I very strongly disagree with your suggestion. Matlab is mostly for numerical work (e.g. what NumPy/SciPy/R/Octave are usually used for). Almost universally, this is not research mathematics (although it is certainly useful for many cutting edge engineering research topics and plenty of applied math work).
Sage can deal with these tasks as well as Matlab, simply by virtue of having interfaces to NumPy/SciPy/Octave/others, but this is not where Sage shines. Sage is indispensable for research math (some examples I understand: group theory, cryptography, abstract algebras; but there are many others that are far beyond my level of math education).
In short, I think you are misrepresenting or missing who Sage is really useful for. Matlab simply does not have these features. The competitors would be Mathematica/Maple/Magma.
You are right. Bad phrasing on my part. Research applied math and research "pure" math even overlap, and the distinction is fuzzy. I do try to distinguish them from engineering research.
Sage can deal with these tasks as well as Matlab, simply by virtue of having interfaces to NumPy/SciPy/Octave/others, but this is not where Sage shines. Sage is indispensable for research math (some examples I understand: group theory, cryptography, abstract algebras; but there are many others that are far beyond my level of math education).
In short, I think you are misrepresenting or missing who Sage is really useful for. Matlab simply does not have these features. The competitors would be Mathematica/Maple/Magma.