
r7521=0
r7522=0
r7523=0
r7524=0
r7525=0
r7526=0
r7527=0
r7528=0
r7529=0
r7530=0
r7531=0
2 2 2
r7532=( - 2*a11 *r7457 - 2*a11 *r7617 - 2*a11 *r7682 + a11*b12*kap*r7391
2 2
- a11*b12*kap*r7448 + b12 *kap*r7682)/(2*b12 )
- a11*r7288 + b12*kap*r7685
r7533=------------------------------
2*b12
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
2*r7229 - r7391
r7561=-----------------
2
r7562=0
4*r7229 - r7391 - r7448
r7563=-------------------------
2
r7564=0
2*r7229 - r7448
r7565=-----------------
2
r7566=0
- 2*a11*r7614 + 2*a11*r7685 - b12*r7288
r7567=------------------------------------------
b12*kap
r7568=0
- 2*a11*r7614 + 2*a11*r7685 - b12*r7288
r7569=------------------------------------------
b12*kap
4*r7229 - r7391
r7570=-----------------
2
r7571=0
4*r7229 - r7448
r7572=-----------------
2
r7573=0
- 2*a11*r7614 + 2*a11*r7685 - b12*r7288
r7574=------------------------------------------
b12*kap
r7575=r7229
r7576=r7685
r7577=0
r7578=r7614
r7579=0
r7580=0
r7582=0
r7583=r7242
r7584=0
r7585=0
2*a11*r7395 + b12*kap*r7391 + 2*b12*kap*r796
r7586=----------------------------------------------
2*b12
r7587=0
2*a11*r7395 + a11*r7457 + 2*b12*kap*r796 + b12*r7407 - b12*r7464
r7588=------------------------------------------------------------------
2*b12
r7589=0
r7590=r7462
2*a11*r7395 + a11*r7457 + 2*b12*kap*r796 + b12*r7407
r7591=------------------------------------------------------
2*b12
a11*r7462 + b12*kap*r7403
r7592=---------------------------
b12
r7593=0
r7594=0
a11*r7411 + b12*kap*r7115
r7595=---------------------------
b12
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=r7685
r7613=0
r7615= - r7682
r7616=0
r7618=0
r7457 - 2*r7682
r7620=-----------------
2
r7621=0
- a11*r7457 + b12*kap*r7391
r7622=------------------------------
b12
r7623=0
r7624=r7288
r7625=0
r7626=0
r7627=0
a11*r7462 + b12*kap*r7403
r7628=---------------------------
b12
- 2*a11*r7407 + 2*a11*r7464 - 2*b12*kap*r7395 - b12*kap*r7457
r7629=----------------------------------------------------------------
2*b12
r7630=0
r7631=0
r7632=0
r7633=0
r7634=0
r7635=0
r7636=0
r7637=0
r7638=0
r7639=0
r7640=0
a11*r7682 + 2*b12*kap*r7229 - b12*kap*r7391
r7641=---------------------------------------------
b12
r7642=0
- 3*a11*r7457 - 2*a11*r7617 + 4*b12*kap*r7229 - b12*kap*r7448
r7643=----------------------------------------------------------------
2*b12
r7644=0
r7645=0
- 3*a11*r7457 - 2*a11*r7617 + 4*b12*kap*r7229 - b12*kap*r7448
r7646=----------------------------------------------------------------
2*b12
- a11*r7288 + b12*kap*r7685
r7647=------------------------------
b12
r7648=0
r7649=0
r7651=0
r7652=0
r7653=0
r7654=0
r7655=0
r7656=0
r7657=0
- a11*r7288 + b12*kap*r7685
r7658=------------------------------
b12
2 2 2
r7659=(2*a11 *r7457 + 2*a11 *r7617 + 2*a11 *r7682 - a11*b12*kap*r7391
2 2
+ a11*b12*kap*r7448 - b12 *kap*r7682)/b12
r7660=0
r7661=0
r7662=0
r7663=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
r7683=0
- r7457 - r7617 + 2*r7682
r7684=----------------------------
3
r7686=0
r7688=0
- r7457 + 2*r7682
r7689=--------------------
2
r7242 + 2*r7685
r7690=-----------------
3
r7691=0
r7692= - r7288
r7693=0
- a11*r7457 + b12*kap*r7391
r7694=------------------------------
b12
r7695=0
r7696=0
r7697=0
2*a11*r7407 - 2*a11*r7464 + 2*b12*kap*r7395 + b12*kap*r7457
r7698=-------------------------------------------------------------
2*b12
a11*r7462 + b12*kap*r7403
r7699=---------------------------
b12
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=0
r7713= - r7288
r7714=0
a11*r7457 + 2*a11*r7617 + 2*a11*r7682 + b12*kap*r7448
r7715=-------------------------------------------------------
b12
r7716=r7288
r7717=0
r7718=0
r7719=0
r7720=0
r7721=0
r7722=0
r7723=0
r7724=0
r7725=0
r7726=0
r7727=0
2 2 2
r7728=( - 2*a11 *r7457 - 2*a11 *r7617 - 2*a11 *r7682 + a11*b12*kap*r7391
2 2
- a11*b12*kap*r7448 + b12 *kap*r7682)/b12
- a11*r7288 + b12*kap*r7685
r7729=------------------------------
b12
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
a11*r7682 + 2*b12*kap*r7229 - b12*kap*r7391
r7746=---------------------------------------------
2*b12
r7747=0
r7748
- 2*a11*r7457 - 2*a11*r7617 - a11*r7682 + 2*b12*kap*r7229 - b12*kap*r7448
=----------------------------------------------------------------------------
2*b12
r7749=0
r7750= - r7288
- a11*r7457 + a11*r7682 + 2*b12*kap*r7229
r7751=--------------------------------------------
2*b12
- a11*r7288 + b12*kap*r7685
r7752=------------------------------
2*b12
r7753=0
r7754=0
2 2
r7755=(a11 *r7407 - a11 *r7464 + 2*a11*b12*kap*r7395 + a11*b12*kap*r7457
2 2 2
+ b12 *kap *r796)/(2*b12 )
r7756=0
r7757=0
r7758=0
r7759=0
r7760=0
r7761=0
r7762=0
- a11*r7288 + b12*kap*r7685
r7763=------------------------------
2*b12
2 2 2
r7764=(2*a11 *r7457 + 2*a11 *r7617 + 2*a11 *r7682 - a11*b12*kap*r7391
2 2
+ a11*b12*kap*r7448 - b12 *kap*r7682)/(2*b12 )
r7765=0
r7766=0
r7767=0
r7768=0
3 3 3 2
r7769=( - 2*a11 *r7457 - 2*a11 *r7617 - 2*a11 *r7682 + a11 *b12*kap*r7391
2 2 3 2
- a11 *b12*kap*r7448 + 2*a11*b12 *kap*r7682 + 2*b12 *kap *r7229
3 2 3
- b12 *kap *r7391)/(2*b12 )
r7770=0
r7771=0
r7772=0
r7773=0
r7774=0
r7775=0
r7776=0
r7777=0
2 2 2
r7778=( - 2*a11 *r7457 - 2*a11 *r7617 - 2*a11 *r7682 + a11*b12*kap*r7391
2 2
- a11*b12*kap*r7448 + b12 *kap*r7682)/(2*b12 )
- a11*r7288 + b12*kap*r7685
r7779=------------------------------
2*b12
r7780=0
r7781=0
r7782=0
r7783=0
r7784=0
r7785=0
r7786=0
r7787=0
r7788=0
3 3 3 2
r7789=( - 2*a11 *r7457 - 2*a11 *r7617 - 2*a11 *r7682 + a11 *b12*kap*r7391
2 2 3 2
- a11 *b12*kap*r7448 + 2*a11*b12 *kap*r7682 + 2*b12 *kap *r7229
3 2 3
- b12 *kap *r7391)/(6*b12 )
r7790=0
r7791=0
a23=0
a22=a11
a13=0
r7276=r7685
- a11*r7391 + a11*r7448 + b12*r7682
r7377=--------------------------------------
2*b12*kap
r7493= - r7617
r7687=r7614
r7197= - r7462
r7581= - r7457
r7116=r7412
r7202= - r7411
r7400=r7403
2*a11*r7614 - 2*a11*r7685 + b12*r7288
r7449=---------------------------------------
b12*kap
r7619=r7242 - 2*r7614 + 2*r7685
3 3 3 2
r7664=( - 2*a11 *r7457 - 2*a11 *r7617 - 2*a11 *r7682 + a11 *b12*kap*r7391
2 2 3 2
- a11 *b12*kap*r7448 + 2*a11*b12 *kap*r7682 + 2*b12 *kap *r7229
3 2 3
- b12 *kap *r7391)/(2*b12 )
r7112=r7115
2 2
r7650=(a11 *r7407 - a11 *r7464 + 2*a11*b12*kap*r7395 + a11*b12*kap*r7457
2 2 2
+ b12 *kap *r796)/b12
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:
r796, r7115, r7229, r7242, r7288, r7403, r7411, r7412,
r7457, r7462, r7614, r7617, r7682, r7685, r7119, r7391,
r7395, r7407, r7448, r7464, a11, a33, 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.
