## 12785 Reputation

8 years, 320 days

## I always prefer a homemade version: plot...

I always prefer a homemade version:

plot3d([u,(u^2-1)*cos(v)+1,(u^2-1)*sin(v)],u=1..2,v=0..2*Pi,
axes=normal,view=[-1..3,-4..6,-5..5],labels=[x,y,z],axes=boxed);

## degrevlex?...

What is degrevlex?

Use e.g.

G:=Basis(K, 'tord', variables={r,u,v,w}); tord;

## You could define the polynomial function...

You could define the polynomial functions and use the composition operator @.

Or, better, use subs.
Notice first that the degrees of a and b must be 1.

a:=a1*x+a0;
a1 x + a0
b:=b1*x+b0;
b1 x + b0
c:=subs(x=a,b);
b1 (a1 x + a0) + b0
coeffs(collect(c-x,x),x):
sol:=solve([%],[a0,a1,b0,b1]):

# So, the general form of a,b is

{'a','b'} = eval({a,b},op(sol));

{a,b} = {x/b1+a0, -a0*b1+b1*x}

# here a0,b1 are arbitrary constants, b1<>0.

Edit: actually c computes b o a, but the final result is of course the same.

## Extrema...

> min(extrema(x,{x^2 + x*y + y^2 = 2}));

## Bug...

It's a bug.

It seems that Apolonius works correctly only if all the 8 circles exist.

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