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

plotting - How to draw lines between specified dots on ListPlot?

I would like to create a plot where I have unconnected dots and some connected. So far, I have figured out how to draw the dots. My code is the following: ListPlot[{{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4,13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full] I have thought using ListLinePlot command, but I don't know how to specify to the command to draw only selected lines between the dots. Do have any suggestions/hints on how to do that? Thank you. Answer One possibility would be to use Epilog with Line : ListPlot[ {{1, 1}, {2, 2}, {3, 3}, {4, 4}, {1, 4}, {2, 5}, {3, 6}, {4, 7}, {1, 7}, {2, 8}, {3, 9}, {4, 10}, {1, 10}, {2, 11}, {3, 12}, {4, 13}, {2.5, 7}}, Ticks -> {{1, 2, 3, 4}, None}, AxesStyle -> Thin, TicksStyle -> Directive[Black, Bold, 12], Mesh -> Full, Epilog -> { Line[ ...

equation solving - Invert and fit implicitly defined curve

I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?

dynamic - How can I make a clickable ArrayPlot that returns input?

I would like to create a dynamic ArrayPlot so that the rectangles, when clicked, provide the input. Can I use ArrayPlot for this? Or is there something else I should have to use? Answer ArrayPlot is much more than just a simple array like Grid : it represents a ranged 2D dataset, and its visualization can be finetuned by options like DataReversed and DataRange . These features make it quite complicated to reproduce the same layout and order with Grid . Here I offer AnnotatedArrayPlot which comes in handy when your dataset is more than just a flat 2D array. The dynamic interface allows highlighting individual cells and possibly interacting with them. AnnotatedArrayPlot works the same way as ArrayPlot and accepts the same options plus Enabled , HighlightCoordinates , HighlightStyle and HighlightElementFunction . data = {{Missing["HasSomeMoreData"], GrayLevel[ 1], {RGBColor[0, 1, 1], RGBColor[0, 0, 1], GrayLevel[1]}, RGBColor[0, 1, 0]}, {GrayLevel[0], GrayLevel...

Blog

Search This Blog