5
{{b12 *r7664,
2 2 1 1 2
a11 *r7276 - a11 *r7687 + ---*a11*b12*kap*r7449 - ---*b12 *kap*r7276,
2 2
3 3 2 2
2*a11 *b12*r7391 - 2*a11 *b12*r7448 + 4*a11 *b12 *kap*r7377
2 2 2 2 3
- 2*a11 *b12 *r7493 - 2*a11 *b12 *r7581 - 2*a11*b12 *kap*r7391
3 4 2
+ 2*a11*b12 *kap*r7448 - 2*b12 *kap *r7377,
3
2*b12 *r7664,
3 3 2 2
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
2 2 2
- 2*a11 *b12*r7581 - 2*a11*b12 *kap*r7391 + 2*a11*b12 *kap*r7448
3 2
- 2*b12 *kap *r7377,
2 2 2 2
2*a11 *b12*kap*r7276 - 2*a11 *b12*kap*r7687 + a11*b12 *kap *r7449
3 2
- b12 *kap *r7276,
3
2*b12 *r7650,
2 2 2 3
2*a11 *b12*r7276 - 2*a11 *b12*r7687 + a11*b12 *kap*r7449 - b12 *kap*r7276,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 2*a11 *b12 *kap*r7391 + 2*a11 *b12 *kap*r7448
3 2 3 4 2 4
- 2*a11*b12 *kap *r7377 + a11*b12 *kap*r7581 + b12 *kap *r7391 + 2*b12 *r7664
,
2*a11*r7276 - 2*a11*r7687 + b12*kap*r7449,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 4*a11 *b12 *kap*r7391 + 4*a11 *b12 *kap*r7448
3 2 3 3
- 6*a11*b12 *kap *r7377 + 2*a11*b12 *kap*r7493 + 2*a11*b12 *kap*r7581
4 2 4 2 4
+ b12 *kap *r7391 - b12 *kap *r7448 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 2*a11 *b12 *kap*r7391 + 2*a11 *b12 *kap*r7448
3 2 4
- 2*a11*b12 *kap *r7377 + 2*b12 *r7664,
2 2 2 2 3 2
2*a11 *b12 *kap*r7276 - 2*a11 *b12 *kap*r7687 + a11*b12 *kap *r7449
4 2
- b12 *kap *r7276,
3 3 2 2 2
4*a11 *b12*kap*r7391 - 4*a11 *b12*kap*r7448 + 8*a11 *b12 *kap *r7377
2 2 2 2 3 2
- 4*a11 *b12 *kap*r7493 - 4*a11 *b12 *kap*r7581 - 4*a11*b12 *kap *r7391
3 2 4 3
+ 4*a11*b12 *kap *r7448 - 4*b12 *kap *r7377,
2
2*a11*a33*b12*r7276 - 2*a11*a33*b12*r7687 + a33*b12 *kap*r7449,
2 2 2 2
2*a11 *b12*r7391 - 2*a11 *b12*r7448 + 4*a11*b12 *kap*r7377 - 2*a11*b12 *r7493
2 3
- a11*b12 *r7581 + b12 *kap*r7448,
2
2*a11*b12*r7276 - 2*a11*b12*r7687 + b12 *kap*r7449,
2 2 2 3 2
a11*a33 *b12 *kap*r7197 - a33 *b12 *kap *r7400,
2 2
2*a11*b12*r7407 - 2*a11*b12*r7464 + 2*b12 *kap*r7395 - b12 *kap*r7581,
a11*r7581 + b12*kap*r7391,
2
2*a11*b12*r7276 - 2*a11*b12*r7687 + b12 *kap*r7449,
a33*b12*r7619 + 2*a33*b12*r7687,
1
a11*r7391 - a11*r7448 + 2*b12*kap*r7377 + ---*b12*r7581,
2
r7687,
b12*r7276,
4*a11*r7391 - 4*a11*r7448 + 8*b12*kap*r7377 + 2*b12*r7493 + 2*b12*r7581,
2
a11*b12*r7391 - a11*b12*r7448 + 2*b12 *kap*r7377,
r7664,
3 3 2 2
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
2 2 2
- 4*a11 *b12*r7581 - 4*a11*b12 *kap*r7391 + 4*a11*b12 *kap*r7448
3 2
- 4*b12 *kap *r7377,
2 3 2 3
2*a11 *a33*b12 *kap*r7276 - 2*a11 *a33*b12 *kap*r7687
4 2 5 2
+ a11*a33*b12 *kap *r7449 - a33*b12 *kap *r7276,
r7650,
2 2 2 3
2*a11 *b12*r7276 - 2*a11 *b12*r7687 + a11*b12 *kap*r7449 - b12 *kap*r7276,
4 4 3 3
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
3 2 2 2 2
- 4*a11 *b12*r7581 - 6*a11 *b12 *kap*r7391 + 6*a11 *b12 *kap*r7448
3 2 3 3
- 8*a11*b12 *kap *r7377 + 2*a11*b12 *kap*r7493 + 3*a11*b12 *kap*r7581
4 2 4 2 4
+ 2*b12 *kap *r7391 - b12 *kap *r7448 + 4*b12 *r7664,
4 4 3 3
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
3 2 2 2 2
- 4*a11 *b12*r7581 - 6*a11 *b12 *kap*r7391 + 6*a11 *b12 *kap*r7448
3 2 3 3
- 8*a11*b12 *kap *r7377 + 2*a11*b12 *kap*r7493 + 3*a11*b12 *kap*r7581
4 2 4 2 4
+ 2*b12 *kap *r7391 - b12 *kap *r7448 + 4*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 2*a11 *b12 *kap*r7391 + 2*a11 *b12 *kap*r7448
3 2 4
- 2*a11*b12 *kap *r7377 + 2*b12 *r7664,
2 2
2*a11*b12*r7407 - 2*a11*b12*r7464 + 2*b12 *kap*r7395 - b12 *kap*r7581,
2 2 2 3 2
a11*a33 *b12 *kap*r7197 - a33 *b12 *kap *r7400,
2
2*a11*b12*r7276 - 2*a11*b12*r7687 + b12 *kap*r7449,
a11*r7581 + b12*kap*r7391,
1
a11*r7391 - a11*r7448 + 2*b12*kap*r7377 + ---*b12*r7581,
2
r7619,
2*b12*r7493,
a11*r7391 - a11*r7448 + 2*b12*kap*r7377,
a33*b12*r7687,
b12*r7276,
2 3
a11*b12 *r7202 - b12 *kap*r7112,
2 2 2 3 2
a11*a33 *b12 *kap*r7197 - a33 *b12 *kap *r7400,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 2*a11*b12 *kap*r7395
2 3 3
- a11*b12 *kap*r7581 - b12 *kap*r7407 - 2*b12 *r7650,
2 2
a33 *b12 *kap*r7197,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 2*a11*b12 *kap*r7395
2 3 3 3
- a11*b12 *kap*r7581 - b12 *kap*r7407 + b12 *kap*r7464 - 2*b12 *r7650,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 2*a11*b12 *kap*r7395
2 3 2 3
- 2*a11*b12 *kap*r7581 - b12 *kap *r7391 - 2*b12 *r7650,
2*a33*b12*r7276 - a33*b12*r7619 - 2*a33*b12*r7687,
r7581,
a33*b12*r7687,
b12*r7276,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4 2 4
- 4*a11*b12 *kap *r7377 + b12 *kap *r7391 + 2*b12 *r7664,
r7449,
4 4 3 3
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
3 2 2 2 2
- 4*a11 *b12*r7581 - 6*a11 *b12 *kap*r7391 + 6*a11 *b12 *kap*r7448
3 2 4 2 4 2 4
- 8*a11*b12 *kap *r7377 + 2*b12 *kap *r7391 - b12 *kap *r7448 + 4*b12 *r7664,
4 4 3 3
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
3 2 2 2 2
- 4*a11 *b12*r7581 - 6*a11 *b12 *kap*r7391 + 6*a11 *b12 *kap*r7448
3 2 4 2 4
- 8*a11*b12 *kap *r7377 + b12 *kap *r7391 + 4*b12 *r7664,
r7449,
r7449,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4 2 4 2 4
- 4*a11*b12 *kap *r7377 + b12 *kap *r7391 - b12 *kap *r7448 + 2*b12 *r7664,
4 4 3 3
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
3 2 2 2 2
- 4*a11 *b12*r7581 - 6*a11 *b12 *kap*r7391 + 6*a11 *b12 *kap*r7448
3 2 4 2 4 2 4
- 8*a11*b12 *kap *r7377 + b12 *kap *r7391 - b12 *kap *r7448 + 4*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 4*a11*b12 *kap *r7377 + 2*b12 *r7664,
2 2 2 3
2*a11 *b12*r7276 - 2*a11 *b12*r7687 + a11*b12 *kap*r7449 - b12 *kap*r7276,
3 3 2 2
a11 *r7391 - a11 *r7448 + 2*a11 *b12*kap*r7377 - a11 *b12*r7493
2 2 2 3 2
- a11 *b12*r7581 - a11*b12 *kap*r7391 + a11*b12 *kap*r7448 - b12 *kap *r7377,
2
2*a11*a33*b12*r7276 - 2*a11*a33*b12*r7687 + a33*b12 *kap*r7449,
2 2
2*a11 *r7391 - 2*a11 *r7448 + 4*a11*b12*kap*r7377 - 2*a11*b12*r7493
2
- a11*b12*r7581 + b12 *kap*r7448,
2
2*a11*a33*b12*r7276 - 2*a11*a33*b12*r7687 + a33*b12 *kap*r7449,
2 2 2 3 2
a11*a33 *b12 *kap*r7197 - a33 *b12 *kap *r7400,
2 2
2*a11*b12*r7407 - 2*a11*b12*r7464 + 2*b12 *kap*r7395 - b12 *kap*r7581,
a11*r7581 + b12*kap*r7391,
2
2*a11*b12*r7276 - 2*a11*b12*r7687 + b12 *kap*r7449,
b12*r7687,
r7493,
a33*b12*r7619,
b12*r7276,
2*a11*r7391 - 2*a11*r7448 + 4*b12*kap*r7377 + b12*r7581,
a11*r7391 - a11*r7448 + 2*b12*kap*r7377,
2
b12 *r7197,
r7464,
2 2
a33 *b12 *kap*r7197,
b12*r7581,
4*a33*b12*r7276 - 2*a33*b12*r7619 - 2*a33*b12*r7687,
b12*r7581,
r7449,
r7448,
r7449,
r7448,
r7448,
r7449,
r7449,
3
a33*b12 *kap*r7116,
2
b12 *r7202,
r7407,
2 2
a33 *b12 *kap*r7197,
b12*r7400,
1
b12*r7395 - ---*b12*r7581,
2
r7400,
3*a33*b12*r7276 - a33*b12*r7400 - a33*b12*r7619 - 2*a33*b12*r7687,
2*b12*r7395 - b12*r7581,
r7395,
r7391,
r7449,
r7391,
r7391,
r7449,
r7449,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
