FeynCalc manual (development version)

FCToTeXReorder[exp, {{v1, v2, ... }, {a1, a2, ... }, {b1, b2, ... }}] is an auxiliary function that helps to bring the given Mathematica expression exp into a form suitable for being inserted into a LaTeX document.

To override the built-in ordering of Plus and Times, the expression is converted into a nested list made of elements of the form {a, b, ... , Plus} or {a, b, ... ,Times} for a sum or a product respectively.

Then, the option SortBy allows to specify two sorting functions that will be used to reorder the terms in both groups.

Most importantly, FCToTeXReorder can be applied to the output of a previous function call. This allows for arbitrarily deep nesting.

Finally, you can check if the final result satisfies your expectations by using FCToTeXPreviewTermOrder.

See also

Examples

exp = (-13629 - 4452*L1 + 24*L2 + 380*NH + 75*L1*NH + 130*NL + 150*L1*NL + 
      130*NV + 150*L1*NV + 20*Sqrt[3]*Pi - 75*Sqrt[3]*NH*Pi + 360*Pi^2 + 66300*z + 
      20628*L1*z + 648*L2*z + 450*NL*z + 900*NV*z + 72*Pi^2*z + 2592*z*Log[z])/81;

aux1 = FCToTeXReorder[exp, {{z}, {Log, L1, L2}, {Log, L1, L2}}]

\left\{\left\{\frac{2}{27} z \left(75 \;\text{NL}+150 \;\text{NV}+12 \pi ^2+11050\right),\{8 z,\text{L2},\text{Times}\},\{32 z,\log (z),\text{Times}\},\left\{\frac{764 z}{3},\text{L1},\text{Times}\right\},\text{Plus}\right\},\left\{\frac{1}{81} \left(-75 \sqrt{3} \pi \;\text{NH}+380 \;\text{NH}+130 \;\text{NL}+130 \;\text{NV}+360 \pi ^2+20 \sqrt{3} \pi -13629\right),\left\{\frac{8}{27},\text{L2},\text{Times}\right\},\left\{\frac{1}{27} (25 \;\text{NH}+50 \;\text{NL}+50 \;\text{NV}-1484),\text{L1},\text{Times}\right\},\text{Plus}\right\},\text{Plus}\right\}

aux1 // FCToTeXPreviewTermOrder

\left(\frac{2}{27} \left(11050+75 \;\text{NL}+150 \;\text{NV}+12 \pi ^2\right) z+8 z \;\text{L2}+32 z \log (z)+\frac{764 z \;\text{L1}}{3}\right)+\left(\frac{1}{81} \left(-13629+380 \;\text{NH}+130 \;\text{NL}+130 \;\text{NV}+20 \sqrt{3} \pi -75 \sqrt{3} \;\text{NH} \pi +360 \pi ^2\right)+\frac{8 \;\text{L2}}{27}+\frac{1}{27} (-1484+25 \;\text{NH}+50 \;\text{NL}+50 \;\text{NV}) \;\text{L1}\right)

aux1 // InputForm

{{(2*(11050 + 75*NL + 150*NV + 12*Pi^2)*z)/27, {8*z, L2, Times}, 
  {32*z, Log[z], Times}, {(764*z)/3, L1, Times}, Plus}, 
 {(-13629 + 380*NH + 130*NL + 130*NV + 20*Sqrt[3]*Pi - 
    75*Sqrt[3]*NH*Pi + 360*Pi^2)/81, {8/27, L2, Times}, 
  {(-1484 + 25*NH + 50*NL + 50*NV)/27, L1, Times}, Plus}, Plus}

res = FCToTeXReorder[aux1, {{L1, L2}, {NH, NV, NL}, {NH, NV, NL}}]

