Re: Re: a LOT of Mathematica bugs (some very old)
- To: mathgroup at smc.vnet.net
- Subject: [mg95079] Re: [mg95046] Re: a LOT of Mathematica bugs (some very old)
- From: Bob Hanlon <hanlonr at cox.net>
- Date: Mon, 5 Jan 2009 03:29:58 -0500 (EST)
- Reply-to: hanlonr at cox.net
In your first example just increase the working precision
Plot[2^-s LerchPhi[-1, s, 1/2], {s, -6.75, -7},
WorkingPrecision -> 20]
Bob Hanlon
On Sun, Jan 4, 2009 at 11:52 AM , Marcelo Surnamed wrote:
> control error
> Plot[2^-s LerchPhi[-1, s, 1/2], {s, -6.75, -7}]
>
>
> Same expression not FullSimplify (ing) - not bug?
> {E^(-(((1 + E) (E + E^(-(1 + E) \[Pi])))/E)),
> E^((-1 - E) (1 + E^(-1 - (1 + E) \[Pi])))} // FullSimplify
>
> **********************************************
> Terrible Performance
>
> x = IE;
> Timing[Do[x = x /. IE -> E^(IE/E), {12}]; x]
>
> {4.687, E^E^(-1 +
> E^(-1 + E^(-1 +
> E^(-1 + E^(-1 +
> E^(-1 + E^(-1 + E^(-1 + E^(-1 + E^(-1 + E^(-1 + IE/E)))))))))))}
>
> mathematica 2.2 do it in a flash :
>
> x=IE;
> Timing[Do[x=x/.IE->E^(IE/E),{12}];x]
>
> {0. Second, Power[E, Power[E,
>
> -1 + Power[E, -1 + Power[E,
>
> -1 + Power[E, -1 + Power[E,
>
> -1 + IE/E
> -1 + E
> -1 + E
> -1 + E
> -1 + E
> -1 + E
> -1 + E ]]]]]]}
>
> try this to hang the system
>
> x = IE;
> Timing[Do[x = x /. IE -> E^(IE/E), {15}]; x]
>
>
>
> SparseArray
>
> ss = SparseArray[{i_, j_, 1} -> 1, {4, 4, 4}]
> ss // MatrixForm
> Map[Sin, ss] // MatrixForm (*Fails*)
> ss // FullForm
> Map[Sin, ss] // FullForm
>
>
>
> *******
> Mathematica eats a lot system memory when this sparseArray
> is (eg 300 x 300 x300) - Is it needed/by design ?
>
> gg = SparseArray[{i_, j_, 1} -> 1, {300, 300, 300}];
> *********
> generated output does not mach the display
>
> ReplaceAll[
> Plus[Times[-1, Power[E, Times[1, Power[x, -1]]]],
> Power[E, Plus[Times[1, Power[x, -1]], Power[x, Times[-1, x]]]]],
> Rule[x, DirectedInfinity[-1]]]
>
> *******************
> Sum[(-x k)^k, {k, 0, Infinity}]
> *******************
> Function tends to Log[2]
> f[k2_] = N[-1 Sum[(1/k) (-1)^k, {k, 1, k2}]] // FullSimplify
>
> But this series diverges
> NSum[ (-1)^k (f[k]/k), {k, 1, Infinity}]
>
> **********************
> version 6 (ok) - 7 results differs
>
> InverseLaplaceTransform[E^((1 - Sqrt[1 + 4*s])/2), s, t]
> ****************