r7377,
a11*r7449 + b12*r7276,
a11*r7449 + b12*r7276,
2*r7377,
2*r7377,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
a11*r7449 + b12*r7276,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
r7377,
2*r7377,
r7377,
4
2*b12 *kap*r7664,
3 3 2 2
a11 *r7391 - a11 *r7448 + 2*a11 *b12*kap*r7377 - a11 *b12*r7493
2 2 2 3 2
- a11 *b12*r7581 - a11*b12 *kap*r7391 + a11*b12 *kap*r7448 - b12 *kap *r7377,
2 2 2
2*a11 *a33*b12*r7276 - 2*a11 *a33*b12*r7687 + a11*a33*b12 *kap*r7449
3
- a33*b12 *kap*r7276,
3
2*b12 *r7650,
2 2 2 3
2*a11 *b12*r7276 - 2*a11 *b12*r7687 + a11*b12 *kap*r7449 - b12 *kap*r7276,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 4*a11 *b12 *kap*r7391 + 4*a11 *b12 *kap*r7448
3 2 3 3
- 6*a11*b12 *kap *r7377 + 2*a11*b12 *kap*r7493 + 2*a11*b12 *kap*r7581
4 2 4 2 4
+ b12 *kap *r7391 - b12 *kap *r7448 + 2*b12 *r7664,
2
2*a11*a33*b12*r7276 - 2*a11*a33*b12*r7687 + a33*b12 *kap*r7449,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 2*a11 *b12 *kap*r7391 + 2*a11 *b12 *kap*r7448
3 2 3 4 2 4
- 2*a11*b12 *kap *r7377 + a11*b12 *kap*r7581 + b12 *kap *r7391 + 2*b12 *r7664
,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 2*a11 *b12 *kap*r7391 + 2*a11 *b12 *kap*r7448
3 2 4
- 2*a11*b12 *kap *r7377 + 2*b12 *r7664,
2 2
2*a11*b12*r7407 - 2*a11*b12*r7464 + 2*b12 *kap*r7395 - b12 *kap*r7581,
2 3 2
a11*a33*b12 *kap*r7197 - a33*b12 *kap *r7400,
2
2*a11*b12*r7276 - 2*a11*b12*r7687 + b12 *kap*r7449,
a11*r7581 + b12*kap*r7391,
2*a11*r7391 - 2*a11*r7448 + 4*b12*kap*r7377 + b12*r7493 + b12*r7581,
a33*b12*r7687,
2*a11*r7391 - 2*a11*r7448 + 4*b12*kap*r7377 + b12*r7581,
a11*r7391 - a11*r7448 + 2*b12*kap*r7377,
a33*b12*r7619 + 2*a33*b12*r7687,
r7276,
2 3
a11*b12 *r7202 - b12 *kap*r7112,
2 3
a11*b12 *r7197 - b12 *kap*r7400,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 2*a11*b12 *kap*r7395
2 3 3 3
- a11*b12 *kap*r7581 - b12 *kap*r7407 + b12 *kap*r7464 - 2*b12 *r7650,
2 2
a33 *b12 *kap*r7197,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 2*a11*b12 *kap*r7395
2 3 3
- a11*b12 *kap*r7581 - b12 *kap*r7407 - 2*b12 *r7650,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 2*a11*b12 *kap*r7395
2 3 2 3
- 2*a11*b12 *kap*r7581 - b12 *kap *r7391 - 2*b12 *r7650,
b12*r7687,
r7581,
2*a33*b12*r7276 - a33*b12*r7619 - 2*a33*b12*r7687,
b12*r7276,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4 2 4 2 4
- 4*a11*b12 *kap *r7377 + b12 *kap *r7391 - b12 *kap *r7448 + 2*b12 *r7664,
r7449,
4 4 3 3
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
3 2 2 2 2
- 4*a11 *b12*r7581 - 6*a11 *b12 *kap*r7391 + 6*a11 *b12 *kap*r7448
3 2 4 2 4 2 4
- 8*a11*b12 *kap *r7377 + 2*b12 *kap *r7391 - b12 *kap *r7448 + 4*b12 *r7664,
4 4 3 3
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
3 2 2 2 2
- 4*a11 *b12*r7581 - 6*a11 *b12 *kap*r7391 + 6*a11 *b12 *kap*r7448
3 2 4 2 4 2 4
- 8*a11*b12 *kap *r7377 + b12 *kap *r7391 - b12 *kap *r7448 + 4*b12 *r7664,
r7449,
r7449,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4 2 4
- 4*a11*b12 *kap *r7377 + b12 *kap *r7391 + 2*b12 *r7664,
4 4 3 3
4*a11 *r7391 - 4*a11 *r7448 + 8*a11 *b12*kap*r7377 - 4*a11 *b12*r7493
3 2 2 2 2
- 4*a11 *b12*r7581 - 6*a11 *b12 *kap*r7391 + 6*a11 *b12 *kap*r7448
3 2 4 2 4
- 8*a11*b12 *kap *r7377 + b12 *kap *r7391 + 4*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 4*a11*b12 *kap *r7377 + 2*b12 *r7664,
r7202,
3
a33*b12 *kap*r7116,
r7197,
r7407,
2*b12*r7395 - b12*r7581,
r7400,
2*b12*r7395 - b12*r7581,
b12*r7395,
b12*r7400,
3*a33*b12*r7276 - a33*b12*r7400 - a33*b12*r7619 - 2*a33*b12*r7687,
r7449,
r7391,
r7449,
r7449,
r7391,
r7391,
r7377,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
2*r7377,
2*r7377,
a11*r7449 + b12*r7276,
a11*r7449 + b12*r7276,
r7377,
2*r7377,
r7377,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
a11*r7449 + b12*r7276,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
r7119,
r7116,
b12*r7112,
r7112,
2*b12*r7112 + b12*r7407,
r7400,
r7400,
3*a33*b12*r7276 - 3*a33*b12*r7400 - a33*b12*r7619 - 2*a33*b12*r7687,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 4*a11*b12 *kap*r7395
2 3
- 2*a11*b12 *kap*r7581 - 2*b12 *r7650,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 4*a11*b12 *kap*r7395
2 3
- 2*a11*b12 *kap*r7581 - 2*b12 *r7650,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 4*a11*b12 *kap*r7395
2 3 2 3
- 2*a11*b12 *kap*r7581 - b12 *kap *r7391 - 2*b12 *r7650,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 4*a11*b12 *kap*r7395
2 3
- 2*a11*b12 *kap*r7581 - 2*b12 *r7650,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 4*a11*b12 *kap*r7395
2 3 2 3
- 2*a11*b12 *kap*r7581 - b12 *kap *r7391 - 2*b12 *r7650,
2 2 2
2*a11 *b12*r7407 - 2*a11 *b12*r7464 + 4*a11*b12 *kap*r7395
2 3 2 3
- 2*a11*b12 *kap*r7581 - 2*b12 *kap *r7391 - 2*b12 *r7650,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
a11*r7449 + b12*r7276,
a11*r7449 + b12*r7276,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
a11*r7449 + b12*r7276,
1 1
---*a11*r7449 + ---*b12*r7276,
2 2
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664,
4 4 3 3
2*a11 *r7391 - 2*a11 *r7448 + 4*a11 *b12*kap*r7377 - 2*a11 *b12*r7493
3 2 2 2 2
- 2*a11 *b12*r7581 - 3*a11 *b12 *kap*r7391 + 3*a11 *b12 *kap*r7448
3 2 4
- 6*a11*b12 *kap *r7377 + 2*b12 *r7664},
a11 - 2*a33,
b12}
Relevance for the application:
The system of equations related to the Hamiltonian HAM:
2 2 2
HAM=u1 *a11 + u1*v2*b12 + u2 *a11 - u2*v1*b12 + u3 *a33
has apart from the Hamiltonian and Casimirs the following 20 first integrals:
4 3 2 3 3 2 2 3 2
FI= - u1 *u3 *a11 - 2*u1 *u3 *v2*a11*b12 - 2*u1 *u2 *u3 *a11
2 3 2 3 2 2 2 3
+ 2*u1 *u2*u3 *v1*a11*b12 - u1 *u3 *v2 *b12 - 2*u1*u2 *u3 *v2*a11*b12
3 2 4 3 2 3 3
+ 2*u1*u2*u3 *v1*v2*b12 - u2 *u3 *a11 + 2*u2 *u3 *v1*a11*b12
2 3 2 2
- u2 *u3 *v1 *b12
3 2 2 2
= - u3 *((u1 + u2 )*a11 + (u1*v2 - u2*v1)*b12)
{HAM,FI} = 0
6 2 3 5 3 4 2 2 3
FI= - u1 *u3*a11 *kap - 3*u1 *u3*v2*a11*b12*kap - 3*u1 *u2 *u3*a11 *kap
4 3 4 2 2 3
+ 3*u1 *u2*u3*v1*a11*b12*kap - 3*u1 *u3*v2 *b12 *kap
3 2 3 3 2 3
- 6*u1 *u2 *u3*v2*a11*b12*kap + 6*u1 *u2*u3*v1*v2*b12 *kap
2 4 2 3 2 3 3
- 3*u1 *u2 *u3*a11 *kap + 6*u1 *u2 *u3*v1*a11*b12*kap
2 2 2 2 3 2 2 2 2 3
- 3*u1 *u2 *u3*v1 *b12 *kap - 3*u1 *u2 *u3*v2 *b12 *kap
2 2 2 2 2 2 4 2 2
- 3*u1 *u3*v1 *v2 *b12 *kap - 3*u1 *u3*v2 *b12 *kap
2 2 2 2 2 4 3
- 3*u1 *u3*v2 *v3 *b12 *kap - 3*u1*u2 *u3*v2*a11*b12*kap
3 2 3 3 2 2
+ 6*u1*u2 *u3*v1*v2*b12 *kap + 6*u1*u2*u3*v1 *v2*b12 *kap
3 2 2 2 2 2
+ 6*u1*u2*u3*v1*v2 *b12 *kap + 6*u1*u2*u3*v1*v2*v3 *b12 *kap
4 2 3
+ 3*u1*u3*v1 *v2*a11*b12*kap + 6*u1*u3*v1 *v2 *a11*b12*kap
2 2 5
+ 6*u1*u3*v1 *v2*v3 *a11*b12*kap + 3*u1*u3*v2 *a11*b12*kap
3 2 4
+ 6*u1*u3*v2 *v3 *a11*b12*kap + 3*u1*u3*v2*v3 *a11*b12*kap
6 2 3 5 3 4 2 2 3
- u2 *u3*a11 *kap + 3*u2 *u3*v1*a11*b12*kap - 3*u2 *u3*v1 *b12 *kap
