Robert Dodier wrote:
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>Eventually I'd like to see a unification of the symbolic and numerical stuff.
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I agree, in some sense.
Beware though that anything that comes from the numerical/ hardware
side of the community has constraints that start with the fixed
finite-size representation premise. That is, you have some number of
bits, which could be 32, 64, 80, 128.. to encode each object. This
leads to problems like trapping overflows, exceptional operands etc.
because there are more than 2^32 (etc) different rational numbers. and
even more real numbers :)
Ideas from the computer algebra community generally are motivated from
how we can "arithmetize" mathematics so as to reflect in the computer
all the properties we are used to, starting with integers.
The hardware community viewpoint cannot even express all integers.
A plausible viewpoint: We can treat the non-exceptional hardware floats
as a special speed-optimized representation for a subset of the rational
numbers. We can construct larger subsets... But Inf and NaN are not
rational numbers.