       Re: reduced functionality of Solve

• To: mathgroup at smc.vnet.net
• Subject: [mg44245] Re: reduced functionality of Solve
• From: CliffMitchel142 at hotmail.com (Cliff Mitchel)
• Date: Fri, 31 Oct 2003 03:01:10 -0500 (EST)
• References: <bnnusd\$5vc\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Try Reduce instead of Solve and FindInstance to get numbers. They seem
to be much more powerful than Solve, and more so than Solve in 4.1.

eg
Reduce[{D[F[W, y], y]*Tan[y] == 2*F[W, y], W == 1000*Sec[y]^2}, {W,
y}]

W == 7000 && C &#8712; Integers && (y == -2*ArcTan[Sqrt[(1/3)*(4 -
Sqrt)]] + 2*Pi*C ||
y == 2*ArcTan[Sqrt[(1/3)*(4 - Sqrt)]] + 2*Pi*C || y ==
-2*ArcTan[Sqrt[(1/3)*(4 + Sqrt)]] + 2*Pi*C ||
y == 2*ArcTan[Sqrt[(1/3)*(4 + Sqrt)]] + 2*Pi*C)

FindInstance[{D[F[W, y], y]*Tan[y] == 2*F[W, y], W == 1000*Sec[y]^2},
{W, y},2]

{{W -> 7000, y -> -2*(31*Pi - ArcTan[Sqrt[(1/3)*(4 + Sqrt)]])}, {W
-> 7000, y -> 2*(51*Pi + ArcTan[Sqrt[(1/3)*(4 + Sqrt)]])}}

FindInstance[{D[F[W, y], y]*Tan[y] == 2*F[W, y], W == 1000*Sec[y]^2},
{W, y},2]//N

{{W->7000.,y->192.82},{W->7000.,y->322.401}}

Andrew Collier <colliera at nu.ac.za> wrote in message news:<bnnusd\$5vc\$1 at smc.vnet.net>...
> hello,
>
> this may be a naive idea but i expected the functionality of software to
> improve with later releases. this, in my opinion, does not seem to be the
> case from mathematica 4.1 to 5.0... or maybe i am just missing something.
>
> in a script i have the following bit of code:
>
> -------------------------------------------------------------------------
> F[W_, y_] := Exp[-W(Cos[y]^2/Tp + Sin[y]^2/Tn)]
>
> Tn = 3000;
> Tp = 2000;
>
> Solve[{D[F[W, y], y] Tan[y] == 2 F[W, y], W == 1000 Sec[y] ^ 2}, {W, y}];
> N[%] // TableForm
> -------------------------------------------------------------------------
>
> now, with mathematica 4.1 this gives:
>
> -------------------------------------------------------------------------
> InverseFunction::ifun:
>    Inverse functions are being used. Values may be lost for multivalued
>     inverses.
>
> Solve::ifun: Inverse functions are being used by Solve, so some solutions may
>      not be found.
>
> In:=
> Out//TableForm= W -> 7000.   y -> -1.95839
>
>                    W -> 7000.   y -> 1.95839
>
>                    W -> 7000.   y -> -1.1832
>
>                    W -> 7000.   y -> 1.1832
> -------------------------------------------------------------------------
>
> which is useful and the kind of result i am after. however, after
> upgrading to mathematica 5.0 the same bit of code gives:
>
> -------------------------------------------------------------------------
> Solve::tdep: The equations appear to involve the variables to be solved for in
>     an essentially non-algebraic way.
>
> In:=
> -------------------------------------------------------------------------
>
> now i read in the manual that Solve "deals primarily with linear and
> polynomial equations", but i would expect that if i got a useful answer
> with 4.1 i should get the same (or better!) with 5.0.
>
> is there some way of getting the old behaviour with the newer version of
> mathematica?
>
> many thanks and best regards,
> andrew collier.

```

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