       Re: the temperamental loop or something wrong with my expression

• To: mathgroup at smc.vnet.net
• Subject: [mg80541] Re: [mg80534] the temperamental loop or something wrong with my expression
• From: DrMajorBob <drmajorbob at bigfoot.com>
• Date: Sun, 26 Aug 2007 02:52:50 -0400 (EDT)
• References: <22937955.1187939639338.JavaMail.root@m35>

```Post that without "In[...]:=" and the outputs, and you'd triple the chance
that anybody will respond. To do anything with your code, we have to
manually, laboriously figure out what's a printed output (guessing in some
cases), delete all of it, find all the Ins and Outs, delete those...

Who'd do that?

Well... I might, but I don't have a lot to do some days!

The first line tells me the likely problem, however... and that's
Simplify. You're using complicated expressions, making them even MORE
complicated... and then trying to Simplify. Frequently.

That can easily take more time than you'll ever have.

When possible you should Simplify once and for all and use Set, not
SetDelayed, for example:

approxFab[f_,t_,p_]=1/384 f^2 (-35-28 Cos[2 t]-Cos[4 t]+8 (Cos[4
p]+Sqrt Sin[4 p]) Sin[t]^4)+1/147456f^4 (5702-86 Cos[4 t]-7 Cos[6 t]-16
Sin[t]^4 (-41 Cos[2 p]+95 Cos[4 p]+Sqrt (41 Sin[2 p]+95 Sin[4 p])+2
Cos[6 p] Sin[t]^2)+Cos[2 t] (4631+16 (-Cos[2 p]+7 Cos[4 p]+Sqrt (Sin[2
p]+7 Sin[4 p])) Sin[t]^4))-1/6144\[ImaginaryI] f^3 (32 (7+Cos[2 t]) Sin[3
p] Sin[t]^3+16 Sqrt Cos[5 p] Sin[t]^5+16 Sin[5 p] Sin[t]^5-Sqrt
Cos[p] (42 Sin[t]+27 Sin[3 t]+Sin[5 t])+Sin[p] (42 Sin[t]+27 Sin[3
t]+Sin[5 t]))//Simplify

(1/147456)f^2 (384 (-35-28 Cos[2 t]-Cos[4 t]+8 (Cos[4 p]+Sqrt Sin[4 p])
Sin[t]^4)+f^2 (5702-86 Cos[4 t]-7 Cos[6 t]-16 Sin[t]^4 (-41 Cos[2 p]+95
Cos[4 p]+Sqrt (41 Sin[2 p]+95 Sin[4 p])+2 Cos[6 p] Sin[t]^2)+Cos[2 t]
(4631+16 (-Cos[2 p]+7 Cos[4 p]+Sqrt (Sin[2 p]+7 Sin[4 p]))
Sin[t]^4))-24 \[ImaginaryI] f (16 Sin[t]^3 (2 (7+Cos[2 t]) Sin[3
p]+(Sqrt Cos[5 p]+Sin[5 p]) Sin[t]^2)-Sqrt Cos[p] (42 Sin[t]+27
Sin[3 t]+Sin[5 t])+Sin[p] (42 Sin[t]+27 Sin[3 t]+Sin[5 t])))

In that case Simplify didn't accomplish much (reducing LeafCount from 248
to 243), but it's worth trying, and Set ("=") will still yield (usually) a
function that executes faster than with SetDelayed (":="). This can't be
done with a function like delconj that uses Part, but even so, delconj
could be simplified to

delconj[eq_] := Conjugate@Total@eq /. Conjugate[x_] -> x

I'm not sure what "/. Conjugate[x_] -> x" accomplishes for you (too many
details for me), but eliminate it if you can. Even if you can't, the above
will be much faster than the original.

Similarly, expandaa becomes:

expandaa[eq_] := CoefficientList[eq, f].f^Range@Length@eq

(Dot product is fast.)

It's doubtful that Expand[Simplify[....]] makes the Integrate in
a\[Alpha]\[Alpha][f_, l_, m_] evaluate faster or better. If the
integration can be done for symbolic f, l, and m, do it just ONCE (not
every time the function is called), like this:

a\[Alpha]\[Alpha][f_, l_, m_] =
Integrate[
Sin[\[Theta]]*
conjSphericalHarmonicY[l,
m, \[Theta], \[Phi]] approxF\[Alpha]\[Alpha][
f, \[Theta], \[Phi]], {\[Theta], 0, Pi}, {\[Phi], 0,
2 Pi}]

That doesn't work as things are, but try to redefine
conjSphericalHarmonicY and approxF\[Alpha]\[Alpha] so that it DOES.

