On Mon, May 01, 2023 at 01:41:22PM +0000, '68th' via FriCAS - computer algebra
system wrote:
> hello,
>
> i'm interested in defining equations for conic sections and plotting them in
> different coordinate systems. i was fine with online graphing calculators
> till i get to the elliptic coordinates, because the calculators only support
> Cartesian and polar ones. i found in the book 'The FriCAS System for Computer
> Mathematics' [7.2.7 Coordinate System Transformations] that FriCAS, which
> i've used some time ago to make and solve some equations, can plot in various
> coordinates, including elliptic. in 7.1.4 Two-Dimensional Options i found the
> following draw command:
>
> > draw(curve(sin(5*t), t), t=0..2*%pi, coordinates==polar)
>
> and it worked as expected, but when i replaced polar with elliptic i got:
<snip>
> i wrote to Ralf Hemmecke and he suggested the following command:
>
> > draw (f,0..%pi, 0..6, coordinates==elliptic(1.::DFLOAT))
>
> i entered 'f=sin(5*t)' followed by the command and it gave me:
>
> > There are 7 exposed and 0 unexposed library operations named draw
1. As Ralf wrote 'elliptic' needs a parameter. The following draws
something:
draw(curve(sin(5*t), t), t=0..2*%pi, coordinates==elliptic(1.::DFLOAT))
2. There are many forms of 'draw' command. Some take expressions
or similar and need name for parameter. Some take function
and do not need parameter name. There are separate forms for
curves ans surfeces, again both in version with parameters and
without. Form that Ralf gave is for drawing functions of two variables.
For curves is space one can use the following form:
f1(t) == sin(5*t)
f2(t) == t
c := curve(f1, f2)$ParametricPlaneCurve(SF -> SF)
draw(c, 0..2*%pi, coordinates==elliptic(1.::DFLOAT))
3. Note that in FriCAS '=' means equality or equation. Assignment
uses ':=', '==' defines functions.
--
Waldek Hebisch
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