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MathGroup Archive 2007

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Re: IsExact

  • To: mathgroup at
  • Subject: [mg80539] Re: IsExact
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at>
  • Date: Sun, 26 Aug 2007 02:51:47 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <falsi4$gfh$>

carlos at wrote:

> Let c be a 1D list of scalar coefficients, numeric or symbolic,
> real or complex. No entry is a list. Examples:
> ClearAll[n,x,y,a,a1,a2,b,r];
> c1={1,2*I/5,E^(25*n),3/4+I,Cos[n*x*Pi],y*Sqrt[-5]};
> c2={a/b,r+2/5,a1,,,,,a2};
> c3={1.5,0,Sqrt[3],0,4};
> c4={(r+0.5)/3,3/7,3+Sin[4*x*y]};
> c5={1,2,3,4,5,6}+0.0;
> c6={N[x]};
> I need a function IsExact[c] that returns False if
> at least one entry of c is floating, or if it contains one
> floating number; else True.  For example, tests on
> c1 and c2  should return True; the others False.
> Any simple way to implement this? It should work on V.5.

I believe you are already aware that any global value for the symbols 
used in the lists may affect the result in one way or another (so the 

Nevertheless, you will have to put a hold on 
N[some_symbolic_expression], since after evaluation the element becomes 
just some_symbolic_expression. Compare the result from c6 and c7.

Below, the function exactQ accepts a one dimensional list and returns 
*True* only if none of its elements has head *Real* or *N*.


exactQ[(lst_List)?VectorQ] := FreeQ[lst, _Real | N]

ClearAll[n, x, y, a, a1, a2, b, r];
c1 = {1, 2*(I/5), E^(25*n), 3/4 + I, Cos[n*x*Pi],
c2 = {a/b, r + 2/5, a1, Null, Null, Null, Null, a2};
c3 = {1.5, 0, Sqrt[3], 0, 4};
c4 = {(r + 0.5)/3, 3/7, 3 + Sin[4*x*y]};
c5 = {1, 2, 3, 4, 5, 6} + 0.;
c6 = {N[x]};
c7 = {HoldForm[N[x]]};

exactQ /@ {c1, c2, c3, c4, c5, c6, c7}

{c6, c7}

{True, True, False, False, False, True, False}


Implemented and tested on Mathematica 5.2 for Microsoft Windows (June 
20, 2005).


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