Mathematical software is

a software for "mathematics". It contains various systems. CAS, Computer Algebra System is one of them. For example, we calculate quotient numbers with CAS.  CAS is supporting polynomials, factorization, derivatives, integrals, group and algebra, etc. General purpose sytems:
  • Mathematica, Maple, Maxima, Reduce, Sage, Giac/XCAS, ...
CAS for research:
  • GAP, PARI/GP,
  • CoCoA, JAS, Macaulay2, Risa/Asir, Singular, ...
  • Cadabra, Polymake, Regina, Snappy, Surf families, ...
Numerical systems:
  • Matlab, Octave, Scilab, BLAS, Julia, ...
Publishing systems is a mathematical software:
  • TeX, LaTeX, (Beamer, a0poster, TikZ)
Statistical software:
  • R, Fathom, ...
Dynamic geometry software:
  • Cabri, Geometer's Sketchpad, Cinderella, GeoGebra, ...
Developing mathematical software is a research area for mathematics.