simonjtyler

(* This code extends Mathematica's Position function to work on SparseArrays. *)
(* Note that Position and Cases have the same optional arguments, so the code is quite simple *)
Unprotect[Position];
Position[A_SparseArray, pat_, others___] := Cases[ArrayRules[A], HoldPattern[_->pat], others][[All,1]]
Protect[Position];

simonjtyler

Cell[TextData[{
 "the chemical formula for hydronium is H",
 Cell[BoxData[
  FormBox[
   SubscriptBox["\[Null]", "3"], TraditionalForm]],
  FormatType->"TraditionalForm"],
 "O",
 Cell[BoxData[
  FormBox[
   SuperscriptBox["\[Null]", "+"], TraditionalForm]],

simonjtyler

Needs["GraphUtilities`"];

Clear[GraphPlotHighlight]

Protect[HighlightColor, HighlightThickness];
Options[GraphPlotHighlight] = Join[Options[GraphPlot], 
    {HighlightColor -> LightBlue, HighlightThickness -> .15}];

GraphPlotHighlight[edges:{((_ -> _) | (List|Tooltip)[_ -> _, _])..}, 
  hl:{___}:{}, opts:OptionsPattern[]] := 

simonjtyler

(* Written for http://stackoverflow.com/q/4126473/421225 *)

(* SlowIntersectQ is too slow to use in EdgeRenderingFunction *)

SlowIntersectQ[{start_,end_},pt_,r_?Positive]/;Length[start]==Length[end]==Length[pt]:=Module[{t},
    TrueQ[NMinValue[{Norm[((1.-t)start+t end)-pt],0<t<1},t,WorkingPrecision->$MachinePrecision]<r]]

(* Since we only care about straight lines, here's a faster implementation *)
(* from: http://stackoverflow.com/q/849211/421225 *)

simonjtyler

SetAttributes[Timeit, HoldAll]
Timeit[x_] := With[{t = Timing[x]}, Module[{out, form},
  If[TrueQ[MemberQ[$OutputForms, Head[t[[2]]]]],
    out = First[t[[2]]]; form = "//" <> ToString[Head[t[[2]]]], 
    out = t[[2]]; form = ""];
  If[out === Null, Null,
    CellPrint[ExpressionCell[t[[2]], "Output",
      CellLabel -> StringJoin["(", ToString[t[[1]]], ")",
        "Out[", ToString[$Line], "]", form, "="]]];
  Unprotect[Out]; Out[$Line] = out; Protect[Out]; out;]];]

simonjtyler

(* http://stackoverflow.com/questions/6367932/generate-a-list-in-mathematica-with-a-conditional-tested-for-each-element/6368770#6368770 *)

(* The code *)

TableIf::usage = "TableIf[expr,{i,\!\(\*SubscriptBox[\(i\), \(max\)]\)},addif] will \
generate a list of values expr when i runs from 1 to \
\!\(\*SubscriptBox[\(i\), \(max\)]\), only including elements if \
addif[expr] returns true. Note that addif can have dependence on the \
iterator variables.
  The default of addif is True&.

simonjtyler

A test of using stackedit
=========================

Some maths
----------

We should note that $1+1=2$ and
$$ f(a) = \frac{1}{2\pi i} \oint_\gamma \frac{f(z)}{z-a}\, dz \,.$$

simonjtyler

In[1]:= n = 400;

In[2]:= TimeAv[Plus@@ReplaceList[Product[y[j], {j, 1, n}], y[i_] rest_ :> x[i] rest];]

During evaluation of In[2]:= Total wall time is 0.554032, 
total cpu time is 0.530403 and total time spent evaluating the expression is 0.53040

During evaluation of In[2]:= The expression was evaluated 6 times, without any blocking of the runs. 
This yields a mean timing of 0.088401 with a standard deviation of 0.0074.

simonjtyler

(* 
  Complete the square for an arbitrary number of variables using a matrix representation. 
  Output a form that cleanly separates out the different terms.
  Other alternatives: http://mathematica.stackexchange.com/q/20051/34
*)

CompleteTheSquare::notquad = "The expression is not quadratic in the variables `1`";
CompleteTheSquare[expr_] := CompleteTheSquare[expr, Variables[expr]]
CompleteTheSquare[expr_, vars_Symbol] := CompleteTheSquare[expr, {vars}]
CompleteTheSquare[expr_, vars : {__Symbol}] := Module[

simonjtyler

(* 
  A simple modification of ListPlot that takes a list of complex numbers instead of a list of {x,y} coordinates
*)
 
ComplexListPlot[pts_List, opts : OptionsPattern[]] := ListPlot[Map[{Re@#, Im@#} &, pts, {-1}], opts, 
                                                        AxesOrigin -> {0, 0}, PlotStyle -> PointSize[Large]]
ComplexListPlot[pt_?NumericQ, opts : OptionsPattern[]] := ComplexListPlot[{pt}, opts]
  
Save[FileNameJoin[{$UserBaseDirectory, "Kernel", "init.m"}], ComplexListPlot]