Re: Question regarding replacement
- To: mathgroup at smc.vnet.net
- Subject: [mg63865] Re: [mg63860] Question regarding replacement
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Fri, 20 Jan 2006 04:32:19 -0500 (EST)
- References: <200601190503.AAA21333@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On 19 Jan 2006, at 06:03, michael_chang86 at hotmail.com wrote:
> Hi,
>
> Often, when manipulating symbolic results, one might want to replace
> some symbols with "simpler" expressions, and typically, I've managed
> this with "/.". However, suppose that
>
> In[1]: a = b c/d
>
> and I know that d/(b c) = theta. Unfortunately,
>
> In[2]: params={d/(b c)->theta}; a/.params
> does *not* yield 1/theta. How can I achieve this simply *without*
> redefining params?
>
> (This (too) simple example is meant to demonstrate some difficulties
> that I typically encounter when trying to replace symbols in *much*
> more complicated expressions, where, sometimes, the symbols that I am
> trying to replace are inverted ... :( )
>
> My apologies in advance, since this seems embarassingly simple, but
> any
> help or suggestions would be greatly appreciated!
>
> Regards,
>
> Michael
>
There is actually in Mathematica an obsolete and no longer documented
function that makes this sort of thing very easy:
b*(c/d) /. AlgebraicRules[{d/(b*c) == theta}, {d, b, c}]
1/theta
AlgebraicRules has been deprecated because the other functionality
for manipulating algebraic expressions is more powerful and reliable,
but unfortunately it is also harder to use. I can see two ways to do
this, both not entirely obvious. One is using GroebnerBasis:
GroebnerBasis[{a - b*(c/d), d/(b*c) - theta}, {theta},
{b, c, d}]
{a*theta - 1}
effectively this is saying a*theta == 1 so a == 1/theta. The other
way is by using PolynomialReduce:
Last[PolynomialReduce[b*(c/d), {d - theta*b*c},
{b, c, d}]]
1/theta
To sue these methods effectively unfortunately requires some
understanding of what GroebnerBasis and PolynomialReduce do, which
actually is non trivial. I still think that it would be a good idea
to bring back to life ALgebraicRUles (deprecated in version 3, I
think), whose syntax is at least much more understandable by users
without much knowledge of modern computational polynomial algebra.
Andrzej Kozlowski
- References:
- Question regarding replacement
- From: "michael_chang86@hotmail.com" <michael_chang86@hotmail.com>
- Question regarding replacement