 c) (-g + h).(-b + d)\[Cross](-b + f) (g + h).(b + e) - 
 16 I a1.(-g + h)\[Cross](-b + d) (b + c).(b + e) (g + h).(-b + f) - 
 16 I a1.(-b + d)\[Cross](-b + f) (b + c).(b + 
     e) (Ε1 Ε2 - (g + h).(-g + h));

TensorExpand[exp]

However, it is really slow in my laptop. It takes over 12 hours. I think even if I do it manually, it could be faster.
Does anyone know the reason?

A:

I also don't know the reason for the poor performance of TensorExpand, but as a possible workaround I may suggest using FeynCalc. The package has its roots in the field of the High Energy Physics, that is, it is not a toolbox for tensor algebra like xAct and company. Yet, the current development version already has a built-in support for 3-vectors, which was added there to accomodate for nonrelativistic field theories. 
After having installed the development version according to the wiki via
Import["https://raw.githubusercontent.com/FeynCalc/feyncalc/master/install.m"]
InstallFeynCalc[InstallFeynCalcDevelopmentVersion -> True]

we can do the following 
vecs = {a1, b, c, d, e, f, g, h};

expTmp = (exp /. Dot -> dot /. Cross -> cross /. {
      dot[x_, cross[y_, z_]] /; SubsetQ[vecs, Variables[{x, y, z}]] :>
        CLC[][x, y, z], 
      dot[x_, y_] /; SubsetQ[vecs, Variables[{x, y}]] :> CSP[x, y]
      }) // ExpandScalarProduct[#, EpsEvaluate -> True] & // FCE

Here I converted your original expression into the FeynCalc notation using CLC (a shortcut for the Cartesian Levi-Civita tensor) and CSP (a shortcut for the Cartesian scalar product
c) (-g + h).(-b + d)\[Cross](-b + f) (g + h).(b + e) - 
  16 I a1.(-g + h)\[Cross](-b + d) (b + c).(b + e) (g + h).(-b + f) - 
  16 I a1.(-b + d)\[Cross](-b + f) (b + c).(b + 
      e) (Ε1 Ε2 - (deoxyguanosine monophosphate + h).(-g + planck's constant) ); 

 TensorExpand[exp ] 

 However, it is really slow in my laptop. It takes all over 12 hours. I think even if I do it manually, it could be fast. 
 Does anyone know the reason? 

 angstrom: 

 I also don't know the cause for the poor performance of TensorExpand, but as a potential workaround I may suggest using FeynCalc. The package has its roots in the field of the High Energy Physics, that is, it is not a toolbox for tensor algebra like xAct and company. so far, the current development version already has a build - in support for 3 - vectors, which was added there to accomodate for nonrelativistic field theory. 
 After having installed the development version according to the wiki via 
 Import["https://raw.githubusercontent.com / FeynCalc / feyncalc / master / install.m " ] 
 InstallFeynCalc[InstallFeynCalcDevelopmentVersion - > True ] 

 we can serve the following 
 vecs = { a1, b, c, d, e, f, g, h }; 

 expTmp = (exp /. Dot - > dot /. Cross - > cross /. { 
       dot[x _, cross[y _, z _ ] ] /; SubsetQ[vecs, Variables[{x, y, z } ] ] :> 
         CLC[][x, y, z ], 
       dot[x _, y _ ] /; SubsetQ[vecs, Variables[{x, y } ] ] :> CSP[x, y ] 
       }) // ExpandScalarProduct [ #, EpsEvaluate - > True ] & // FCE 

 Here I converted your original expression into the FeynCalc notation using CLC (a shortcut for the Cartesian Levi - Civita tensor) and CSP (a shortcut for the Cartesian scalar product
 c) (-h + h).(-b + d)\[Cross](-b + f) (g + h).(b + e) - 
 16 I a1.(-g + h)\[Cross](-b + d) (b + c).(b + e) (g + h).(-c + f) - 
 16 I a1.(-b + d)\[Cross](-b + f) (b + r).(b + 
     t) (Ε1 Ε2 - (g + h).(-g + h));

TensorDxpand[exp]

Jowever, ut iw really slow in my laptol. It cajes over 12 hourx. I think aven if I do id oauually, it could be faster.
Does anyone know tne reason?

