Name: Rolf Mertig Date: 06/21/12-12:20:45 AM Z

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Am 20.06.2012 17:21, schrieb Feng Feng:
> Dear All,
>
> I have found that The Tr operation is terriblely slow in FeynCalc 6.0, while the same code run very faster with fc5beta3.
>
> Here is my testing code, and has anyone else experienced the same problem?
>
> ===========================
> «HighEnergyPhysics`fc`
>
> exp = (mc + GSD[k1]).GAD[c[li3]].(mc + GSD[k1 + k2 + p - q]).GAD[
*> c[\\\\\\\\\\\\\\\\[Gamma]]].(-mc

• GSD[p] - GSD[q]).GA[*
  > 5].(mc + GSD[p] + GSD[q]).GAD[c[li2]].(-mc + GSD[k2]).GAD[
  > li2].(mc + GSD[p] + GSD[q]).GA[
  *> 5].(-mc + GSD[p] - GSD[q]).GAD[\\\\\\\\\\\\\\\\[Gamma]].(mc
• GSD[k2 + 2 p])*
  > .GAD[li3] // FCI
  >
  > (*$VeryVerbose=5;*)
  >
  > DateString[]
  > Tr[exp]
  > DateString[]
  >
  >
  Please use Mathematica 8 and FeynCalc 8.1.0
  Then on a reasonably fast computer it takes half a minute to do the trace.
  That is not extremely fast, but also not extremely slow, I think.

Rolf

Mathematica 8.0 for Linux x86 (64-bit)
Copyright 1988-2011 Wolfram Research, Inc.

In[1]:= !!t
<<HighEnergyPhysics`fc` ;
s2v[a_Symbol,b_Symbol]:=s2v[a]=Symbol[ToString[a]<>ToString[b]];
exp = (mc + GSD[k1]).GAD[li3].(mc + GSD[k1 + k2 + p

• q]).GAD[
      gam].(-mc + GSD[p] - GSD[q]).GA[5].(mc + GSD[p + q]).GAD[
      li2].(-mc + GSD[k2]).GAD[li2].(mc + GSD[p + q]).GA[5].
  (-mc + GSD[p - q]).GAD[gam].(mc - GSD[k2 + 2 p]) .GAD[li3];

Print[“time needed for the trace = “,
AbsoluteTiming[trres=Tr[exp];]//First];

Print[“the result is : “,
InputForm[result = Collect2[FCE[trres]/.SPD->s2v, mc, Factoring ->
Simplify, IsolateNames -> X]]];
Print[“where : “];
??X

In[1]:= <<t
Loading FeynCalc from /usr/share/Mathematica/Applications/HighEnergyPhysics
FeynCalc 8.1.0 Type ?FeynCalc for help or visit http://www.feyncalc.org/
$PrePrint is set to FeynCalcForm. Use FI and FC to change the display
format.
Loading FeynArts, see www.feynarts.de for documentation
FeynArts 3.4 patched for use with FeynCalc
time needed for the trace = 31.681195
the result is : -4*D^3*mc^8 + 4*mc^2*HoldForm[X[17]]

   4*mc^4*HoldForm[X[28]] + 4*mc^6*HoldForm[X[32]] -

   4*HoldForm[X[3]]^3*HoldForm[X[47]]
where :
Global`X

X[3] = -2 + D

X[4] = -6*pp + 5*D*pp + 4*D*pq - 6*qq + D*qq + 4*k2p*HoldForm[X[3]] +
     2*k2q*HoldForm[X[3]]

X[5] = 8 - 10*D + D^2

X[6] = 16*pq - 20*D*pq + 2*D^2*pq - 8*qq + 2*D*qq - D^2*qq +
     k2q*HoldForm[X[3]]^2 - pp*HoldForm[X[5]]