I hope some of that helps!

Bobby

On Fri, 24 Aug 2007 01:06:10 -0500, Jack Yu <Jack.Yu at astro.cf.ac.uk> wrote:

> Hi
> I have defined a function whose value I want to know  for a range of two
> of its arguments.  So to save time, I use a Do loop.  However, after a
> few loops, it just doesn't produce any more result, even though at the
> top it still says: 'Running ...'. I know that when I do this by manually
> changing the arguments without using a Do loop, they all evaluate.  So I
> thought it's to do with Do, and after reading somewhere in this forum
> that For and While are faster, I tried them as well, but they still
> become stuck after a few loops.  The best I can do using a loop is to
> split the range of the variables into smaller ones; for some reason,
> this sometimes work, but sometimes it still doesn't work.  The quickest
> I can do is actually just do them individually without using a loop.  I
> find this a bit puzzling and would really appreciate if anyone can help
> me with this.
>
> The Notebook is here:
> ***********************************************
> In:=
> delconj[eq_] :=
>     Apply[Plus,(Conjugate[
>             Simplify[
>               Table[Expand[eq][[i]],{i,1,
>                   Length[Expand[eq]]}]]]) /. {Conjugate[x_]\[Rule]x}];
>
> In:=
> conjSphericalHarmonicY[l_,m_,\[Theta]_,\[Phi]_]:=
>     delconj[1+SphericalHarmonicY[l,m,\[Theta],\[Phi]]]-1;
>
> In:=
> conjY[eq_]:= Conjugate[eq] /. Conjugate[x_]\[Rule]x;
>
> In:=
> expandaa[eq_]:=(aaa=eq;bbb=CoefficientList[aaa,f];
>       Apply[Plus,Table[bbb[[i]]f^(i-1),{i,1,Length[bbb]}]]);
>
> In:=
> \!\(\(approxF\[Alpha]\[Alpha][f_, \[Theta]_, \[Phi]_] :=
>       1\/12\ \((Cos[\[Theta]]\^2\ \((3 + Cos[4\ \[Phi]])\) +
>               4\ \((1 +
>                     Cos[\[Theta]]\^4)\)\ Cos[\[Phi]]\^2\ Sin[\[Phi]]\^2)\)\ f\
> \^2 + \(1\/147456\) \((\((\(-11278\) - 9307\ Cos[2\ \[Theta]] +
>                   94\ Cos[4\ \[Theta]] + 11\ Cos[6\ \[Theta]] +
>                   128\ \((\(-5\) + Cos[2\ \[Theta]])\)\ Cos[
>                       2\ \[Phi]]\ Sin[\[Theta]]\^4 -
>                   64\ \((\(-37\) + 5\ Cos[2\ \[Theta]])\)\ Cos[
>                       4\ \[Phi]]\ Sin[\[Theta]]\^4 -
>                   32\ Cos[6\ \[Phi]]\ Sin[\[Theta]]\^6)\)\ f\^4)\);\)\)
>
> In:=
> \!\(\(approxF\[Alpha]\[Beta][f_, \[Theta]_, \[Phi]_] :=
>       1\/384\ \((\(-35\) - 28\ Cos[2\ \[Theta]] - Cos[4\ \[Theta]] +
>               8\ Sin[\[Theta]]\^4\ \((Cos[
>                       4\ \[Phi]] + \@3\ Sin[
>                         4\ \[Phi]])\))\)\ f\^2 + \(-\(\(1\/6144\) \((\
> \[ImaginaryI]\ \((16\ \@3\ Cos[
>                         5\ \[Phi]]\ Sin[\[Theta]]\^5 -
> \@3\ Cos[\[Phi]]\ \
> \((42\ Sin[\[Theta]] + 27\ Sin[3\ \[Theta]] +
>                           Sin[5\ \[Theta]])\) + \((42\ Sin[\[Theta]] +
>                           27\ Sin[3\ \[Theta]] +
>                           Sin[5\ \[Theta]])\)\ Sin[\[Phi]] +
>                     32\ \((7
> + Cos[2\ \[Theta]])\)\ Sin[\[Theta]]\^3\ Sin[
>                         3\ \[Phi]] +
>                     16\ Sin[\[Theta]]\^5\ Sin[
>                         5\ \[Phi]])\)\ f\^3)\)\)\) + \(1\/147456\)
> \((\((5702 \
> - 86\ Cos[4\ \[Theta]] - 7\ Cos[6\ \[Theta]] -
>                   16\ Sin[\[Theta]]\^4\ \((\(-41\)\ Cos[2\ \[Phi]] +
>                         95\ Cos[4\ \[Phi]] +
>                         2\ Cos[
>                             6\ \[Phi]]\ Sin[\[Theta]]\^2
> + \@3\ \((41\ Sin[
>                                   2\ \[Phi]] + 95\ Sin[4\ \[Phi]])\))\) +
>                   Cos[2\ \[Theta]]\ \((4631 +
