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}]

```

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