Differential equations for integrals associated with smooth Fano polytope
Paper
Hiromasa Nakayama, Nobuki Takayama,
Computing differential equations for integrals associated to smooth Fano polytope doi (final version).
Draft version at arxiv .
Asir main program : sfp.rr
Smooth Fano 2-polytope
- 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)