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%typeset_mode True

var('xi, eta')

x_nodes = [-1, 1]
xi_LGL = [-1.0,           \
          -0.87174014851, \
          -0.591700181433,\
          -0.209299217902,\
          0.209299217902, \
          0.591700181433, \
          0.87174014851,  \
          1.0]

eta_LGL = [-1.0,          \
          -0.87174014851, \
          -0.591700181433,\
          -0.209299217902,\
          0.209299217902, \
          0.591700181433, \
          0.87174014851,  \
          1.0]
(ξ\displaystyle \xi, η\displaystyle \eta)
#L_i(\xi)
L_0_xi =  ((xi - (xi_LGL[1])) / (xi_LGL[0] - xi_LGL[1]))\
        * ((xi - (xi_LGL[2])) / (xi_LGL[0] - xi_LGL[2]))\
        * ((xi - (xi_LGL[3])) / (xi_LGL[0] - xi_LGL[3]))\
        * ((xi - (xi_LGL[4])) / (xi_LGL[0] - xi_LGL[4]))\
        * ((xi - (xi_LGL[5])) / (xi_LGL[0] - xi_LGL[5]))\
        * ((xi - (xi_LGL[6])) / (xi_LGL[0] - xi_LGL[6]))\
        * ((xi - (xi_LGL[7])) / (xi_LGL[0] - xi_LGL[7]))

L_1_xi =  ((xi - (xi_LGL[0])) / (xi_LGL[1] - xi_LGL[0]))\
        * ((xi - (xi_LGL[2])) / (xi_LGL[1] - xi_LGL[2]))\
        * ((xi - (xi_LGL[3])) / (xi_LGL[1] - xi_LGL[3]))\
        * ((xi - (xi_LGL[4])) / (xi_LGL[1] - xi_LGL[4]))\
        * ((xi - (xi_LGL[5])) / (xi_LGL[1] - xi_LGL[5]))\
        * ((xi - (xi_LGL[6])) / (xi_LGL[1] - xi_LGL[6]))\
        * ((xi - (xi_LGL[7])) / (xi_LGL[1] - xi_LGL[7]))
        
L_2_xi =  ((xi - (xi_LGL[0])) / (xi_LGL[2] - xi_LGL[0])) \
        * ((xi - (xi_LGL[1])) / (xi_LGL[2] - xi_LGL[1])) \
        * ((xi - (xi_LGL[3])) / (xi_LGL[2] - xi_LGL[3])) \
        * ((xi - (xi_LGL[4])) / (xi_LGL[2] - xi_LGL[4])) \
        * ((xi - (xi_LGL[5])) / (xi_LGL[2] - xi_LGL[5])) \
        * ((xi - (xi_LGL[6])) / (xi_LGL[2] - xi_LGL[6])) \
        * ((xi - (xi_LGL[7])) / (xi_LGL[2] - xi_LGL[7]))

L_3_xi =  ((xi - (xi_LGL[0])) / (xi_LGL[3] - xi_LGL[0])) \
        * ((xi - (xi_LGL[1])) / (xi_LGL[3] - xi_LGL[1])) \
        * ((xi - (xi_LGL[2])) / (xi_LGL[3] - xi_LGL[2])) \
        * ((xi - (xi_LGL[4])) / (xi_LGL[3] - xi_LGL[4])) \
        * ((xi - (xi_LGL[5])) / (xi_LGL[3] - xi_LGL[5])) \
        * ((xi - (xi_LGL[6])) / (xi_LGL[3] - xi_LGL[6])) \
        * ((xi - (xi_LGL[7])) / (xi_LGL[3] - xi_LGL[7]))
        
L_4_xi =  ((xi - (xi_LGL[0])) / (xi_LGL[4] - xi_LGL[0])) \
        * ((xi - (xi_LGL[1])) / (xi_LGL[4] - xi_LGL[1])) \
        * ((xi - (xi_LGL[2])) / (xi_LGL[4] - xi_LGL[2])) \
        * ((xi - (xi_LGL[3])) / (xi_LGL[4] - xi_LGL[3])) \
        * ((xi - (xi_LGL[5])) / (xi_LGL[4] - xi_LGL[5])) \
        * ((xi - (xi_LGL[6])) / (xi_LGL[4] - xi_LGL[6])) \
        * ((xi - (xi_LGL[7])) / (xi_LGL[4] - xi_LGL[7]))