\left\{\left\{\left\{\frac{4}{27} \left(5525+6 \pi ^2\right) z,\left\{\frac{50 z}{9},\text{NL},\text{Times}\right\},\left\{\frac{100 z}{9},\text{NV},\text{Times}\right\},\text{Plus}\right\},\{8 z,\text{L2},\text{Times}\},\{32 z,\log (z),\text{Times}\},\left\{\frac{764 z}{3},\text{L1},\text{Times}\right\},\text{Plus}\right\},\left\{\left\{\frac{1}{81} \left(-13629+20 \sqrt{3} \pi +360 \pi ^2\right),\left\{\frac{130}{81},\text{NL},\text{Times}\right\},\left\{\frac{130}{81},\text{NV},\text{Times}\right\},\left\{\frac{5}{81} \left(76-15 \sqrt{3} \pi \right),\text{NH},\text{Times}\right\},\text{Plus}\right\},\left\{\frac{8}{27},\text{L2},\text{Times}\right\},\left\{\left\{-\frac{1484}{27},\left\{\frac{25}{27},\text{NH},\text{Times}\right\},\left\{\frac{50}{27},\text{NL},\text{Times}\right\},\left\{\frac{50}{27},\text{NV},\text{Times}\right\},\text{Plus}\right\},\text{L1},\text{Times}\right\},\text{Plus}\right\},\text{Plus}\right\}

res // FCToTeXPreviewTermOrder

\left(\left(\frac{4}{27} \left(5525+6 \pi ^2\right) z+\frac{50 z \;\text{NL}}{9}+\frac{100 z \;\text{NV}}{9}\right)+8 z \;\text{L2}+32 z \log (z)+\frac{764 z \;\text{L1}}{3}\right)+\left(\left(\frac{1}{81} \left(-13629+20 \sqrt{3} \pi +360 \pi ^2\right)+\frac{130 \;\text{NL}}{81}+\frac{130 \;\text{NV}}{81}+\frac{5}{81} \left(76-15 \sqrt{3} \pi \right) \;\text{NH}\right)+\frac{8 \;\text{L2}}{27}+\left(-\frac{1484}{27}+\frac{25 \;\text{NH}}{27}+\frac{50 \;\text{NL}}{27}+\frac{50 \;\text{NV}}{27}\right) \;\text{L1}\right)

exp = ((L2*(-5 + nc)*(1 + nc)*(-32*nc - 32*nc^2))/nc^3 + (L1*(1 + nc)*(672*nc + 256*nc^2 + 
          32*nc^3 - 40*nc^2*NH - 80*nc^2*NL - 80*nc^2*NV))/(3*nc^3) + ((1 + nc)*(14544*nc + 
          7872*nc^2 - 1440*nc^3 - 1216*nc^2*NH - 416*nc^2*NL - 416*nc^2*NV - 192*Sqrt[3]*nc*Pi + 
          240*Sqrt[3]*nc^2*NH*Pi - 384*nc^3*Pi^2 - 1440*nc^2*NV*z))/(36*nc^3) + 
      ((1 + nc)*(14544*nc + 7872*nc^2 - 1440*nc^3 - 1216*nc^2*NH - 416*nc^2*NL - 
           416*nc^2*NV - 192*Sqrt[3]*nc*Pi + 240*Sqrt[3]*nc^2*NH*Pi - 384*nc^3*Pi^2 + 
           11520*nc*z + 15984*nc^2*z + 3312*nc^3*z - 1440*nc^2*NL*z - 2880*nc^2*NV*z - 
           768*nc^3*Pi^2*z))/(36*nc^3))/2

\frac{1}{2} \left(\frac{\text{L1} (\text{nc}+1) \left(32 \;\text{nc}^3-40 \;\text{nc}^2 \;\text{NH}-80 \;\text{nc}^2 \;\text{NL}-80 \;\text{nc}^2 \;\text{NV}+256 \;\text{nc}^2+672 \;\text{nc}\right)}{3 \;\text{nc}^3}+\frac{\text{L2} (\text{nc}-5) (\text{nc}+1) \left(-32 \;\text{nc}^2-32 \;\text{nc}\right)}{\text{nc}^3}+\frac{1}{36 \;\text{nc}^3}(\text{nc}+1) \left(-384 \pi ^2 \;\text{nc}^3-1440 \;\text{nc}^3-1216 \;\text{nc}^2 \;\text{NH}+240 \sqrt{3} \pi \;\text{nc}^2 \;\text{NH}-416 \;\text{nc}^2 \;\text{NL}-1440 \;\text{nc}^2 \;\text{NV} z-416 \;\text{nc}^2 \;\text{NV}+7872 \;\text{nc}^2-192 \sqrt{3} \pi \;\text{nc}+14544 \;\text{nc}\right)+\frac{1}{36 \;\text{nc}^3}(\text{nc}+1) \left(-768 \pi ^2 \;\text{nc}^3 z+3312 \;\text{nc}^3 z-384 \pi ^2 \;\text{nc}^3-1440 \;\text{nc}^3-1216 \;\text{nc}^2 \;\text{NH}+240 \sqrt{3} \pi \;\text{nc}^2 \;\text{NH}-1440 \;\text{nc}^2 \;\text{NL} z-416 \;\text{nc}^2 \;\text{NL}-2880 \;\text{nc}^2 \;\text{NV} z-416 \;\text{nc}^2 \;\text{NV}+15984 \;\text{nc}^2 z+7872 \;\text{nc}^2+11520 \;\text{nc} z-192 \sqrt{3} \pi \;\text{nc}+14544 \;\text{nc}\right)\right)

