Re: List Operations

• To: mathgroup at smc.vnet.net
• Subject: [mg65710] Re: [mg65681] List Operations
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Sun, 16 Apr 2006 01:45:17 -0400 (EDT)
• References: <200604140832.EAA22085@smc.vnet.net> <6921F99C-AC55-4966-B588-F29487922B0D@mimuw.edu.pl> <FA248633-57A1-4440-81B7-AB73A59A8AE6@mimuw.edu.pl>
• Sender: owner-wri-mathgroup at wolfram.com

```On 15 Apr 2006, at 16:54, Andrzej Kozlowski wrote:

>
> On 15 Apr 2006, at 10:10, Andrzej Kozlowski wrote:
>
>>
>> On 14 Apr 2006, at 17:32, LectorZ wrote:
>>
>>> Hi guys,
>>>
>>> My question:
>>>
>>> mylist={{1,a, b},{1,a, b},{1,a,
>>> b},{2,b,z},{2,b,z},{2,b,z},{2,b,z},....,{n,x,y},{n,x,y},
>>> {n,x,y},...{n,x,y}}
>>>
>>> The sublists are of different length.
>>>
>>> I need to calculate the product between the 2nd and 3rd element of
>>> every sublist (e.g. a*b) and then add them up according to the 1st
>>> element: sum of all products where the 1st element is 1, 2, ...n.
>>>
>>> The result should be a list like that:
>>> {{1,a*b+a*b+a*b},{2,b*z+b*z+b*z+b*z}, ...,{n, x*y+x*y+x*y+...+x*y}}
>>>
>>> Thank you for your help.
>>>
>>> LZ
>>>
>>
>> It is impossible in Mathematica to get  Mathematica to output
>> something in the form a+a+a and the like instead of 3a , without
>> using HoldForm. So, you should  either use something like this:
>>
>> mylist = {{1, a, b}, {1, a, b}, {1, a,
>> b}, {2, b, z}, {2, b, z}, {2, b, z}, {2, b, z}};
>>
>>
>>
>> mylist /. {i_, x_, y_} -> {i, x*y} //. {a___, {i_, x_}, {i_, y_},
>> b___} -> {a, {i, x + y}, b}
>>
>> {{1, 3*a*b}, {2, 4*b*z}}
>>
>> or if you really want it to look as you wrote it:
>>
>>
>> SetAttributes[plus,{Flat,OneIdentity}]
>>
>>
>> Format[plus[x___]]:=HoldForm[Plus[x]]
>>
>>
>> mylist /. {i_, x_, y_} -> {i, x*y} //. {a___, {i_, x_}, {i_, y_},
>> b___} -> {a, {i, HoldForm[x + y]}, b}
>>
>>
>> {{1,a*b+a*b+a*b},{2,b z+b*z+b*z+b*z}}
>>
>> Andrzej Kozlowski
>>
>
>
> Sorry, I copied and pasted not what I intended. The second example
> should have been:
>
>
> SetAttributes[plus,{Flat,OneIdentity}];
>
> Format[plus[x___]]:=HoldForm[Plus[x]];
>
> Split[mylist /. {i_, x_, y_} -> {i, x*y}, #1[[1]] == #2[[1]]
> & ] //. {a___, {i_, x_}, {i_, y_}, b___} ->
>    {a, {i, plus[x, y]}, b}
>
>
> {{{1, a*b + a*b + a*b}}, {{2, b*z + b*z + b*z + b*z}}}
>
>
>
>

Another silly mistake: there is no need for Split in the above. This
will do just as well:

SetAttributes[plus,{Flat,OneIdentity}];

Format[plus[x___]]:=HoldForm[Plus[x]];

mylist /. {i_, x_, y_} -> {i, x*y} //. {a___, {i_, x_}, {i_, y_},
b___} -> {a, {i, plus[x, y]}, b}

Andrzej Kozlowski

```

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