2 4 2 2 2 2 2 2 2
- 3*u2 *u3*v1 *b12 *kap - 3*u2 *u3*v1 *v2 *b12 *kap
2 2 2 2 2 5
- 3*u2 *u3*v1 *v3 *b12 *kap - 3*u2*u3*v1 *a11*b12*kap
3 2 3 2
- 6*u2*u3*v1 *v2 *a11*b12*kap - 6*u2*u3*v1 *v3 *a11*b12*kap
4 2 2
- 3*u2*u3*v1*v2 *a11*b12*kap - 6*u2*u3*v1*v2 *v3 *a11*b12*kap
4 6 2 4 2 2
- 3*u2*u3*v1*v3 *a11*b12*kap - u3*v1 *a11 - 3*u3*v1 *v2 *a11
4 2 2 2 4 2 2 2 2 2
- 3*u3*v1 *v3 *a11 - 3*u3*v1 *v2 *a11 - 6*u3*v1 *v2 *v3 *a11
2 4 2 6 2 4 2 2 2 4 2
- 3*u3*v1 *v3 *a11 - u3*v2 *a11 - 3*u3*v2 *v3 *a11 - 3*u3*v2 *v3 *a11
6 2
- u3*v3 *a11
2 2 2 2 2
=u3*(3*((v2 + v3 + v1 - (u1 + u2 )*kap)*a11 - (u1*v2 - u2*v1)*b12*kap)
2 2 2 2 2 2 2 2
*(u1*v2 - u2*v1)*b12*kap - ((u1 + u2 ) *kap + (v1 + v2 + v3 )
2 2 2 2 2 2
- (v2 + v3 + v1 )*(u1 + u2 )*kap)*a11 )
2 2 2 2 2
*(v2 + v3 + v1 + (u1 + u2 )*kap)
{HAM,FI} = 0
4 3 2 3 3 2 2 3 2
FI=u1 *u3 *a11 + 2*u1 *u3 *v2*a11*b12 + 2*u1 *u2 *u3 *a11
2 3 2 3 2 2 2 3 2 2
- 2*u1 *u2*u3 *v1*a11*b12 + u1 *u3 *v1 *b12 + u1 *u3 *v2 *b12
2 3 4 2 4 3 2
+ 2*u1*u2 *u3 *v2*a11*b12 + 2*u1*u3 *v1*v3*b12 + u2 *u3 *a11
3 3 2 3 2 2 2 3 2 2
- 2*u2 *u3 *v1*a11*b12 + u2 *u3 *v1 *b12 + u2 *u3 *v2 *b12
4 2 5 2 2
+ 2*u2*u3 *v2*v3*b12 + u3 *v3 *b12
3 2 2 2 2 2
=u3 *(((2*u2*v2 + u3*v3 + 2*u1*v1)*u3*v3 + (u1 + u2 )*(v1 + v2 ))*b12
2 2 2 2
+ ((u1 + u2 )*a11 + 2*(u1*v2 - u2*v1)*b12)*(u1 + u2 )*a11)
{HAM,FI} = 0
4 3 3 3 2 2 3
FI=u1 *u3 *a11*kap + u1 *u3 *v2*b12*kap + 2*u1 *u2 *u3 *a11*kap
2 3 2 3 2 2 3 2
- u1 *u2*u3 *v1*b12*kap + u1 *u3 *v1 *a11 + u1 *u3 *v2 *a11
2 3 2 2 3 3 2
+ u1 *u3 *v3 *a11 + u1*u2 *u3 *v2*b12*kap + u1*u3 *v1 *v2*b12
3 3 3 2 4 3 3 3
+ u1*u3 *v2 *b12 + u1*u3 *v2*v3 *b12 + u2 *u3 *a11*kap - u2 *u3 *v1*b12*kap
2 3 2 2 3 2 2 3 2 3 3
+ u2 *u3 *v1 *a11 + u2 *u3 *v2 *a11 + u2 *u3 *v3 *a11 - u2*u3 *v1 *b12
3 2 3 2
- u2*u3 *v1*v2 *b12 - u2*u3 *v1*v3 *b12
3 2 2 2 2 2
=u3 *(v2 + v3 + v1 + (u1 + u2 )*kap)
2 2
*((u1 + u2 )*a11 + (u1*v2 - u2*v1)*b12)
{HAM,FI} = 0
6 2 3 2 4 5 3
FI=u1 *u3*(a11 *kap - b12 *kap ) + 3*u1 *u3*v2*a11*b12*kap
4 2 2 3 2 4 4 3
+ u1 *u2 *u3*(3*a11 *kap - 3*b12 *kap ) - 3*u1 *u2*u3*v1*a11*b12*kap
4 2 2 3 3 2 3
- 3*u1 *u3*v3 *b12 *kap + 6*u1 *u2 *u3*v2*a11*b12*kap
3 2 2 3 2 4 2 3 2 4
+ 6*u1 *u3 *v1*v3*b12 *kap + u1 *u2 *u3*(3*a11 *kap - 3*b12 *kap )
2 3 3 2 2 2 2 3
- 6*u1 *u2 *u3*v1*a11*b12*kap - 6*u1 *u2 *u3*v3 *b12 *kap
2 2 2 3 2 3 2 2 3
+ 6*u1 *u2*u3 *v2*v3*b12 *kap + 3*u1 *u3 *v3 *b12 *kap
2 2 2 2 2 2 2 2 2 2
- 3*u1 *u3*v1 *v3 *b12 *kap - 3*u1 *u3*v2 *v3 *b12 *kap
2 4 2 2 4 3
- 3*u1 *u3*v3 *b12 *kap + 3*u1*u2 *u3*v2*a11*b12*kap
2 2 2 3 2 3 2 2
+ 6*u1*u2 *u3 *v1*v3*b12 *kap + 6*u1*u3 *v1 *v3*b12 *kap
2 2 2 2 2 3 2 2
+ 6*u1*u3 *v1*v2 *v3*b12 *kap + 6*u1*u3 *v1*v3 *b12 *kap
4 2 3
- 3*u1*u3*v1 *v2*a11*b12*kap - 6*u1*u3*v1 *v2 *a11*b12*kap
2 2 5
- 6*u1*u3*v1 *v2*v3 *a11*b12*kap - 3*u1*u3*v2 *a11*b12*kap
3 2 4
- 6*u1*u3*v2 *v3 *a11*b12*kap - 3*u1*u3*v2*v3 *a11*b12*kap
6 2 3 2 4 5 3
+ u2 *u3*(a11 *kap - b12 *kap ) - 3*u2 *u3*v1*a11*b12*kap
4 2 2 3 3 2 2 3
- 3*u2 *u3*v3 *b12 *kap + 6*u2 *u3 *v2*v3*b12 *kap
2 3 2 2 3 2 2 2 2 2
+ 3*u2 *u3 *v3 *b12 *kap - 3*u2 *u3*v1 *v3 *b12 *kap
2 2 2 2 2 2 4 2 2
- 3*u2 *u3*v2 *v3 *b12 *kap - 3*u2 *u3*v3 *b12 *kap
2 2 2 2 2 3 2 2
+ 6*u2*u3 *v1 *v2*v3*b12 *kap + 6*u2*u3 *v2 *v3*b12 *kap
2 3 2 2 5
+ 6*u2*u3 *v2*v3 *b12 *kap + 3*u2*u3*v1 *a11*b12*kap
3 2 3 2
+ 6*u2*u3*v1 *v2 *a11*b12*kap + 6*u2*u3*v1 *v3 *a11*b12*kap
4 2 2
+ 3*u2*u3*v1*v2 *a11*b12*kap + 6*u2*u3*v1*v2 *v3 *a11*b12*kap
4 3 2 2 2 2
+ 3*u2*u3*v1*v3 *a11*b12*kap + 3*u3 *v1 *v3 *b12 *kap
3 2 2 2 2 3 4 2 2 6 2 2
+ 3*u3 *v2 *v3 *b12 *kap + 3*u3 *v3 *b12 *kap + u3*v1 *(a11 - b12 *kap)
4 2 2 2 4 2 2 2
+ u3*v1 *v2 *(3*a11 - 3*b12 *kap) + u3*v1 *v3 *(3*a11 - 3*b12 *kap)
2 4 2 2 2 2 2 2 2
+ u3*v1 *v2 *(3*a11 - 3*b12 *kap) + u3*v1 *v2 *v3 *(6*a11 - 6*b12 *kap)
2 4 2 2 6 2 2
+ u3*v1 *v3 *(3*a11 - 3*b12 *kap) + u3*v2 *(a11 - b12 *kap)
4 2 2 2 2 4 2 2
+ u3*v2 *v3 *(3*a11 - 3*b12 *kap) + u3*v2 *v3 *(3*a11 - 3*b12 *kap)
6 2 2
+ u3*v3 *(a11 - b12 *kap)
2 2 2 2 2 2 2 2
=u3*((((u1 + u2 ) *kap + (v1 + v2 + v3 )
2 2 2 2 2
- (v2 + v3 + v1 )*(u1 + u2 )*kap)*a11
2 2 2 2 2
- 3*(v2 + v3 + v1 - (u1 + u2 )*kap)*(u1*v2 - u2*v1)*b12*kap)*a11 +
2 2 2 2 2
((3*(2*u2*v2 + u3*v3 + 2*u1*v1)*u3*v3 + (v2 - 2*v3 + v1 )*(u1 + u2 ))
2 2 2 2 2 2 2 2 2
*kap - ((u1 + u2 ) *kap + (v1 + v2 + v3 ) ))*b12 *kap)
2 2 2 2 2
*(v2 + v3 + v1 + (u1 + u2 )*kap)
{HAM,FI} = 0
7
FI=u3
7
=u3
{HAM,FI} = 0
5 2 3 4 2 3 4 2 2 3
FI=3*u1 *u3*v1*b12 *kap + 3*u1 *u2*u3*v2*b12 *kap + 3*u1 *u3 *v3*b12 *kap
3 2 2 3 3 3 2 2
+ 6*u1 *u2 *u3*v1*b12 *kap + 4*u1 *u3*v1 *b12 *kap
3 2 2 2 2 3 2 3
+ 6*u1 *u3*v1*v3 *b12 *kap + 6*u1 *u2 *u3*v2*b12 *kap
2 2 2 2 3 2 2 2 2
+ 6*u1 *u2 *u3 *v3*b12 *kap + 12*u1 *u2*u3*v1 *v2*b12 *kap
2 2 2 2 2 2 3 2 2
+ 6*u1 *u2*u3*v2*v3 *b12 *kap + 6*u1 *u3 *v3 *b12 *kap
2 3 2 3
+ 12*u1 *u3*v1 *v2*a11*b12*kap + 12*u1 *u3*v1*v2 *a11*b12*kap
2 2 4 2 3
+ 12*u1 *u3*v1*v2*v3 *a11*b12*kap + 3*u1*u2 *u3*v1*b12 *kap
2 2 2 2 2 2 2 2
+ 12*u1*u2 *u3*v1*v2 *b12 *kap + 6*u1*u2 *u3*v1*v3 *b12 *kap
4 2 2
- 12*u1*u2*u3*v1 *a11*b12*kap - 12*u1*u2*u3*v1 *v3 *a11*b12*kap
4 2 2
+ 12*u1*u2*u3*v2 *a11*b12*kap + 12*u1*u2*u3*v2 *v3 *a11*b12*kap
3 2 2 2 2 2
- 6*u1*u3 *v1*v3 *b12 *kap + 12*u1*u3 *v1 *v2*v3*a11*b12*kap
2 3 2 3
+ 12*u1*u3 *v2 *v3*a11*b12*kap + 12*u1*u3 *v2*v3 *a11*b12*kap
5 2 2
+ u1*u3*v1 *( - 6*a11 + 3*b12 *kap)
3 2 2 2
+ u1*u3*v1 *v2 *( - 12*a11 + 6*b12 *kap)
3 2 2 2
+ u1*u3*v1 *v3 *( - 12*a11 + 6*b12 *kap)
4 2 2
+ u1*u3*v1*v2 *( - 6*a11 + 3*b12 *kap)
2 2 2 2
+ u1*u3*v1*v2 *v3 *( - 12*a11 + 6*b12 *kap)
4 2 2 5 2 3
+ u1*u3*v1*v3 *( - 6*a11 + 3*b12 *kap) + 3*u2 *u3*v2*b12 *kap
4 2 2 3 3 3 2 2
+ 3*u2 *u3 *v3*b12 *kap + 4*u2 *u3*v2 *b12 *kap
3 2 2 2 2 2 3 2 2
+ 6*u2 *u3*v2*v3 *b12 *kap + 6*u2 *u3 *v3 *b12 *kap
2 3 2 3
- 12*u2 *u3*v1 *v2*a11*b12*kap - 12*u2 *u3*v1*v2 *a11*b12*kap
2 2 3 2 2 2
- 12*u2 *u3*v1*v2*v3 *a11*b12*kap - 6*u2*u3 *v2*v3 *b12 *kap
2 3 2 2
- 12*u2*u3 *v1 *v3*a11*b12*kap - 12*u2*u3 *v1*v2 *v3*a11*b12*kap
2 3 4 2 2
- 12*u2*u3 *v1*v3 *a11*b12*kap + u2*u3*v1 *v2*( - 6*a11 + 3*b12 *kap)
2 3 2 2
+ u2*u3*v1 *v2 *( - 12*a11 + 6*b12 *kap)
2 2 2 2
+ u2*u3*v1 *v2*v3 *( - 12*a11 + 6*b12 *kap)
5 2 2
+ u2*u3*v2 *( - 6*a11 + 3*b12 *kap)
3 2 2 2
+ u2*u3*v2 *v3 *( - 12*a11 + 6*b12 *kap)
4 2 2 4 3 2 2
+ u2*u3*v2*v3 *( - 6*a11 + 3*b12 *kap) - 2*u3 *v3 *b12 *kap
2 4 2 2
+ u3 *v1 *v3*( - 6*a11 + 3*b12 *kap)
2 2 2 2 2
+ u3 *v1 *v2 *v3*( - 12*a11 + 6*b12 *kap)
2 2 3 2 2
+ u3 *v1 *v3 *( - 12*a11 + 6*b12 *kap)
2 4 2 2
+ u3 *v2 *v3*( - 6*a11 + 3*b12 *kap)
2 2 3 2 2 2 5 2 2
+ u3 *v2 *v3 *( - 12*a11 + 6*b12 *kap) + u3 *v3 *( - 6*a11 + 3*b12 *kap)
2 2 2
= - u3*((2*((2*u2*v2 + u3*v3)*u3*v3 - (2*v2 + 3*v3 )*u2
2 2 2
- (2*v1 + 3*v3 )*u1 - 2*(2*u2*v2 - u3*v3)*u1*v1)*kap
2 2 2 2 2 2 2 2 2
