problem with elliptic coordinates

[68th]

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:

There are 1 exposed and 2 unexposed library operations named coordinates having 1 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op coordinates to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation.

Cannot find a definition or applicable library operation named coordinates with argument type(s) Variable(elliptic)

Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

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 having 4 argument(s) but none was determined to be applicable. Use HyperDoc Browse, or issue )display op draw to learn more about the available operations. Perhaps package-calling the operation or using coercions on the arguments will allow you to apply the operation.

Cannot find a definition or applicable library operation named draw with argument type(s) Variable(f) Segment(Pi) Segment(NonNegativeInteger) List(DrawOption)

Perhaps you should use "@" to indicate the required return type, or "$" to specify which version of the function you need.

what should i do to draw in elliptic coordinates?

)show CoordinateSystems

CoordinateSystems(R: Join(Field,TranscendentalFunctionCategory,RadicalCategory)) is a package constructor

Abbreviation for CoordinateSystems is COORDSYS

This constructor is exposed in this frame.

------------------------------- Operations --------------------------------

cartesian : Point(R) -> Point(R)      cylindrical : Point(R) -> Point(R)

parabolic : Point(R) -> Point(R)      polar : Point(R) -> Point(R)

spherical : Point(R) -> Point(R)

bipolar : R -> (Point(R) -> Point(R))

bipolarCylindrical : R -> (Point(R) -> Point(R))

conical : (R, R) -> (Point(R) -> Point(R))

elliptic : R -> (Point(R) -> Point(R))

ellipticCylindrical : R -> (Point(R) -> Point(R))

oblateSpheroidal : R -> (Point(R) -> Point(R))

parabolicCylindrical : Point(R) -> Point(R)

paraboloidal : Point(R) -> Point(R)

prolateSpheroidal : R -> (Point(R) -> Point(R))

toroidal : R -> (Point(R) -> Point(R))

[Waldek Hebisch]

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

[68th]

yes, this command finally gives me a plot in elliptic coordinates:

draw(curve(sin(5t), t), t=0..2%pi, coordinates==elliptic(1.::DFLOAT))

thank you!

------- Original Message -------

On Monday, May 1st, 2023 at 3:10 PM, Waldek Hebisch <de...@fricas.math.uni.wroc.pl> wrote:


> 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(5t), 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(5t), 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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[68th]

------- Original Message -------
On Monday, May 1st, 2023 at 3:10 PM, Waldek Hebisch de...@fricas.math.uni.wroc.pl wrote:

... 'elliptic' needs a parameter.

what's the meaning of this parameter?

[68th]

------- Original Message -------

On Monday, May 8th, 2023 at 5:54 AM, '68th' via FriCAS - computer algebra system <fricas...@googlegroups.com> wrote:

what's the meaning of this parameter?

it's the distance from the pole to each of the two foci.

[Ralf Hemmecke]

Either look here

http://fricas.github.io/api/CoordinateSystems.html?highlight=elliptic

or there

https://github.com/fricas/fricas/blob/master/src/algebra/coordsys.spad#L55

https://github.com/fricas/fricas/blob/master/src/algebra/coordsys.spad#L146

Ralf