FORM vs. Wolfram: simple examples

test11.frm

* Example:
*   form -D M=10 -D N=15 test11.frm
Symbol x1,...,x`M';
Local F = (x1+...+x`M')^`N';
.end

test11.m

(*
 * Example:
 *   wolframscript -f test11.m 10 15
 *)
m = $ScriptCommandLine[[2]] // ToExpression;
n = $ScriptCommandLine[[3]] // ToExpression;

f = Sum[Symbol["x" <> ToString[i]], {i, 1, m}]^n;

Print["Input: ", f];

{t, f} = f // Expand // Timing;

Print["Timing: ", t, " seconds"]
Print["Number of terms: ", f // Length];
Print["Bytes used :", f // ByteCount];

test21.frm

* Example:
*   form -D N=12 test21.frm

Index j;  * fermion line
Auto Index mu;  * Lorentz indices

Local F = g_(j,mu1,...,mu`N');
Print +s;
.sort:input;

tracen j;
*Print +s;
*.sort:result;

.end

test21.m

(*
 * Example:
 *   wolframscript -f test21.m 12
 *)
n = $ScriptCommandLine[[2]] // ToExpression;

$FeynCalcStartupMessages = False;
<< FeynCalc`;

f = GAD @@ Table[
  Symbol["mu" <> ToString[i]], {i, 1, n}
];

Print["Input: ", f];

{t, f} = Tr[f] // Expand // Timing;

Print["Timing: ", t, " seconds"];
Print["Number of terms: ", f // Length];
Print["Bytes used :", f // ByteCount];

test31.frm

* Example:
*   form -D N=12 test31.frm

Index j;  * fermion line

Symbol D,[D-4],ep;
Dimension D:[D-4];
Auto Index mu;  * Lorentz indices

Local F = g_(j,mu1,...,mu`N',mu1,...,mu`N');
Print +s;
.sort:input;

tracen j;
.sort
id D = 4 - 2 * ep;
id [D-4] = - 2 * ep;
Print;
.sort:result;

.end

test31.m

(*
 * Example:
 *   wolframscript -f test31.m 12
 *)
n = $ScriptCommandLine[[2]] // ToExpression;

$FeynCalcStartupMessages = False;
<< FeynCalc`;

f = Table[
  Symbol["mu" <> ToString[i]], {i, 1, n}
];
f = GAD @@ Join[f, f];

Print["Input: ", f];

{t, f} = Tr[f] /. D -> 4 - 2 ep // Expand // Timing;

Print["Result: ", f];
Print["Timing: ", t, " seconds"];
Print["Number of terms: ", f // Length];
Print["Bytes used :", f // ByteCount];