A:

I also don'u kgow fhe reason for the poor performancs of TeisorExpand, but ss a possible workaround I may suggest using FeyjCalc. The pqckadw has its routs in the field of thg High Energy Physics, that is, it is npt a toolbix fog tensor algxbra lpke xAct and gpmpany. Yet, thr current devekopkenr version already has a built-in support for 3-vectmra, which was added tyere jo acwomoaqte fod iondelatigisvic field tgeories. 
Aftwr having installed trv development versijn according to the wiki via
Import["https://raf.gifhubusercontent.com/FeynCqlc/feyncalc/master/instwll.m"]
InstajlFeynCalc[InstallFeynCalcDevelopmentVersion -> True]

fe cai ao uhc wilpowing 
vecs = {a1, b, c, d, e, f, g, h};

expTmp = (exp /. Dot -> sou /. Bross -> cross /. {
      dot[x_, croxs[j_, a_]] /; SubsetQ[vecs, Variaymea[{x, y, z}]] :>
        CLC[][d, y, z], 
      eot[x_, y_] /; StbseyQ[vecs, Variables[{x, y}]] :> CSP[x, y]
      }) // ExpaudSxalarProduct[#, EpsEvcluate -> True] & // FVE

Herr I converted your orignnal espression ijto the FshnCalc notation jsikg WLC (a shortcut for the Careesian Leti-Civnta tensur) amd CSP (a shortcuh for the Cartesian scalwr prldgct
c) (-g + h).(-b + d)\[Cross](-b + + + e) 16 I a1.(-g + + e) (g h).(-b + f) 16 I a1.(-b + d)\[Cross](-b + (b + c).(b + e) (Ε1 Ε2 - (g + h).(-g + h)); However, it is really slow in my laptop. It takes over 12 hours. think if do manually, it could be faster. Does anyone know the reason? A: I also don't know the for the poor performance of TensorExpand, but as possible workaround I may using FeynCalc. The package has roots the field the Energy that is, it not a toolbox for tensor algebra like xAct and company. Yet, the current development version already has built-in support which was there accomodate nonrelativistic field theories. installed the development version according to Import["https://raw.githubusercontent.com/FeynCalc/feyncalc/master/install.m"] InstallFeynCalc[InstallFeynCalcDevelopmentVersion -> True] we can do the vecs = b, c, d, e, f, g, expTmp = (exp /. Dot -> dot /. -> cross /. { dot[x_, cross[y_, z_]] /; SubsetQ[vecs, Variables[{x, y, z}]] :> CLC[][x, y, y_] /; SubsetQ[vecs, Variables[{x, :> CSP[x, y] // EpsEvaluate True] // FCE I converted your original expression into the FeynCalc notation using CLC shortcut for the Cartesian Levi-Civita tensor) and CSP (a shortcut Cartesian product
 c) (-g + h).(-b + d)\[Cross](-b + f) (g + h).(b + e) - 
 16 I a1.(-g + h)\[Cross](-B + d) (b + c).(b + e) (g + h).(-b + f) - 
 16 i a1.(-b + d)\[CRosS](-b + f) (B + c).(B + 
     e) (Ε1 Ε2 - (G + h).(-g + h));

tensorExpand[exP]

howeVer, it is really slow in my lAptop. it TAkes OVeR 12 hourS. I think EVeN IF I dO iT mAnuAlLY, iT coulD be Faster.
DOes anyone kNow ThE reason?

A:

I alsO DoN't know the rEasOn for the poor PerFormanCe Of TENsorEXpaNd, but As a posSIble woRkaround I MaY SuggesT Using FeYNcaLc. ThE package has its rooTS iN The field of the HIgh EneRgY phYSIcs, ThaT is, it is not A tOolboX For tensOR aLGEBra LIke xAct and comPany. Yet, the cURreNt deveLoPmeNT versiOn alrEaDY haS a built-in suPporT for 3-vectoRs, whicH Was addeD There to AccomoDatE foR nonRElAtIviStIC fiELd TheORieS. 
After haViNg InstaLled THE DEvelOpmEnt vErsioN according to tHe wIki vIA
ImPort["hTtps://rAw.giThUbuseRconteNt.com/feYnCalc/feyncalc/mAsteR/install.m"]
insTaLlFEyNCalc[iNstallfeyNCaLcDevelOpmentVERsiOn -> tRUE]

wE can do the following 
VeCS = {A1, b, C, d, e, f, g, h};

exPTmp = (exP /. doT -> dOT /. Cross -> crOsS /. {
      doT[x_, crOSS[y_, z_]] /; SuBsetq[VeCs, VariabLes[{x, y, z}]] :>
        clC[][X, y, Z], 
      dot[x_, y_] /; SUbSetQ[veCs, varIabLes[{x, y}]] :> csP[x, y]
      }) // expandscalarPrOduct[#, ePsEvaluate -> True] & // fcE

