# Lepton expression syntax and features

Lepton supports the following operators in expressions:

The following mathematical functions are available:

Numbers may be given in either decimal or exponential form. All of the
following are valid numbers: [5]{.title-ref}, [-3.1]{.title-ref},
[1e6]{.title-ref}, and [3.12e-2]{.title-ref}.

As an extension to the standard Lepton syntax, it is also possible to
use LAMMPS [variables](variable) in the format \"v_name\". Before
evaluating the expression, \"v_name\" will be replaced with the value of
the variable \"name\". This is compatible with all kinds of scalar
variables, but not with vectors, arrays, local, or per-atom variables.
If necessary, a custom scalar variable needs to be defined that can
access the desired (single) item from a non-scalar variable. As an
example, the following lines will instruct LAMMPS to ramp the force
constant for a harmonic bond from 100.0 to 200.0 during the next run:

``` LAMMPS
variable fconst equal ramp(100.0, 200)
bond_style lepton
bond_coeff 1 1.5 "v_fconst * (r^2)"
```

An expression may be followed by definitions for intermediate values
that appear in the expression. A semicolon \";\" is used as a delimiter
between value definitions. For example, the expression:

``` C
a^2+a*b+b^2; a=a1+a2; b=b1+b2
```

is exactly equivalent to

``` C
(a1+a2)^2+(a1+a2)*(b1+b2)+(b1+b2)^2
```

The definition of an intermediate value may itself involve other
intermediate values. Whitespace and quotation characters (\'\'\' and
\'\"\') are ignored. All uses of a value must appear *before* that
value\'s definition. For efficiency reasons, the expression string is
parsed, optimized, and then stored in an internal, pre-parsed
representation for evaluation.

Evaluating a Lepton expression is typically between 2.5 and 5 times
slower than the corresponding compiled and optimized C++ code. If
additional speed or GPU acceleration (via GPU or KOKKOS) is required,
the interaction can be represented as a table. Suitable table files can
be created either internally using the [pair_write](pair_write) or
[bond_write](bond_write) command or through the Python scripts in the
[tools/tabulate](tabulate) folder.