- 3*((u1 + u2 ) *kap + (v1 + v2 + v3 ) ))*b12 *kap + 6
2 2 2
*(a11*v1 + a11*v2 + a11*v3 - 2*b12*kap*u1*v2 + 2*b12*kap*u2*v1)
2 2 2
*(v1 + v2 + v3 )*a11)*(u2*v2 + u3*v3 + u1*v1)
{HAM,FI} = 0
6 3 2 2 3
FI=u1 *u3*( - 2*a11 *kap + 2*a11*b12 *kap )
5 2 2 3 3
+ u1 *u3*v2*( - 6*a11 *b12*kap + 3*b12 *kap )
4 2 3 2 2 3
+ u1 *u2 *u3*( - 6*a11 *kap + 6*a11*b12 *kap )
4 2 2 3 3 4 2 2 2
+ u1 *u2*u3*v1*(6*a11 *b12*kap - 3*b12 *kap ) + 3*u1 *u3*v1 *a11*b12 *kap
4 2 2 2 4 2 2 2
- 3*u1 *u3*v2 *a11*b12 *kap + 3*u1 *u3*v3 *a11*b12 *kap
3 2 2 2 3 3
+ u1 *u2 *u3*v2*( - 12*a11 *b12*kap + 6*b12 *kap )
3 2 2 3 2 3 2
+ 12*u1 *u2*u3*v1*v2*a11*b12 *kap + 6*u1 *u3*v1 *v2*b12 *kap
3 3 3 2 3 2 3 2
+ 4*u1 *u3*v2 *b12 *kap + 6*u1 *u3*v2*v3 *b12 *kap
2 4 3 2 2 3
+ u1 *u2 *u3*( - 6*a11 *kap + 6*a11*b12 *kap )
2 3 2 2 3 3
+ u1 *u2 *u3*v1*(12*a11 *b12*kap - 6*b12 *kap )
2 2 2 2 2 2 3 3 2
+ 6*u1 *u2 *u3*v3 *a11*b12 *kap - 6*u1 *u2*u3*v1 *b12 *kap
2 2 3 2
- 6*u1 *u2*u3*v1*v3 *b12 *kap
4 2 2 3 3
+ u1*u2 *u3*v2*( - 6*a11 *b12*kap + 3*b12 *kap )
3 2 2 2 3 3 2
+ 12*u1*u2 *u3*v1*v2*a11*b12 *kap + 6*u1*u2 *u3*v2 *b12 *kap
2 2 3 2 4 3
+ 6*u1*u2 *u3*v2*v3 *b12 *kap + 3*u1*u3*v1 *v2*b12 *kap
2 3 3 2 2 3
+ 6*u1*u3*v1 *v2 *b12 *kap + 6*u1*u3*v1 *v2*v3 *b12 *kap
5 3 3 2 3 4 3
+ 3*u1*u3*v2 *b12 *kap + 6*u1*u3*v2 *v3 *b12 *kap + 3*u1*u3*v2*v3 *b12 *kap
6 3 2 2 3
+ u2 *u3*( - 2*a11 *kap + 2*a11*b12 *kap )
5 2 2 3 3 4 2 2 2
+ u2 *u3*v1*(6*a11 *b12*kap - 3*b12 *kap ) - 3*u2 *u3*v1 *a11*b12 *kap
4 2 2 2 4 2 2 2
+ 3*u2 *u3*v2 *a11*b12 *kap + 3*u2 *u3*v3 *a11*b12 *kap
3 3 3 2 3 2 3 2
- 4*u2 *u3*v1 *b12 *kap - 6*u2 *u3*v1*v2 *b12 *kap
3 2 3 2 5 3
- 6*u2 *u3*v1*v3 *b12 *kap - 3*u2*u3*v1 *b12 *kap
3 2 3 3 2 3
- 6*u2*u3*v1 *v2 *b12 *kap - 6*u2*u3*v1 *v3 *b12 *kap
4 3 2 2 3
- 3*u2*u3*v1*v2 *b12 *kap - 6*u2*u3*v1*v2 *v3 *b12 *kap
4 3 6 2 4 2 2
- 3*u2*u3*v1*v3 *b12 *kap - u3*v1 *a11*b12 - 3*u3*v1 *v2 *a11*b12
4 2 2 2 4 2 2 2 2 2
- 3*u3*v1 *v3 *a11*b12 - 3*u3*v1 *v2 *a11*b12 - 6*u3*v1 *v2 *v3 *a11*b12
2 4 2 6 2 4 2 2
- 3*u3*v1 *v3 *a11*b12 - u3*v2 *a11*b12 - 3*u3*v2 *v3 *a11*b12
2 4 2 6 2
- 3*u3*v2 *v3 *a11*b12 - u3*v3 *a11*b12
2 2 2 2 2 2 2 2 2 2 2 2
=u3*(((3*((u1 + u2 ) *kap + (v1 + v2 + v3 ) ) + 2*(3*u1 *v1 + 2*u1 *v2
2 2 2 2 2 2 2 2
+ 3*u1 *v3 + 2*u1*u2*v1*v2 + 2*u2 *v1 + 3*u2 *v2 + 3*u2 *v3 )
3
*kap)*(u1*v2 - u2*v1)*b12
2 2 2 2 2 2
- 2*((u1 + u2 )*a11 + 3*(u1*v2 - u2*v1)*b12)*(u1 + u2 ) *a11 *kap)
2 2 3 3 2 2 2 3 2 2 2 2
*kap + (2*(u1 + u2 ) *kap - (v1 + v2 + v3 ) + 3*(u1 *v1 - u1 *v2
2 2 2 2 2 2 2 2
+ u1 *v3 + 4*u1*u2*v1*v2 - u2 *v1 + u2 *v2 + u2 *v3 )
2 2 2 2
*(u1 + u2 )*kap )*a11*b12 )
{HAM,FI} = 0
6 3 5 2 4 2 3
FI= - u1 *u3*a11 - 3*u1 *u3*v2*a11 *b12 - 3*u1 *u2 *u3*a11
4 2 4 2 2 3 2 2
+ 3*u1 *u2*u3*v1*a11 *b12 - 3*u1 *u3*v2 *a11*b12 - 6*u1 *u2 *u3*v2*a11 *b12
3 2 3 3 3 2 4 3
+ 6*u1 *u2*u3*v1*v2*a11*b12 - u1 *u3*v2 *b12 - 3*u1 *u2 *u3*a11
2 3 2 2 2 2 2
+ 6*u1 *u2 *u3*v1*a11 *b12 - 3*u1 *u2 *u3*v1 *a11*b12
2 2 2 2 2 2 3
- 3*u1 *u2 *u3*v2 *a11*b12 + 3*u1 *u2*u3*v1*v2 *b12
4 2 3 2
- 3*u1*u2 *u3*v2*a11 *b12 + 6*u1*u2 *u3*v1*v2*a11*b12
2 2 3 6 3 5 2
- 3*u1*u2 *u3*v1 *v2*b12 - u2 *u3*a11 + 3*u2 *u3*v1*a11 *b12
4 2 2 3 3 3
- 3*u2 *u3*v1 *a11*b12 + u2 *u3*v1 *b12
2 2 3
= - u3*((u1 + u2 )*a11 + (u1*v2 - u2*v1)*b12)
{HAM,FI} = 0
3 2 2 2 2 2 2 2
FI=u1 *u3*v1*v2 *b12 *kap - 2*u1 *u2*u3*v1 *v2*b12 *kap
2 3 2 2 2 2 2 2 2
+ u1 *u2*u3*v2 *b12 *kap + u1 *u3 *v2 *v3*b12 *kap
2 3 2 3
- 2*u1 *u3*v1 *v2*a11*b12*kap - 2*u1 *u3*v1*v2 *a11*b12*kap
2 2 2 3 2 2
- 2*u1 *u3*v1*v2*v3 *a11*b12*kap + u1*u2 *u3*v1 *b12 *kap
2 2 2 2 2 2 2
- 2*u1*u2 *u3*v1*v2 *b12 *kap - 2*u1*u2*u3 *v1*v2*v3*b12 *kap
4 2 2
+ 2*u1*u2*u3*v1 *a11*b12*kap + 2*u1*u2*u3*v1 *v3 *a11*b12*kap
4 2 2
- 2*u1*u2*u3*v2 *a11*b12*kap - 2*u1*u2*u3*v2 *v3 *a11*b12*kap
2 2 2 3
- 2*u1*u3 *v1 *v2*v3*a11*b12*kap - 2*u1*u3 *v2 *v3*a11*b12*kap
2 3 5 2 3 2 2
- 2*u1*u3 *v2*v3 *a11*b12*kap + u1*u3*v1 *a11 + 2*u1*u3*v1 *v2 *a11
3 2 2 4 2 2 2 2
+ 2*u1*u3*v1 *v3 *a11 + u1*u3*v1*v2 *a11 + 2*u1*u3*v1*v2 *v3 *a11
4 2 3 2 2 2 2 2 2 2 2
+ u1*u3*v1*v3 *a11 + u2 *u3*v1 *v2*b12 *kap + u2 *u3 *v1 *v3*b12 *kap
2 3 2 3
+ 2*u2 *u3*v1 *v2*a11*b12*kap + 2*u2 *u3*v1*v2 *a11*b12*kap
2 2 2 3
+ 2*u2 *u3*v1*v2*v3 *a11*b12*kap + 2*u2*u3 *v1 *v3*a11*b12*kap
2 2 2 3
+ 2*u2*u3 *v1*v2 *v3*a11*b12*kap + 2*u2*u3 *v1*v3 *a11*b12*kap
4 2 2 3 2 2 2 2
+ u2*u3*v1 *v2*a11 + 2*u2*u3*v1 *v2 *a11 + 2*u2*u3*v1 *v2*v3 *a11
5 2 3 2 2 4 2
+ u2*u3*v2 *a11 + 2*u2*u3*v2 *v3 *a11 + u2*u3*v2*v3 *a11
2 4 2 2 2 2 2 2 2 3 2
+ u3 *v1 *v3*a11 + 2*u3 *v1 *v2 *v3*a11 + 2*u3 *v1 *v3 *a11
2 4 2 2 2 3 2 2 5 2
+ u3 *v2 *v3*a11 + 2*u3 *v2 *v3 *a11 + u3 *v3 *a11
2 2 2 2
=u3*((v2 + v3 + v1 )*a11 - (u1*v2 - u2*v1)*b12*kap) *(u2*v2 + u3*v3 + u1*v1)
{HAM,FI} = 0
3 3 2 3 2 4 2 3
FI=u1 *u3 *v1*a11 + u1 *u2*u3 *v2*a11 + u1 *u3 *v3*a11 + u1 *u3 *v1*v2*b12
2 3 3 2 3 2
+ u1*u2 *u3 *v1*a11 - u1*u2*u3 *v1 *b12 + u1*u2*u3 *v2 *b12
4 3 3 2 4 2 3
+ u1*u3 *v2*v3*b12 + u2 *u3 *v2*a11 + u2 *u3 *v3*a11 - u2 *u3 *v1*v2*b12
4
- u2*u3 *v1*v3*b12
3 2 2
=u3 *((u1 + u2 )*a11 + (u1*v2 - u2*v1)*b12)*(u2*v2 + u3*v3 + u1*v1)
{HAM,FI} = 0
6 3 5 2 4 2 3
FI= - 2*u1 *u3*a11 - 6*u1 *u3*v2*a11 *b12 - 6*u1 *u2 *u3*a11
4 2 4 3 2 4 2 2
+ 6*u1 *u2*u3*v1*a11 *b12 + 3*u1 *u3 *a11*b12 *kap - 3*u1 *u3*v1 *a11*b12
4 2 2 3 2 2
- 6*u1 *u3*v2 *a11*b12 - 12*u1 *u2 *u3*v2*a11 *b12
3 2 3 3 3
+ 6*u1 *u2*u3*v1*v2*a11*b12 + 3*u1 *u3 *v2*b12 *kap
3 2 2 3 2 3 3 3 3
- 6*u1 *u3 *v1*v3*a11*b12 - 3*u1 *u3*v1 *v2*b12 - 2*u1 *u3*v2 *b12
2 4 3 2 3 2 2 2 3 2
- 6*u1 *u2 *u3*a11 + 12*u1 *u2 *u3*v1*a11 *b12 + 6*u1 *u2 *u3 *a11*b12 *kap
2 2 2 2 2 2 2 2
- 9*u1 *u2 *u3*v1 *a11*b12 - 9*u1 *u2 *u3*v2 *a11*b12
2 3 3 2 2 2
- 3*u1 *u2*u3 *v1*b12 *kap - 6*u1 *u2*u3 *v2*v3*a11*b12
2 3 3 2 3 2 2 2 3 2 2
+ 3*u1 *u2*u3*v1 *b12 + 3*u1 *u3 *v1 *a11*b12 + 3*u1 *u3 *v2 *a11*b12
2 2 3 4 2
- 6*u1 *u3 *v1*v2*v3*b12 - 6*u1*u2 *u3*v2*a11 *b12
3 2 2 3 3
+ 6*u1*u2 *u3*v1*v2*a11*b12 + 3*u1*u2 *u3 *v2*b12 *kap
2 2 2 2 3 3
- 6*u1*u2 *u3 *v1*v3*a11*b12 - 3*u1*u2 *u3*v2 *b12
2 2 3 2 2 3 3 2 3
+ 6*u1*u2*u3 *v1 *v3*b12 - 6*u1*u2*u3 *v2 *v3*b12 + 3*u1*u3 *v1 *v2*b12
3 3 3 6 3 5 2
+ 3*u1*u3 *v2 *b12 - 2*u2 *u3*a11 + 6*u2 *u3*v1*a11 *b12
4 3 2 4 2 2 4 2 2
+ 3*u2 *u3 *a11*b12 *kap - 6*u2 *u3*v1 *a11*b12 - 3*u2 *u3*v2 *a11*b12
3 3 3 3 2 2 3 3 3
- 3*u2 *u3 *v1*b12 *kap - 6*u2 *u3 *v2*v3*a11*b12 + 2*u2 *u3*v1 *b12
3 2 3 2 3 2 2 2 3 2 2
+ 3*u2 *u3*v1*v2 *b12 + 3*u2 *u3 *v1 *a11*b12 + 3*u2 *u3 *v2 *a11*b12
2 2 3 3 3 3 3 2 3
+ 6*u2 *u3 *v1*v2*v3*b12 - 3*u2*u3 *v1 *b12 - 3*u2*u3 *v1*v2 *b12
2 2 2 2 2
=u3*((3*((v1 + v2 )*u3 - 2*u2*v2*v3)*u3 - (2*v1 + 3*v2 )*u2
2 2 2
- (3*v1 + 2*v2 )*u1 - 2*(u2*v2 + 3*u3*v3)*u1*v1
2 2 2 2
+ 3*(u1 + u2 )*kap*u3 )*b12
2 2 2 2
- 2*((u1 + u2 )*a11 + 2*(u1*v2 - u2*v1)*b12)*(u1 + u2 )*a11)
2 2
*((u1 + u2 )*a11 + (u1*v2 - u2*v1)*b12)
{HAM,FI} = 0
