TARCER examples

The timings below are for the Linux  version of Mathematica 3.0 on a Pentium Pro 200 with 96 MB RAM.

<< tarcer23.mx

This switches the comment mechanism on. Changing True to False will suppress the comment notebook.

$Comment = True;

Off[General::"spell"]; Off[General::"spell1"];

Simple Examples

This reduces (for (p^2) = (M^2)) 
(Subscript[F, {1, 0}{1, M}{1, M}{1, 0}{1, M}]^((d))) =
∫∫   
      (((d^d) (Subscript[q, 1]) (d^d) 
          (Subscript[q, 2]))/([(Subscript[q, 1]^2)] [(Subscript[q, 2]^2) - (M^2)] [
              ((((Subscript[q, 1]) - p))^2) - (M^2)] [((((Subscript[q, 2]) - p))^2)])) [
          ((((Subscript[q, 1]) - (Subscript[q, 2])))^2) - (M^2)]

ex1 = 
   TarcerRecurse[TFI[d, M^2, 
     {{1, 0}, {1, M}, {1, M}, {1, 0}, 
      {1, M}}]]

This expands up to the constant term.

TarcerExpand[ex1,  d -> 4 + ε]

Moment Examples

eg2[m_]:=TFI[d, M^2,Δp,{m,0}, 
     {{2, M}, 1, 1, {1,M}, 
      {1, M}}]

TarcerRecurse[eg2[0]]

TarcerExpand[%, d -> 4 + ε, 0]

TarcerRecurse[eg2[1]]

TarcerExpand[%, d -> 4 + ε, 0]

General massive examples

Typesetting rules:

\(MakeBoxes[pp, fmt_] := 
      InterpretationBox[SuperscriptBox["p", 2], pp]; 

    MakeBoxes[m2, fmt_] := InterpretationBox[SubscriptBox["m", 2], m2]; 

    MakeBoxes[m3, fmt_] := InterpretationBox[SubscriptBox["m", 3], m3]; 

    MakeBoxes[m4, fmt_] := InterpretationBox[SubscriptBox["m", 4], m4]; 
    \)

(Subscript[Y, 234]^1)

\(Timing[

      y1234\  = \ 
        TarcerRecurse[\ 
          TFI[D, pp, {1, 0, 0, 0, 0}, {0, \ {1, m4}, {1, m2}, 0, {1, m3}}]\ ]
          
]\)

(Subscript[Y, 234]^11)

\(Timing[

      y11234\  = \ 
        TarcerRecurse[\ 
          TFI[D, pp, {2, 0, 0, 0, 0}, {0, \ {1, m4}, {1, m2}, 0, {1, m3}}]\ ]
          
]\)

(Subscript[Y, 234]^5)

\(Timing[

      y5234\  = \ 
        TarcerRecurse[\ 
          TFI[D, pp, {0, 0, 1, 0, 0}, {0, \ {1, m4}, {1, m2}, 0, {1, m3}}]\ ]
          
]\)