From: maple@rogers.com   
      
   On Saturday, October 30, 2021 at 9:03:43 AM UTC-4, acer wrote:   
   > On Saturday, October 30, 2021 at 3:03:32 AM UTC-4, Nasser M. Abbasi wrote:   
   > > since sqrt of number is taken as the positive root, why   
   > > then Maple 2021.1 says it can't show this is true or not? Is   
   > > there something deep I am overlooking here?   
   > >   
   > > if evalb( 5^(1/2) < (5^(1/2)+1) ) then   
   > > "yes, smaller";   
   > > fi;   
   > >   
   > > Error, cannot determine if this expression is true or false: 5^(1/2) <   
   5^(1/2)+1   
   > >   
   > > if 5^(1/2) < (5^(1/2)+1) then   
   > > "yes, smaller";   
   > > fi;   
   > >   
   > > Error, cannot determine if this expression is true or false: 5^(1/2) <   
   5^(1/2)+1   
   > >   
   > > But in Mathematica it did not complain   
   > >   
   > > 5^(1/2) < (5^(1/2) + 1)   
   > > True   
   > >   
   > > This is very strange. Does your CAS have any problem showing   
   > > that 5^(1/2) is smaller than 5^(1/2)+1?   
   > >   
   > > In Maple, it can do it if I convert everything to float   
   > >   
   > > if evalf(5^(1/2)) < evalf((5^(1/2)+1)) then   
   > > "yes, smaller";   
   > > fi;   
   > >   
   > > "yes, smaller"   
   > >   
   > > --Nasser   
   > You are simply using the wrong command, `evalb`, instead of an appropriate   
   command such as `is`.   
   >   
   > > evalb( 5^(1/2) < (5^(1/2)+1) );   
   > 1/2 1/2   
   > 5 < 5 + 1   
   >   
   > > is( 5^(1/2) < (5^(1/2)+1) );   
   > true   
   >   
   > Your incorrect preconceptions as to the designed functionality of the   
   `evalb` command are getting in your way here.   
      
   I could add that the functionality changes according to the `type` of the   
   input, for a clear programmatic distinction.   
      
   The `evalb` command tests an inequality if the arguments are of type   
   `numeric`, in Maple's technical sense of the `type` command. And that type   
   does not include exact radicals (though it does include, say, rationals and   
   floats).   
      
   For strict equality testing the functionality is also according to that same   
   `numeric` type. But in this case the remaining cases are subjested to a pure   
   address check (which is a structural rather than a mathematical comparison).   
      
   --- SoupGate-Win32 v1.05   
    * Origin: you cannot sedate... all the things you hate (1:229/2)