code: def eqs_10x8():
      return [
          (a_33 * a_34 + a_33 * a_44 + a_43 * a_44) * x3
          + (a_33 * a_34 + a_33 * a_44 + a_43 * a_44) * x4
          + (a_12 * a_34 + a_12 * a_44 + a_22 * a_34 + a_22 * a_44) * x5
          + (a_12 * a_44 + a_22 * a_44) * x6
          + (a_12 * a_33 + a_22 * a_33) * x7
          - a_12 * a_33
          - a_12 * a_43
          - a_22 * a_33
          - a_22 * a_43,
          (a_33 + a_34 + a_43 + a_44) * x3
          + (a_33 + a_34 + a_43 + a_44) * x4
          + (a_12 + a_22 + a_34 + a_44) * x5
          + (a_12 + a_22 + a_44) * x6
          + (a_12 + a_22 + a_33) * x7
          - a_12
          - a_22
          - a_33
          - a_43,
          x3 + x4 + x5 + x6 + x7 - 1,
          (
              a_12 * a_33 * a_34
              + a_12 * a_33 * a_44
              + a_12 * a_43 * a_44
              + a_22 * a_33 * a_34
              + a_22 * a_33 * a_44
              + a_22 * a_43 * a_44
          )
          * x0
          + (
              a_22 * a_33 * a_34
              + a_22 * a_33 * a_44
              + a_22 * a_43 * a_44
          )
          * x1
          + (
              a_12 * a_33 * a_34
              + a_12 * a_33 * a_44
              + a_12 * a_43 * a_44
              + a_22 * a_33 * a_34
              + a_22 * a_33 * a_44
              + a_22 * a_43 * a_44
          )
          * x2
          + (
              a_11 * a_33 * a_34
              + a_11 * a_33 * a_44
              + a_11 * a_43 * a_44
              + a_31 * a_33 * a_34
              + a_31 * a_33 * a_44
              + a_31 * a_43 * a_44
          )
          * x3
          + (
              a_11 * a_33 * a_34
              + a_11 * a_33 * a_44
              + a_11 * a_43 * a_44
              + a_21 * a_33 * a_34
              + a_21 * a_33 * a_44
              + a_21 * a_43 * a_44
              + a_31 * a_33 * a_34
              + a_31 * a_33 * a_44
              + a_31 * a_43 * a_44
          )
          * x4
          + (
              a_11 * a_12 * a_34
              + a_11 * a_12 * a_44
              + a_11 * a_22 * a_34
              + a_11 * a_22 * a_44
              + a_12 * a_31 * a_34
              + a_12 * a_31 * a_44
              + a_21 * a_22 * a_34
              + a_21 * a_22 * a_44
              + a_22 * a_31 * a_34
              + a_22 * a_31 * a_44
          )
          * x5
          + (
              a_11 * a_12 * a_44
              + a_11 * a_22 * a_44
              + a_12 * a_31 * a_44
              + a_21 * a_22 * a_44
              + a_22 * a_31 * a_44
          )
          * x6
          + (
              a_11 * a_12 * a_33
              + a_11 * a_22 * a_33
              + a_12 * a_31 * a_33
              + a_21 * a_22 * a_33
              + a_22 * a_31 * a_33
          )
          * x7
          - a_11 * a_12 * a_33
          - a_11 * a_12 * a_43
          - a_11 * a_22 * a_33
          - a_11 * a_22 * a_43
          - a_12 * a_31 * a_33
          - a_12 * a_31 * a_43
          - a_21 * a_22 * a_33
          - a_21 * a_22 * a_43
          - a_22 * a_31 * a_33
          - a_22 * a_31 * a_43,
          (
              a_12 * a_33
              + a_12 * a_34
              + a_12 * a_43
              + a_12 * a_44
              + a_22 * a_33
              + a_22 * a_34
              + a_22 * a_43
              + a_22 * a_44
              + a_33 * a_34
              + a_33 * a_44
              + a_43 * a_44
          )
          * x0
          + (
              a_22 * a_33
              + a_22 * a_34
              + a_22 * a_43
              + a_22 * a_44
              + a_33 * a_34
              + a_33 * a_44
              + a_43 * a_44
          )
          * x1
          + (
              a_12 * a_33
              + a_12 * a_34
              + a_12 * a_43
              + a_12 * a_44
