simonjtyler

from typing import List

class Primes:
  "Singleton to dynamically generate primes when required and until out of memory"
  
  _instance = None
  _primes: List[int]
  _max_num_checked: int

  def __new__(cls, init_primes=[2]):

simonjtyler

void main() {
  for (var i = 0; i <= 30; i++) {
  	print('fibonacci($i) = ${fibonacci(i)}');
  }
  
  print('\n'
        'Function fibonacci is of type ${fibonacci.runtimeType}'
        ' and has memoized the values ${fibonacci.vals}');
}

simonjtyler

(* Old code, made redundant by RepeatedTiming, but put here for safe keeping *)
(* Also in a AUG 15TH, 2011 pastebin  https://pastebin.com/Nv7rH2vE *)
(*http://stackoverflow.com/questions/4198961/what-is-in-your-mathematica-tool-bag/4199042#4199042*)

Unprotect[TimeAv];

TimeAv::usage = "\!\(\*
StyleBox[\"TimeAv\", \"TI\"]\)\!\(\*
StyleBox[\"[\", \"TI\"]\)\!\(\*
StyleBox[\"expr_\", \"TI\"]\)\!\(\*

simonjtyler

from colorsys import hsv_to_rgb

def hue2rgb(hue, saturation=1, value=0.8, rgb_scale = 1):
    """Given a hue, this function returns a RGB value.
    hue is a number between 0 and 1 that represents a color on the color wheel in RGB order.
    hue2rgb(0) = red,  hue2rgb(1/3) = green,  hue2rgb(2/3) = blue"""
    return tuple(rgb_scale*c for c in hsv_to_rgb(hue, saturation, value))

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]

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

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

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

(* 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

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;]];]