The tests made are as follows.

Test if x rational.

Test if x is algebraic of degree 6 (default) or less.

Test if x is a function of a rational number e.g. $\ln \left(5\right)$.

Test if x is a function of an algebraic number of degree 6 or less.

Test if x is of the form $a_1+a_2\sqrt{t}+\frac{a_3}{\sqrt{t}}+a_{4}t+\frac{a_5}{t}+\mathrm{...}+a_n{t}^k$ where $t$ is a known transcendental constant e.g. $\mathrm{\pi }$ or $\ⅇ$ or $\ln \left(2\right)$.

(optional) Test if x is a function of the above form.

Test if x is of the form $a_1{t}_1+a_2{t}_2+a_n{t}_n+\mathrm{...}+a_0$ where $t_i$ are known algebraic or transcendental constants.

(optional) Test if x is a function of the above form.

Test if x is of the form $t_1^{a_1}{t}_2^{a_2}\mathrm{...}{t}_n^{a_n}$ where $t_i$ are certain constants and $a_i$ are rational.

(optional) Test if x is a function of the above form.

The test for rational constants is made by looking at the continued fraction expansion of x.  The test for an algebraic number up to degree 6, that is, a root of a polynomial $m\left(z\right)$ of degree 6 or less, is made by applying Bailey and Ferguson's IntegerRelations[PSLQ] algorithm to $\[x^0,x^1,x^2,...,x^6\]$ to compute the minimal polynomial $m\left(z\right)$ for x and then solving for the roots and selecting the right one. If the solve command is not able to solve for the root in terms of radicals, the answer may be returned in the form of a RootOf.

The remaining arguments to the identify command are treated as options.  They are equations of the form option=value. The following options are supported.

all

The option all=true specifies trying all tests, including the optional ones. The option all=false specifies only the tests that are explicitly asked for, as specified below.

BasisSizeAlg

The option BasisSizeAlg=n specifies when testing whether x is an algebraic number, to search up to degree $n$ (default is 6).

BasisPolyConst

The option BasisPolyConst=B1 specifies the use of basis $\mathrm{B1}$, a list of real constants (default is $\left[\mathrm{\pi }\,\ⅇ\,\ln \left(2\right)\right]$, when making test 5, that is, $t$ is chosen from this list.

BasisSizePoly

The option BasisSizePoly=n specifies the value of $n$ to use in test 5.

BasisSumConst

The option BasisSumConst=B2 specifies the use of basis $\mathrm{B2}$, a list of real constants (default is $\left[1\,\sqrt{2}\,\sqrt{3}\,\mathrm{\pi }\,\ln \left(2\right)\,\ln \left(3\right)\,\mathrm{\zeta }\left(3\right)\,\mathrm{\zeta }\left(5\right)\right]$) when making test 7, that is, $t_i$ is chosen from this list.

BasisSizeSum

The option BasisSizeSum=n specifies the value of $n$ to use in test 7 (default 3).

BasisProdConst

The option BasisProdConst=B3 specifies the use of basis $\mathrm{B3}$, a list of real constants (default is $\left[2\,3\,5\,7\,\mathrm{\pi }\,\ⅇ\,\ln \left(2\right)\,\ln \left(3\right)\,\mathrm{\zeta }\left(3\right)\,\mathrm{\zeta }\left(5\right)\right]$) when making test 9, that is, $t_i$ is chosen from this list.

BasisSizeProd

The option BasisSizeProd=n specifies the value of $n$ to use in test 9 (default 3).

extension

The option extension=B specifies adding the elements of $B$, a list of real constants, to the bases $\mathrm{B1},\mathrm{B2},\mathrm{B3}$, when making tests 5, 7, and 9.

LearnBasis

The option LearnBasis=true specifies the use of nonrational constants found in tests 1-4 when making tests 5-10.  The default for this option is false.

Rational, Algebraic, FuncRat, FuncAlg, PolyConst, SumConst, and ProdConst

The options Rational=false, Algebraic=false, FuncRat=false, FuncAlg=false, PolyConst=false, SumConst=false, and ProdConst=false specify not to perform tests 1, 2, 3, 4, 5, 7, and 9 respectively.

FuncPoly, FuncSum, and FuncProd

The options FuncPoly=true, FuncSum=true, FuncProd=true specify the performance of tests 6, 8 and 10 respectively.