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[MUG] testeq
Author: Bill Whiten    Posted: 16/08/2001 07:13:07 GDT
>> From: (Bill Whiten) In Maple Vr5.1 Mac: > ex1:=n*k!/n!/(k-n)!*p^n*(1 - p)^(k-n); n (k - n) n k! p (1 - p) ex1 := ---------------------- n! (k - n)! > ex2:=k*(k-1)!/(k-n)!/(n-1)!*p^(n-1)*(1 - p)^(k-n)*p; (-1 + n) (k - n) k (k - 1)! p (1 - p) p ex2 := ------------------------------------- (k - n)! (-1 + n)! > testeq(ex1,ex2); false > simplify(ex1-ex2); 0 > simplify(ex1/ex2); 1 > ----------- Bill Whiten, Julius Kruttschnitt Mineral Research Centre, The University Of Queensland, Tel: int +61 7 3365 5888 Isles Rd, Indooroopilly, Fax: int +61 7 3365 5999 Brisbane Qld 4068, AUSTRALIA.

[MUG] Re: testeq
Author: Maple User Group    Posted: 22/08/2001 16:11:03 GDT
>> From: Maple User Group |On Thu, 16 Aug 2001, Bill Whiten wrote: |> In Maple Vr5.1 Mac: |> |> > ex1:=n*k!/n!/(k-n)!*p^n*(1 - p)^(k-n); |> > ex2:=k*(k-1)!/(k-n)!/(n-1)!*p^(n-1)*(1 - p)^(k-n)*p; -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 17 Aug 2001 15:16:20 -0700 (PDT) From: Robert Israel To: Subject: testeq This bug seems to be fixed in Maple 6, to the extent that the result is FAIL rather than "false". Note that the help for testeq does not mention factorial: - This function will succeed over expressions formed with rational constants, independent variables, and I, combined by arithmetic operations, exponentials, trigonometrics and a few others. It may also succeed with some expressions involving radicals, Pi as an argument of trigonometrics, and algebraic constants and functions. If the expressions do not fall in this class, testeq returns FAIL. Testeq may also return FAIL if it cannot find an appropriate modulus that works after seven trials. So FAIL should be an acceptable result in this context. Still, it's curious that Maple 6 does not come up with "true" here, because it does produce "true" for testeq(k*(k-1)!, k!). Robert Israel Department of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Fri, 17 Aug 2001 23:10:12 -0400 (EDT) From: Carl DeVore To: Subject: testeq You do not need such a complicated example to catch this bug. In Maple 5.1, try > testeq(n*(n-1)!, n!); and you still get "false". There seems to be much flip-flopping among versions with how testeq handles this expression. Maple 6 returns "true". Maple 7 returns "FAIL". FAIL is not incorrect per se, but if Maple 6 can find the answer, why not Maple 7? The testeq command does not try to simplify the difference. Therefore, I think that testeq is intended for expressions where the simplify command would take too long. To verify equality, first try simplifying the difference. -- Carl Devore Maple programs written for hire. Maple advisor for hire. -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Sun, 19 Aug 2001 16:24:13 +0100 (BST) From: J H Davenport To: Subject: testeq Maple 6 returns 'FAIL' for me, which is not the same as false. The HELP for testeq in Maple 6 says: This function will succeed over expressions formed with rational constants, independent variables, and I, combined by arithmetic operations, exponentials, trigonometrics and a few others. It may also succeed with some expressions involving radicals, Pi as an argument of trigonometrics, and algebraic constants and functions. If the expressions do not fall in this class, testeq returns FAIL. Testeq may also return FAIL if it cannot find an appropriate modulus that works after seven trials. A quick use of printlevel shows that it is the second case (no modulus) which is happening, essentially because Maple is refusing to work out the factorials (which are converted into Gamma) since the arguments are too large. James Davenport -=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=-=*=- Date: Tue, 21 Aug 2001 11:02:23 +0200 From: Helmut Kahovec To: Subject: testeq Well, this weakness of testeq() is present in the Windows version of MapleV/Release5.1, too. It can be easily removed by changing the third and fourth source code line of testeq() from testeq := proc(a, b) local expr, e1, e2, i, ig, preverror, s, t; 1 if nargs = 1 and type(a,algebraic) then 2 expr := a elif nargs = 1 and type(a,`=`) and type(op(1,a),algebraic) and type(op(2,a),algebraic) then 3 expr := op(1,a)-op(2,a) elif nargs = 2 and type(a,algebraic) and type(b,algebraic) then 4 expr := a-b else 5 ERROR(`invalid arguments`) fi; ... to testeq := proc(a, b) local expr, e1, e2, i, ig, preverror, s, t; 1 if nargs = 1 and type(a,algebraic) then 2 expr := a elif nargs = 1 and type(a,`=`) and type(op(1,a),algebraic) and type(op(2,a),algebraic) then 3 expr := simplify(op(1,a)-op(2,a)) elif nargs = 2 and type(a,algebraic) and type(b,algebraic) then 4 expr := simplify(a-b) else 5 ERROR(`invalid arguments`) fi; ... Then we get: > restart; > ex1:=n*k!/n!/(k-n)!*p^n*(1-p)^(k-n); > ex2:=k*(k-1)!/(k-n)!/(n-1)!*p^(n-1)*(1-p)^(k-n)*p; > testeq(ex1,ex2),testeq(ex1=ex2); true, true With kind regards, Helmut

[MUG] Re: testeq
Author: Carl DeVore    Posted: 23/08/2001 20:53:48 GDT
>> From: Carl DeVore > Date: Tue, 21 Aug 2001 11:02:23 +0200 > From: Helmut Kahovec > > Well, this weakness of testeq() is present in the Windows version of > MapleV/Release5.1, too. It can be easily removed by changing the third > and fourth source code line of testeq() > to > 3 expr := simplify(op(1,a)-op(2,a)) > elif nargs = 2 and type(a,algebraic) and type(b,algebraic) > then > 4 expr := simplify(a-b) My assumption is that the testeq command was intended to be used on expressions that would take a very long time to simplify.

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