Split into pieces that depend on L1, L2 and those then don’ t . Then collect terms in the first group w.r.t L1, L2 . Collect terms in the second group w.r.t. z . Use ExpandAll as the factoring function in both groups . Sort the resulting terms in the first group such, that terms containing L1 come first, then those with L2 and finally all the rest . Put terms that depend on z in the second group first .

out1 = FCToTeXReorder[exp, {{L1, L2}, {L1, L2}, {z}}, Split -> True, Factoring -> {Function[x, 
      ExpandAll[x]], Function[x, ExpandAll[x]]}, SortBy -> {Function[x, Which[! FreeQ2[x, {L1}], 1, 
       ! FreeQ2[x, {L2}], 2, True, 30]], Function[x, Which[! FreeQ2[x, {z}], 1, True, 3]]}]

\left\{\left\{\left\{\frac{112}{\text{nc}^2}-\frac{20 \;\text{NH}}{3 \;\text{nc}}-\frac{40 \;\text{NL}}{3 \;\text{nc}}-\frac{40 \;\text{NV}}{3 \;\text{nc}}+\frac{16 \;\text{nc}}{3}+\frac{464}{3 \;\text{nc}}-\frac{20 \;\text{NH}}{3}-\frac{40 \;\text{NL}}{3}-\frac{40 \;\text{NV}}{3}+48,\text{L1},\text{Times}\right\},\left\{\frac{80}{\text{nc}^2}-16 \;\text{nc}+\frac{144}{\text{nc}}+48,\text{L2},\text{Times}\right\},\text{Plus}\right\},\left\{\left\{\frac{160}{\text{nc}^2}-\frac{20 \;\text{NL}}{\text{nc}}-\frac{60 \;\text{NV}}{\text{nc}}-\frac{32 \pi ^2 \;\text{nc}}{3}+46 \;\text{nc}+\frac{382}{\text{nc}}-20 \;\text{NL}-60 \;\text{NV}-\frac{32 \pi ^2}{3}+268,z,\text{Times}\right\},-\frac{16 \pi }{\sqrt{3} \;\text{nc}^2}+\frac{404}{\text{nc}^2}-\frac{304 \;\text{NH}}{9 \;\text{nc}}+\frac{20 \pi \;\text{NH}}{\sqrt{3} \;\text{nc}}-\frac{104 \;\text{NL}}{9 \;\text{nc}}-\frac{104 \;\text{NV}}{9 \;\text{nc}}-\frac{32 \pi ^2 \;\text{nc}}{3}-40 \;\text{nc}-\frac{16 \pi }{\sqrt{3} \;\text{nc}}+\frac{1868}{3 \;\text{nc}}-\frac{304 \;\text{NH}}{9}+\frac{20 \pi \;\text{NH}}{\sqrt{3}}-\frac{104 \;\text{NL}}{9}-\frac{104 \;\text{NV}}{9}-\frac{32 \pi ^2}{3}+\frac{536}{3},\text{Plus}\right\},\text{Plus}\right\}

Now work with the innermost brackets and put terms that contain z first . All the other terms should be sorted, such that NH, NV and NL terms appear in this order.

out2 = FCToTeXReorder[out1, {{}, {}, {}}, Split -> False, Factoring -> {Function[x, ExpandAll[x]], 
     Function[x, ExpandAll[x]]}, SortBy -> {Function[x, Which[! FreeQ2[x, {z}], 1, ! FreeQ2[x, {NH}], 
       2, ! FreeQ2[x, {NV}], 3, ! FreeQ2[x, {NL}], 4, True, 5]], Function[x, Which[! FreeQ2[x, {z}], 
       1, ! FreeQ2[x, {NH}], 2, ! FreeQ2[x, {NV}], 3, ! FreeQ2[x, {NL}], 4, True, 5]]}]

