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)

```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]
> ****************

```

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