The evalb command forces the evaluation of expressions involving relational operators, using a three-valued logic system.  The return values are true, false, and FAIL. If evaluation is not possible, an unevaluated expression is returned.

Normally expressions containing the relational operators =, <>, <, <=, >, and >= are treated as algebraic equations or inequalities by Maple.  However, when passed as arguments to the evalb command (or when appearing in a Boolean context in an if or while statement), they are evaluated to true or false if possible.

Note that expressions involving > and >= are converted into equivalent expressions involving < and <=, respectively.

An evalb call using <, <=, >, or >= returns evaluated only with arguments of type extended_numeric, complex, or string. For more on string comparisons, see the section Operations on Entire Strings in Using Strings in Maple.

Important: The evalb command does not simplify expressions. It may return false for a relation that is true. In such a case, apply a simplification to the relation before using evalb.

Important: The evalb command does not perform arithmetic for inequalities involving <, <=, >, or >=. It may return unevaluated when a relation is true. In such a case, perform the arithmetic operations before using evalb.

The evalb command is thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe.

$x=x$

$x=x$

$\mathrm{evalb}\left(x=x\right)$

$\mathrm{true}$

$\mathrm{evalb}\left(x=y\right)$

$\mathrm{false}$

$a≔2\&colon;$

$b≔2\&colon;$

$\mathrm{evalb}\left(a=b\right)$

$\mathrm{true}$

$\mathrm{evalb}\left(Float\left(\mathrm{\infty }\right)<\mathrm{\infty }\right)$

$\mathrm{false}$

$\mathrm{evalb}\left(Float\left(\mathrm{undefined}\right)<\mathrm{undefined}\right)$

$\mathrm{false}$

$\mathrm{evalb}\left(\mathrm{\Re }\left(x\right)\ne \mathrm{\Re }\left(x+1\right)\right)$

$\mathrm{true}$

$\mathrm{evalb}\left(y<x\right)$

$y<x$

$\mathrm{evalb}\left(2+3\mathrm{I}<3+4\mathrm{I}\right)$

$\mathrm{FAIL}$

$\mathrm{evalb}\left(\mathrm{\Re }\left(x\right)<\mathrm{\Re }\left(x+1\right)\right)$

$\mathrm{\Re }\left(x\right)<1+\mathrm{\Re }\left(x\right)$

$\mathrm{evalb}\left(\mathrm{\Re }\left(x\right)-\mathrm{\Re }\left(x+1\right)<0\right)$

$\mathrm{true}$

$\mathrm{evalb}\left(\mathrm{\Re }\left(x\right)\le \mathrm{\Re }\left(x\right)\right)$

$\mathrm{true}$

$\mathrm{evalb}\left(2<\mathrm{sqrt}\left(5\right)\right)$

$2<\sqrt{5}$

$\mathrm{evalb}\left(2<\mathrm{evalf}\left(\mathrm{sqrt}\left(5\right)\right)\right)$

$\mathrm{true}$

$\mathrm{is}\left(2<\mathrm{sqrt}\left(5\right)\right)$

$\mathrm{true}$

$\mathrm{evalb}\left(\mathrm{StringTools}\left[\mathrm{Search}\right]\left(''2''\&comma;''This\; sentence\; does\; not\; contain\; any\; numbers.''\right)=0\right)$

$\mathrm{true}$

$\mathrm{evalb}\left(\mathrm{coeff}\left(x^3+2x^2-5\&comma;x\right)\ne 0\right)$

$\mathrm{false}$

$\mathrm{evalb}\left(\mathrm{coeff}\left(x^3+2x^2-5\&comma;x^2\right)\ne 0\right)$

$\mathrm{true}$