\left\{\left\{\left\{\left\{-\frac{20 \;\text{NH}}{3},-\frac{20 \;\text{NH}}{3 \;\text{nc}},-\frac{40 \;\text{NV}}{3},-\frac{40 \;\text{NV}}{3 \;\text{nc}},-\frac{40 \;\text{NL}}{3},-\frac{40 \;\text{NL}}{3 \;\text{nc}},48,\frac{112}{\text{nc}^2},\frac{464}{3 \;\text{nc}},\frac{16 \;\text{nc}}{3},\text{Plus}\right\},\text{L1},\text{Times}\right\},\left\{\left\{48,\frac{80}{\text{nc}^2},\frac{144}{\text{nc}},-16 \;\text{nc},\text{Plus}\right\},\text{L2},\text{Times}\right\},\text{Plus}\right\},\left\{\left\{\left\{-60 \;\text{NV},-\frac{60 \;\text{NV}}{\text{nc}},-20 \;\text{NL},-\frac{20 \;\text{NL}}{\text{nc}},268,\frac{160}{\text{nc}^2},\frac{382}{\text{nc}},46 \;\text{nc},-\frac{32 \pi ^2}{3},-\frac{32 \pi ^2 \;\text{nc}}{3},\text{Plus}\right\},z,\text{Times}\right\},\left\{-\frac{304 \;\text{NH}}{9},-\frac{304 \;\text{NH}}{9 \;\text{nc}},\frac{20 \pi \;\text{NH}}{\sqrt{3}},\frac{20 \pi \;\text{NH}}{\sqrt{3} \;\text{nc}},-\frac{104 \;\text{NV}}{9},-\frac{104 \;\text{NV}}{9 \;\text{nc}},-\frac{104 \;\text{NL}}{9},-\frac{104 \;\text{NL}}{9 \;\text{nc}},\frac{536}{3},\frac{404}{\text{nc}^2},\frac{1868}{3 \;\text{nc}},-40 \;\text{nc},-\frac{16 \pi }{\sqrt{3} \;\text{nc}^2},-\frac{16 \pi }{\sqrt{3} \;\text{nc}},-\frac{32 \pi ^2}{3},-\frac{32 \pi ^2 \;\text{nc}}{3},\text{Plus}\right\},\text{Plus}\right\},\text{Plus}\right\}

FCToTeXPreviewTermOrder[out2]

\left(\left(-\frac{20 \;\text{NH}}{3}-\frac{20 \;\text{NH}}{3 \;\text{nc}}-\frac{40 \;\text{NV}}{3}-\frac{40 \;\text{NV}}{3 \;\text{nc}}-\frac{40 \;\text{NL}}{3}-\frac{40 \;\text{NL}}{3 \;\text{nc}}+48+\frac{112}{\text{nc}^2}+\frac{464}{3 \;\text{nc}}+\frac{16 \;\text{nc}}{3}\right) \;\text{L1}+\left(48+\frac{80}{\text{nc}^2}+\frac{144}{\text{nc}}-16 \;\text{nc}\right) \;\text{L2}\right)+\left(\left(-60 \;\text{NV}-\frac{60 \;\text{NV}}{\text{nc}}-20 \;\text{NL}-\frac{20 \;\text{NL}}{\text{nc}}+268+\frac{160}{\text{nc}^2}+\frac{382}{\text{nc}}+46 \;\text{nc}-\frac{32 \pi ^2}{3}-\frac{32 \;\text{nc} \pi ^2}{3}\right) z+\left(-\frac{304 \;\text{NH}}{9}-\frac{304 \;\text{NH}}{9 \;\text{nc}}+\frac{20 \;\text{NH} \pi }{\sqrt{3}}+\frac{20 \;\text{NH} \pi }{\sqrt{3} \;\text{nc}}-\frac{104 \;\text{NV}}{9}-\frac{104 \;\text{NV}}{9 \;\text{nc}}-\frac{104 \;\text{NL}}{9}-\frac{104 \;\text{NL}}{9 \;\text{nc}}+\frac{536}{3}+\frac{404}{\text{nc}^2}+\frac{1868}{3 \;\text{nc}}-40 \;\text{nc}-\frac{16 \pi }{\sqrt{3} \;\text{nc}^2}-\frac{16 \pi }{\sqrt{3} \;\text{nc}}-\frac{32 \pi ^2}{3}-\frac{32 \;\text{nc} \pi ^2}{3}\right)\right)