>                         16\ Sin[\[Theta]]\^4\ \((\(-Cos[2\ \[Phi]]\) +
>                               7\ Cos[
>                                   4\ \[Phi]] + \@3\ \((Sin[2\ \[Phi]] +
>                                     7\ Sin[
>                                         4\ \[Phi]])\))\))\))\)\ f\^4)\);\)\)
>
> In:=
> a\[Alpha]\[Alpha][f_,l_,m_]:=
>     Integrate[
>       Expand[Simplify[
>           Sin[\[Theta]]*
>             conjSphericalHarmonicY[l,
>               m,\[Theta],\[Phi]]approxF\[Alpha]\[Alpha][
>               f,\[Theta],\[Phi]]]],{\[Theta],0,Pi},{\[Phi],0,2Pi}];
>
> In:=
> a\[Alpha]\[Beta][f_,l_,m_]:=
>     Integrate[
>       Expand[Simplify[
>           Sin[\[Theta]]*
>             conjSphericalHarmonicY[l,m,\[Theta],\[Phi]]approxF\[Alpha]\[Beta][
>               f,\[Theta],\[Phi]]]],{\[Theta],0,Pi},{\[Phi],0,2Pi}];
>
> In:=
> \!\(\(a\[Beta]\[Beta][f_, l_, m_] :=
>       Exp[\(-I\)*m*\((\(2  Pi\)\/3)\)] a\[Alpha]\[Alpha][f, l, m];\)\)
>
> In:=
> \!\(\(a\[Gamma]\[Gamma][f_, l_, m_] :=
>       Exp[\(-I\)*m*\((\(4  Pi\)\/3)\)] a\[Alpha]\[Alpha][f, l, m];\)\)
>
> In:=
> \!\(\(a\[Beta]\[Gamma][f_, l_, m_] :=
>       Exp[\(-I\)*m*\((\(2  Pi\)\/3)\)] a\[Alpha]\[Beta][f, l, m];\)\)
>
> In:=
> \!\(\(a\[Gamma]\[Alpha][f_, l_, m_] :=
>       Exp[\(-I\)*m*\((\(4  Pi\)\/3)\)] a\[Alpha]\[Beta][f, l, m];\)\)
>
> In:=
> a\[Alpha]\[Gamma][f_,l_,m_]:= (-1)^m*conjY[a\[Alpha]\[Beta][f,l,m]];
>
> In:=
> \!\(\(a\[Beta]\[Alpha][f_, l_, m_] := \((\(-1\))\)^m*
>         Exp[\(-I\)*m*\((\(2  Pi\)\/3)\)] conjY[a\[Alpha]\[Beta][f, l,
> m]];\)\)
>
> In:=
> \!\(\(a\[Gamma]\[Beta][f_, l_, m_] := \((\(-1\))\)^m*
>         Exp[\(-I\)*m*\((\(4  Pi\)\/3)\)] conjY[a\[Alpha]\[Beta][f, l,
> m]];\)\)
>
> In:=
> \!\(\(aET[f_, l_,
>         m_] := \ \(1\/\(3 \@ 2\)\) \((a\[Alpha]\[Alpha][f, l, m] -
>             2  a\[Beta]\[Beta][f, l, m] + a\[Gamma]\[Gamma][f, l, m] +
>             a\[Alpha]\[Beta][f, l, m] - 2  a\[Beta]\[Alpha][f, l, m] +
>             a\[Gamma]\[Beta][f, l, m] -
>             2  a\[Beta]\[Gamma][f, l, m] + \((a\[Alpha]\[Gamma][f, l, m]
> +
>                 a\[Gamma]\[Alpha][f, l, m])\))\);\)\)
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,6,2]]]]]
>
> Out=
> \!\({53.921514`8.183307071248283\ Second, \(\((3\ \[ImaginaryI] -
> \@3)\)\ \
> f\^4\ \@\(\[Pi]\/910\)\)\/4752}\)
>
> Do[Print["aET(f,",l,m,")=",
>     expandaa[FullSimplify[ComplexExpand[aET[f,l,m]]]]],{l,0,6},{m,0,l} ]
>
> aET(f,\[InvisibleSpace]0\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]1\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]1\[InvisibleSpace]1\
> \[InvisibleSpace]")="\[InvisibleSpace]\(1\/168\ \((\(-\[ImaginaryI]\) + \
> \@3)\)\ f\^3\ \@\[Pi]\)\),
>     SequenceForm[ "aET(f,", 1, 1, ")=",
>       Times[
>         Rational[ 1, 168],
>         Plus[
>           Complex[ 0, -1],
>           Power[ 3,
>             Rational[ 1, 2]]],
>         Power[ f, 3],
>         Power[ Pi,
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]2\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]2\[InvisibleSpace]1\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]2\[InvisibleSpace]2\
> \[InvisibleSpace]")="\[InvisibleSpace]\(1\/864\ \((\(-3\)\ \[ImaginaryI]
> + \
> \@3)\)\ f\^4\ \@\(\[Pi]\/5\)\)\),
>     SequenceForm[ "aET(f,", 2, 2, ")=",
>       Times[
>         Rational[ 1, 864],
>         Plus[
>           Complex[ 0, -3],
>           Power[ 3,
>             Rational[ 1, 2]]],
>         Power[ f, 4],
>         Power[
>           Times[
>             Rational[ 1, 5], Pi],
