On 6 April 2015 at 18:38, Waldek Hebisch <[email protected]> wrote:
> Bill Page wrote:
>>
>> At the risk of unnecessarily complicating your example which I presume
>> was intended to address other issues, I would say that it is not
>> accurate to say that "we implement equality so this is true". In fact
>> it is not so easy even to represent 'x*(y+z)' as something of type
>> Expression
>
> OK, I was oversimplifying. One important point it that if we
> consider two expressions as equal, then there is no need to
> represent differences between them. We may just store
> some standarized version. In particular we may go to
> so called normal form or canonical form. This is explanined
> in chapter 2 of book by J.H. Davenport, Y. Siret, E. Tournier,
> "Computer Algebra -- Systems and Algorithms for Algebraic Computation"
> which is available at
>
> http://staff.bath.ac.uk/masjhd/masternew.pdf
>
Yes, I think this is a bit dated but still a good reference. Thank
you. For example:
page 80, quote:
Brown's storage method [1969] raises this question of regularity. Given
a normal representation, he proposes to construct a canonical representa-
tion. All the expressions which have already been calculated are stored,
a_1, ... a_n. When a new expression b is calculated, for all the a_i we test
whether b is equal to this a_i (by testing whether a_i−b i s zero). If b=a_i,
we replace b by a_i ,otherwise a_{n+1} becomes b, which is a new expression.
This method of storing yields a canonical representation, which, however,
is not at all regular, because it depends entirely on the order in which the
expressions appear. Moreover, it is not effi cient, for we have to store all the
expressions and compare each result calculated with all the other stored
expressions.
end_quote
> Also concept of normal and canonical forms is explained
> if A = B by Petkovsek, Wilf and Zeilberger.
>
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