Re: reduced functionality of Solve

*To*: mathgroup at smc.vnet.net*Subject*: [mg44239] Re: [mg44222] reduced functionality of Solve*From*: Andrzej Kozlowski <akoz at mimuw.edu.pl>*Date*: Fri, 31 Oct 2003 03:01:05 -0500 (EST)*References*: <200310290834.DAA05917@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

On 29 Oct 2003, at 17:34, Andrew Collier wrote: > 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[5]:= > Out[5]//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[5]:= > ----------------------------------------------------------------------- > -- > > 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. > > -- > Andrew B. Collier > Antarctic Research Fellow tel: +27 31 2601157 > Space Physics Research Institute fax: +27 31 2616550 > University of Natal, Durban, 4041, South Africa > > > On the contrary, the functionality of Mathematica in this area has been considerably enhanced. But what has happened at the same time is that Solve has given up moonlighting as a general purpose solver and returned to its day job as an algebraic solver. The other job has been taken over by Reduce, that does it in a proper professional manner: F[W_, y_] := Exp[(-W)*(Cos[y]^2/Tp + Sin[y]^2/Tn)] Tn = 3000; Tp = 2000; Reduce[{D[F[W, y], y]*Tan[y] == 2*F[W, y], W == 1000*Sec[y]^2}, {W, y}] W == 7000 && C[1] $B":(B Integers && (y == 2*Pi*C[1] - 2*ArcTan[Sqrt[(1/3)*(4 - Sqrt[7])]] || y == 2*Pi*C[1] + 2*ArcTan[Sqrt[(1/3)*(4 - Sqrt[7])]] || y == 2*Pi*C[1] - 2*ArcTan[Sqrt[(1/3)*(4 + Sqrt[7])]] || y == 2*Pi*C[1] + 2*ArcTan[Sqrt[(1/3)*(4 + Sqrt[7])]]) Andrzej Kozlowski Yokohama, Japan http://www.mimuw.edu.pl/~akoz/

**References**:**reduced functionality of Solve***From:*Andrew Collier <colliera@nu.ac.za>