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]3\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]3\[InvisibleSpace]1\
> \[InvisibleSpace]")="\[InvisibleSpace]\(1\/72\ \((\(-\[ImaginaryI]\)
> + \@3)\)\
> \ f\^3\ \@\(\[Pi]\/14\)\)\),
>     SequenceForm[ "aET(f,", 3, 1, ")=",
>       Times[
>         Rational[ 1, 72],
>         Plus[
>           Complex[ 0, -1],
>           Power[ 3,
>             Rational[ 1, 2]]],
>         Power[ f, 3],
>         Power[
>           Times[
>             Rational[ 1, 14], Pi],
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]3\[InvisibleSpace]2\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]3\[InvisibleSpace]3\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]4\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]4\[InvisibleSpace]1\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]4\[InvisibleSpace]2\
> \[InvisibleSpace]")="\[InvisibleSpace]\(\[ImaginaryI]\ \((\[ImaginaryI]
> + \
> \@3)\)\ f\^4\ \@\(\[Pi]\/5\)\)\/3168\),
>     SequenceForm[ "aET(f,", 4, 2, ")=",
>       Times[
>         Complex[ 0,
>           Rational[ 1, 3168]],
>         Plus[
>           Complex[ 0, 1],
>           Power[ 3,
>             Rational[ 1, 2]]],
>         Power[ f, 4],
>         Power[
>           Times[
>             Rational[ 1, 5], Pi],
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]4\[InvisibleSpace]3\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]4\[InvisibleSpace]4\
> \[InvisibleSpace]")="\[InvisibleSpace]\(-\(\(17\ \[ImaginaryI]\ \((\(-\
> \[ImaginaryI]\) + \@3)\)\ f\^4\ \@\(\[Pi]\/35\)\)\/3168\)\)\),
>     SequenceForm[ "aET(f,", 4, 4, ")=",
>       Times[
>         Complex[ 0,
>           Rational[ -17, 3168]],
>         Plus[
>           Complex[ 0, -1],
>           Power[ 3,
>             Rational[ 1, 2]]],
>         Power[ f, 4],
>         Power[
>           Times[
>             Rational[ 1, 35], Pi],
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]5\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]5\[InvisibleSpace]1\
> \[InvisibleSpace]")="\[InvisibleSpace]\(\((\(-\[ImaginaryI]\)
> + \@3)\)\ f\^3\ \
> \@\(\[Pi]\/55\)\)\/1008\),
>     SequenceForm[ "aET(f,", 5, 1, ")=",
>       Times[
>         Rational[ 1, 1008],
>         Plus[
>           Complex[ 0, -1],
>           Power[ 3,
>             Rational[ 1, 2]]],
>         Power[ f, 3],
>         Power[
>           Times[
>             Rational[ 1, 55], Pi],
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]5\[InvisibleSpace]2\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]5\[InvisibleSpace]3\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]5\[InvisibleSpace]4\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]5\[InvisibleSpace]5\
> \[InvisibleSpace]")="\[InvisibleSpace]\(1\/72\ \((3
> + \[ImaginaryI]\ \@3)\)\ \
> f\^3\ \@\(\[Pi]\/154\)\)\),
>     SequenceForm[ "aET(f,", 5, 5, ")=",
>       Times[
>         Rational[ 1, 72],
>         Plus[ 3,
>           Times[
>             Complex[ 0, 1],
>             Power[ 3,
>               Rational[ 1, 2]]]],
>         Power[ f, 3],
>         Power[
>           Times[
>             Rational[ 1, 154], Pi],
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]6\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> Do[Print["aET(f,",l,m,")=",
>     expandaa[FullSimplify[ComplexExpand[aET[f,l,m]]]]],{l,6,8},{m,0,l}]
>
> aET(f,\[InvisibleSpace]6\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]6\[InvisibleSpace]1\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]6\[InvisibleSpace]2\
> \[InvisibleSpace]")="\[InvisibleSpace]\(\((3\ \[ImaginaryI] -
