Re: Mistake in applying a rule
- To: mathgroup at smc.vnet.net
- Subject: [mg80681] Re: Mistake in applying a rule
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Tue, 28 Aug 2007 06:43:37 -0400 (EDT)
- Organization: The Open University, Milton Keynes, UK
- References: <fb0f17$f05$1@smc.vnet.net>
Steven Siew wrote:
> I'm trying to show that Integrate[Cos[x-a]] is Sin[x-a] + C
>
> I manage to get Simplify @ Integrate[Cos[x-a]] to give -Sin[a-x]
>
> This is fine because Sin[-x] is equal to -Sin[x]
>
> But when I apply the rule Times[-1,Sin[Plus[g_,Times[-1,h_]]]] ->
> Sin[h-g] it fails.
<snip>
Mathematica reorders the expressions in canonical order before
evaluating them. Also, evaluated expressions are returned in canonical
order too. For instance,
In[1]:= {x^2 + x + a, Cos[x - a], Sin[x - a]}
Out[1]= {a + x + x^2, Cos[a - x], -Sin[a - x]}
To keep the elements of an expression in a specific (user-defined)
order, you can use *HoldForm* as in
In[2]:= Simplify[Integrate[Cos[x - a], x]] /. -Sin[(g_) - (h_)] ->
HoldForm @ Sin[h - g]
Out[2]= Sin[x - a]
HTH,
--
Jean-Marc