Re: Re: Radicals simplify
- To: mathgroup at smc.vnet.net
- Subject: [mg106435] Re: [mg106399] Re: Radicals simplify
- From: "David Park" <djmpark at comcast.net>
- Date: Tue, 12 Jan 2010 04:50:49 -0500 (EST)
- References: <hic37h$5ef$1@smc.vnet.net> <hieujs$mtu$1@smc.vnet.net> <549721.1263255174908.JavaMail.root@n11>
The problem is that Mathematica automatically combines expressions such as x Sqrt[x]. To display that form it is necessary to wrap x in a HoldForm so that it won't recombine. In Mathematica it is often necessary to write routines to obtain the form you want. Here is a somewhat general routine that may work for you: factorIntegerPower::usage = "factorIntegerPower[expr] will factor out integer powers from a \ symbolic radical power x^p where p is Rational. The integer power is \ kept in a HoldForm. It is assumes that x represents a positive Real."; factorIntegerPower[expr_] := expr /. x_^p_Rational :> Module[{floor, frac}, floor = Floor[p]; frac = p - floor; If[floor == 0, x^frac, HoldForm @@ {x^floor} x^frac] ] {11 x^(3/2), y^(73/15), y^(2/15), x^(-14/11)} // factorIntegerPower {11 Sqrt[x] x, y^(13/15) y^4, y^(2/15), x^(8/11) 1/x^2} David Park djmpark at comcast.net http://home.comcast.net/~djmpark/ From: francix [mailto:fracix at hotmail.com] "dh" <dh at metrohm.com> ha scritto nel messaggio news:hieujs$mtu$1 at smc.vnet.net... > > > Hi, > > why do you think x(x^2 y^3)^(1/4) is simpler than (x^6 y^3)^(1/4)? > > Mathematica needs some criterion for this decision. The default criterion is the > > "LeafCount[..]". If that does not suit you, you must define another > > criterion. > > Daniel Thank you all for your answer. I understand your explanations, but I have the impression that in this case Mathematica uses numbers in a different way from letters. If I do Simplify[2 Sqrt[2] + 4 Sqrt[2]] I get 6 Sqrt[2] or Simplify[5 Sqrt[50] + 6 Sqrt[18]] I get 43 Sqrt[2] Instead if I do Simplify[5 x Sqrt[x] + 6 x Sqrt[x], x >= 0] or Simplify[5 Sqrt[x^3] + 6 x Sqrt[x], x >= 0] I get 11 x^(3/2) instead of 11xSqrt[x] As you know the last one is the result normally found in Algebra books. So, there is no solution?