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Re: Solve Function

• To: mathgroup at smc.vnet.net
• Subject: [mg44975] Re: Solve Function
• From: "Curt Fischer" <crf3 at po.cwru.edu>
• Date: Thu, 11 Dec 2003 05:28:29 -0500 (EST)
• References: <br6oqv$2lb$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

"Gregory Lypny" <gregory.lypny at videotron.ca> wrote in message
news:br6oqv$2lb$1 at smc.vnet.net...
> Hello Everyone,
>
> I've got a question about the Solve function.  I read in the
> Mathematica Book that Solve can handle a set of simultaneous equations
> (page 88) and that the syntax for the function is to list each equation
> followed by the variables to solve for.  What if all of the equations
> have the same form, say, because they're constraints in the first-order
> conditions of an optimization?  I'm wondering whether Solve can handle
> a neater specification in matrix form, something along the lines of
>
> Solve[f[x]==g[x], x],
>
> where x is a vector of variables {x1, x2, x3, ... , xn}.  It would save
> a lot of typing.  I've tried to feed solve a variable defined as an
> array, but I keep getting errors to the effect that the equation is not
> well formed.

This is possible but as far as I know only in version 5.0.  What version are
you using?  Anyway, even if not possible, you should still be able to use
Thread[] to turn a matrix equation into a list of regular equations.

Here's a problem I solved.

In[2]:=
? Solve

\!\(\*
  RowBox[{"\<\"Solve[eqns, vars] attempts to solve an equation or set of \
equations for the variables vars. Solve[eqns, vars, elims] attempts to solve
\
the equations for vars, eliminating the variables elims.\"\>", " ",
    ButtonBox[
      StyleBox["More.",
        "SR"],
      ButtonData:>"Solve",
      Active->True,
      ButtonStyle->"RefGuideLink"]}]\)

In[3]:=
A={{a,b},{c,d}};

In[4]:=
X={x,y};

In[5]:=
B={e,f};

In[6]:=
\!\(Solve[A . X\^2\  + \ 2  X == B, X]\)
Out[6]=

{a horrible mess of formulae many pages long; see if it works on your
machine...}

If that doesn't work, try doing it like this:

In[7]:=

\!\(Thread[A . X\^2\  + \ 2  X == B]\)
Out[7]=
\!\({2\ x + a\ x\^2 + b\ y\^2 \[Equal] e,
    c\ x\^2 + 2\ y + d\ y\^2 \[Equal] f}\)

In[8]:=
Solve[%,X]

Out[8]=

{the same horrible mess that I omitted earlier}
-- 
Curt Fischer