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

• To: mathgroup at smc.vnet.net
• Subject: [mg98038] Re: [mg98002] Looking for help with "Reduce" command for use with
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 28 Mar 2009 05:45:09 -0500 (EST)

```pts = {x, y} /. {Reduce[
{x^3 + y^3 == 6 x*y, -4 <= x <= 3,
Element[x, Integers], Element[y, Reals]},
{x, y}] // ToRules} /. Root[a__] :> N[Root[a]]

{{-4, 2.214295128870666}, {-3, 1.3601929545492113},
{-2, 0.6443707092521711}, {-1, 0.1659055841222127}, {0, 0},
{1, -2.528917957294362}, {1, 0.16744919110853515},
{1, 2.3614687661858267}, {2, -3.7587704831436337},
{2, 0.6945927106677213}, {2, 3.064177772475912},
{3, (1/2)*(-3 - 3*Sqrt[5])}, {3, (1/2)*(-3 + 3*Sqrt[5])}, {3, 3}}

Bob Hanlon

---- Gary Church <gary.church1 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

```

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