On 09/01/2021 11:57, S.Y. Lee wrote:
I have previously questioned that Wolfram have a == b -> a/c == b/c
transformation in conditional expression format
https://reference.wolfram.com/language/ref/DivideSides.html and why
you were not attempting to implement same like this,
But now I'd may agree on that if we treat such examples as polynomial
algebra, those transformation can make mathematical sense without
connection to the assumptions behind.
And I believe that in this sense, differentiation and integration can
similarly avoid such hoax without treatment of assumptions.
But now I have an another question if the manipulation works in
algebraically robust way,
For example, we have lots of pitfalls of expression tree manipulation
that some simple examples like "x / x" work,
but we soon end up with some more complicated examples like "
exp(x+1)/exp(1)" doesn't work robustly,
and the only way to cope with them are appending
.expand().cancel().together().simplify(), ... to the tail which is
pretty much black-boxed and not robust at all.
So this is one of the problem that I'm skeptical about how they can be
used as a backend for automatic symbolic manipulations, rather than
some convenience tools for end users.
And for such purposes I believe that we rather have to make object
like PolyEquation.
I suppose I think the problem is that many users DO use SymPy as a tool
to do calculations - not as something to build into something else. As
you acknowledge, such convenience functions are almost essential to make
good use of an equation class interactively, even though they can
produce mistakes when wrongly used (as can subs).
One possibility might be to place 'dangerous' functions, such as
DivideSides, in a submodule of SymPy so that they are only loaded if the
user, or the system builder, deems it appropriate - very much as users
can choose to import the symbols from sympy.abc at their discretion.
Obviously such functions would not be used by default by simplify if it
were applied to equation objects.
David
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