What software can I use to visualize transformations of the plane?

[sari]

For example, I would like to visualize the transformation

u=cot^-1(1/α y/x)
v=αx²+y²/α

 

[bigfooted]

mathematics packages:
matlab, maple, maxima, octave, scilab
graphics packages:
tecplot, gnuplot.

There are probably dozens (hundreds?) more, but these are the ones I use.

 

[sari]

Thanks! Are any of those free?

 

[bigfooted]

you have to pay for tecplot, MATLAB and maple, but if you are a student then your university might get you a discount.

 

[PJC01]

There are many software options available for visualizing transformations of the plane. Some popular options include Geogebra, Desmos, and Wolfram Mathematica. These programs allow you to input equations and manipulate them to visualize the resulting transformations on the plane. For your specific example, you can input the equations u=cot^-1(1/α y/x) and v=αx^2+y^2/α into any of these software programs and adjust the values of α to see how it affects the resulting transformation. These programs also have various tools and features that can help you analyze and understand the transformations in more detail. Overall, using a visualization software can greatly enhance your understanding of transformations in the plane and aid in your scientific research.