       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:= {x^2 + x + a, Cos[x - a], Sin[x - a]}

Out= {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:= Simplify[Integrate[Cos[x - a], x]] /. -Sin[(g_) - (h_)] ->
HoldForm @ Sin[h - g]

Out= Sin[x - a]

HTH,
--
Jean-Marc

```

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