5 5 6
FI=u1*u3 *v1 + u2*u3 *v2 + u3 *v3
5
=u3 *(u2*v2 + u3*v3 + u1*v1)
{HAM,FI} = 0
2 5 5 2 5 5
FI=u1 *u3 *a11 + u1*u3 *v2*b12 + u2 *u3 *a11 - u2*u3 *v1*b12
5 2 2
=u3 *((u1 + u2 )*a11 + (u1*v2 - u2*v1)*b12)
{HAM,FI} = 0
3 3 2 3 2 4 2 3
FI=u1 *u3 *v1*kap + u1 *u2*u3 *v2*kap + u1 *u3 *v3*kap + u1*u2 *u3 *v1*kap
3 3 3 2 3 2 3 3
+ u1*u3 *v1 + u1*u3 *v1*v2 + u1*u3 *v1*v3 + u2 *u3 *v2*kap
2 4 3 2 3 3 3 2 4 2
+ u2 *u3 *v3*kap + u2*u3 *v1 *v2 + u2*u3 *v2 + u2*u3 *v2*v3 + u3 *v1 *v3
4 2 4 3
+ u3 *v2 *v3 + u3 *v3
3 2 2 2 2 2
=u3 *(v2 + v3 + v1 + (u1 + u2 )*kap)*(u2*v2 + u3*v3 + u1*v1)
{HAM,FI} = 0
5 2 4 2 4 2 2
FI= - u1 *u3*v1*a11*kap - u1 *u2*u3*v2*a11*kap - u1 *u3 *v3*a11*kap
4 2 3 2 2
- 2*u1 *u3*v1*v2*b12*kap - 2*u1 *u2 *u3*v1*a11*kap
3 2 2 3 2 2
+ 2*u1 *u2*u3*v1 *b12*kap - 2*u1 *u2*u3*v2 *b12*kap
3 2 2 2 3 2
- 2*u1 *u3 *v2*v3*b12*kap - 2*u1 *u2 *u3*v2*a11*kap
2 2 2 2 2 2 2
- 2*u1 *u2 *u3 *v3*a11*kap + 2*u1 *u2*u3 *v1*v3*b12*kap
2 3 2 3
- 2*u1 *u3*v1 *v2*b12*kap - 2*u1 *u3*v1*v2 *b12*kap
2 2 4 2
- 2*u1 *u3*v1*v2*v3 *b12*kap - u1*u2 *u3*v1*a11*kap
3 2 2 3 2 2
+ 2*u1*u2 *u3*v1 *b12*kap - 2*u1*u2 *u3*v2 *b12*kap
2 2 2 4
- 2*u1*u2 *u3 *v2*v3*b12*kap + 2*u1*u2*u3*v1 *b12*kap
2 2 4
+ 2*u1*u2*u3*v1 *v3 *b12*kap - 2*u1*u2*u3*v2 *b12*kap
2 2 2 2
- 2*u1*u2*u3*v2 *v3 *b12*kap - 2*u1*u3 *v1 *v2*v3*b12*kap
2 3 2 3 5
- 2*u1*u3 *v2 *v3*b12*kap - 2*u1*u3 *v2*v3 *b12*kap + u1*u3*v1 *a11
3 2 3 2 4
+ 2*u1*u3*v1 *v2 *a11 + 2*u1*u3*v1 *v3 *a11 + u1*u3*v1*v2 *a11
2 2 4 5 2
+ 2*u1*u3*v1*v2 *v3 *a11 + u1*u3*v1*v3 *a11 - u2 *u3*v2*a11*kap
4 2 2 4 2 3 2 2
- u2 *u3 *v3*a11*kap + 2*u2 *u3*v1*v2*b12*kap + 2*u2 *u3 *v1*v3*b12*kap
2 3 2 3
+ 2*u2 *u3*v1 *v2*b12*kap + 2*u2 *u3*v1*v2 *b12*kap
2 2 2 3
+ 2*u2 *u3*v1*v2*v3 *b12*kap + 2*u2*u3 *v1 *v3*b12*kap
2 2 2 3 4
+ 2*u2*u3 *v1*v2 *v3*b12*kap + 2*u2*u3 *v1*v3 *b12*kap + u2*u3*v1 *v2*a11
2 3 2 2 5
+ 2*u2*u3*v1 *v2 *a11 + 2*u2*u3*v1 *v2*v3 *a11 + u2*u3*v2 *a11
3 2 4 2 4
+ 2*u2*u3*v2 *v3 *a11 + u2*u3*v2*v3 *a11 + u3 *v1 *v3*a11
2 2 2 2 2 3 2 4
+ 2*u3 *v1 *v2 *v3*a11 + 2*u3 *v1 *v3 *a11 + u3 *v2 *v3*a11
2 2 3 2 5
+ 2*u3 *v2 *v3 *a11 + u3 *v3 *a11
2 2 2 2 2
=u3*((v2 + v3 + v1 - (u1 + u2 )*kap)*a11 - 2*(u1*v2 - u2*v1)*b12*kap)
2 2 2 2 2
*(v2 + v3 + v1 + (u1 + u2 )*kap)*(u2*v2 + u3*v3 + u1*v1)
{HAM,FI} = 0
3 3 2 2 2 2 2 2 2
FI=u1 *u3*v1 + 3*u1 *u2*u3*v1 *v2 + 3*u1 *u3 *v1 *v3 + 3*u1*u2 *u3*v1*v2
2 3 2 3 3 2 2 2
+ 6*u1*u2*u3 *v1*v2*v3 + 3*u1*u3 *v1*v3 + u2 *u3*v2 + 3*u2 *u3 *v2 *v3
3 2 4 3
+ 3*u2*u3 *v2*v3 + u3 *v3
3
=u3*(u1*v1 + u2*v2 + u3*v3)
{HAM,FI} = 0
6 3 4 2 3 4 2 2 4 2 2
FI=u1 *u3*kap + 3*u1 *u2 *u3*kap + 3*u1 *u3*v1 *kap + 3*u1 *u3*v2 *kap
4 2 2 2 4 3 2 2 2 2
+ 3*u1 *u3*v3 *kap + 3*u1 *u2 *u3*kap + 6*u1 *u2 *u3*v1 *kap
2 2 2 2 2 2 2 2 2 4
+ 6*u1 *u2 *u3*v2 *kap + 6*u1 *u2 *u3*v3 *kap + 3*u1 *u3*v1 *kap
2 2 2 2 2 2 2 4
+ 6*u1 *u3*v1 *v2 *kap + 6*u1 *u3*v1 *v3 *kap + 3*u1 *u3*v2 *kap
2 2 2 2 4 6 3 4 2 2
+ 6*u1 *u3*v2 *v3 *kap + 3*u1 *u3*v3 *kap + u2 *u3*kap + 3*u2 *u3*v1 *kap
4 2 2 4 2 2 2 4
+ 3*u2 *u3*v2 *kap + 3*u2 *u3*v3 *kap + 3*u2 *u3*v1 *kap
2 2 2 2 2 2 2 4
+ 6*u2 *u3*v1 *v2 *kap + 6*u2 *u3*v1 *v3 *kap + 3*u2 *u3*v2 *kap
2 2 2 2 4 6 4 2
+ 6*u2 *u3*v2 *v3 *kap + 3*u2 *u3*v3 *kap + u3*v1 + 3*u3*v1 *v2
4 2 2 4 2 2 2 2 4 6
+ 3*u3*v1 *v3 + 3*u3*v1 *v2 + 6*u3*v1 *v2 *v3 + 3*u3*v1 *v3 + u3*v2
4 2 2 4 6
+ 3*u3*v2 *v3 + 3*u3*v2 *v3 + u3*v3
2 2 2 2 2 3
=u3*(v2 + v3 + v1 + (u1 + u2 )*kap)
{HAM,FI} = 0
2 5 2 5 5 2 5 2 5 2
FI=u1 *u3 *kap + u2 *u3 *kap + u3 *v1 + u3 *v2 + u3 *v3
5 2 2 2 2 2
=u3 *(v2 + v3 + v1 + (u1 + u2 )*kap)
{HAM,FI} = 0
4 3 2 2 2 3 2 2 3 2 2 3 2
FI=u1 *u3 *kap + 2*u1 *u2 *u3 *kap + 2*u1 *u3 *v1 *kap + 2*u1 *u3 *v2 *kap
2 3 2 4 3 2 2 3 2 2 3 2
+ 2*u1 *u3 *v3 *kap + u2 *u3 *kap + 2*u2 *u3 *v1 *kap + 2*u2 *u3 *v2 *kap
2 3 2 3 4 3 2 2 3 2 2 3 4
+ 2*u2 *u3 *v3 *kap + u3 *v1 + 2*u3 *v1 *v2 + 2*u3 *v1 *v3 + u3 *v2
3 2 2 3 4
+ 2*u3 *v2 *v3 + u3 *v3
3 2 2 2 2 2 2
=u3 *(v2 + v3 + v1 + (u1 + u2 )*kap)
{HAM,FI} = 0
And again in machine readable form:
HAM=u1**2*a11 + u1*v2*b12 + u2**2*a11 - u2*v1*b12 + u3**2*a33$
FI= - u1**4*u3**3*a11**2 - 2*u1**3*u3**3*v2*a11*b12 - 2*u1**2*u2**2*u3**3*a11**2
+ 2*u1**2*u2*u3**3*v1*a11*b12 - u1**2*u3**3*v2**2*b12**2 - 2*u1*u2**2*u3**3*v2*
a11*b12 + 2*u1*u2*u3**3*v1*v2*b12**2 - u2**4*u3**3*a11**2 + 2*u2**3*u3**3*v1*a11
*b12 - u2**2*u3**3*v1**2*b12**2$
FI= - u1**6*u3*a11**2*kap**3 - 3*u1**5*u3*v2*a11*b12*kap**3 - 3*u1**4*u2**2*u3*
a11**2*kap**3 + 3*u1**4*u2*u3*v1*a11*b12*kap**3 - 3*u1**4*u3*v2**2*b12**2*kap**3
- 6*u1**3*u2**2*u3*v2*a11*b12*kap**3 + 6*u1**3*u2*u3*v1*v2*b12**2*kap**3 - 3*u1
**2*u2**4*u3*a11**2*kap**3 + 6*u1**2*u2**3*u3*v1*a11*b12*kap**3 - 3*u1**2*u2**2*
u3*v1**2*b12**2*kap**3 - 3*u1**2*u2**2*u3*v2**2*b12**2*kap**3 - 3*u1**2*u3*v1**2
*v2**2*b12**2*kap**2 - 3*u1**2*u3*v2**4*b12**2*kap**2 - 3*u1**2*u3*v2**2*v3**2*
b12**2*kap**2 - 3*u1*u2**4*u3*v2*a11*b12*kap**3 + 6*u1*u2**3*u3*v1*v2*b12**2*kap
**3 + 6*u1*u2*u3*v1**3*v2*b12**2*kap**2 + 6*u1*u2*u3*v1*v2**3*b12**2*kap**2 + 6*
u1*u2*u3*v1*v2*v3**2*b12**2*kap**2 + 3*u1*u3*v1**4*v2*a11*b12*kap + 6*u1*u3*v1**
2*v2**3*a11*b12*kap + 6*u1*u3*v1**2*v2*v3**2*a11*b12*kap + 3*u1*u3*v2**5*a11*b12
*kap + 6*u1*u3*v2**3*v3**2*a11*b12*kap + 3*u1*u3*v2*v3**4*a11*b12*kap - u2**6*u3
*a11**2*kap**3 + 3*u2**5*u3*v1*a11*b12*kap**3 - 3*u2**4*u3*v1**2*b12**2*kap**3 -
3*u2**2*u3*v1**4*b12**2*kap**2 - 3*u2**2*u3*v1**2*v2**2*b12**2*kap**2 - 3*u2**2
*u3*v1**2*v3**2*b12**2*kap**2 - 3*u2*u3*v1**5*a11*b12*kap - 6*u2*u3*v1**3*v2**2*
a11*b12*kap - 6*u2*u3*v1**3*v3**2*a11*b12*kap - 3*u2*u3*v1*v2**4*a11*b12*kap - 6
*u2*u3*v1*v2**2*v3**2*a11*b12*kap - 3*u2*u3*v1*v3**4*a11*b12*kap - u3*v1**6*a11
**2 - 3*u3*v1**4*v2**2*a11**2 - 3*u3*v1**4*v3**2*a11**2 - 3*u3*v1**2*v2**4*a11**
2 - 6*u3*v1**2*v2**2*v3**2*a11**2 - 3*u3*v1**2*v3**4*a11**2 - u3*v2**6*a11**2 -
3*u3*v2**4*v3**2*a11**2 - 3*u3*v2**2*v3**4*a11**2 - u3*v3**6*a11**2$
FI=u1**4*u3**3*a11**2 + 2*u1**3*u3**3*v2*a11*b12 + 2*u1**2*u2**2*u3**3*a11**2 -
2*u1**2*u2*u3**3*v1*a11*b12 + u1**2*u3**3*v1**2*b12**2 + u1**2*u3**3*v2**2*b12**
2 + 2*u1*u2**2*u3**3*v2*a11*b12 + 2*u1*u3**4*v1*v3*b12**2 + u2**4*u3**3*a11**2 -
2*u2**3*u3**3*v1*a11*b12 + u2**2*u3**3*v1**2*b12**2 + u2**2*u3**3*v2**2*b12**2
+ 2*u2*u3**4*v2*v3*b12**2 + u3**5*v3**2*b12**2$
FI=u1**4*u3**3*a11*kap + u1**3*u3**3*v2*b12*kap + 2*u1**2*u2**2*u3**3*a11*kap -
u1**2*u2*u3**3*v1*b12*kap + u1**2*u3**3*v1**2*a11 + u1**2*u3**3*v2**2*a11 + u1**
2*u3**3*v3**2*a11 + u1*u2**2*u3**3*v2*b12*kap + u1*u3**3*v1**2*v2*b12 + u1*u3**3
*v2**3*b12 + u1*u3**3*v2*v3**2*b12 + u2**4*u3**3*a11*kap - u2**3*u3**3*v1*b12*
kap + u2**2*u3**3*v1**2*a11 + u2**2*u3**3*v2**2*a11 + u2**2*u3**3*v3**2*a11 - u2
*u3**3*v1**3*b12 - u2*u3**3*v1*v2**2*b12 - u2*u3**3*v1*v3**2*b12$
FI=u1**6*u3*(a11**2*kap**3 - b12**2*kap**4) + 3*u1**5*u3*v2*a11*b12*kap**3 + u1