> \@3)\)\ f\^4\ \
> \@\(\[Pi]\/910\)\)\/4752\),
>     SequenceForm[ "aET(f,", 6, 2, ")=",
>       Times[
>         Rational[ 1, 4752],
>         Plus[
>           Complex[ 0, 3],
>           Times[ -1,
>             Power[ 3,
>               Rational[ 1, 2]]]],
>         Power[ f, 4],
>         Power[
>           Times[
>             Rational[ 1, 910], Pi],
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]6\[InvisibleSpace]3\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \!\(\*
>   InterpretationBox[\("aET(f,"\[InvisibleSpace]6\[InvisibleSpace]4\
> \[InvisibleSpace]")="\[InvisibleSpace]\(-\(\(\[ImaginaryI]\ \((\(-\
> \[ImaginaryI]\) + \@3)\)\ f\^4\ \@\(\[Pi]\/91\)\)\/3168\)\)\),
>     SequenceForm[ "aET(f,", 6, 4, ")=",
>       Times[
>         Complex[ 0,
>           Rational[ -1, 3168]],
>         Plus[
>           Complex[ 0, -1],
>           Power[ 3,
>             Rational[ 1, 2]]],
>         Power[ f, 4],
>         Power[
>           Times[
>             Rational[ 1, 91], Pi],
>           Rational[ 1, 2]]]],
>     Editable->False]\)
>
> aET(f,\[InvisibleSpace]6\[InvisibleSpace]5\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]6\[InvisibleSpace]6\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]7\[InvisibleSpace]0\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]7\[InvisibleSpace]1\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> aET(f,\[InvisibleSpace]7\[InvisibleSpace]2\[InvisibleSpace])=\[InvisibleSpace]\
> 0
>
> \$Aborted
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,7,3]]]]]
>
> Out=
> {54.478757 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,7,4]]]]]
>
> Out=
> {76.970704 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,7,5]]]]]
>
> Out=
> {60.329395 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,7,6]]]]]
>
> Out=
> {32.853831 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,7,7]]]]]
>
> Out=
> {32.139781 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,0]]]]]
>
> Out=
> {69.877317 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,1]]]]]
>
> Out=
> {91.335676 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,2]]]]]
>
> Out=
> {88.233249 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,3]]]]]
>
> Out=
> {77.997297 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,4]]]]]
>
> Out=
> {79.343742 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,5]]]]]
>
> Out=
> {62.095294 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,6]]]]]
>
> Out=
> {49.984301 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,7]]]]]
>
> Out=
> {33.587836 Second,0}
>
> In:=
> AbsoluteTiming[expandaa[FullSimplify[ComplexExpand[aET[f,8,8]]]]]
>
> Out=
> {32.811034 Second,0}
>
> ********************************************
>
> aET[f,l,m] is the function I want to evaluate for {l,0,8} and for each=
=

> l, {m,-l,l}.  As can be seen in the first Do loop, it stopped at  =

> aET[f,6,0]; I deleted 'Aborted'. And as can be seen in the second Do  =

> loop, it stopped at aET[f,7,2].  I finished the rest just by using the=
=

> expression expandaa[FullSimplify[ComplexExpand[aET[f,l,m]]]] again and=
=

> again.  When I was doing this I noticed that the above expression  =

> sometimes gets stuck and I have to do it one step at a time. e.g  =

> aET[f,l,m], then ComplexExpand[aET[f,l,m]], then  =

> FullSimplify[ComplexExpand[aET[f,l,m]]] and so on, then the whole  =

> expression will work afterwards.  This is also very strange.
>
>

-- =

DrMajorBob at bigfoot.com

```

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