L_5_xi =  ((xi - (xi_LGL[0])) / (xi_LGL[5] - xi_LGL[0])) \
        * ((xi - (xi_LGL[1])) / (xi_LGL[5] - xi_LGL[1])) \
        * ((xi - (xi_LGL[2])) / (xi_LGL[5] - xi_LGL[2])) \
        * ((xi - (xi_LGL[3])) / (xi_LGL[5] - xi_LGL[3])) \
        * ((xi - (xi_LGL[4])) / (xi_LGL[5] - xi_LGL[4])) \
        * ((xi - (xi_LGL[6])) / (xi_LGL[5] - xi_LGL[6])) \
        * ((xi - (xi_LGL[7])) / (xi_LGL[5] - xi_LGL[7]))
        
L_6_xi =  ((xi - (xi_LGL[0])) / (xi_LGL[6] - xi_LGL[0])) \
        * ((xi - (xi_LGL[1])) / (xi_LGL[6] - xi_LGL[1])) \
        * ((xi - (xi_LGL[2])) / (xi_LGL[6] - xi_LGL[2])) \
        * ((xi - (xi_LGL[3])) / (xi_LGL[6] - xi_LGL[3])) \
        * ((xi - (xi_LGL[4])) / (xi_LGL[6] - xi_LGL[4])) \
        * ((xi - (xi_LGL[5])) / (xi_LGL[6] - xi_LGL[5])) \
        * ((xi - (xi_LGL[7])) / (xi_LGL[6] - xi_LGL[7]))
        

L_7_xi =  ((xi - (xi_LGL[0])) / (xi_LGL[7] - xi_LGL[0])) \
        * ((xi - (xi_LGL[1])) / (xi_LGL[7] - xi_LGL[1])) \
        * ((xi - (xi_LGL[2])) / (xi_LGL[7] - xi_LGL[2])) \
        * ((xi - (xi_LGL[3])) / (xi_LGL[7] - xi_LGL[3])) \
        * ((xi - (xi_LGL[4])) / (xi_LGL[7] - xi_LGL[4])) \
        * ((xi - (xi_LGL[5])) / (xi_LGL[7] - xi_LGL[5])) \
        * ((xi - (xi_LGL[6])) / (xi_LGL[7] - xi_LGL[6])) \
        
# L_i(\eta)
L_0_eta = ((eta - (xi_LGL[1])) / (xi_LGL[0] - eta_LGL[1]))\
        * ((eta - (xi_LGL[2])) / (xi_LGL[0] - eta_LGL[2]))\
        * ((eta - (xi_LGL[3])) / (xi_LGL[0] - eta_LGL[3]))\
        * ((eta - (xi_LGL[4])) / (xi_LGL[0] - eta_LGL[4]))\
        * ((eta - (xi_LGL[5])) / (xi_LGL[0] - eta_LGL[5]))\
        * ((eta - (xi_LGL[6])) / (xi_LGL[0] - eta_LGL[6]))\
        * ((eta - (xi_LGL[7])) / (xi_LGL[0] - eta_LGL[7]))

L_1_eta = ((eta - (xi_LGL[0])) / (xi_LGL[1] - eta_LGL[0]))\
        * ((eta - (xi_LGL[2])) / (xi_LGL[1] - eta_LGL[2]))\
        * ((eta - (xi_LGL[3])) / (xi_LGL[1] - eta_LGL[3]))\
        * ((eta - (xi_LGL[4])) / (xi_LGL[1] - eta_LGL[4]))\
        * ((eta - (xi_LGL[5])) / (xi_LGL[1] - eta_LGL[5]))\
        * ((eta - (xi_LGL[6])) / (xi_LGL[1] - eta_LGL[6]))\
        * ((eta - (xi_LGL[7])) / (xi_LGL[1] - eta_LGL[7]))
        
L_2_eta = ((eta - (xi_LGL[0])) / (xi_LGL[2] - eta_LGL[0])) \
        * ((eta - (xi_LGL[1])) / (xi_LGL[2] - eta_LGL[1])) \
        * ((eta - (xi_LGL[3])) / (xi_LGL[2] - eta_LGL[3])) \
        * ((eta - (xi_LGL[4])) / (xi_LGL[2] - eta_LGL[4])) \
        * ((eta - (xi_LGL[5])) / (xi_LGL[2] - eta_LGL[5])) \
        * ((eta - (xi_LGL[6])) / (xi_LGL[2] - eta_LGL[6])) \
        * ((eta - (xi_LGL[7])) / (xi_LGL[2] - eta_LGL[7]))

