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Works in 7.0.1, not in 8.0.4 ??

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124290] Works in 7.0.1, not in 8.0.4 ??
  • From: James Stein <mathgroup at stein.org>
  • Date: Mon, 16 Jan 2012 17:06:17 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I wrote some code in 2010 (posted below).
It gave correct results under Mathematica v7.0.1 (posted further below)
It gives nothing except errors under Mathematica v8.0.4 (as shown still
further below).
Can anyone shed light on this discrepancy?
The same file was run on both versions, immediately after a Quit[] command.
(Both Mathematica versions were Macintosh.)

Code:
Clear[xp,yp,zp];(* pole   coordinates *)
Clear[xs,ys,zs];(* sphere coordinates *)
Clear[xm,ym,zm];(* map    coordinates *)
eq0=xs^2+ys^2+zs^2==1;       (* sphere *)
(* constraints on colinear points,x,y,z: *)
eq1=(ym-yp) (xs-xp)==(xm-xp) (ys-yp);
eq2=(ym-yp) (zs-zp)==(zm-zp) (ys-yp);
(* two sets polar projection parameters *)
eq3={xp,yp,zp,zm}=={0,0,-1,0};(* N *)
eq4={xp,yp,zp,zm}=={0,0,+1,0};(* S *)
(* map from S -> M *)
Simplify[Solve[{eq1,eq2,eq3},{xm,ym}]]
Simplify[Solve[{eq1,eq2,eq4},{xm,ym}]]
(* map from M -> S *)
Simplify[Solve[{eq0,eq1,eq2,eq3},{xs,ys,zs}]][[2]]
(* m2s (S): *)
Simplify[Solve[{eq0,eq1,eq2,eq4},{xs,ys,zs}]][[2]]

Output from v7.0.1:  (printed nicely, but can't display in email)

{{xm->xs/(1+zs),ym->ys/(1+zs)}}

{{xm -> -(xs/(-1 + zs)), ym -> -(ys/(-1 + zs))}}

{xs->(2 xm)/(1+xm^2+ym^2),zs->-1+2/(1+xm^2+ym^2),ys->(2 ym)/(1+xm^2+ym^2)}

{xs -> (2 xm)/(1 + xm^2 + ym^2), zs -> 1 - 2/(1 + xm^2 + ym^2),
 ys -> (2 ym)/(1 + xm^2 + ym^2)}


Output from v8.0.4:

{}

{}

Part::partw: Part 2 of {} does not exist. >>
{}[[2]]

Part::partw: Part 2 of {} does not exist. >>
{}[[2]]


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