Surely it is better if the best algorithms and most useful mathematical
knowledge are already implemented in a standard, widely available
program for immediate use. At best, the mathematician user could well
use the program without knowing all the technical refinements that make
the computation possible---though in our view a basic knowledge on the
part of the user is indispensable, providing confidence that the
algorithms are not being totally umis-used. At worst, it provides a
common basis or language for communication and exchange, one which has
been carefully crafted for precision, accuracy and consistency, much
like the traditional logical formalism behind conventional
mathematics.
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