Re: Why can't I solve this SIMPLE problem?

*To*: mathgroup at christensen.cybernetics.net*Subject*: [mg1225] Re: Why can't I solve this SIMPLE problem?*From*: bob Hanlon <hanlon at pafosu2.hq.af.mil>*Date*: Fri, 26 May 1995 02:59:56 -0400

In Mathematica if you define R as Sqrt[x^2 + y^2] it will always make that substitution for R. Consequently, you must avoid the direct assignment. Try this: z /. Solve[{R == Sqrt[x^2 + y^2], z == D[Sqrt[x^2 + y^2], x]}, z, y] this will return x/R. You can also write this as: temp = Sqrt[x^2 + y^2]; z /. Solve[{R == temp, z == D[temp, x]}, z, y] Bob Hanlon ---------- Forwarded message ---------- >From: fateman at peoplesparc.cs.berkeley.edu (Richard J Fateman) >Subject: Re: Why can't I solve this SIMPLE problem? > Date: 23 May 1995 18:17:36 GMT In article <1995May23.152242.21102 at tron.bwi.wec.com>, Mark W. Brown <MWBrown at AOL.com> wrote: >I've been trying to solve a VERY simple symbolic problem, and >none of the packages I have can do it. I tried the symbolic >processor in MATHCAD (a subset of MAPLE, I believe) and the >shareware program SYMBMATH. Here's the problem: > >Given: R = sqrt(x^2 + y^2) >Find: derivative dR/dx >Solution Found: dR/dx = x/sqrt(x^2+y^2) >Desired Solution: dR/dx = x/R > >Why don't these programs recognize that the square root in the >denominator of the solution has been DEFINED as the variable R >and substitute? I have been unsuccessful using substitute because >it apparently only works for simple variables (like x) and not >expressions (like sqrt(x^2 + y^2). This simple problem has become >my test bench when I evaluate symbolic processors. ............ There are quite a number of system-independent symbolic algebra systems bugs, and this one is a classic example. By representing x/sqrt(x^2+y^2) as x* (x^2+y^2)^(-1/2), Maple and some other systems fail to find any subexpression that is equal to (x^2+y^2)^(1/2) because there isn't one. If you try substituting 1/R for 1/sqrt(x^2+y^2), it will likely work as you expect on almost any system. For at least 20 years, Macsyma has done this (by in effect substituting for 1/r...). automatically. I do not know if one can coax other systems to "do the right thing" automatically too. I think it is not too expensive to check for this extra case most of the time; and I think is unreasonable to require every user to understand the internal representation of expressions in a computer algebra system to get it to work. Apparently other people disagree with me. Here's macsyma: (c1) r:sqrt(x^2+y^2)$ (c2) diff(r,x); x (d2) ------------- 2 2 sqrt(y + x ) (c3) subst('r, sqrt(x^2+y^2),%); x (d3) - r (c4) inpart(d2,2); /* pick out 2nd factor in internal representation */ 1 (d4) ------------- 2 2 sqrt(y + x ) (c5) inpart(d4,2);/* pick out exponent [2nd part] of internal rep. */ 1 (d5) - - 2 There is another possible problem, and that is that you are using your system wrong, and not substituting "quote r" for r's value, and therefore trying to substitute sqrt(x^2+y^2) for sqrt(x^2+y^2)... so nothing can change. -- Richard J. Fateman fateman at cs.berkeley.edu 510 642-1879