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MathGroup Archive 2009

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Re: Working with Lists

  • To: mathgroup at smc.vnet.net
  • Subject: [mg104369] Re: [mg104327] Working with Lists
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Thu, 29 Oct 2009 02:57:56 -0500 (EST)
  • Reply-to: hanlonr at cox.net

f = Array[a, {4, 2}]

{{a[1, 1], a[1, 2]}, {a[2, 1], 
     a[2, 2]}, {a[3, 1], a[3, 2]}, 
   {a[4, 1], a[4, 2]}}

c1 = f[[All, 1]]

{a[1, 1], a[2, 1], a[3, 1], a[4, 1]}

c2 = f[[All, 2]]

{a[1, 2], a[2, 2], a[3, 2], a[4, 2]}

f == Thread[{c1, c2}]

True

f == Transpose[{c1, c2}]

True


f2 = {{0, 1}, {7, 1}, {12, 2}};

rd = {1 -> 1/4, 2 -> 1/2};

f2 /. {x_, y_} :> {x, y /. rd}

{{0, 1/4}, {7, 1/4}, {12, 1/2}}

{#[[1]], #[[2]] /. rd} & /@ f2

{{0, 1/4}, {7, 1/4}, {12, 1/2}}

Thread[{f2[[All, 1]], f2[[All, 2]] /. rd}]

{{0, 1/4}, {7, 1/4}, {12, 1/2}}


Read the documentation:

http://reference.wolfram.com/mathematica/tutorial/VectorsAndMatrices.html

http : // reference.wolfram.com/mathematica/ref/List.html

http : // reference.wolfram.com/mathematica/ref/Sequence.html

http : // reference.wolfram.com/mathematica/ref/VectorQ.html

http://reference.wolfram.com/mathematica/ref/Array.html

http://reference.wolfram.com/mathematica/ref/MatrixQ.html

http://reference.wolfram.com/mathematica/ref/Table.html

http://reference.wolfram.com/mathematica/ref/Grid.html

http://reference.wolfram.com/mathematica/tutorial/ListsOverview.html


Bob Hanlon

---- BenT <brtubb at pdmusic.org> wrote: 

=============
I have several practical problems which I need to solve, and
understand, preferable in a generic matter well, before needing to
apply them specifically pertaining to:

using a "generic" example:

f={{1,2,},{3,4,},{5,6},{7,8}}

NOTE: the use of 1 thru 8 for the values is purely arbitrary so please
to do not apply any "simplifications" based on their present values.

I know have to obtain the sum of all of the elements in each of the
lists by using

Apply[Plus,f]

and from it, I can use the Part function or "[[]]" method of obtaining
each result as needed.

asum=Apply[Plus,f][[1]]
bsum=Apply[Plus,f][[2]]

What I further need are methods to:

(1) obtain separate lists, call them a and b which contain just the
1st and 2nd elements of each sublist respectively

(2) then after further, if eny modification of either list's data (a
copletely separate issue), I need to know the method of how to merge
them, and replace the original data.

I know how to apply Rule's to transform data on a list of single
elements, but not for "larger" lists.

Consider this code:

f={{0,1},{7,1},{12,2}}

rd={1->1/4,2=1/2}

How can I apply the rd "rule" (or any Rule) to just the second
elements' 2nd values in the f list? And more importantly how are such
things done generically?

And someone please define distinct differences between:

(1) list
(2) sequence
(2) vector
(2) array
(3) matrix/table

I'm using Mathemata Version 7, but am only a "hobbies" at it. Music is
my primary interest.

--- Benjamin Tubb




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