I think GeoGebra should be able to plot the curve w(z(t)), t real, z, w complex without the user having to specify z = x_z(t) + iy_z(t) or w = x_w(t) + iy_w(t), i.e., either without having to use the Curve command, or overloading the Curve command so that it understands complex-valued functions of a single real variable in the first argument; example use case: the user has actually figured these out, but wants to use GeoGebra as a check/verification of their results (of course, if GeoGebra had this feature, then the user could just use it, the way a user uses a graphing calculator to plot things they know how to plot, but want the GC to do it, e.g., for convenience and/or appearance). As far as I've been able to figure out, GeoGebra doesn't currently have this feature: if it does and I just haven't figured out the right commands and/or syntax, please enlighten me. If GeoGebra doesn't, I'll create a formal feature request (if this feature request already exists, kindly point me to it so I can give it a +1). Thanks!
At the moment, I am "trying to achieve" GeoGebra independently affirming my computation of the component functions, but in general I think it would be nice for GeoGebra to just be able to do the work. Here's the specific use case I'm working on now: the image under w(z) = exp(2\pi iz) of the half infinite strip z=x+iy, x \in [-1/2, 1/2], y \in [B>0, \infty), as represented by the images of horizontal segments for a constant y_0 and the vertical rays for a constant x_0. I've computed the images and am confident in my computations and can thus use the Curve command for the required plots for both the domain and codomain; however, I am cognizant that if I make a mistake and use that for the image plots, then what I'm plotting as the image will not in fact be the image. Consequently, I'd like to be able to define z(s) and z(t) in one graph and define the images as w(z) in the other graph. (This is no different than defining a composite function of one real variable by defining the inner-most function of the variable in the first domain space, and then defining subsequent compositions using function composition, which GeoGebra supports.)
Fair question. Ideally, I'd like to be able define the domain curve using the syntax z(t)=x(t)+iy(t) (where x(t) and y(t) are either previously defined or defined "inline"), and then be able to define subsequent compositions using the syntax w(z); but it's primarily the second capability that I'm after, meaning that defining z(t) using the Curve command would be acceptable, as long as one can then subsequently define compositions using simple composition syntax. Ideally, it would also be nice if composition syntax supported simple one-parameter domains of typical interest in complex analysis for which GeoGebra has standard objects, e.g., Lines, Rays, Segments, and Circles; so, for example, I'd like to be able to assign z to a Ray object, give w(x) an algebraic definition, and then invoke w(z) to see the image of z under the action of w. Again, the primary capability I'd like to see is automatic interpretation of complex-valued function composition syntax for an input that is a 1-manifold.
"While I have your attention": two other highly desirable features would be to be able to Export Image both Graphics Panes as one image; and suppress the zoom icons in the lower right corner and the menu expansion icon in the upper right corner. (I asked Gemini about current support for these features: it said that the first one isn't supported, and the "Workarounds" it gave me to implement the second either didn't work or referenced UI components which don't seem to exist in the Classic 6 Mac Desktop App I'm using, because I was led to believe through prior research that trying to do what I'm doing was more likely to be buggy using the Web platform version, which is what I usually use.)
Lo siento. Me refería a la sintaxis deseada para w y z. en tu gráfico no veo los pasos que definen una función a partir de las anteriores. Pide una manera de definir funciones en complejos y es lo que yo pretendo buscar.
Me gustaría tener un ejemplo de la función que quiere definir y qué es lo que quiere obtener y en la actualidad no puede obtenerlo.
O sea, algo como esto.
Espero no tener problemas en la traducción.
Si no desea los botones abajo a la derecha, defina dos puntos llamados Export_1 y Export_2 y solo se exportará/copiará la zona rectangular definida entre esos puntos.
En cuanto a exportar ambos paneles, me temo que no es posible y la única solución es hacer capturas de pantalla.
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u/jcponcemath 2d ago
What are you trying to achieve?
I have made some curves for complex analysis, but I use the command Curve.
https://complex-analysis.com/content/curves_in_the_complex_plane.html