On Polynomial Curves in the Affine Plane

• Our preprint: On Polynomial Curves in the Affine Plane (13pages)
• The used software: Asir and Singular
• Installation of Asir
  • Windows
  • UNIX
• Installation of Singular
  • Windows
  • UNIX
• Groebner basis computation
  • For Asir users
    • {6,21,4}:
      The construction of the polynomial system of {6,21,4} using Asir.
      We replace variables in our preprint as following:
      a_2=a, a_3=b, a_4=c, a_5=d, a_6=e, b_{12}=f, b_{18}=g
      
      The procedure for Groebner basis computation of {6,21,4} on Asir.
      
      Data files:
      
      • polynomial system 6-21-4_poly_13 (binary)
      • check polynomial 6-21-4_chkpoly (binary)
      • Groebner basis w.r.t. weighted LEX ordering 6-21-4_gr (binary)
    • {6,22,17}:
      The construction of the polynomial system of {6,22,17} using Asir.
      We replace variables in our preprint as following:
      a_2=a, a_3=b, a_4=c, a_5=d, a_6=e, b_2=f, b_8=k, b_{12}=o, b_{14}=q, b_{18}=u, b_{20}=w
      
      The procedure for Groebner basis computation of {6,22,17} on Asir.
      
      Data files:
      
      • polynomial system 6-22-17_poly_17 (binary)
      • check polynomial 6-22-17_chkpoly (binary)
      • Groebner basis w.r.t. weighted LEX ordering 6-22-17_gr (binary)
  • For Singular users
    • {6,21,4}:
      The procedure for Groebner basis computation of {6,21,4} on Singular.
      
      Data files:
      
      • polynomial system 6-21-4_poly_13_txt (text)
      • check polynomial 6-21-4_chkpoly_txt (text)
      • Groebner basis w.r.t. weighted LEX ordering 6-21-4_gr.mp (binary)
    • {6,22,17}:
      The procedure for Groebner basis computation of {6,22,17} on Singular.
      
      Data files:
      
      • polynomial system 6-22-17_poly_17_txt (text)
      • check polynomial 6-22-17_chkpoly_txt (text)
      • Groebner basis w.r.t. weighted LEX ordering 6-22-17_gr.mp (binary)