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%typeset_mode True

var('xi')

xi_LGL = [-1.0,           \
          -0.87174014851, \
          -0.591700181433,\
          -0.209299217902,\
          0.209299217902, \
          0.591700181433, \
          0.87174014851,  \
          1.0]
(x\displaystyle x, ξ\displaystyle \xi)
#Assigning L_0 and L_1 as the lagrange basis polynomials.
L_0 =     ((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_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_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_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_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_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_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_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_0.simplify_full()
L_1.simplify_full()
L_2.simplify_full()
L_3.simplify_full()
L_4.simplify_full()
L_5.simplify_full()
L_6.simplify_full()
L_7.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
import numpy as np

xi_set = np.linspace(-1, 1, 10)

for xi_ in xi_set:
    print L_0(xi = xi_),
print '\n'
for xi_ in xi_set:
    print L_1(xi = xi_),
print '\n'
for xi_ in xi_set:
    print L_2(xi = xi_),
1.00000000000000 -0.132053542476430 0.0258385534173595 0.0466392318246838 -0.0295830894993247 -0.0236664715994598 0.0233196159123419 0.00738244383353131 -0.0165066928095537 0.000000000000000 0.000000000000000 0.758576206458160 -0.0882186919073414 -0.140270136955740 0.0839718544026725 0.0649858563619554 -0.0626703672768669 -0.0195428257173647 0.0432111816452180 -0.000000000000000 -0.000000000000000 0.487391303737210 0.981920359634066 0.371926962822827 -0.169103048286541 -0.115634278542167 0.103881206003751 0.0309356866966560 -0.0662242146131606 0.000000000000000