Oneloop massless scalar and tensor integral reduction by means of Tarasov's recurrence relations (adapted from O. V. Tarasov's Maple codes).
oneloop v1.0
Usage: oneloop i2|i3|i4|i5 [--di <shift>] --n1 <n1> --n2 <n2> ...
Options:
-h, --help Show help message
-v, --version Show version of this program
Subcommand: i2 - Computes massless 2-point integral I2[s12] in (d + di) dimensions
--n1 <arg> Exponent of the first propagator
--n2 <arg> Exponent of the second propagator
--di <arg> Dimension shift (must be even)
-c, --characteristic <arg> Characteristic of the used ring
--database <arg> Alternative path to database file
-f, --factorize Factorize coefficient at each integral summand
-i, --indices <arg> Tensor indices
--no-database Disable use of database (each expression will be
calculated from scratch)
-o, --output-format <arg> Format of output. Possible values: FORM, MMA,
Maple. Default is MMA.
--s12 <arg> Optional value for kinematic invariant s12
-t, --table-print Print each summand of the result on a new line
-h, --help Show help message
Subcommand: i3 - Computes massless 3-point integral I3[s23, s13, s12] in (d + di) dimensions
--n1 <arg> Exponent of the first propagator
--n2 <arg> Exponent of the second propagator
--n3 <arg> Exponent of the third propagator
--di <arg> Dimension shift (must be even)
-c, --characteristic <arg> Characteristic of the used ring
--database <arg> Alternative path to database file
-f, --factorize Factorize coefficient at each integral summand
-i, --indices <arg> Tensor indices
--no-database Disable use of database (each expression will be
calculated from scratch)
-o, --output-format <arg> Format of output. Possible values: FORM, MMA,
Maple. Default is MMA.
--s12 <arg> Optional value for kinematic invariant s12
--s13 <arg> Optional value for kinematic invariant s13
--s23 <arg> Optional value for kinematic invariant s23
-t, --table-print Print each summand of the result on a new line
-h, --help Show help message
Subcommand: i4 - Computes massless 4-point integral I4[s12, s23, s34, s14, s24, s13] in (d + di) dimensions
--n1 <arg> Exponent of the first propagator
--n2 <arg> Exponent of the second propagator
--n3 <arg> Exponent of the third propagator
--n4 <arg> Exponent of the fourth propagator
--di <arg> Dimension shift (must be even)
-c, --characteristic <arg> Characteristic of the used ring
--database <arg> Alternative path to database file
-f, --factorize Factorize coefficient at each integral summand
-i, --indices <arg> Tensor indices
--no-database Disable use of database (each expression will be
calculated from scratch)
-o, --output-format <arg> Format of output. Possible values: FORM, MMA,
Maple. Default is MMA.
--s12 <arg> Optional value for kinematic invariant s12
--s13 <arg> Optional value for kinematic invariant s13
--s14 <arg> Optional value for kinematic invariant s14
--s23 <arg> Optional value for kinematic invariant s23
--s24 <arg> Optional value for kinematic invariant s24
--s34 <arg> Optional value for kinematic invariant s24
-t, --table-print Print each summand of the result on a new line
-h, --help Show help message
Subcommand: i5 - Computes massless 5-point integral I5[s12, s23, s34, s45, s15, s13, s14, s24, s25, s35] in (d + di) dimensions
--n1 <arg> Exponent of the first propagator
--n2 <arg> Exponent of the second propagator
--n3 <arg> Exponent of the third propagator
--n4 <arg> Exponent of the fourth propagator
--n5 <arg> Exponent of the fifth propagator
--di <arg> Dimension shift (must be even)
-c, --characteristic <arg> Characteristic of the used ring
--database <arg> Alternative path to database file
-f, --factorize Factorize coefficient at each integral summand
-i, --indices <arg> Tensor indices
--no-database Disable use of database (each expression will be
calculated from scratch)
-o, --output-format <arg> Format of output. Possible values: FORM, MMA,
Maple. Default is MMA.
--s12 <arg> Optional value for kinematic invariant s12
--s13 <arg> Optional value for kinematic invariant s13
--s14 <arg> Optional value for kinematic invariant s14
--s15 <arg> Optional value for kinematic invariant s15
--s23 <arg> Optional value for kinematic invariant s23
--s24 <arg> Optional value for kinematic invariant s24
--s25 <arg> Optional value for kinematic invariant s25
--s34 <arg> Optional value for kinematic invariant s24
--s35 <arg> Optional value for kinematic invariant s25
--s45 <arg> Optional value for kinematic invariant s25
-t, --table-print Print each summand of the result on a new line
-h, --help Show help message
Install MMA wrapper using
Import["https://raw.githubusercontent.com/PoslavskySV/rings.oneloop/develop/mma/Install.m"]; DoInstall[];
Then run e.g.
<< oneloop`
I3[1, 1, 1, 2, Factorize -> True, Characteristic -> 0, Indices -> "mn"]