Skip to main content

customization - Display Log with desired notation in output


I wish to display logarithms with different bases in the single-term rather than numerator/denominator form during output:


Log[17]/Log[2]   ->  Log2[17]

Log[13]/Log[10]  ->  Log10[13]
Log[99]/Log[11]  ->  Log[11, 99]

What is the best way to apply formatting rules like this?



Answer



One can use $PrePrint and ReplaceAll to effect this:


$PrePrint = # /. {
     Log[n_]/Log[2]  :> Defer @ Log2[n],
     Log[n_]/Log[10] :> Defer @ Log10[n],
     Log[n_]/Log[b_] :> Defer @ Log[b, n]

     } &;

Or MakeBoxes:


MakeBoxes[Log[n_]/Log[2], fmt_]  := ToBoxes[Defer @ Log2[n], fmt]
MakeBoxes[Log[n_]/Log[10], fmt_] := ToBoxes[Defer @ Log10[n], fmt]
MakeBoxes[Log[n_]/Log[b_], fmt_] := ToBoxes[Defer @ Log[b, n], fmt]

It is also possible to use Format but in this case it requires unprotecting Times:


Unprotect[Times];


Format[Log[n_]/Log[2]]  := Defer @ Log2[n]
Format[Log[n_]/Log[10]] := Defer @ Log10[n]
Format[Log[n_]/Log[b_]] := Defer @ Log[b, n]

Protect[Times];

These assignments are made to a special class of rules: FormatValues. Because these are only used in formatting this should not slow down internal operations using Times, unlike overloading UpValues or DownValues.


Each method relies on Defer to prevent an infinite recursion yet allow evaluation of output when it is given as input.


Result:


Mathematica graphics



Comments

Post a Comment

Popular posts from this blog

front end - keyboard shortcut to invoke Insert new matrix

I frequently need to type in some matrices, and the menu command Insert > Table/Matrix > New... allows matrices with lines drawn between columns and rows, which is very helpful. I would like to make a keyboard shortcut for it, but cannot find the relevant frontend token command (4209405) for it. Since the FullForm[] and InputForm[] of matrices with lines drawn between rows and columns is the same as those without lines, it's hard to do this via 3rd party system-wide text expanders (e.g. autohotkey or atext on mac). How does one assign a keyboard shortcut for the menu item Insert > Table/Matrix > New... , preferably using only mathematica? Thanks! Answer In the MenuSetup.tr (for linux located in the $InstallationDirectory/SystemFiles/FrontEnd/TextResources/X/ directory), I changed the line MenuItem["&New...", "CreateGridBoxDialog"] to read MenuItem["&New...", "CreateGridBoxDialog", MenuKey["m", Modifiers-...
Post a Comment
Read more

How to thread a list

I have data in format data = {{a1, a2}, {b1, b2}, {c1, c2}, {d1, d2}} Tableform: I want to thread it to : tdata = {{{a1, b1}, {a2, b2}}, {{a1, c1}, {a2, c2}}, {{a1, d1}, {a2, d2}}} Tableform: And I would like to do better then pseudofunction[n_] := Transpose[{data2[[1]], data2[[n]]}]; SetAttributes[pseudofunction, Listable]; Range[2, 4] // pseudofunction Here is my benchmark data, where data3 is normal sample of real data. data3 = Drop[ExcelWorkBook[[Column1 ;; Column4]], None, 1]; data2 = {a #, b #, c #, d #} & /@ Range[1, 10^5]; data = RandomReal[{0, 1}, {10^6, 4}]; Here is my benchmark code kptnw[list_] := Transpose[{Table[First@#, {Length@# - 1}], Rest@#}, {3, 1, 2}] &@list kptnw2[list_] := Transpose[{ConstantArray[First@#, Length@# - 1], Rest@#}, {3, 1, 2}] &@list OleksandrR[list_] := Flatten[Outer[List, List@First[list], Rest[list], 1], {{2}, {1, 4}}] paradox2[list_] := Partition[Riffle[list[[1]], #], 2] & /@ Drop[list, 1] RM[list_] := FoldList[Transpose[{First@li...
Post a Comment
Read more

functions - Get leading series expansion term?

Given a function f[x] , I would like to have a function leadingSeries that returns just the leading term in the series around x=0 . For example: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x)] x and leadingSeries[(1/x + 2 + (1 - 1/x^3)/4)/(4 + x)] -(1/(16 x^3)) Is there such a function in Mathematica? Or maybe one can implement it efficiently? EDIT I finally went with the following implementation, based on Carl Woll 's answer: lds[ex_,x_]:=( (ex/.x->(x+O[x]^2))/.SeriesData[U_,Z_,L_List,Mi_,Ma_,De_]:>SeriesData[U,Z,{L[[1]]},Mi,Mi+1,De]//Quiet//Normal) The advantage is, that this one also properly works with functions whose leading term is a constant: lds[Exp[x],x] 1 Answer Update 1 Updated to eliminate SeriesData and to not return additional terms Perhaps you could use: leadingSeries[expr_, x_] := Normal[expr /. x->(x+O[x]^2) /. a_List :> Take[a, 1]] Then for your examples: leadingSeries[(1/x + 2)/(4 + 1/x^2 + x), x] leadingSeries[Exp[x], x] leadingSeries[(1/x + 2 + (1 - 1/x...
Post a Comment
Read more