X[7] = 32*k2q^2 - 48*D*k2q^2 + 24*D^2*k2q^2 - 4*D^3*k2q^2

• 64*k2q*pp -
       64*D*k2q*pp - 16*D^2*k2q*pp + 16*D^3*k2q*pp - 32*D*pp^2
• 34*D^2*pp^2 -
       7*D^3*pp^2 - 64*k2q*pq + 32*D*k2q*pq + 16*D^2*k2q*pq - 8*D^3*k2q*pq +
       64*D*pp*pq - 64*D^2*pp*pq + 16*D^3*pp*pq - 8*D^2*pq^2 - 4*D^3*pq^2 +
       64*k2q*qq - 64*D*k2q*qq + 16*D^2*k2q*qq - 32*D*pp*qq + 36*D^2*pp*qq -
       6*D^3*pp*qq + 2*D^2*qq^2 + D^3*qq^2 + 2*k2k2*HoldForm[X[3]]^2*
        HoldForm[X[4]] + 4*k2p*HoldForm[X[3]]*HoldForm[X[6]]

X[8] = -2 + 5*D

X[9] = 2*k2p*HoldForm[X[3]] + qq*HoldForm[X[3]] + pp*HoldForm[X[8]]

X[10] = 5*pp - 4*pq + qq

X[11] = -4*pq + k2q*HoldForm[X[3]] - D*HoldForm[X[10]]

X[12] = pp - 2*pq + qq

X[13] = -16 + 9*D

X[14] = 2*pq + qq

X[15] = pp*HoldForm[X[13]] + D*HoldForm[X[14]]

X[16] = 4*k2p^2*HoldForm[X[3]]^2 + 2*k2k2*HoldForm[X[3]]*HoldForm[X[9]]

•      4*k2p*HoldForm[X[3]]*HoldForm[X[11]]
• D*HoldForm[X[12]]*HoldForm[X[15]]

X[17] = 64*k1k1*k2p^2 - 96*D*k1k1*k2p^2 + 48*D^2*k1k1*k2p^2 -
     8*D^3*k1k1*k2p^2 + 128*k1k2*k2p^2 - 192*D*k1k2*k2p^2 +
     96*D^2*k1k2*k2p^2 - 16*D^3*k1k2*k2p^2 - 16*k1k1*k2k2*pp

