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.