Symbolic Limits

Experimental symbolic limit support is provided by the limit function, documented below. See SymbolicLimits.jl for more information and implementation details.

Symbolics.limit — Function

limit(expr, var, h[, side::Symbol])

Compute the limit of expr as var approaches h.

side indicates the direction from which var approaches h. It may be one of :left, :right, or :both. If side is :both and the two sides do not align, an error is thrown. Side defaults to :both for finite h, :left for h = Inf, and :right for h = -Inf.

expr must be composed of log, exp, constants, and the rational operators +, -, *, and /. This limitation may eventually be relaxed.

Warning

Because symbolic limit computation is undecidable, this function necessarily employs heuristics and may occasionally return wrong answers. Nevertheless, please report wrong answers as issues as we aim to have heuristics that produce correct answers in all practical cases.

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SymPy Integration

SymPy also includes limits as well, and the SymPy.jl extensions allow for automatically converting Symbolics expressions for use in its solvers.

Symbolics.sympy_limit — Function

sympy_limit(expr, var, val)

Computes limit of expr as var approaches val using SymPy.

Arguments

expr: Symbolics expression.
var: Symbolics variable.
val: Symbolics expression or number.

Returns

Symbolics limit.

Example

@variables x
expr = 1/x
result = sympy_limit(expr, x, 0)

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