FIRE-Examples

For examples on FIRE 5 download the full package from GIT

The following is an example with the box diagram (with an old version of FIRE):

Get["d:/groebner/mreduction/SBases_2.0.0.m"];

Get["d:/groebner/mreduction/FIRE_2.6.4.m"];

Get["d:/groebner/IBP/IBP.m"]

Internal={k};

External={p1,p2,p4};

Propagators={-k^2,-(k+p1)^2,-(k+p1+p2)^2,-(k+p1+p2+p4)^2};

PrepareIBP[];

reps= {p1^2®0,p2^2®0,p4^2®0,p1 p2®s/2,p2 p4®t/2,p1 p4®-s/2-t/2};

startinglist={IBP[k,k] ,IBP[k,p1] ,IBP[k,p2],IBP[k,p4] }/.reps;

RESTRICTIONS={{-1,-1,0,0},{0,-1,-1,0},{0,0,-1,-1}, {-1,0,0,-1}};

SYMMETRIES={{3,2,1,4},{1,4,3,2},{3,4,1,2}};

Prepare[];

SaveStart["box"];

Burn[];

F[{2,2,2,2}]

EVALUATING {0,{2,2,2,2}}

Working in {0,{1,1,1,1}}

LAPORTA STARTED: 1 integrals for evaluation

{0,{2,2,2,2}}

12 IBP's generated: 0.0312500 seconds.

7 new relations produced: 0.1250000 seconds.

IRREDUCIBLE INTEGRAL: {0,{1,1,1,1}}

52 IBP's generated: 0.1250000 seconds.

19 new relations produced: 0.4375000 seconds.

Relations produced: 24

Working in {0,{1,1,1,-1}}

Relations produced: 12

Working in {0,{-1,1,1,1}}

Relations produced: 3

Working in {0,{1,-1,1,1}}

LAPORTA STARTED: 10 integrals for evaluation

{0,{2,0,1,3}}

36 IBP's generated: 0.1093750 seconds.

23 new relations produced: 0.3281250 seconds.

48 IBP's generated: 0.1093750 seconds.

22 new relations produced: 0.4531250 seconds.

Relations produced: 28

Working in {0,{1,1,-1,1}}

LAPORTA STARTED: 8 integrals for evaluation

{0,{2,2,0,2}}

36 IBP's generated: 0.0937500 seconds.

23 new relations produced: 0.3125000 seconds.

48 IBP's generated: 0.1093750 seconds.

22 new relations produced: 0.4218750 seconds.

{0,{4,1,0,1}}

72 IBP's generated: 0.1562500 seconds.

1 new relations produced: 0.ґ10^{-8
seconds.}

Relations produced: 38

Working in {0,{1,-1,1,-1}}

LAPORTA STARTED: 5 integrals for evaluation

{0,{3,0,2,0}}

32 IBP's generated: 0.0625000 seconds.

19 new relations produced: 0.3281250 seconds.

IRREDUCIBLE INTEGRAL: {0,{1,0,1,0}}

32 IBP's generated: 0.0625000 seconds.

4 new relations produced: 0.0312500 seconds.

Relations produced: 24

Working in {0,{-1,1,-1,1}}

LAPORTA STARTED: 5 integrals for evaluation

{0,{-1,2,0,2}}

32 IBP's generated: 0.0625000 seconds.

19 new relations produced: 0.3437500 seconds.

IRREDUCIBLE INTEGRAL: {0,{0,1,0,1}}

Relations produced: 23

SORTING THE LIST OF 152 INTEGRALS: 0.0156250 seconds.

Substituting 152 values: 0.2656250 seconds.

Total time: 4.7500000 seconds

-(4 (-7+d) (-5+d) (-3+d) (-664 s+228 d s-26 d^{2 s+d3 s-160 t+36
d t-2 d2 t) G[{0,1,0,1}])/((-8+d) (-6+d) s3 t4)-(4 (-7+d) (-5+d) (-3+d) (-160
s+36 d s-2 d2 s-664 t+228 d t-26 d2 t+d3 t) G[{1,0,1,0}])/((-8+d) (-6+d) s4
t3)-((-7+d) (-5+d) (-20 s2+2 d s2-88 s t+18 d s t-d2 s t-20 t2+2 d t2)
G[{1,1,1,1}])/(s3 t3)}

^{(* and now with the s- bases *)}

^{BuildBasis[\{1, 1, 1, 1\},\{\{1, 1, 1, 1\},\{1, 1, 1, 0\},\{1, 1, 0,
0\},\{1, 0, 0, 0\}\}]}

^{BuildBasis[\{-1, 1, 1, 1\},\{\{1, 1, 1, 1\},\{1, 1, 1, 0\},\{1, 1, 0,
0\},\{1, 0, 0, 0\}\}]}

^{BuildBasis[\{1, -1, 1, 1\},\{\{1, 1, 1, 1\},\{1, 1, 1, 0\},\{1, 1, 0,
0\},\{1, 0, 0, 0\}\}]}

^{BuildBasis[\{-1, 1, -1, 1\},\{\{1, 1, 1, 1\},\{1, 1, 1, 0\},\{1, 1, 0,
0\},\{1, 0, 0, 0\}\}]}

^{BuildBasis[\{1, -1, 1, -1\},\{\{1, 1, 1, 1\},\{1, 1, 1, 0\},\{1, 1, 0,
0\},\{1, 0, 0, 0\}\}]}

^Burn[];

F[{2,2,2,2}]

EVALUATING {0,{2,2,2,2}}

Working in {0,{1,1,1,1}}

IRREDUCIBLE INTEGRAL: {0,{1,1,1,1}}

Relations produced: 14

Working in {0,{-1,1,1,1}}

Relations produced: 7

Working in {0,{1,-1,1,1}}

Relations produced: 12

Working in {0,{1,-1,1,-1}}

IRREDUCIBLE INTEGRAL: {0,{1,0,1,0}}

Relations produced: 24

Working in {0,{-1,1,-1,1}}

IRREDUCIBLE INTEGRAL: {0,{0,1,0,1}}

Relations produced: 13

GENERATING 70 NEW RELATIONS: 0.2656250 seconds.

SORTING THE LIST OF 70 INTEGRALS: 0.ґ10^{-8
seconds.}

Substituting 70 values: 0.1250000 seconds.

Total time: 0.3906250 seconds

A notebook with this example can be downloaded here.