Things to code in Mathomatic that might be good ideas
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Simplify nested radicals like ((9 + 4*(2^.5))^.5) to (1 + 2*(2^.5)).  This
may be difficult, I don't know how this is generally done.  Heuristics are
not acceptable for this.  Test expression:

  ((2+(3^.5))/((2^.5)+(2+(3^.5))^.5)+(2-(3^.5))/((2^.5)-(2-(3^.5))^.5))^2

should simplify to 2.

Add complex number factorials, when an accurate floating point complex number
gamma calculating function is found.

Add constant of integration option to the integrate command.  Would just add
the variable "C" to the result after every integration.

Use the GNU Scientific Library (GSL) to automatically solve any degree
numeric polynomial equation, like "psolve.c" does, when symbolic solving
fails.  Unfortunately, this will make Mathomatic dependent on GSL, so I may
not do this.