              + a_22 * a_33
              + a_22 * a_34
              + a_22 * a_43
              + a_22 * a_44
              + a_33 * a_34
              + a_33 * a_44
              + a_43 * a_44
          )
          * x2
          + (
              a_11 * a_33
              + a_11 * a_34
              + a_11 * a_43
              + a_11 * a_44
              + a_31 * a_33
              + a_31 * a_34
              + a_31 * a_43
              + a_31 * a_44
              + a_33 * a_34
              + a_33 * a_44
              + a_43 * a_44
          )
          * x3
          + (
              a_11 * a_33
              + a_11 * a_34
              + a_11 * a_43
              + a_11 * a_44
              + a_21 * a_33
              + a_21 * a_34
              + a_21 * a_43
              + a_21 * a_44
              + a_31 * a_33
              + a_31 * a_34
              + a_31 * a_43
              + a_31 * a_44
              + a_33 * a_34
              + a_33 * a_44
              + a_43 * a_44
          )
          * x4
          + (
              a_11 * a_12
              + a_11 * a_22
              + a_11 * a_34
              + a_11 * a_44
              + a_12 * a_31
              + a_12 * a_34
              + a_12 * a_44
              + a_21 * a_22
              + a_21 * a_34
              + a_21 * a_44
              + a_22 * a_31
              + a_22 * a_34
              + a_22 * a_44
              + a_31 * a_34
              + a_31 * a_44
          )
          * x5
          + (
              a_11 * a_12
              + a_11 * a_22
              + a_11 * a_44
              + a_12 * a_31
              + a_12 * a_44
              + a_21 * a_22
              + a_21 * a_44
              + a_22 * a_31
              + a_22 * a_44
              + a_31 * a_44
          )
          * x6
          + (
              a_11 * a_12
              + a_11 * a_22
              + a_11 * a_33
              + a_12 * a_31
              + a_12 * a_33
              + a_21 * a_22
              + a_21 * a_33
              + a_22 * a_31
              + a_22 * a_33
              + a_31 * a_33
          )
          * x7
          - a_11 * a_12
          - a_11 * a_22
          - a_11 * a_33
          - a_11 * a_43
          - a_12 * a_31
          - a_12 * a_33
          - a_12 * a_43
          - a_21 * a_22
          - a_21 * a_33
          - a_21 * a_43
          - a_22 * a_31
          - a_22 * a_33
          - a_22 * a_43
          - a_31 * a_33
          - a_31 * a_43,
          (a_12 + a_22 + a_33 + a_34 + a_43 + a_44) * x0
          + (a_22 + a_33 + a_34 + a_43 + a_44) * x1
          + (a_12 + a_22 + a_33 + a_34 + a_43 + a_44) * x2
          + (a_11 + a_31 + a_33 + a_34 + a_43 + a_44) * x3
          + (a_11 + a_21 + a_31 + a_33 + a_34 + a_43 + a_44) * x4
          + (a_11 + a_12 + a_21 + a_22 + a_31 + a_34 + a_44) * x5
          + (a_11 + a_12 + a_21 + a_22 + a_31 + a_44) * x6
          + (a_11 + a_12 + a_21 + a_22 + a_31 + a_33) * x7
          - a_11
          - a_12
          - a_21
          - a_22
          - a_31
          - a_33
          - a_43,
          x0 + x1 + x2 + x3 + x4 + x5 + x6 + x7 - 1,
          (a_12 * a_34 + a_12 * a_44 + a_22 * a_34 + a_22 * a_44) * x2
          + (a_31 * a_34 + a_31 * a_44) * x3
          + (a_31 * a_34 + a_31 * a_44) * x4
          + (a_12 * a_31 + a_22 * a_31) * x7
          - a_12 * a_31
          - a_22 * a_31,
          (a_12 + a_22 + a_34 + a_44) * x2
          + a_31 * x3
          + a_31 * x4
          + a_31 * x7
          - a_31,
          x2,
      ]
  
imports: from sympy.polys.rings import ring
  from sympy.polys.fields import field
  from sympy.polys.domains import ZZ, QQ
  from sympy.polys.solvers import solve_lin_sys
label_desc: Use image node_id 13 for calling a global function with example usage: eqs_10x8() and returns: list