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.

Implement functions as macros.  This would require an simple, interactive macro
pre-processor for all expression input.  It would handle everything except
logarithms.  If only a C Pre-Processor (cpp) could be piped into Mathomatic!
All that is needed is the "#define" directive.