# NAME

Math::NumSeq::Expression -- mathematical expression values

# SYNOPSIS

```
use Math::NumSeq::Expression;
my $seq = Math::NumSeq::Expression->new (expression => '2*i+1');
my ($i, $value) = $seq->next;
```

# DESCRIPTION

A string expression evaluated at i=0, 1, 2, etc, by Perl or a choice of evaluator modules.

This is designed to take expression strings from user input though could be used for something quick from program code too. The expression syntax in the evaluator modules varies in subtle ways.

## Perl

The default `expression_evaluator => 'Perl'`

evaluates with Perl itself. This is always available. Expressions are run with the `Safe`

module to restrict to arithmetic (see Safe).

The i index is in a `$i`

variable and an `i()`

function. The `i()`

function is prototyped like a constant.

```
i+1
2*$i - 2
```

The functions made available include

```
atan2 sin cos exp log \ Perl builtins
sqrt rand /
min max List::Util
floor ceil POSIX module
cbrt hypot erf erfc expm1 \
j0 j1 jn lgamma_r log10 | Math::Libm
log1p pow rint y0 y1 yn /
tan asin acos atan \
csc cosec sec cot cotan | Math::Trig
acsc acosec asec acot acotan |
sinh cosh tanh |
csch cosech sech coth cotanh |
asinh acosh atanh |
acsch acosech asech acoth acotanh /
```

## Math-Symbolic

`expression_evaluator => 'MS'`

selects the `Math::Symbolic`

module, if available.

The expression is parsed with `Math::Symbolic->parse_from_string()`

and should use a single variable for the i index in the sequence. The variable can be any name, not just "i"

```
2*i+1
x^2 + x + 1 # any single variable
```

The usual `$ms->simplify()`

is applied to perhaps reduce the expression a bit, then `to_sub()`

for actual evaluation.

## Math-Expression-Evaluator

`expression_evaluator => 'MEE'`

selects the `Math::Expression::Evaluator`

module, if available.

The expression should use a single input variable, which can be any name, and takes the i index in the sequence. Temporary variables can be used by assigning to them,

```
x^2 + x + 1 # any single variable
t=2*i; t^2 # temporary variables assigned
```

The expression is run with `$mee->compiled()`

. It turns the expression into a Perl subr for actual evaluation.

## Language-Expr

`expression_evaluator => 'LE'`

selects the `Language::Expr`

module, if available.

The expression should use a single variable, of any name, which will be the i index in the sequence. See Language::Expr::Manual::Syntax for the expression syntax.

` $x*$x + $x + 1`

The expression is compiled with Language::Expr::Compiler::perl for evaluation.

# FUNCTIONS

See "FUNCTIONS" in Math::NumSeq for behaviour common to all sequence classes.

## Random Access

# BUGS

`Safe.pm`

seems a bit of a slowdown. Is that right or is it supposed to validate ops during the eval which compiles a subr?

# SEE ALSO

Math::NumSeq, Safe Math::Symbolic, Math::Expression::Evaluator, Language::Expr

# HOME PAGE

http://user42.tuxfamily.org/math-numseq/index.html

# LICENSE

Copyright 2010, 2011, 2012, 2013, 2014, 2016 Kevin Ryde

Math-NumSeq is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 3, or (at your option) any later version.

Math-NumSeq is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with Math-NumSeq. If not, see <http://www.gnu.org/licenses/>.