Re: Looking for help with "Reduce" command for use with my Calculus

*To*: mathgroup at smc.vnet.net*Subject*: [mg98033] Re: Looking for help with "Reduce" command for use with my Calculus*From*: Raffy <raffy at mac.com>*Date*: Sat, 28 Mar 2009 05:44:13 -0500 (EST)*References*: <gqiaa6$oot$1@smc.vnet.net>

On Mar 27, 3:37 am, Gary Church <gary.chur... at comcast.net> wrote: > Hello, > > My first post to this newsgroup :-) > > I'm a mathematics instructor at a two-year college. Currently, I'm > trying to explain implicit differentiation and implicitly defined > functions to my students. > > To illustrate, I'm using the famous folium of Descartes: > x^3 + y^3 = 6xy > > I want to generate all the pairs of real (x,y) solutions for x taking > integer values from -4 to 3, and to then plot these pairs as points on > the curve defined by the equation. > > So far I've come up with: > > pts = Table[{i, Reduce[curve /. {x -> i}, y, Reals] // N}, {i, -4, 3}] > > which gives me a table with rows like: > > -4 y=2.2143 > > or like: > > 2 y=-3.75877 \[Or] y=0.694593 \[Or] y=3.06418 > > where the "\[Or]" is the logical "or" symbol. > > Of course this is not what I want. I want a list of pairs like: > > (-4,2.2143), (2,-3.75877), (2,0.694693), (2,3.06418), etc... > > so I can plot them as points. > > Can any of you Mathematica mavens provide this neophyte with an elegant > solution? > > Thanks much, > Gary Join @@ N @ Table[ Cases[Reduce[x^3 + y^3 == 6 x y, y, Reals], y == u_ :> {x, u}, {0, Infinity}], {x, -4, 3}]