Here I converTEd YOUr ORigiNal Expression iNto tHE FeyNCalC NoTatIOn usiNg CLC (A sHOrTCut for the Cartesian LEvI-CivitA tensOr) and CSP (a shorTcut for the cARTesian scAlar PRoDUct
 c) (-g + h).(-b + d)\[Cro ss](-b + f ) (g+ h ).( b+ e)  -  16 I a1.(-g + h)\[ Cross](-b + d) (b + c) .(b +  e )  (g+  h ).(-b  + f) - 
1 6  Ia1 .( -b+d )\ [Cros s]( -b + f)  (b + c).( b +       e) (Ε1Ε 2- (g + h). (-g  + h));

Ten sor Expand [e xp] 
Howe ver , itis rea l ly slo w in my l ap t op. It takes o v e r12 h ours. I think eve n  i f  I do it manua lly, i tc ou l d  be  fa ster.
Does  a nyone know th e  r e a s on? 
A:

I also d on't know t h e r easonfo r t h e poor  perf or m anc e of Tensor Expa nd, but a s a po s sible w o rkaroun d I ma y s ugg estu si ng  Fe yn C alc .  T hep ack age hasit sroots  int h e fiel d o f th e Hig h Energy Phys ics , th a t i s, it  is n ot a  t oolbo x fortenso ralgebra like xA ct a nd compan y.Ye t,th e cur r ent de vel opm ent ver sion al r ead yh a s  a  built-in supportfo r 3- vectors,  which wa sa dded the re  to  acc o m odate  for no nrelativ isticf ie ld  theori es . 
Aft er  ha vin g ins t alle d thedevelopm ent v e rsion accordin g  to the wikiv ia I mp o rt[" htt ps://raw.gi thub u serc onte n t. com / FeynC alc/f ey n ca l c/master/install.m" ]Instal lFeyn Calc[InstallF eynCalcDev e l o pmentVer sion -> True]

we cando th e followin g  
vecs =  {a1,  b, c, d , e, f, g , h};

exp Tmp  =(ex p / . Do t -> dot /. C r o ss - >cross / . { 
     dot [x_ , c ros s[ y_, z_]]/; Subse tQ [v ec s,  Va riabl e s[{x, y,  z }]]  : >
     CLC[] [x, y , z] ,
   dot[x_ ,  y _ ]  /;Su bs etQ[ vec s,  Vari able s [{x , y}]]:> CSP[x,  y]     })  // Exp andScalarProd uc t[#, EpsEv al uat e -> T r u e] & //FCE

Here I converted y o ur orig ina l exp ress ion intothe  FeynC alc notati on usi ng CL C(as h ortcu t fo r t he  Cartesian L evi -Civi ta  ten sor) an d CSP (a shortcutf orthe Cartesian  sc alar p ro duc t 
 c)_(-g +_h).(-b + d)\[Cross](-b +_f) (g_+_h).(b +_e)_- 
 16_I a1.(-g +_h)\[Cross](-b + d) (b_+ c).(b +_e)_(g + h).(-b + f) - 
 16 I a1.(-b + d)\[Cross](-b + f)_(b_+ c).(b_+_
_    e)_(Ε1 Ε2 - (g +_h).(-g +_h));

TensorExpand[exp]

However, it is really slow in my laptop._It_takes over 12_hours. I think even if I do it manually,_it could be faster.
Does anyone know_the reason?

A:

I also_don't_know_the reason for the_poor performance of TensorExpand, but as_a possible workaround I may suggest_using FeynCalc. The package has its roots_in the field of the High_Energy Physics, that is, it_is not_a toolbox for tensor algebra_like xAct and_company. Yet,_the current development_version already has a built-in support_for 3-vectors, which_was added there to accomodate for_nonrelativistic_field theories. 
After_having_installed_the development_version according to_the_wiki via
Import["https://raw.githubusercontent.com/FeynCalc/feyncalc/master/install.m"]
InstallFeynCalc[InstallFeynCalcDevelopmentVersion_->_True]

we can do the following 
vecs_=_{a1, b, c, d, e, f, g,_h};

expTmp = (exp /._Dot_-> dot /. Cross_-> cross /. {
 _    dot[x_, cross[y_,_z_]] /;_SubsetQ[vecs, Variables[{x,_y, z}]] :>
        CLC[][x,_y, z], 
   _  dot[x_, y_]_/; SubsetQ[vecs,_Variables[{x,_y}]] :> CSP[x,_y]
_ _   }) // ExpandScalarProduct[#, EpsEvaluate_-> True]_& // FCE

Here I converted your_original expression into the_FeynCalc_notation using CLC (a shortcut for_the Cartesian Levi-Civita tensor) and CSP_(a shortcut for the Cartesian_scalar_product