Force scientific notation in tick labels of ListLogLogPlot

I am trying to custom-format tick labels on a ListLogLogPlot. By searching Mathgroup archives, it looks like the usual way to mess with tick labels is to extract t开发者_高级运维hem using AbsoluteOptions, run a replacement rule with the custom format, and then explicitly feed them to the plotting function with the Ticks->{...} option. However, the following doesn't work for ListLogLogPlot:

foo = ListLogLogPlot[Range[20]^3, Frame -> True];
ticks=(FrameTicks /. AbsoluteOptions[foo, FrameTicks])

Any ideas on how to deal with this?..

Edit: lots of good answers here! Accepting Mr. Wizard's since it proved to be the most concise way to solve the immediate problem at hand, but I see myself using the other methods suggested in the future.

One can use replacements to mess with the labels directly, bypassing Option/AbsoluteOptions:

ListLogLogPlot[Range[20]^3, Frame -> True] /.
   (FrameTicks -> x_) :>
      (FrameTicks -> (x /. {a_?NumericQ, b_Integer, s___} :>
         {a, Superscript[10, Log10@b], s} ))

Thanks to Alexey Popkov this is now improved and less fragile.

Like Sjoerd, I generally prefer to write a function that computes the ticks on the fly:

PowerTicks[label_][min_, max_] := Block[{min10, max10},
  min10 = Floor[Log10[min]];
  max10 = Ceiling[Log10[max]];
  Join[Table[{10^i, 
     If[label, Superscript[10, i], Spacer[{0, 0}]]}, {i, min10, 
     max10}],
   Flatten[
    Table[{k 10^i, 
      Spacer[{0, 0}], {0.005, 0.`}, {Thickness[0.001`]}}, {i, min10, 
      max10}, {k, 9}], 1]]
  ]

ListLogLogPlot[Range[20]^3, Frame -> True, 
 FrameTicks -> {{PowerTicks[True], 
    PowerTicks[False]}, {PowerTicks[True], PowerTicks[False]}}]

To complement Brett's answer, look at the CustomTicks package in LevelScheme. It provides two functions for generating tick marks 'LinTicksandLogTicks`, and each has a host of formatting options. Currently, it requires you to perform the logarithm yourself, i.e.

Plot[ {Log[10,Cosh[x]], Log[10, Sinh[x]]}, {x, 0, 4}, Frame -> True,
      FrameTicks -> { LinTicks, LogTicks, None, None }]

gives

For a list of data, obviously you'd have to use Log[Base, data] with ListPlot, but it is workable. I have submitted a patch to Mark Caprio so that the following would do the exact same thing as above

LogPlot[ {Cosh[x], Sinh[x]}, {x, 0, 4}, Frame -> True,
      FrameTicks -> { LinTicks, LogTicks, None, None }]

If the patch is accepted the old form of LogTicks would be accessible by setting the option PlotType to Linear, Logarithmic is default. The advantage of using CustomTicks is that other bases are easy

and it automatically formats it like you want.

Edit: I'd also like to point out, that CustomTicks is loadable by itself, separate from the rest of LevelScheme. And, as it is a small package, there isn't all that much additional overhead.

Looks like a bug to me. Simple calling AbsoluteOptions[foo] yields error messages. Plain old Options[foo] works fine, though.

Send an email with this code in it to support@Wolfram.com. They will be able to tell you if there's a known better workaround.