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