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Davenport J.H. (ed.) Proc. EUROCAL 87 (selected papers)(LNCS 378, 1987)(L)(T)(30s).djvu |
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Size 0.6Mb Date Dec 18, 2004 |
# use alg canonical for a canonical form
expr := full_subs(substitutions, expr);
return(expr);
Description
The above algorithm works as follows: It gets all of the radicals in the expression in order of their depen-
dependencies (i.e...
Our algorithms are randomized
in the Las Vegas sense, that is they can fail but they will never give an incorrect answer...
The remaining lemmas enable us to conclude that Я, computed in step B), has that pro-
property unless the random entries of R, chosen in step 1, form a root of a certain polynomial 7t...
It would be possible to write a package, using these facilities, which
checked for hidden relations, but this would be much slower...
Suggestions for the bound in step (i) include the height of the input polynomial (which is
fooled by cases like factorising *2-2 over Q(a) where (a-999J-2=0), the heuristic bound in
395
[Wang76], and even a constant bound, on the principle that any useful factorisation would be
fairly small...
We repeat until all the vectors have
been incorporated:
for к = 1 to n do
(b, , b*_i, bk) = reduce{b, bk)
NB each time round the loop b-, Ьк_л are already reduced...
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