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Looking for help with "Reduce" command for use with my Calculus course.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg98002] Looking for help with "Reduce" command for use with my Calculus course.
  • From: Gary Church <gary.church1 at comcast.net>
  • Date: Fri, 27 Mar 2009 05:38:15 -0500 (EST)

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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