Date: Sep 13, 2013 2:50 AM
Author: quasi
Subject: Re: Building an Equation to find (Maximum Y) ie Highest Point on a curve!

mervynmccrabbe@gmail.com wrote:
>
>IS there some sort of FREE downloadable utility or website where
>I could plug in 2 equations and get a lovely elegant solution in
>terms of one variable only?


I used Maple, which is not free.

To get the y-only equation, I used the Maple command block
shown below

#---
restart:
with(Groebner):
r1:=x^4+y^4+a*(x^2)-a*(y^2)+2*(x^2)*(y^2)-b*x*y+c:
subs(y=y(x),%):
diff(%,x):
subs(diff(y(x),x)=y1,%):
subs(y(x)=y,%):
r2:=subs(y1=0,%):
rels:=[r1,r2]:
vars:=[x,y]:
bas:=gbasis(rels,plex(op(vars))):
collect(bas[1],y)=0;
#---

quasi