•      24*D*k1k1*k2k2*pp - 12*D^2*k1k1*k2k2*pp + 2*D^3*k1k1*k2k2*pp -
       16*k1k2*k2k2*pp + 24*D*k1k2*k2k2*pp - 12*D^2*k1k2*k2k2*pp +
       2*D^3*k1k2*k2k2*pp + 96*k1k1*k2p*pp - 144*D*k1k1*k2p*pp
•      72*D^2*k1k1*k2p*pp - 12*D^3*k1k1*k2p*pp + 192*k1k2*k2p*pp -
       320*D*k1k2*k2p*pp + 168*D^2*k1k2*k2p*pp - 28*D^3*k1k2*k2p*pp -
       8*D^2*k2k2*k2p*pp + 4*D^3*k2k2*k2p*pp - 24*D^2*k2p^2*pp
•      12*D^3*k2p^2*pp + 64*k1k1*k2q*pp - 32*D*k1k1*k2q*pp -
       16*D^2*k1k1*k2q*pp + 8*D^3*k1k1*k2q*pp + 96*k1k2*k2q*pp
•      80*D*k1k2*k2q*pp - 8*D^2*k1k2*k2q*pp + 12*D^3*k1k2*k2q*pp -
       16*D^2*k2k2*k2q*pp + 8*D^3*k2k2*k2q*pp - 40*D^2*k2p*k2q*pp +
       20*D^3*k2p*k2q*pp + 16*D^2*k2q^2*pp - 8*D^3*k2q^2*pp - 32*D*k1k1*pp^2 +
       30*D^2*k1k1*pp^2 - 7*D^3*k1k1*pp^2 + 24*k1k2*pp^2 - 88*D*k1k2*pp^2 +
       70*D^2*k1k2*pp^2 - 15*D^3*k1k2*pp^2 + D^3*k2k2*pp^2 + 4*D*k2p*pp^2 -
       20*D^2*k2p*pp^2 + 12*D^3*k2p*pp^2 + 20*D*k2q*pp^2 - 52*D^2*k2q*pp^2 +
       20*D^3*k2q*pp^2 + 2*D^3*pp^3 - 64*k1k1*k2p*pq + 32*D*k1k1*k2p*pq +
       16*D^2*k1k1*k2p*pq - 8*D^3*k1k1*k2p*pq - 160*k1k2*k2p*pq
•      176*D*k1k2*k2p*pq - 40*D^2*k1k2*k2p*pq - 4*D^3*k1k2*k2p*pq +
       16*D^2*k2k2*k2p*pq - 8*D^3*k2k2*k2p*pq + 48*D^2*k2p^2*pq
•      24*D^3*k2p^2*pq - 32*k1k2*k2q*pq + 48*D*k1k2*k2q*pq -
       24*D^2*k1k2*k2q*pq + 4*D^3*k1k2*k2q*pq - 16*D^2*k2p*k2q*pq +
       8*D^3*k2p*k2q*pq - 32*k1k2*pp*pq + 64*D*k1k2*pp*pq -
  40*D^2*k1k2*pp*pq +
       8*D^3*k1k2*pp*pq - 16*D*k2p*pp*pq + 64*D^2*k2p*pp*pq
• 28*D^3*k2p*pp*pq +
       16*D*k2q*pp*pq + 16*D^2*k2q*pp*pq - 12*D^3*k2q*pp*pq - 2*D^3*pp^2*pq +
       8*D^2*k1k1*pq^2 - 4*D^3*k1k1*pq^2 + 32*k1k2*pq^2 - 24*D^2*k1k2*pq^2 +
       4*D^3*k1k2*pq^2 - 4*D^3*k2k2*pq^2 + 16*D*k2p*pq^2 - 48*D^2*k2p*pq^2 +
       8*D^3*k2p*pq^2 + 16*D*k2q*pq^2 - 16*D^2*k2q*pq^2 + 8*D^3*k2q*pq^2 -
       8*D^3*pp*pq^2 + 8*D^3*pq^3 - 16*k1k1*k2k2*qq + 24*D*k1k1*k2k2*qq -
       12*D^2*k1k1*k2k2*qq + 2*D^3*k1k1*k2k2*qq - 16*k1k2*k2k2*qq +
       24*D*k1k2*k2k2*qq - 12*D^2*k1k2*k2k2*qq + 2*D^3*k1k2*k2k2*qq -
       32*k1k1*k2p*qq + 48*D*k1k1*k2p*qq - 24*D^2*k1k1*k2p*qq
•      4*D^3*k1k1*k2p*qq + 32*k1k2*k2p*qq - 16*D*k1k2*k2p*qq
•      8*D^2*k2k2*k2p*qq - 4*D^3*k2k2*k2p*qq + 24*D^2*k2p^2*qq
•      12*D^3*k2p^2*qq - 8*D^2*k2p*k2q*qq + 4*D^3*k2p*k2q*qq
• 32*D*k1k1*pp*qq -
       36*D^2*k1k1*pp*qq + 10*D^3*k1k1*pp*qq + 16*k1k2*pp*qq
• 16*D*k1k2*pp*qq +
       4*D^2*k1k2*pp*qq + 2*D^3*k1k2*pp*qq + 2*D^3*k2k2*pp*qq
• 40*D*k2p*pp*qq +
       56*D^2*k2p*pp*qq - 12*D^3*k2p*pp*qq - 40*D*k2q*pp*qq
• 40*D^2*k2q*pp*qq -
       12*D^3*k2q*pp*qq + 4*D^3*pp^2*qq - 32*k1k2*pq*qq + 32*D*k1k2*pq*qq -
       8*D^2*k1k2*pq*qq + 16*D*k2p*pq*qq - 32*D^2*k2p*pq*qq
• 12*D^3*k2p*pq*qq -
       16*D*k2q*pq*qq + 16*D^2*k2q*pq*qq - 4*D^3*k2q*pq*qq - 4*D^3*pp*pq*qq -
       2*D^2*k1k1*qq^2 + D^3*k1k1*qq^2 - 8*k1k2*qq^2 + 8*D*k1k2*qq^2 -
       2*D^2*k1k2*qq^2 + D^3*k1k2*qq^2 + D^3*k2k2*qq^2 + 20*D*k2p*qq^2 -
       20*D^2*k2p*qq^2 + 8*D^3*k2p*qq^2 + 4*D*k2q*qq^2 - 4*D^2*k2q*qq^2 +
       2*D^3*pp*qq^2 - 2*D^3*pq*qq^2 + k1p*HoldForm[X[7]] -
       k1q*HoldForm[X[3]]*HoldForm[X[16]]

