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[MUG] Curious simplification
| [MUG] Curious simplification |
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Author: Greg Gamble
Posted: Thu, 5 Dec 2002 17:23:15 +0800
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>> From: "Greg Gamble" "gregg"
Hi again,
Apologies for the last inane request. My real query was based on trying
to find a general way to treat student inequality responses to check their
equivalence with a correct response e.g.
x < 2 or x > 2
is treated as different to
2 < x or 2 > x
In Maple:
> evalb((x < 2 or x > 2) = (2 < x or 2 > x));
false
> evalb({solve(x < 2 or x > 2)} = {solve(2 < x or 2 > x)});
true
... so this suggests using {solve(...)} to compare such expressions.
However, if one tries this with <> one gets:
> solve(x<>2);
x
(which means `any value' as I interpret it) and differs from:
> solve(x < 2 or x > 2);
RealRange(-infinity, Open(2)), RealRange(Open(2), infinity)
I'm using Maple 7 and, looking at the docs, <> is not included as a
an operator for expressions of form solve(ineq). Anyway, I'm wondering if
anyone can see a nice way to uniformly recognise domains and ranges written
in inequality form.
Regards,
Greg Gamble
> -----Original Message-----
> From: Greg Gamble "mailto:gregg"
> Sent: Thursday, 5 December 2002 4:51 PM
> To: "maple-list"
> Subject: Curious simplification
>
>
> Hi,
>
> Can anyone explain the following Maple evaluation?
>
> > x<>2 or x>3;
> true
>
> Regards,
> Greg Gamble
>
> // Greg Gamble, Dept. of Maths & Stats //
> // Curtin University, Bentley WA 6102 //
> // Mailto: "gregg" //
> // WWW: http://www.maths.curtin.edu.au/~gregg //
>
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| [MUG] Re: Curious simplification |
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Author: Carl Devore
Posted: Wed, 11 Dec 2002 01:37:12 -0500
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>> From: Carl Devore "devore"
On Thu, 5 Dec 2002, Greg Gamble wrote:
> ... so this suggests using {solve(...)} to compare such expressions.
> However, if one tries this with <> one gets:
> > solve(x<>2);
> x
> (which means `any value' as I interpret it) and differs from:
>
> > solve(x < 2 or x > 2);
> RealRange(-infinity, Open(2)), RealRange(Open(2), infinity)
Because of complex numbers, 'x<>2' is not the same as 'x>2 or x<2'. But
if you include a trivial directional inequality in the solve, it will
"reduce" the inequalities:
> solve( {x<>2, x<infinity} );
{x<2}, {2<x}
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| [MUG] Re: Curious simplification |
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Author: Greg Gamble
Posted: Fri, 13 Dec 2002 10:48:19 +0800
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>> From: "Greg Gamble" "gregg"
On Wednesday, 11 December 2002 2:37 PM, Carl Devore wrote:
> On Thu, 5 Dec 2002, Greg Gamble wrote:
> > ... so this suggests using {solve(...)} to compare such expressions.
> > However, if one tries this with <> one gets:
> > > solve(x<>2);
> > x
> > (which means `any value' as I interpret it) and differs from:
> >
> > > solve(x < 2 or x > 2);
> > RealRange(-infinity, Open(2)),
> RealRange(Open(2), infinity)
>
> Because of complex numbers, 'x<>2' is not the same as 'x>2 or x<2'.
Thanks Carl ... I keep forgetting about Complex Numbers!!
After sending the email, I found that by defining a function
SolveInequality, I could map inequality expressions (of the type I was
expecting from students) uniformly to a set of RealRange expressions. My
function, however, replaced
expressions of form 'x <> a' by their 'x < a or x > a' equivalent,
explicitly,
by a call to a ReplaceNEQ function I defined. ...
> But if you include a trivial directional inequality in the solve, it will
> "reduce" the inequalities:
>
> > solve( {x<>2, x<infinity} );
> {x<2}, {2<x}
... Thus my code, of course, had precisely the sort of implied assumption
that Maple tries to avoid (I assumed I was working over the Real numbers).
So
I really should define a function SolveRealInequality (instead of
SolveInequality)
defined as follows:
SolveRealInequality := proc(ineq::boolean, var)::set;
description
"Returns the solution of the inequality ineq as a set of ",
"RealRange expressions";
local i;
{ seq( solve( op(i) ),
i = { solve({subs(var = `x`, ineq), x < infinity}) }
) };
end;
In this way, SolveRealInequality returns a canonical representation for
equivalent inequalities representing Real intervals, e.g.
> SolveRealInequality(x<>2, x);
{RealRange(-infinity, Open(2)), RealRange(Open(2), infinity)}
> SolveRealInequality(x>2 or x<2, x);
{RealRange(-infinity, Open(2)), RealRange(Open(2), infinity)}
> SolveRealInequality(2>x or 2<x, x);
{RealRange(-infinity, Open(2)), RealRange(Open(2), infinity)}
... so that seems to achieve what I was after (the first arguments of each
of these when tested pairwise for equality, Maple returns false).
However, there really seems to be a bug (I am using Maple 7) ...
> solve(x<2 or x>2 or x=2);
RealRange(-infinity, Open(2)), RealRange(Open(2), infinity)
whereas:
> solve(x<=2 or x>2);
x
Is there a reason for this behaviour? I'm a little troubled also by the
return
of x here also. It's not documented anywhere that I can see, what it's
supposed
to mean ... even looking through the code of `solve` there is no comment
indicating the reason for this return value. I interpret it as `any x', i.e.
`no restriction
on x', but if that's the case why do you also get ...
> solve(x<>2);
x
? I don't find this sensible. Can someone please explain it?
Regards,
Greg Gamble
// Greg Gamble, Dept. of Maths & Stats //
// Curtin University, Bentley WA 6102 //
// Mailto: "gregg" //
// WWW: http://www.maths.curtin.edu.au/~gregg //
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