Position of largest element in a list

Here is an etoolbox:

documentclass{article}

usepackage{expl3,etoolbox}

ExplSyntaxOn
  cs_new_eq:NN calc fp_eval:n
ExplSyntaxOff

defvalueA{7}
defvalueB{19}
defvalueC{41}
defvalueD{31}
defvalueE{25}
defvalueF{17}
defvalueG{7}
defvalueH{3}

makeatletter
newcounter{maxindex}
newcommand{findmaxindex}[1]{%
  @tempcnta=0% Counter for stepping through elements
  setlength{@tempdima}{-maxdimen}% "Smallest" number as a length/dimension
  renewcommand*{do}[1]{%
    advance@tempcnta by 1% Step to next element
    ifdimgreater{##1pt}{@tempdima}{setlength{@tempdima}{##1pt}setcounter{maxindex}{@tempcnta}}{}}% Found larger element
  docsvlist{#1}% process list to find maximum number and index
}
makeatother

setlength{parindent}{0pt}% Just for this example
begin{document}

I have the list
[
  7, 19, 41, 31, 25, 17, 7, 3
]
in which the largest element is $calc{max(7, 19, 41, 31, 25, 17, 7, 3)}$.

findmaxindex{7, 19, 41, 31, 25, 17, 7, 3}% Find maximum number index
The position number of the largest element in this themaxindex.

bigskip

I have the list
[
  valueH,valueG,valueF,valueE,valueD,valueC,valueB,valueA
]
in which the largest element is $calc{max(valueH,valueG,valueF,valueE,valueD,valueC,valueB,valueA)}$.

findmaxindex{valueH,valueG,valueF,valueE,valueD,valueC,valueB,valueA}% Find maximum number index
The position number of the largest element in this themaxindex.

end{document}

Note that it will choose as index of the first elements that is largest. The index of the maximum number is stored in the counter maxindex, available for print via themaxindent.

The idea is to step through the list and mark each element that is found to be greater than the previous greatest element found. Using dimensions allows for working with decimal numbers.

Another expandable solution. No package used. (for this situation dealing only with integers, for decimals one can replace ifnum with ifdim up to some extent; for even more complicated situations there is, among others, xint).

documentclass{article}

defvalueA{7}
defvalueB{19}
defvalueC{41}
defvalueD{31}
defvalueE{25}
defvalueF{17}
defvalueG{7}
defvalueH{3}

defmylist{valueA,valueB,valueC,valueD,valueE,valueF,valueG,valueH}

makeatletter
% the two routines maxoflist and maxposition are not optimal if the
% list elements require some costly expansion to compute their values
% this could be improved, if needed, to do this expansion only once
% I here design the thing for either litteral digit tokens or 
% count registers or the like

% naturally one could also do a single routine with a two element
% output: (earliest) position and value of the maximum

% maximum
defmaxoflist #1{romannumeral0expandafter
                    maxoflist@aromannumeral-`0#1,,}
defmaxoflist@a #1,{maxoflist@c {numexpr#1relax}}
defmaxoflist@c #1#2,{%
    ifxrelax #2relaxexpandaftermaxoflist@end
    elseifnum#2>#1expandafterexpandafterexpandaftermaxoflist@update
               elseexpandafterexpandafterexpandaftermaxoflist@next
    fifi {#1}{#2}}
defmaxoflist@end    #1#2{expandafterspacethe#1}
defmaxoflist@update #1#2{maxoflist@c {numexpr#2relax}}
defmaxoflist@next   #1#2{maxoflist@c {#1}}

% max position
defmaxposition #1{romannumeral0expandafter
                    maxposition@aromannumeral-`0#1,,}
defmaxposition@a #1,{maxposition@c 21{numexpr#1relax}}
defmaxposition@b #1%
   {expandaftermaxposition@cexpandafter {thenumexpr #1+@ne}}%
defmaxposition@c #1#2#3#4,{%
    ifxrelax #4relaxexpandaftermaxposition@end
    elseifnum#4>#3expandafterexpandafterexpandaftermaxposition@update
               elseexpandafterexpandafterexpandaftermaxposition@next
    fifi {#1}{#2}{#3}{#4}}
defmaxposition@end #1#2#3#4{ #2}
defmaxposition@update #1#2#3#4{maxposition@b {#1}{#1}{numexpr#4relax}}
defmaxposition@next   #1#2#3#4{maxposition@b {#1}{#2}{#3}}
makeatother


begin{document}

noindent I have the list
[
mylist
]
in which the largest element is $maxoflistmylist$ (but that is 
of no importance to me).[baselineskip]
How can I get LaTeX{} to extracting the position number 
of the largest element in a list? (In the example above, 
the answer is of course `$maxpositionmylist$'.)

end{document}

With pgfmath:

documentclass[a4paper]{article}
usepackage{tikz}
begin{document}
defmylist{7, 19, 41, 31, 25, 17, 7, 3}
pgfmathtruncatemacroMax{max(mylist)}

foreach[count=Pos] k in mylist {
pgfmathsetmacrotest{k==Max ?  Pos :  0}
ifnumtest=0 else xdefMaxPos{test} fi
}

In {mylist} the maximum is  {Max} at list-position MaxPos.
end{document}