X[18] = 2*k2p + 2*pp - pq + qq

X[19] = 6*k2p + 10*pp - pq + qq

X[20] = pq + qq

X[21] = 4*k2p + 5*pp + pq + 2*qq

X[22] = D^3*HoldForm[X[18]] - 2*D^2*HoldForm[X[19]] - 8*HoldForm[X[20]] +
     4*D*HoldForm[X[21]]

X[23] = k2k2*HoldForm[X[3]]^3 + 2*HoldForm[X[22]]

X[24] = -8 + D

X[25] = D*qq + pp*HoldForm[X[24]]

X[26] = k2p*HoldForm[X[3]]^2 + D*HoldForm[X[25]]

X[27] = k2k2*HoldForm[X[3]]^2 + 2*HoldForm[X[26]]

X[28] = -24*k1p*k2k2 + 20*D*k1p*k2k2 - 2*D^2*k1p*k2k2 - D^3*k1p*k2k2 +
     8*k1q*k2k2 - 12*D*k1q*k2k2 + 6*D^2*k1q*k2k2 - D^3*k1q*k2k2 +
32*k1p*k2p -
     8*D^2*k1p*k2p - 16*k1q*k2p + 8*D*k1q*k2p + 4*D^2*k1q*k2p

•      2*D^3*k1q*k2p + 8*D^2*k2k2*k2p - 4*D^3*k2k2*k2p + 24*D^2*k2p^2 -
       12*D^3*k2p^2 + 48*k1p*k2q - 40*D*k1p*k2q + 4*D^2*k1p*k2q
•      2*D^3*k1p*k2q - 8*D^2*k2p*k2q + 4*D^3*k2p*k2q + 16*D*k1p*pp -
       36*D^2*k1p*pp + 2*D^3*k1p*pp + 4*D^2*k1q*pp - 2*D^3*k1q*pp -
       6*D^3*k2k2*pp - 24*D*k2p*pp + 32*D^2*k2p*pp - 28*D^3*k2p*pp -
       8*D*k2q*pp - 8*D^2*k2q*pp + 12*D^3*k2q*pp + 8*D^2*pp^2 - 15*D^3*pp^2 -
       32*D*k1p*pq + 16*D^2*k1p*pq - 16*D*k2p*pq + 16*D^2*k2p*pq -
       4*D^3*k2p*pq - 16*D*k2q*pq + 16*D^2*k2q*pq - 4*D^3*k2q*pq +
  8*D^2*pp*pq +
       8*D^3*pp*pq + 16*D^2*pq^2 - 12*D^3*pq^2 + 16*D*k1p*qq - 4*D^2*k1p*qq +
       2*D^3*k1p*qq + 4*D^2*k1q*qq - 2*D^3*k1q*qq + 2*D^3*k2k2*qq +
       24*D*k2p*qq - 16*D^2*k2p*qq + 8*D^3*k2p*qq + 8*D*k2q*qq
• 8*D^2*k2q*qq -
       24*D^2*pp*qq + 18*D^3*pp*qq - 8*D^2*pq*qq + D^3*qq^2 +
       k1k2*HoldForm[X[23]] + k1k1*HoldForm[X[3]]*HoldForm[X[27]]