**4*u2**2*u3*(3*a11**2*kap**3 - 3*b12**2*kap**4) - 3*u1**4*u2*u3*v1*a11*b12*kap
**3 - 3*u1**4*u3*v3**2*b12**2*kap**3 + 6*u1**3*u2**2*u3*v2*a11*b12*kap**3 + 6*u1
**3*u3**2*v1*v3*b12**2*kap**3 + u1**2*u2**4*u3*(3*a11**2*kap**3 - 3*b12**2*kap**
4) - 6*u1**2*u2**3*u3*v1*a11*b12*kap**3 - 6*u1**2*u2**2*u3*v3**2*b12**2*kap**3 +
6*u1**2*u2*u3**2*v2*v3*b12**2*kap**3 + 3*u1**2*u3**3*v3**2*b12**2*kap**3 - 3*u1
**2*u3*v1**2*v3**2*b12**2*kap**2 - 3*u1**2*u3*v2**2*v3**2*b12**2*kap**2 - 3*u1**
2*u3*v3**4*b12**2*kap**2 + 3*u1*u2**4*u3*v2*a11*b12*kap**3 + 6*u1*u2**2*u3**2*v1
*v3*b12**2*kap**3 + 6*u1*u3**2*v1**3*v3*b12**2*kap**2 + 6*u1*u3**2*v1*v2**2*v3*
b12**2*kap**2 + 6*u1*u3**2*v1*v3**3*b12**2*kap**2 - 3*u1*u3*v1**4*v2*a11*b12*kap
- 6*u1*u3*v1**2*v2**3*a11*b12*kap - 6*u1*u3*v1**2*v2*v3**2*a11*b12*kap - 3*u1*
u3*v2**5*a11*b12*kap - 6*u1*u3*v2**3*v3**2*a11*b12*kap - 3*u1*u3*v2*v3**4*a11*
b12*kap + u2**6*u3*(a11**2*kap**3 - b12**2*kap**4) - 3*u2**5*u3*v1*a11*b12*kap**
3 - 3*u2**4*u3*v3**2*b12**2*kap**3 + 6*u2**3*u3**2*v2*v3*b12**2*kap**3 + 3*u2**2
*u3**3*v3**2*b12**2*kap**3 - 3*u2**2*u3*v1**2*v3**2*b12**2*kap**2 - 3*u2**2*u3*
v2**2*v3**2*b12**2*kap**2 - 3*u2**2*u3*v3**4*b12**2*kap**2 + 6*u2*u3**2*v1**2*v2
*v3*b12**2*kap**2 + 6*u2*u3**2*v2**3*v3*b12**2*kap**2 + 6*u2*u3**2*v2*v3**3*b12
**2*kap**2 + 3*u2*u3*v1**5*a11*b12*kap + 6*u2*u3*v1**3*v2**2*a11*b12*kap + 6*u2*
u3*v1**3*v3**2*a11*b12*kap + 3*u2*u3*v1*v2**4*a11*b12*kap + 6*u2*u3*v1*v2**2*v3
**2*a11*b12*kap + 3*u2*u3*v1*v3**4*a11*b12*kap + 3*u3**3*v1**2*v3**2*b12**2*kap
**2 + 3*u3**3*v2**2*v3**2*b12**2*kap**2 + 3*u3**3*v3**4*b12**2*kap**2 + u3*v1**6
*(a11**2 - b12**2*kap) + u3*v1**4*v2**2*(3*a11**2 - 3*b12**2*kap) + u3*v1**4*v3
**2*(3*a11**2 - 3*b12**2*kap) + u3*v1**2*v2**4*(3*a11**2 - 3*b12**2*kap) + u3*v1
**2*v2**2*v3**2*(6*a11**2 - 6*b12**2*kap) + u3*v1**2*v3**4*(3*a11**2 - 3*b12**2*
kap) + u3*v2**6*(a11**2 - b12**2*kap) + u3*v2**4*v3**2*(3*a11**2 - 3*b12**2*kap)
+ u3*v2**2*v3**4*(3*a11**2 - 3*b12**2*kap) + u3*v3**6*(a11**2 - b12**2*kap)$
FI=u3**7$
FI=3*u1**5*u3*v1*b12**2*kap**3 + 3*u1**4*u2*u3*v2*b12**2*kap**3 + 3*u1**4*u3**2*
v3*b12**2*kap**3 + 6*u1**3*u2**2*u3*v1*b12**2*kap**3 + 4*u1**3*u3*v1**3*b12**2*
kap**2 + 6*u1**3*u3*v1*v3**2*b12**2*kap**2 + 6*u1**2*u2**3*u3*v2*b12**2*kap**3 +
6*u1**2*u2**2*u3**2*v3*b12**2*kap**3 + 12*u1**2*u2*u3*v1**2*v2*b12**2*kap**2 +
6*u1**2*u2*u3*v2*v3**2*b12**2*kap**2 + 6*u1**2*u3**2*v3**3*b12**2*kap**2 + 12*u1
**2*u3*v1**3*v2*a11*b12*kap + 12*u1**2*u3*v1*v2**3*a11*b12*kap + 12*u1**2*u3*v1*
v2*v3**2*a11*b12*kap + 3*u1*u2**4*u3*v1*b12**2*kap**3 + 12*u1*u2**2*u3*v1*v2**2*
b12**2*kap**2 + 6*u1*u2**2*u3*v1*v3**2*b12**2*kap**2 - 12*u1*u2*u3*v1**4*a11*b12
*kap - 12*u1*u2*u3*v1**2*v3**2*a11*b12*kap + 12*u1*u2*u3*v2**4*a11*b12*kap + 12*
u1*u2*u3*v2**2*v3**2*a11*b12*kap - 6*u1*u3**3*v1*v3**2*b12**2*kap**2 + 12*u1*u3
**2*v1**2*v2*v3*a11*b12*kap + 12*u1*u3**2*v2**3*v3*a11*b12*kap + 12*u1*u3**2*v2*
v3**3*a11*b12*kap + u1*u3*v1**5*( - 6*a11**2 + 3*b12**2*kap) + u1*u3*v1**3*v2**2
*( - 12*a11**2 + 6*b12**2*kap) + u1*u3*v1**3*v3**2*( - 12*a11**2 + 6*b12**2*kap)
+ u1*u3*v1*v2**4*( - 6*a11**2 + 3*b12**2*kap) + u1*u3*v1*v2**2*v3**2*( - 12*a11
**2 + 6*b12**2*kap) + u1*u3*v1*v3**4*( - 6*a11**2 + 3*b12**2*kap) + 3*u2**5*u3*
v2*b12**2*kap**3 + 3*u2**4*u3**2*v3*b12**2*kap**3 + 4*u2**3*u3*v2**3*b12**2*kap
**2 + 6*u2**3*u3*v2*v3**2*b12**2*kap**2 + 6*u2**2*u3**2*v3**3*b12**2*kap**2 - 12
*u2**2*u3*v1**3*v2*a11*b12*kap - 12*u2**2*u3*v1*v2**3*a11*b12*kap - 12*u2**2*u3*
v1*v2*v3**2*a11*b12*kap - 6*u2*u3**3*v2*v3**2*b12**2*kap**2 - 12*u2*u3**2*v1**3*
v3*a11*b12*kap - 12*u2*u3**2*v1*v2**2*v3*a11*b12*kap - 12*u2*u3**2*v1*v3**3*a11*
b12*kap + u2*u3*v1**4*v2*( - 6*a11**2 + 3*b12**2*kap) + u2*u3*v1**2*v2**3*( - 12
*a11**2 + 6*b12**2*kap) + u2*u3*v1**2*v2*v3**2*( - 12*a11**2 + 6*b12**2*kap) +
u2*u3*v2**5*( - 6*a11**2 + 3*b12**2*kap) + u2*u3*v2**3*v3**2*( - 12*a11**2 + 6*
b12**2*kap) + u2*u3*v2*v3**4*( - 6*a11**2 + 3*b12**2*kap) - 2*u3**4*v3**3*b12**2
*kap**2 + u3**2*v1**4*v3*( - 6*a11**2 + 3*b12**2*kap) + u3**2*v1**2*v2**2*v3*( -
12*a11**2 + 6*b12**2*kap) + u3**2*v1**2*v3**3*( - 12*a11**2 + 6*b12**2*kap) +
u3**2*v2**4*v3*( - 6*a11**2 + 3*b12**2*kap) + u3**2*v2**2*v3**3*( - 12*a11**2 +
6*b12**2*kap) + u3**2*v3**5*( - 6*a11**2 + 3*b12**2*kap)$
FI=u1**6*u3*( - 2*a11**3*kap**2 + 2*a11*b12**2*kap**3) + u1**5*u3*v2*( - 6*a11**
2*b12*kap**2 + 3*b12**3*kap**3) + u1**4*u2**2*u3*( - 6*a11**3*kap**2 + 6*a11*b12
**2*kap**3) + u1**4*u2*u3*v1*(6*a11**2*b12*kap**2 - 3*b12**3*kap**3) + 3*u1**4*
u3*v1**2*a11*b12**2*kap**2 - 3*u1**4*u3*v2**2*a11*b12**2*kap**2 + 3*u1**4*u3*v3
**2*a11*b12**2*kap**2 + u1**3*u2**2*u3*v2*( - 12*a11**2*b12*kap**2 + 6*b12**3*
kap**3) + 12*u1**3*u2*u3*v1*v2*a11*b12**2*kap**2 + 6*u1**3*u3*v1**2*v2*b12**3*
kap**2 + 4*u1**3*u3*v2**3*b12**3*kap**2 + 6*u1**3*u3*v2*v3**2*b12**3*kap**2 + u1
**2*u2**4*u3*( - 6*a11**3*kap**2 + 6*a11*b12**2*kap**3) + u1**2*u2**3*u3*v1*(12*
a11**2*b12*kap**2 - 6*b12**3*kap**3) + 6*u1**2*u2**2*u3*v3**2*a11*b12**2*kap**2
- 6*u1**2*u2*u3*v1**3*b12**3*kap**2 - 6*u1**2*u2*u3*v1*v3**2*b12**3*kap**2 + u1*
u2**4*u3*v2*( - 6*a11**2*b12*kap**2 + 3*b12**3*kap**3) + 12*u1*u2**3*u3*v1*v2*
a11*b12**2*kap**2 + 6*u1*u2**2*u3*v2**3*b12**3*kap**2 + 6*u1*u2**2*u3*v2*v3**2*
b12**3*kap**2 + 3*u1*u3*v1**4*v2*b12**3*kap + 6*u1*u3*v1**2*v2**3*b12**3*kap + 6
*u1*u3*v1**2*v2*v3**2*b12**3*kap + 3*u1*u3*v2**5*b12**3*kap + 6*u1*u3*v2**3*v3**
2*b12**3*kap + 3*u1*u3*v2*v3**4*b12**3*kap + u2**6*u3*( - 2*a11**3*kap**2 + 2*
a11*b12**2*kap**3) + u2**5*u3*v1*(6*a11**2*b12*kap**2 - 3*b12**3*kap**3) - 3*u2
**4*u3*v1**2*a11*b12**2*kap**2 + 3*u2**4*u3*v2**2*a11*b12**2*kap**2 + 3*u2**4*u3
*v3**2*a11*b12**2*kap**2 - 4*u2**3*u3*v1**3*b12**3*kap**2 - 6*u2**3*u3*v1*v2**2*
b12**3*kap**2 - 6*u2**3*u3*v1*v3**2*b12**3*kap**2 - 3*u2*u3*v1**5*b12**3*kap - 6
*u2*u3*v1**3*v2**2*b12**3*kap - 6*u2*u3*v1**3*v3**2*b12**3*kap - 3*u2*u3*v1*v2**
4*b12**3*kap - 6*u2*u3*v1*v2**2*v3**2*b12**3*kap - 3*u2*u3*v1*v3**4*b12**3*kap -
u3*v1**6*a11*b12**2 - 3*u3*v1**4*v2**2*a11*b12**2 - 3*u3*v1**4*v3**2*a11*b12**2
- 3*u3*v1**2*v2**4*a11*b12**2 - 6*u3*v1**2*v2**2*v3**2*a11*b12**2 - 3*u3*v1**2*
v3**4*a11*b12**2 - u3*v2**6*a11*b12**2 - 3*u3*v2**4*v3**2*a11*b12**2 - 3*u3*v2**
2*v3**4*a11*b12**2 - u3*v3**6*a11*b12**2$
FI= - u1**6*u3*a11**3 - 3*u1**5*u3*v2*a11**2*b12 - 3*u1**4*u2**2*u3*a11**3 + 3*
u1**4*u2*u3*v1*a11**2*b12 - 3*u1**4*u3*v2**2*a11*b12**2 - 6*u1**3*u2**2*u3*v2*
a11**2*b12 + 6*u1**3*u2*u3*v1*v2*a11*b12**2 - u1**3*u3*v2**3*b12**3 - 3*u1**2*u2
**4*u3*a11**3 + 6*u1**2*u2**3*u3*v1*a11**2*b12 - 3*u1**2*u2**2*u3*v1**2*a11*b12
**2 - 3*u1**2*u2**2*u3*v2**2*a11*b12**2 + 3*u1**2*u2*u3*v1*v2**2*b12**3 - 3*u1*
u2**4*u3*v2*a11**2*b12 + 6*u1*u2**3*u3*v1*v2*a11*b12**2 - 3*u1*u2**2*u3*v1**2*v2