L_3_eta = ((eta - (xi_LGL[0])) / (xi_LGL[3] - eta_LGL[0])) \
        * ((eta - (xi_LGL[1])) / (xi_LGL[3] - eta_LGL[1])) \
        * ((eta - (xi_LGL[2])) / (xi_LGL[3] - eta_LGL[2])) \
        * ((eta - (xi_LGL[4])) / (xi_LGL[3] - eta_LGL[4])) \
        * ((eta - (xi_LGL[5])) / (xi_LGL[3] - eta_LGL[5])) \
        * ((eta - (xi_LGL[6])) / (xi_LGL[3] - eta_LGL[6])) \
        * ((eta - (xi_LGL[7])) / (xi_LGL[3] - eta_LGL[7]))
        
L_4_eta = ((eta - (xi_LGL[0])) / (xi_LGL[4] - eta_LGL[0])) \
        * ((eta - (xi_LGL[1])) / (xi_LGL[4] - eta_LGL[1])) \
        * ((eta - (xi_LGL[2])) / (xi_LGL[4] - eta_LGL[2])) \
        * ((eta - (xi_LGL[3])) / (xi_LGL[4] - eta_LGL[3])) \
        * ((eta - (xi_LGL[5])) / (xi_LGL[4] - eta_LGL[5])) \
        * ((eta - (xi_LGL[6])) / (xi_LGL[4] - eta_LGL[6])) \
        * ((eta - (xi_LGL[7])) / (xi_LGL[4] - eta_LGL[7]))


L_5_eta = ((eta - (xi_LGL[0])) / (xi_LGL[5] - eta_LGL[0])) \
        * ((eta - (xi_LGL[1])) / (xi_LGL[5] - eta_LGL[1])) \
        * ((eta - (xi_LGL[2])) / (xi_LGL[5] - eta_LGL[2])) \
        * ((eta - (xi_LGL[3])) / (xi_LGL[5] - eta_LGL[3])) \
        * ((eta - (xi_LGL[4])) / (xi_LGL[5] - eta_LGL[4])) \
        * ((eta - (xi_LGL[6])) / (xi_LGL[5] - eta_LGL[6])) \
        * ((eta - (xi_LGL[7])) / (xi_LGL[5] - eta_LGL[7]))
        
L_6_eta = ((eta - (xi_LGL[0])) / (xi_LGL[6] - eta_LGL[0])) \
        * ((eta - (xi_LGL[1])) / (xi_LGL[6] - eta_LGL[1])) \
        * ((eta - (xi_LGL[2])) / (xi_LGL[6] - eta_LGL[2])) \
        * ((eta - (xi_LGL[3])) / (xi_LGL[6] - eta_LGL[3])) \
        * ((eta - (xi_LGL[4])) / (xi_LGL[6] - eta_LGL[4])) \
        * ((eta - (xi_LGL[5])) / (xi_LGL[6] - eta_LGL[5])) \
        * ((eta - (xi_LGL[7])) / (xi_LGL[6] - eta_LGL[7]))
        

L_7_eta = ((eta - (xi_LGL[0])) / (xi_LGL[7] - eta_LGL[0])) \
        * ((eta - (xi_LGL[1])) / (xi_LGL[7] - eta_LGL[1])) \
        * ((eta - (xi_LGL[2])) / (xi_LGL[7] - eta_LGL[2])) \
        * ((eta - (xi_LGL[3])) / (xi_LGL[7] - eta_LGL[3])) \
        * ((eta - (xi_LGL[4])) / (xi_LGL[7] - eta_LGL[4])) \
        * ((eta - (xi_LGL[5])) / (xi_LGL[7] - eta_LGL[5])) \
        * ((eta - (xi_LGL[6])) / (xi_LGL[7] - eta_LGL[6])) \

L_0_xi.simplify_full()
L_1_xi.simplify_full()
L_2_xi.simplify_full()
L_3_xi.simplify_full()
L_4_xi.simplify_full()
L_5_xi.simplify_full()
L_6_xi.simplify_full()
L_7_xi.simplify_full()

