Differential equations for integrals associated with smooth Fano polytope

Asir main program : sfp.rr

Smooth Fano 2-polytope

• Fano(2, 0)
  • Points : {(1,0), (0,1), (-1,1)}
  • Differential equations : sfp20_output
  • Program : sfp20.rr

• Fano(2, 1)
  • Points : {(1,0), (0,1), (-1,0), (0,-1)}
  • Differential equations : sfp21_output
  • Program : sfp21.rr

• Fano(2, 2)
  • Points : {(1,0), (0,1), (-1,1), (0,-1)}
  • Differential equations : sfp22_output
  • Program : sfp22.rr

• Fano(2, 3)
  • Points : {(1,0), (0,1), (-1,1), (1,-1), (-1,0)}
  • Differential equations : sfp23_output
  • Program : sfp23.rr

• Fano(2, 4)
  • Points : {(1,0), (0,1), (-1,1), (1,-1), (-1,0), (0,-1)}
  • Differential equations : sfp24_output
  • Program : sfp24.rr

Smooth Fano 3-polytope

• Fano(3, 0)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,-1,1)}
  • Differential equations : sfp30_output
  • Program : sfp30.rr

• Fano(3, 1)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,0), (0,-1,-1)}
  • Differential equations : sfp31_output
  • Program : sfp31.rr

• Fano(3, 2)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,-1,1), (0,0,-1)}
  • Differential equations : sfp32_output
  • Program : sfp32.rr

• Fano(3, 3)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,1), (0,-1,-1)}
  • Differential equations : sfp33_output
  • Program : sfp33.rr

• Fano(3, 4)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,-1,2), (0,0,-1)}
  • Differential equations : sfp34_output
  • Program : sfp34.rr

• Fano(3, 5)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,-1,2), (0,1,-1), (0,0,-1)}
  • Differential equations : sfp35_app_output
  • Program : sfp35_app.rr

• Fano(3, 6)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,1), (1,0,-1), (-1,-1,0)}
  • Differential equations : sfp36_app_output
  • Program : sfp36_app.rr

• Fano(3, 7)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,1), (0,-1,0), (0,0,-1)}
  • Differential equations : sfp37_app_output
  • Program : sfp37_app.rr

• Fano(3, 8)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,1), (0,0,-1), (0,-1,-1)}
  • Differential equations : sfp38_app_output
  • Program : sfp38_app.rr

• Fano(3, 9)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,0), (0,-1,0), (0,0,-1)}
  • Differential equations : sfp39_app_output
  • Program : sfp39_app.rr

• Fano(3, 10)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,1), (0,-1,1), (0,0,-1)}
  • Differential equations : sfp310_app_output
  • Program : sfp310_app.rr

• Fano(3, 11)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,1), (0,1,-1), (0,-1,0)}
  • Differential equations : sfp311_app_output
  • Program : sfp311_app.rr

• Fano(3, 15)
  • Points : {(1,0,0), (0,1,0), (0,0,1), (-1,0,1), (1,0,-1), (1,0,-1), (-1,0,0), (0,-1,0)}
  • Differential equations : sfp315_app_output
  • Program : sfp315_app.rr

File format of output file

• sfp(D, I) : Fano(D, I)
• F : integrand
• Ann F^s : annihilating ideal of F^s
• Ann F^(-1) : annihilating ideal of F^(-1)
• weyl_minipoly, generic_bfct, S0 ...etc : informations of integration algorithm
• the last line : differential equations for the integral associated with smooth Fano polytope Fano(D, I)