Union & precision <<take 2>>

• To: mathgroup at smc.vnet.net
• Subject: [mg8627] Union & precision <<take 2>>
• From: Gadi Oron <oron at manet.pmmh.espci.fr>
• Date: Fri, 12 Sep 1997 04:10:41 -0400
• Organization: Acces regional Ile-de-France (Univ. Paris VI/VII) - France
• Sender: owner-wri-mathgroup at wolfram.com

```Hello again,

This is the second chapter im my adventure of trying to use Union taking
into account the precision.

As suggested by the replies to my last message (thanx) the use of
SameTest-> testfunc should do the thing.

Since my sets contain only one of the two structures
"eline[{x1,y1},{x2,y2}]" and "Circle[{x,y},r]" I wrote the following:

pre=10^(-4);
norm[v_List]:=Sqrt[v.v];

Clear[test];

test[lhs_Circle,rhs_Circle]:=
(norm[lhs[[1]]-rhs[[1]]]<pre && Abs[lhs[[2]]-rhs[[2]]]<pre );

test[lhs_eline , rhs_eline]:=
(norm[lhs[[1]]-rhs[[1]]]<pre && norm[lhs[[2]]-rhs[[2]]]<pre);

test[lhs_,rhs_]:=TrueQ[(lhs==rhs)];

Now, it seems to work all right: Check :

test[Circle[{0.192450089729875202`,0.277777777777777767`},
0.0555555555555555535`],
Circle[{0.192450089729875308`,0.277777777777777901`},
0.0555555555555555802`]]

Gives : True.

Also :

Union[{Circle[{0.192450089729875202`,0.277777777777777767`},
0.0555555555555555535`],
Circle[{0.192450089729875308`,0.277777777777777901`},
0.0555555555555555802`]},SameTest->test]

Gives (right):

{Circle[{0.19245,0.277778},0.0555556]}

But (surprise):

Union[{Circle[{0.192450089729875202`,0.277777777777777767`},
0.0555555555555555535`],
Circle[{0.192450089729875202`,0.722222222222222232`},
0.0555555555555555535`],
Circle[{0.192450089729875308`,0.277777777777777901`},
0.0555555555555555802`]},SameTest->test]

Gives (!!) :

{Circle[{0.19245,0.277778},0.0555556],Circle[{0.19245,0.722222},0.0555556],
Circle[{0.19245,0.277778},0.0555556]}

Notice that the set is not well ordered and that we have 2 of the
element equal by the SameTest.

What is going wrong??

Thank you.

P.S. Sorry for the illisibility, I have put in the full form of the
numbers in order to show the precision.

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```

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