L_0_eta.simplify_full()
L_1_eta.simplify_full()
L_2_eta.simplify_full()
L_3_eta.simplify_full()
L_4_eta.simplify_full()
L_5_eta.simplify_full()
L_6_eta.simplify_full()
L_7_eta.simplify_full()
−3.35156250001 ξ7+3.35156250001 ξ6+3.86718750001 ξ5−3.86718750001 ξ4−1.0546875 ξ3+1.0546875 ξ2+0.0390624999999 ξ−0.0390624999999\displaystyle -3.35156250001 \, \xi^{7} + 3.35156250001 \, \xi^{6} + 3.86718750001 \, \xi^{5} - 3.86718750001 \, \xi^{4} - 1.0546875 \, \xi^{3} + 1.0546875 \, \xi^{2} + 0.0390624999999 \, \xi - 0.0390624999999
8.14072271825 ξ7−7.09659483138 ξ6−11.347477684 ξ5+9.89205188146 ξ4+3.33160871212 ξ3−2.90429707348 ξ2−0.124853746365 ξ+0.108840023398\displaystyle 8.14072271825 \, \xi^{7} - 7.09659483138 \, \xi^{6} - 11.347477684 \, \xi^{5} + 9.89205188146 \, \xi^{4} + 3.33160871212 \, \xi^{3} - 2.90429707348 \, \xi^{2} - 0.124853746365 \, \xi + 0.108840023398
−10.3581368289 ξ7+6.12891144098 ξ6+18.6833551584 ξ5−11.054944637 ξ4−8.6700371412 ξ3+5.13006254948 ξ2+0.34481881174 ξ−0.204029353468\displaystyle -10.3581368289 \, \xi^{7} + 6.12891144098 \, \xi^{6} + 18.6833551584 \, \xi^{5} - 11.054944637 \, \xi^{4} - 8.6700371412 \, \xi^{3} + 5.13006254948 \, \xi^{2} + 0.34481881174 \, \xi - 0.204029353468
11.3898137485 ξ7−2.38387910961 ξ6−24.032962502 ξ5+5.03008025554 ξ4+15.6735080469 ξ3−3.280452976 ξ2−3.0303592934 ξ+0.63425183007\displaystyle 11.3898137485 \, \xi^{7} - 2.38387910961 \, \xi^{6} - 24.032962502 \, \xi^{5} + 5.03008025554 \, \xi^{4} + 15.6735080469 \, \xi^{3} - 3.280452976 \, \xi^{2} - 3.0303592934 \, \xi + 0.63425183007
−11.3898137485 ξ7−2.38387910961 ξ6+24.032962502 ξ5+5.03008025554 ξ4−15.6735080469 ξ3−3.280452976 ξ2+3.0303592934 ξ+0.63425183007\displaystyle -11.3898137485 \, \xi^{7} - 2.38387910961 \, \xi^{6} + 24.032962502 \, \xi^{5} + 5.03008025554 \, \xi^{4} - 15.6735080469 \, \xi^{3} - 3.280452976 \, \xi^{2} + 3.0303592934 \, \xi + 0.63425183007
10.3581368289 ξ7+6.12891144098 ξ6−18.6833551584 ξ5−11.054944637 ξ4+8.6700371412 ξ3+5.13006254948 ξ2−0.34481881174 ξ−0.204029353468\displaystyle 10.3581368289 \, \xi^{7} + 6.12891144098 \, \xi^{6} - 18.6833551584 \, \xi^{5} - 11.054944637 \, \xi^{4} + 8.6700371412 \, \xi^{3} + 5.13006254948 \, \xi^{2} - 0.34481881174 \, \xi - 0.204029353468
−8.14072271825 ξ7−7.09659483138 ξ6+11.347477684 ξ5+9.89205188146 ξ4−3.33160871212 ξ3−2.90429707348 ξ2+0.124853746365 ξ+0.108840023398\displaystyle -8.14072271825 \, \xi^{7} - 7.09659483138 \, \xi^{6} + 11.347477684 \, \xi^{5} + 9.89205188146 \, \xi^{4} - 3.33160871212 \, \xi^{3} - 2.90429707348 \, \xi^{2} + 0.124853746365 \, \xi + 0.108840023398
3.35156250001 ξ7+3.35156250001 ξ6−3.86718750001 ξ5−3.86718750001 ξ4+1.0546875 ξ3+1.0546875 ξ2−0.0390624999999 ξ−0.0390624999999\displaystyle 3.35156250001 \, \xi^{7} + 3.35156250001 \, \xi^{6} - 3.86718750001 \, \xi^{5} - 3.86718750001 \, \xi^{4} + 1.0546875 \, \xi^{3} + 1.0546875 \, \xi^{2} - 0.0390624999999 \, \xi - 0.0390624999999
