RE: Rearranging expressions in a user-defined form
- To: mathgroup at smc.vnet.net
- Subject: [mg94121] RE: [mg94083] Rearranging expressions in a user-defined form
- From: "David Park" <djmpark at comcast.net>
- Date: Fri, 5 Dec 2008 05:32:12 -0500 (EST)
- References: <24833256.1228395441799.JavaMail.root@m02>
Alexei,
I agree that it is generally better to do things by Mathematica operations
than by cutting and pasting or retyping.
I have always been interested in the problem of manipulating expressions so
they follow textbook expressions or are in a convenient form. I have put a
number of routines in the Presentations that make this easier. One gap in
Mathematica is the ability to operate on a subset of level parts in an
expression, and reinsert the result back into the expression. One of the
routines in Presentations is MapLevelParts (there is also a
MapLevelPatterns) that does this. We can just use that on your second
example:
Needs["Presentations`Master`"]
a b + a c + c d + c a - g d - g a
% // MapLevelParts[Factor, {{1, 2, 4}}]
% // MapLevelParts[Factor, {{1, 3}}]
a b + 2 a c + c d - a g - d g
c d + a (b + 2 c - g) - d g
d (c - g) + a (b + 2 c - g)
You have thrown a spanner into the first example in that Mathematica will
immediately combine the two a c terms. There are several ways to handle
this. The first way uses a routine CreateSubexpression from Presentations. A
Subexpression will not combine with other terms. It has a Tooltip on it. It
is very convenient when one has a subexpression, often a product of factors
that one wants to treat as a unit in some expression and prevent routines
such as Simplify from breaking up. Here we just use it to split the 2ac term
into two terms, one in a Subexpression. Then we can use MapLevelParts to do
the two factorings. The term in parentheses is the Subexpression. (You can
have it with or without parentheses.)
a b + a c + c d + c a - g d - g a
MapAt[(#/2 + CreateSubexpression[#/2]) &, %, 2]
% // MapLevelParts[Factor, {{1, 2}}] // ReleaseSubexpressions[]
% // MapLevelParts[Factor, {{1, 3, 4, 5}}]
a b + 2 a c + c d - a g - d g
a b + a c + c d - a g - d g + (a c)
a c + a (b + c) + c d - a g - d g
a (b + c) + (a + d) (c - g)
For a long time I have had a routine EvaluateAtPattern that allows functions
to be applied to patterns within Held expressions. I also had an EvaluateAt
routine but did not put it in Presentations. As a result of your question I
now have, but not yet in the current release at the download site. With
EvaluateAt we can write your initial expression in a HoldForm and then do
your first case as:
expr = HoldForm[a b + a c + c d + c a - g d - g a]
% // EvaluateAt[{1, 4}, CreateSubexpression] // ReleaseHold
% // MapLevelParts[Factor, {{1, 2}}] // ReleaseSubexpressions[]
% // MapLevelParts[Factor, {{1, 3, 4, 5}}]
a b + a c + c d + c a - g d - g a
a b + a c + c d - a g - d g + (a c)
a c + a (b + c) + c d - a g - d g
a (b + c) + (a + d) (c - g)
So that is one way to manipulate expressions into desired forms.
David Park
djmpark at comcast.net
http://home.comcast.net/~djmpark
From: Alexei Boulbitch [mailto:Alexei.Boulbitch at iee.lu]
Dear MathGroup,
in symbolic transformations of mathematical expressions I often need to
group or transform differently different parts
of these expression, just to make them more visible , or more easy to
analyze or so. Just to give a simplest example,
assume that we have an expression:
expr = ab + ac + cd + ca- gd - ga
and I need to have it once in the form like say,
expr=a (b + c) + (c - g) (d + a)
and another time in the form say,
expr=a (b + 2 c - g) + d (c - g)
or I will need to group it in some third, fourth ... form. You indeed
understand that I gave the example easily treatable without computer,
while I have in mind much more complex transformations of real interest.
This evidently may be done by copy-pasting parts of the expression in
question and
transforming then separately and then again copy-pasting and thus,
collecting the results together. That's exactly what I do in such a case.
However, this may easily become a source of errors: such as copying
without a sign, or copying a part of the expression, rather than the
whole one and so on.
Finally it considerably slows you down.
Could you think of tricks to instruct Mathematica to group only certain
terms and not others, and to take certain
factors out of parentheses, while leave others, according to your choice?
Thank you, Alexei
--
Alexei Boulbitch, Dr., Habil.
Senior Scientist
IEE S.A.
ZAE Weiergewan
11, rue Edmond Reuter
L-5326 Contern
Luxembourg
Phone: +352 2454 2566
Fax: +352 2454 3566
Website: www.iee.lu
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