Dr. John May

## 2616 Reputation

17 years, 4 days
Maplesoft
Pasadena, California, United States

## Social Networks and Content at Maplesoft.com

I have been a part of the Mathematical Software Group at Maplesoft since 2007. I have a Ph.D in Mathematics from North Carolina State University as well as Masters and Bachelors degrees from the University of Oregon. I have been working on research in computational mathematics since 1997. I currently work on symbolic solvers and visualization as well as other subsystems of Maple.

## I can't seem to replicate this as a bug....

I can't seem to replicate this as a bug. In Maple 14,

`solve({b4*y^3+b1*x*y^2+b2*x^2*y+b3*x^3, a*y+a1*x+a2*x*y+a3*x^2+a4*y^2}, {x,y});`

gives me the same answer as Maple 13 in both 32 and 64 bit Linux.  Are you on a different platform?

## I can't seem to replicate this as a bug....

I can't seem to replicate this as a bug. In Maple 14,

`solve({b4*y^3+b1*x*y^2+b2*x^2*y+b3*x^3, a*y+a1*x+a2*x*y+a3*x^2+a4*y^2}, {x,y});`

gives me the same answer as Maple 13 in both 32 and 64 bit Linux.  Are you on a different platform?

## avoiding conversion...

Without declaring A first, the assignment "A[i,j]:=lcm(i,j):" implicitly creates a table.  In a case like this example, you know how big your data is, and you know you want it in a Matrix in the end, so you can avoid all the post-processing and table creation overhead by either 1. declaring A to be a matrix before the loop (i.e. "A := Matrix(10,10, 0);") or 2. (preferred) construct A using the Matrix constructor:

A := Matrix(10,10,lcm);

and avoid the loop entirely.

## @Clare So I'll be impressed if you can r...

@Clare So I'll be impressed if you can render pac-man navigating his entire maze.

## @Robert Israel Oops! There appears...

@Robert Israel Oops!  There appears to have been a cut and paste malfunction.  PP actually has a small circle in the middle of the path, so it is a little more complicated than that:

```PP :=
[piecewise(t < 0, -(1/8)*t^2,
t < .8*Pi, -(2/15)*cos(t)*(30*sin(t)+60*sin(t)*cos(t)^6-90*sin(t)*cos(t)^4),
t < Pi, (1/10)*sin(10*t-8.0*Pi)+.5242497001,
-(2/15)*cos(t+.2*Pi)*(-30*sin(t+.2*Pi)-60*sin(t+.2*Pi)                   *cos(t+.2*Pi)^6+90*sin(t+.2*Pi)*cos(t+.2*Pi)^4)),

piecewise(t < 0, t,
t < .8*Pi, 4*sin(t)^2,
t < Pi, (1/10)*cos(10*t-8.0*Pi)+.381966011,                     4*sin(t+.2*Pi)^2),

piecewise(t < 0, t, 0) ];
```

I also editted my original post with the correct value of PP to create the plot

## @hirnyk I was hoping for daily birth dat...

@hirnyk I was hoping for daily birth data from Australia, but I used the monthly data you posted to plot Austrailian births from 1998-2007 (2008 Decemeber numbers looked incomplete) renormalized, fit with a curve (using ?CurveFitting,Spline ), and overlaid on the US data:

To my eye it looks a little less seasonal perhaps due to seperate winter and Christmas/New Year conception spikes? (the white month labels at the bottom are the approximate months of conception)

Heres the new worksheet: birthday-distributi.mw

## @Robert Israel There is a nice box plot ...

@Robert Israel There is a nice box plot of the weekend phenomena here http://www.stanford.edu/~dgleich/notebook/2009/04/birthday_distribution.html too (using the US 1978 live birth data).  I imagine that a lot of mothers do not want to give birth on Christmas either - that probably also contributes to the dip.

## @Axel Vogt I tried to find birth data fo...

@Axel Vogt I tried to find birth data for Australia (to no avail) to see if that big bump is due to Christmas, or just to winter. :D  If anyone can dig something up, I'd love to see it.

## @Robert Israel I had the same problem, b...

@Robert Israel I had the same problem, but it seems to work fine if I change the main while loop from "p=100" to "p<>0"

```while p <> 0 do
a := Array(1 .. 100, datatype = integer[1]);
p := Sockets:-ReadBinary(a, sock);
s(n+1 .. n+p) := a[1 .. p];
n := n+p;
end do:
```

## @Robert Israel I had the same problem, b...

@Robert Israel I had the same problem, but it seems to work fine if I change the main while loop from "p=100" to "p<>0"

```while p <> 0 do
a := Array(1 .. 100, datatype = integer[1]);
p := Sockets:-ReadBinary(a, sock);
s(n+1 .. n+p) := a[1 .. p];
n := n+p;
end do:
```

## Here is a shot at an in then out flythro...

Here is a shot at an in then out flythrough based on Robert's post:

`S:= [-2/15*cos(t)*(3*cos(v)+5*sin(t)*cos(v)*cos(t)-30*sin(t)-60*sin(t)*cos(t)^6 +90*sin(t)*cos(t)^4), -1/15*sin(t)*(80*cos(v)*cos(t)^7*sin(t)+48*cos(v)*cos(t)^6 -80*cos(v)*cos(t)^5*sin(t)-48*cos(v)*cos(t)^4-5*cos(v)*cos(t)^3*sin(t) -3*cos(v)*cos(t)^2+5*sin(t)*cos(v)*cos(t)+3*cos(v)-60*sin(t)), 2/15*sin(v)*(3+5*sin(t)*cos(t))]; P := eval(S, {cos(v)=0, sin(v)=0, t=-t}); Q := eval(S, {cos(v)=0, sin(v)=0, t=t+Pi*0.2});  ﻿PP:= [piecewise(t<0,-t^2/8,t<.8*Pi,P[1],t<Pi,sin(10*(t-.8*Pi))/10+0.5242497001,Q[1]),          piecewise(t<0,t,t<.8*Pi,P[2],t<Pi,cos(10*(t-.8*Pi))/10+.381966011, Q[2]),          piecewise(t<0,t, 0)];S:= [S[1],S[3],S[2]];PP := [PP[1],PP[3],PP[2]];`

I found it really helpful to plot the space curve:

`sc:=plots:-spacecurve(PP,t=-1.5..1.7*Pi,color=black,thickness=2);kb:=plot3d(S, t = 0 .. Pi, v = 0 .. 2*Pi, scaling = constrained, grid=[100, 30], transparency=0.5);plots:-display([kb,sc]);`

And then the plot

`plot3d(S, t = 0 .. Pi, v = 0 .. 2*Pi, scaling = constrained, lightmodel = light3, colour=t, grid=[150, 30],           viewpoint=[path=[PP,t=-1.5..1.65*Pi],look=forward, fieldofview=75, frames=100]);`

## @Robert Israel I probably should have...

@Robert Israel I probably should have been more specific, and said "Shannon Entropy" measured just with character counting a la ?StringTools:-Entropy or ?ImageTools:-Entropy .  Clearly that sort of measure can not really say anything about LZ compressibility, but so much of what I found written on the web conflated entropy (typically immediately defined to be Shannon Entropy) with compressibility when as per @JacquesC it would be better to save comparisons to compressibility for information theoritical measures of complexity (or a more subtle discussion of entropy).

## @Robert Israel Excellent!...

@Robert Israel Excellent!

## @Robert Israel Very nice!...

@Robert Israel Very nice!

## Jabulani...

I'll be impressed if someone can plot one of the actual 2010 World Cup balls: http://en.wikipedia.org/wiki/Adidas_Jabulani

John

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