−3.35156250001 η7+3.35156250001 η6+3.86718750001 η5−3.86718750001 η4−1.0546875 η3+1.0546875 η2+0.0390624999999 η−0.0390624999999\displaystyle -3.35156250001 \, \eta^{7} + 3.35156250001 \, \eta^{6} + 3.86718750001 \, \eta^{5} - 3.86718750001 \, \eta^{4} - 1.0546875 \, \eta^{3} + 1.0546875 \, \eta^{2} + 0.0390624999999 \, \eta - 0.0390624999999
8.14072271825 η7−7.09659483138 η6−11.347477684 η5+9.89205188146 η4+3.33160871212 η3−2.90429707348 η2−0.124853746365 η+0.108840023398\displaystyle 8.14072271825 \, \eta^{7} - 7.09659483138 \, \eta^{6} - 11.347477684 \, \eta^{5} + 9.89205188146 \, \eta^{4} + 3.33160871212 \, \eta^{3} - 2.90429707348 \, \eta^{2} - 0.124853746365 \, \eta + 0.108840023398
−10.3581368289 η7+6.12891144098 η6+18.6833551584 η5−11.054944637 η4−8.6700371412 η3+5.13006254948 η2+0.34481881174 η−0.204029353468\displaystyle -10.3581368289 \, \eta^{7} + 6.12891144098 \, \eta^{6} + 18.6833551584 \, \eta^{5} - 11.054944637 \, \eta^{4} - 8.6700371412 \, \eta^{3} + 5.13006254948 \, \eta^{2} + 0.34481881174 \, \eta - 0.204029353468
11.3898137485 η7−2.38387910961 η6−24.032962502 η5+5.03008025554 η4+15.6735080469 η3−3.280452976 η2−3.0303592934 η+0.63425183007\displaystyle 11.3898137485 \, \eta^{7} - 2.38387910961 \, \eta^{6} - 24.032962502 \, \eta^{5} + 5.03008025554 \, \eta^{4} + 15.6735080469 \, \eta^{3} - 3.280452976 \, \eta^{2} - 3.0303592934 \, \eta + 0.63425183007
−11.3898137485 η7−2.38387910961 η6+24.032962502 η5+5.03008025554 η4−15.6735080469 η3−3.280452976 η2+3.0303592934 η+0.63425183007\displaystyle -11.3898137485 \, \eta^{7} - 2.38387910961 \, \eta^{6} + 24.032962502 \, \eta^{5} + 5.03008025554 \, \eta^{4} - 15.6735080469 \, \eta^{3} - 3.280452976 \, \eta^{2} + 3.0303592934 \, \eta + 0.63425183007
10.3581368289 η7+6.12891144098 η6−18.6833551584 η5−11.054944637 η4+8.6700371412 η3+5.13006254948 η2−0.34481881174 η−0.204029353468\displaystyle 10.3581368289 \, \eta^{7} + 6.12891144098 \, \eta^{6} - 18.6833551584 \, \eta^{5} - 11.054944637 \, \eta^{4} + 8.6700371412 \, \eta^{3} + 5.13006254948 \, \eta^{2} - 0.34481881174 \, \eta - 0.204029353468
−8.14072271825 η7−7.09659483138 η6+11.347477684 η5+9.89205188146 η4−3.33160871212 η3−2.90429707348 η2+0.124853746365 η+0.108840023398\displaystyle -8.14072271825 \, \eta^{7} - 7.09659483138 \, \eta^{6} + 11.347477684 \, \eta^{5} + 9.89205188146 \, \eta^{4} - 3.33160871212 \, \eta^{3} - 2.90429707348 \, \eta^{2} + 0.124853746365 \, \eta + 0.108840023398
3.35156250001 η7+3.35156250001 η6−3.86718750001 η5−3.86718750001 η4+1.0546875 η3+1.0546875 η2−0.0390624999999 η−0.0390624999999\displaystyle 3.35156250001 \, \eta^{7} + 3.35156250001 \, \eta^{6} - 3.86718750001 \, \eta^{5} - 3.86718750001 \, \eta^{4} + 1.0546875 \, \eta^{3} + 1.0546875 \, \eta^{2} - 0.0390624999999 \, \eta - 0.0390624999999
L_0_xi_eta = L_0_xi * L_0_eta
L_0_xi_eta.simplify_full()