*b12**3 - u2**6*u3*a11**3 + 3*u2**5*u3*v1*a11**2*b12 - 3*u2**4*u3*v1**2*a11*b12
**2 + u2**3*u3*v1**3*b12**3$
FI=u1**3*u3*v1*v2**2*b12**2*kap**2 - 2*u1**2*u2*u3*v1**2*v2*b12**2*kap**2 + u1**
2*u2*u3*v2**3*b12**2*kap**2 + u1**2*u3**2*v2**2*v3*b12**2*kap**2 - 2*u1**2*u3*v1
**3*v2*a11*b12*kap - 2*u1**2*u3*v1*v2**3*a11*b12*kap - 2*u1**2*u3*v1*v2*v3**2*
a11*b12*kap + u1*u2**2*u3*v1**3*b12**2*kap**2 - 2*u1*u2**2*u3*v1*v2**2*b12**2*
kap**2 - 2*u1*u2*u3**2*v1*v2*v3*b12**2*kap**2 + 2*u1*u2*u3*v1**4*a11*b12*kap + 2
*u1*u2*u3*v1**2*v3**2*a11*b12*kap - 2*u1*u2*u3*v2**4*a11*b12*kap - 2*u1*u2*u3*v2
**2*v3**2*a11*b12*kap - 2*u1*u3**2*v1**2*v2*v3*a11*b12*kap - 2*u1*u3**2*v2**3*v3
*a11*b12*kap - 2*u1*u3**2*v2*v3**3*a11*b12*kap + u1*u3*v1**5*a11**2 + 2*u1*u3*v1
**3*v2**2*a11**2 + 2*u1*u3*v1**3*v3**2*a11**2 + u1*u3*v1*v2**4*a11**2 + 2*u1*u3*
v1*v2**2*v3**2*a11**2 + u1*u3*v1*v3**4*a11**2 + u2**3*u3*v1**2*v2*b12**2*kap**2
+ u2**2*u3**2*v1**2*v3*b12**2*kap**2 + 2*u2**2*u3*v1**3*v2*a11*b12*kap + 2*u2**2
*u3*v1*v2**3*a11*b12*kap + 2*u2**2*u3*v1*v2*v3**2*a11*b12*kap + 2*u2*u3**2*v1**3
*v3*a11*b12*kap + 2*u2*u3**2*v1*v2**2*v3*a11*b12*kap + 2*u2*u3**2*v1*v3**3*a11*
b12*kap + u2*u3*v1**4*v2*a11**2 + 2*u2*u3*v1**2*v2**3*a11**2 + 2*u2*u3*v1**2*v2*
v3**2*a11**2 + u2*u3*v2**5*a11**2 + 2*u2*u3*v2**3*v3**2*a11**2 + u2*u3*v2*v3**4*
a11**2 + u3**2*v1**4*v3*a11**2 + 2*u3**2*v1**2*v2**2*v3*a11**2 + 2*u3**2*v1**2*
v3**3*a11**2 + u3**2*v2**4*v3*a11**2 + 2*u3**2*v2**2*v3**3*a11**2 + u3**2*v3**5*
a11**2$
FI=u1**3*u3**3*v1*a11 + u1**2*u2*u3**3*v2*a11 + u1**2*u3**4*v3*a11 + u1**2*u3**3
*v1*v2*b12 + u1*u2**2*u3**3*v1*a11 - u1*u2*u3**3*v1**2*b12 + u1*u2*u3**3*v2**2*
b12 + u1*u3**4*v2*v3*b12 + u2**3*u3**3*v2*a11 + u2**2*u3**4*v3*a11 - u2**2*u3**3
*v1*v2*b12 - u2*u3**4*v1*v3*b12$
FI= - 2*u1**6*u3*a11**3 - 6*u1**5*u3*v2*a11**2*b12 - 6*u1**4*u2**2*u3*a11**3 + 6
*u1**4*u2*u3*v1*a11**2*b12 + 3*u1**4*u3**3*a11*b12**2*kap - 3*u1**4*u3*v1**2*a11
*b12**2 - 6*u1**4*u3*v2**2*a11*b12**2 - 12*u1**3*u2**2*u3*v2*a11**2*b12 + 6*u1**
3*u2*u3*v1*v2*a11*b12**2 + 3*u1**3*u3**3*v2*b12**3*kap - 6*u1**3*u3**2*v1*v3*a11
*b12**2 - 3*u1**3*u3*v1**2*v2*b12**3 - 2*u1**3*u3*v2**3*b12**3 - 6*u1**2*u2**4*
u3*a11**3 + 12*u1**2*u2**3*u3*v1*a11**2*b12 + 6*u1**2*u2**2*u3**3*a11*b12**2*kap
- 9*u1**2*u2**2*u3*v1**2*a11*b12**2 - 9*u1**2*u2**2*u3*v2**2*a11*b12**2 - 3*u1
**2*u2*u3**3*v1*b12**3*kap - 6*u1**2*u2*u3**2*v2*v3*a11*b12**2 + 3*u1**2*u2*u3*
v1**3*b12**3 + 3*u1**2*u3**3*v1**2*a11*b12**2 + 3*u1**2*u3**3*v2**2*a11*b12**2 -
6*u1**2*u3**2*v1*v2*v3*b12**3 - 6*u1*u2**4*u3*v2*a11**2*b12 + 6*u1*u2**3*u3*v1*
v2*a11*b12**2 + 3*u1*u2**2*u3**3*v2*b12**3*kap - 6*u1*u2**2*u3**2*v1*v3*a11*b12
**2 - 3*u1*u2**2*u3*v2**3*b12**3 + 6*u1*u2*u3**2*v1**2*v3*b12**3 - 6*u1*u2*u3**2
*v2**2*v3*b12**3 + 3*u1*u3**3*v1**2*v2*b12**3 + 3*u1*u3**3*v2**3*b12**3 - 2*u2**
6*u3*a11**3 + 6*u2**5*u3*v1*a11**2*b12 + 3*u2**4*u3**3*a11*b12**2*kap - 6*u2**4*
u3*v1**2*a11*b12**2 - 3*u2**4*u3*v2**2*a11*b12**2 - 3*u2**3*u3**3*v1*b12**3*kap
- 6*u2**3*u3**2*v2*v3*a11*b12**2 + 2*u2**3*u3*v1**3*b12**3 + 3*u2**3*u3*v1*v2**2
*b12**3 + 3*u2**2*u3**3*v1**2*a11*b12**2 + 3*u2**2*u3**3*v2**2*a11*b12**2 + 6*u2
**2*u3**2*v1*v2*v3*b12**3 - 3*u2*u3**3*v1**3*b12**3 - 3*u2*u3**3*v1*v2**2*b12**3
$
FI=u1*u3**5*v1 + u2*u3**5*v2 + u3**6*v3$
FI=u1**2*u3**5*a11 + u1*u3**5*v2*b12 + u2**2*u3**5*a11 - u2*u3**5*v1*b12$
FI=u1**3*u3**3*v1*kap + u1**2*u2*u3**3*v2*kap + u1**2*u3**4*v3*kap + u1*u2**2*u3
**3*v1*kap + u1*u3**3*v1**3 + u1*u3**3*v1*v2**2 + u1*u3**3*v1*v3**2 + u2**3*u3**
3*v2*kap + u2**2*u3**4*v3*kap + u2*u3**3*v1**2*v2 + u2*u3**3*v2**3 + u2*u3**3*v2
*v3**2 + u3**4*v1**2*v3 + u3**4*v2**2*v3 + u3**4*v3**3$
FI= - u1**5*u3*v1*a11*kap**2 - u1**4*u2*u3*v2*a11*kap**2 - u1**4*u3**2*v3*a11*
kap**2 - 2*u1**4*u3*v1*v2*b12*kap**2 - 2*u1**3*u2**2*u3*v1*a11*kap**2 + 2*u1**3*
u2*u3*v1**2*b12*kap**2 - 2*u1**3*u2*u3*v2**2*b12*kap**2 - 2*u1**3*u3**2*v2*v3*
b12*kap**2 - 2*u1**2*u2**3*u3*v2*a11*kap**2 - 2*u1**2*u2**2*u3**2*v3*a11*kap**2
+ 2*u1**2*u2*u3**2*v1*v3*b12*kap**2 - 2*u1**2*u3*v1**3*v2*b12*kap - 2*u1**2*u3*
v1*v2**3*b12*kap - 2*u1**2*u3*v1*v2*v3**2*b12*kap - u1*u2**4*u3*v1*a11*kap**2 +
2*u1*u2**3*u3*v1**2*b12*kap**2 - 2*u1*u2**3*u3*v2**2*b12*kap**2 - 2*u1*u2**2*u3
**2*v2*v3*b12*kap**2 + 2*u1*u2*u3*v1**4*b12*kap + 2*u1*u2*u3*v1**2*v3**2*b12*kap
- 2*u1*u2*u3*v2**4*b12*kap - 2*u1*u2*u3*v2**2*v3**2*b12*kap - 2*u1*u3**2*v1**2*
v2*v3*b12*kap - 2*u1*u3**2*v2**3*v3*b12*kap - 2*u1*u3**2*v2*v3**3*b12*kap + u1*
u3*v1**5*a11 + 2*u1*u3*v1**3*v2**2*a11 + 2*u1*u3*v1**3*v3**2*a11 + u1*u3*v1*v2**
4*a11 + 2*u1*u3*v1*v2**2*v3**2*a11 + u1*u3*v1*v3**4*a11 - u2**5*u3*v2*a11*kap**2
- u2**4*u3**2*v3*a11*kap**2 + 2*u2**4*u3*v1*v2*b12*kap**2 + 2*u2**3*u3**2*v1*v3
*b12*kap**2 + 2*u2**2*u3*v1**3*v2*b12*kap + 2*u2**2*u3*v1*v2**3*b12*kap + 2*u2**
2*u3*v1*v2*v3**2*b12*kap + 2*u2*u3**2*v1**3*v3*b12*kap + 2*u2*u3**2*v1*v2**2*v3*
b12*kap + 2*u2*u3**2*v1*v3**3*b12*kap + u2*u3*v1**4*v2*a11 + 2*u2*u3*v1**2*v2**3
*a11 + 2*u2*u3*v1**2*v2*v3**2*a11 + u2*u3*v2**5*a11 + 2*u2*u3*v2**3*v3**2*a11 +
u2*u3*v2*v3**4*a11 + u3**2*v1**4*v3*a11 + 2*u3**2*v1**2*v2**2*v3*a11 + 2*u3**2*
v1**2*v3**3*a11 + u3**2*v2**4*v3*a11 + 2*u3**2*v2**2*v3**3*a11 + u3**2*v3**5*a11
$
FI=u1**3*u3*v1**3 + 3*u1**2*u2*u3*v1**2*v2 + 3*u1**2*u3**2*v1**2*v3 + 3*u1*u2**2
*u3*v1*v2**2 + 6*u1*u2*u3**2*v1*v2*v3 + 3*u1*u3**3*v1*v3**2 + u2**3*u3*v2**3 + 3
*u2**2*u3**2*v2**2*v3 + 3*u2*u3**3*v2*v3**2 + u3**4*v3**3$
FI=u1**6*u3*kap**3 + 3*u1**4*u2**2*u3*kap**3 + 3*u1**4*u3*v1**2*kap**2 + 3*u1**4
*u3*v2**2*kap**2 + 3*u1**4*u3*v3**2*kap**2 + 3*u1**2*u2**4*u3*kap**3 + 6*u1**2*
u2**2*u3*v1**2*kap**2 + 6*u1**2*u2**2*u3*v2**2*kap**2 + 6*u1**2*u2**2*u3*v3**2*
kap**2 + 3*u1**2*u3*v1**4*kap + 6*u1**2*u3*v1**2*v2**2*kap + 6*u1**2*u3*v1**2*v3
**2*kap + 3*u1**2*u3*v2**4*kap + 6*u1**2*u3*v2**2*v3**2*kap + 3*u1**2*u3*v3**4*
kap + u2**6*u3*kap**3 + 3*u2**4*u3*v1**2*kap**2 + 3*u2**4*u3*v2**2*kap**2 + 3*u2
**4*u3*v3**2*kap**2 + 3*u2**2*u3*v1**4*kap + 6*u2**2*u3*v1**2*v2**2*kap + 6*u2**
2*u3*v1**2*v3**2*kap + 3*u2**2*u3*v2**4*kap + 6*u2**2*u3*v2**2*v3**2*kap + 3*u2
**2*u3*v3**4*kap + u3*v1**6 + 3*u3*v1**4*v2**2 + 3*u3*v1**4*v3**2 + 3*u3*v1**2*
v2**4 + 6*u3*v1**2*v2**2*v3**2 + 3*u3*v1**2*v3**4 + u3*v2**6 + 3*u3*v2**4*v3**2
+ 3*u3*v2**2*v3**4 + u3*v3**6$
FI=u1**2*u3**5*kap + u2**2*u3**5*kap + u3**5*v1**2 + u3**5*v2**2 + u3**5*v3**2$
FI=u1**4*u3**3*kap**2 + 2*u1**2*u2**2*u3**3*kap**2 + 2*u1**2*u3**3*v1**2*kap + 2
*u1**2*u3**3*v2**2*kap + 2*u1**2*u3**3*v3**2*kap + u2**4*u3**3*kap**2 + 2*u2**2*
u3**3*v1**2*kap + 2*u2**2*u3**3*v2**2*kap + 2*u2**2*u3**3*v3**2*kap + u3**3*v1**
4 + 2*u3**3*v1**2*v2**2 + 2*u3**3*v1**2*v3**2 + u3**3*v2**4 + 2*u3**3*v2**2*v3**
2 + u3**3*v3**4$