The identify command uses the LLL and PSLQ routines to identify exact constants from decimal numbers, for example, given  outputs

The process is described as follows. Consider . The identify command first tests if  is close to a small rational constant. Next identify tests if  is close to an algebraic number. To do this, identify first tests if  is a root of a quadratic polynomial.  It computes .  PSLQ outputs  an integer relation with small integer coefficients satisfying , which is small.  From this relation you have the minimal polynomial for , namely . The identify command then solves for  to obtain  from which it determines that . The algorithms in the identify routine can find other relations, for example:

with(IntegerRelations);

Digits := 20;

x := 0.31783724519578224473;

PSLQ([1,x,x^2,x^3,x^4]);

solve(y^4-10*y^2+1, y);

identify(x);

Each command in the IntegerRelations package can be accessed by using either the long form or the short form of the command name in the command calling sequence.

As the underlying implementation of the IntegerRelations package is a module, it is also possible to use the form IntegerRelations:-command to access a command from the package. For more information,  see Module Members.