Depends on how you want to approach things. I find that by far the best option is Mathematica. Although, Mathematica is expensive, for commercial use, it is quite affordable otherwise. Mathematica is however not everybody's cup of tea. If you can not afford Mathematica consider, Python + numpy, scipy, sympy combo, or octave if you can afford it Matlab would be fine too.
Image 1 A vector streamfield quickly generated in Mathematica, and touched up in Illustrator.
Nothing says you can not use several applications together. Any of the above + illustrator makes a formidable tool set.
Drawing the field manually is not out of the question. Although you could easily script the field generation. I have made a similar, but crude, parametric curve drawing routine as you find in inkscape. You can find it here. It wouldn't take much work to convert it to draw vector fields if your point distribution is known.