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Topic: Building an Equation to find (Maximum Y) ie Highest Point on a curve!
Replies: 14   Last Post: Sep 14, 2013 3:40 PM

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 quasi Posts: 12,067 Registered: 7/15/05
Re: Building an Equation to find (Maximum Y) ie Highest Point on a curve!
Posted: Sep 13, 2013 2:50 AM

mervynmccrabbe@gmail.com wrote:
>
>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