(11.2329711915 η7−11.2329711915 η6−12.9611206055 η5+12.9611206055 η4+3.53485107423 η3−3.53485107423 η2−0.130920410156 η+0.130920410156)ξ7+0.130920410156 η7+(−11.2329711915 η7+11.2329711915 η6+12.9611206055 η5−12.9611206055 η4−3.53485107423 η3+3.53485107423 η2+0.130920410156 η−0.130920410156)ξ6−0.130920410156 η6+(−12.9611206055 η7+12.9611206055 η6+14.9551391602 η5−14.9551391602 η4−4.07867431643 η3+4.07867431643 η2+0.151062011719 η−0.151062011719)ξ5−0.151062011719 η5+(12.9611206055 η7−12.9611206055 η6−14.9551391602 η5+14.9551391602 η4+4.07867431643 η3−4.07867431643 η2−0.151062011719 η+0.151062011719)ξ4+0.151062011719 η4+(3.53485107423 η7−3.53485107423 η6−4.07867431643 η5+4.07867431643 η4+1.11236572266 η3−1.11236572266 η2−0.0411987304688 η+0.0411987304688)ξ3+0.0411987304688 η3+(−3.53485107423 η7+3.53485107423 η6+4.07867431643 η5−4.07867431643 η4−1.11236572266 η3+1.11236572266 η2+0.0411987304688 η−0.0411987304688)ξ2−0.0411987304688 η2+(−0.130920410156 η7+0.130920410156 η6+0.151062011719 η5−0.151062011719 η4−0.0411987304688 η3+0.0411987304688 η2+0.00152587890624 η−0.00152587890624)ξ−0.00152587890624 η+0.00152587890624\displaystyle {\left(11.2329711915 \, \eta^{7} - 11.2329711915 \, \eta^{6} - 12.9611206055 \, \eta^{5} + 12.9611206055 \, \eta^{4} + 3.53485107423 \, \eta^{3} - 3.53485107423 \, \eta^{2} - 0.130920410156 \, \eta + 0.130920410156\right)} \xi^{7} + 0.130920410156 \, \eta^{7} + {\left(-11.2329711915 \, \eta^{7} + 11.2329711915 \, \eta^{6} + 12.9611206055 \, \eta^{5} - 12.9611206055 \, \eta^{4} - 3.53485107423 \, \eta^{3} + 3.53485107423 \, \eta^{2} + 0.130920410156 \, \eta - 0.130920410156\right)} \xi^{6} - 0.130920410156 \, \eta^{6} + {\left(-12.9611206055 \, \eta^{7} + 12.9611206055 \, \eta^{6} + 14.9551391602 \, \eta^{5} - 14.9551391602 \, \eta^{4} - 4.07867431643 \, \eta^{3} + 4.07867431643 \, \eta^{2} + 0.151062011719 \, \eta - 0.151062011719\right)} \xi^{5} - 0.151062011719 \, \eta^{5} + {\left(12.9611206055 \, \eta^{7} - 12.9611206055 \, \eta^{6} - 14.9551391602 \, \eta^{5} + 14.9551391602 \, \eta^{4} + 4.07867431643 \, \eta^{3} - 4.07867431643 \, \eta^{2} - 0.151062011719 \, \eta + 0.151062011719\right)} \xi^{4} + 0.151062011719 \, \eta^{4} + {\left(3.53485107423 \, \eta^{7} - 3.53485107423 \, \eta^{6} - 4.07867431643 \, \eta^{5} + 4.07867431643 \, \eta^{4} + 1.11236572266 \, \eta^{3} - 1.11236572266 \, \eta^{2} - 0.0411987304688 \, \eta + 0.0411987304688\right)} \xi^{3} + 0.0411987304688 \, \eta^{3} + {\left(-3.53485107423 \, \eta^{7} + 3.53485107423 \, \eta^{6} + 4.07867431643 \, \eta^{5} - 4.07867431643 \, \eta^{4} - 1.11236572266 \, \eta^{3} + 1.11236572266 \, \eta^{2} + 0.0411987304688 \, \eta - 0.0411987304688\right)} \xi^{2} - 0.0411987304688 \, \eta^{2} + {\left(-0.130920410156 \, \eta^{7} + 0.130920410156 \, \eta^{6} + 0.151062011719 \, \eta^{5} - 0.151062011719 \, \eta^{4} - 0.0411987304688 \, \eta^{3} + 0.0411987304688 \, \eta^{2} + 0.00152587890624 \, \eta - 0.00152587890624\right)} \xi - 0.00152587890624 \, \eta + 0.00152587890624