X[29] = 2*k1k2 + 4*k1p + k2p + k2q

X[30] = k1k1 + k1k2 + 3*k1p - k1q - 2*k2p + 2*k2q + 4*pp + 4*pq

X[31] = k1k1 + k1k2 + k1p - k1q + k2k2 + 2*pq + 2*qq

X[32] = -8*k1k2 + 4*D*HoldForm[X[29]] - 2*D^2*HoldForm[X[30]] +
     D^3*HoldForm[X[31]]

X[33] = pp - 2*pq - qq

X[34] = 8*k2q*pp - pp^2 + 4*pq^2 - 2*pp*qq - qq^2 + 4*k2p*HoldForm[X[33]]

X[35] = 3*pp - 6*pq - qq

X[36] = 5*pp - 2*pq + qq

X[37] = 3*pp^2 - 8*pp*pq + 4*pq^2 + 2*pp*qq - qq^2 + 2*k2q*HoldForm[X[36]]

X[38] = 4*k2q*pp*HoldForm[X[12]] + 2*k2p^2*HoldForm[X[35]] +
     k2p*HoldForm[X[37]]

X[39] = k2k2*HoldForm[X[34]] + 2*HoldForm[X[38]]

X[40] = pp + 2*pq - qq

X[41] = 3*pp^2 - 12*pq^2 + 8*k2p*qq + 6*pp*qq + 3*qq^2

4*k2q*HoldForm[X[40]]

X[42] = -3*pp^2 + 8*pp*pq - 4*pq^2 - 2*pp*qq + qq^2 + 2*k2q*HoldForm[X[36]]

X[43] = -3*pp + 6*pq + qq

X[44] = pp^2 - 4*pp*pq + 4*pq^2 - qq^2 + k2q*HoldForm[X[43]]

X[45] = k2q*HoldForm[X[42]] - 2*k2p*HoldForm[X[44]]

X[46] = k2k2*HoldForm[X[41]] - 2*HoldForm[X[45]]

X[47] = -8*k1k1*k2q^2*pp - 16*k1k2*k2q^2*pp + k1k1*k2k2*pp^2 +
     k1k2*k2k2*pp^2 + 2*k1k1*k2p*pp^2 + 8*k1k1*k2q*pp^2 + 12*k1k2*k2q*pp^2 -
     2*k1k2*pp^3 + 16*k1k1*k2p*k2q*pq + 32*k1k2*k2p*k2q*pq -
     8*k1k1*k2p*pp*pq - 12*k1k2*k2p*pp*pq - 4*k1k2*k2q*pp*pq

•      2*k1k2*pp^2*pq - 4*k1k1*k2k2*pq^2 - 4*k1k2*k2k2*pq^2 +
  8*k1k1*k2p*pq^2 +
       24*k1k2*k2p*pq^2 - 8*k1k2*k2q*pq^2 + 8*k1k2*pp*pq^2 - 8*k1k2*pq^3 -
       8*k1k1*k2p^2*qq - 16*k1k2*k2p^2*qq + 2*k1k1*k2k2*pp*qq
•      2*k1k2*k2k2*pp*qq - 12*k1k1*k2p*pp*qq - 20*k1k2*k2p*pp*qq -
       8*k1k1*k2q*pp*qq - 4*k1k2*k2q*pp*qq - 4*k1k2*pp^2*qq +
  8*k1k1*k2p*pq*qq +
       12*k1k2*k2p*pq*qq + 4*k1k2*k2q*pq*qq + 4*k1k2*pp*pq*qq
• k1k1*k2k2*qq^2 +
       k1k2*k2k2*qq^2 + 2*k1k1*k2p*qq^2 - 4*k1k2*k2p*qq^2 - 2*k1k2*pp*qq^2 +
       2*k1k2*pq*qq^2 + k1q*HoldForm[X[39]] + k1p*HoldForm[X[46]]

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