A structured verification is a Maple expression other than a symbol which can be interpreted as a verification. A typical example would be $\left[\mathrm{simplify}\,\mathrm{simplify}\right]$. This specifies that the two objects must be lists with two operands, and that each pair of operands must have the property that their difference when simplified, equals zero.

This help page first gives a formal grammatical description of the valid structured verifications, then notes on some of the special verifications, and lastly, examples.

In the formal definition below, read "::=" to mean "is defined to be", "|" to mean "or", and "*" to mean "zero or more occurrences of".

The square brackets [ and ] are used to check for a fixed argument sequence.  The verification $\left[\mathrm{boolean}\,\mathrm{simplify}\right]$ checks the equality of two lists, each with exactly 2 arguments, the first checked with simple equality and the second with simplify.

The set brackets { and } are used for alternation.  The verification {set(float(10)),list(float(10))} matches either lists or sets of floating-point numbers which are considered equal if they are within 10 units in the last place.

The verification $\mathrm{boolean}$ does a simple comparison.

The verifications $\mathrm{identical}\left(\mathrm{expr}\right)$ compares two objects, complex(numeric) or string, to the expression expr.

The verification $\mathrm{anyfunc}\left(\mathrm{t1},...,\mathrm{tn}\right)$ matches any two functions with $n$ arguments where the arguments agree according to the appropriate verifications.

The verification specfunc(ver, n) matches functions $n$ with 0 or more arguments where the arguments agree according to the verification ver.  Thus verify(f, g, specfunc(ver, n)) is equivalent to all five of the forms, type(f, function), type(g, function), $\mathrm{op}\left(0\,f\right)=n$, $\mathrm{op}\left(0\,g\right)=n$, and verify([op(f)], [op(g)], list(ver)).

$\mathrm{verify}\left(\mathrm{string}\,\mathrm{string}\,\mathrm{identical}\left(\mathrm{string}\right)\right)$

$\mathrm{true}$

$\mathrm{verify}\left(\mathrm{evalf}\left(\mathrm{abs}\left(1\,x+\mathrm{sqrt}\left(1-{\cos \left(2\right)}^2\right)\right)\right)\,\mathrm{abs}\left(1\,x+\sin \left(2.\right)\right)\,'\mathrm{abs}\left(1\,\mathrm{polynom}\left(\mathrm{float}\left(1\right)\,x\right)\right)'\right)$

$\mathrm{true}$

$\mathrm{verify}\left({\left(x^2-1\right)}^{2.0002}\,{\left(\left(x-1\right)\left(x+1\right)\right)}^{2.00003}\,'{\mathrm{normal}}^{\mathrm{float}\left(1.\times {10}^6\right)}'\right)$

$\mathrm{true}$

$\mathrm{evalb}\left(\left[2.\,1-x^2\right]=\left[2\,\left(1-x\right)\left(1+x\right)\right]\right)$

$\mathrm{false}$

$\mathrm{verify}\left(\left[2.0000001\,1-x^2\right]\,\left[2\,\left(1-x\right)\left(1+x\right)\right]\,'\left[\mathrm{float}\left(10000.\right)\,\mathrm{expand}\right]'\right)$

$\mathrm{true}$

$\mathrm{verify}\left(\left\{0.32\right\}\,\left\{0.319996\,0.320002\right\}\,'\mathrm{set}\left(\mathrm{float}\left(100000.\right)\right)'\right)$

$\mathrm{true}$

$\mathrm{verify}\left(\mathrm{evalr}\left(\sin \left(\mathrm{INTERVAL}\left(-1..-1.5\right)\right)\right)\,\mathrm{INTERVAL}\left(-0.9974949866..-\sin \left(1\right)\right)\,'\mathrm{INTERVAL}\left(\mathrm{float}\left(1\right)..\mathrm{boolean}\right)'\right)$

$\mathrm{true}$

$\mathrm{solns}≔\mathrm{dsolve}\left(\mathrm{D}\left(f\right)\left(x\right)=f\left(x\right)\,\left\{f\left(x\right)\right\}\right)$

$\mathrm{solns}≔f\left(x\right)=\mathrm{c\_\_1}{\ⅇ}^x$

$\mathrm{verify}\left(\mathrm{solns}\,f\left(x\right)=\mathrm{\_C1}\left(\cosh \left(x\right)+\sinh \left(x\right)\right)\,\mathrm{boolean}=\mathrm{testeq}\right)$

$\mathrm{true}$

$\mathrm{zero}≔\left\{0.\,c-a^{\log \left[a\right]\left(c\right)}\,{\cos \left(x\right)}^2+{\sin \left(x\right)}^2-1\,x^2-1-\left(x-1\right)\left(x+1\right)\right\}$

$\mathrm{zero}≔\left\{0.\,c-a^{\frac{\ln \left(c\right)}{\ln \left(a\right)}}\,x^2-1-\left(x-1\right)\left(x+1\right)\,{\cos \left(x\right)}^2+{\sin \left(x\right)}^2-1\right\}$

$\mathrm{verify}\left(\left\{0\right\}\,\mathrm{zero}\,\mathrm{set}\left(\mathrm{simplify}\right)\right)$

$\mathrm{true}$