Interoperability

Three optional package extensions turn SymbolicUncertainties.jl into a hub for broader Julia scientific-computing workflows. Each activates automatically when the triggering package is loaded.

Latexify.jl — calibration-certificate LaTeX

using Symbolics, SymbolicUncertainties, Latexify

@variables V I σV σI
R = (V ± σV) / (I ± σI)

latex(R)
# e.g. "\\frac{V}{I} \\pm \\sqrt{\\frac{σV^{2}}{I^{2}} + \\frac{V^{2} σI^{2}}{I^{4}}}"

"\\begin{equation}\n\\frac{V}{I}\n\\end{equation}\n \\pm \\begin{equation}\n\\sqrt{\\mathtt{{\\sigma}V}^{2} ~ \\left( \\frac{1}{I} \\right)^{2} + \\mathtt{{\\sigma}I}^{2} ~ \\left( \\frac{ - V}{I^{2}} \\right)^{2}}\n\\end{equation}\n"

The fallback's ArgumentError is replaced by the SymbolicUncertaintiesLatexifyExt extension. Use the returned String directly in your LaTeX calibration-certificate template.

Measurements.jl — convert a substituted measurement

Bridge to the standard Julia uncertainty type for numerical pipelines:

using Symbolics, SymbolicUncertainties, DynamicQuantities
import Measurements

# A mass of 5.000 g with u_c = 0.1 mg. `Measurement` carries the
# number and its dispersion; the unit rides alongside it.
m = 5.0 ± 0.0001
Measurements.Measurement(m) * us"g"

5.0 ± 0.0001 g

substitute does not auto-promote — the conversion is explicit:

@variables V I σV σI
R = (V ± σV) / (I ± σI)

ohm = Dict(V => 5.0us"V", σV => 0.01us"V", I => 0.5us"A", σI => 0.001us"A")

# `Measurement` needs plain numbers, so the values are stripped for the
# conversion — and the unit of the answer is taken from
# [`evaluate`](@ref), which derives it from the model rather than
# leaving it to be asserted here.
R_num = Symbolics.substitute(R, Dict(k => ustrip(v) for (k, v) in ohm))

Measurements.Measurement(R_num) * oneunit(evaluate(R, ohm).val)

10.0 ± 0.028 A⁻¹ V

Conversion fails with ArgumentError when either m.val or m.err is still symbolic — call substitute first.

DataFrames.jl — tabular uncertainty_budget output

Opt into a DataFrame rendering via the as = :dataframe keyword; the default :budget returns the UncertaintyBudget value itself, which already indexes and iterates as a vector of its rows:

using SymbolicUncertainties, Symbolics, DataFrames

@variables V σV R1 σR1 R2 σR2
Vout = propagate(
    (v, r1, r2) -> v * r2 / (r1 + r2),
    [V ± σV, R1 ± σR1, R2 ± σR2],
)

df = uncertainty_budget(
    Vout,
    [V, R1, R2],
    [σV, σR1, σR2];
    as = :dataframe,
)
# df isa DataFrame with 3 rows and columns
#   variable, sigma, sensitivity, contribution, relative

Export to CSV, join with other tabular data, apply filters — the full DataFrames.jl ergonomics are available. When DataFrames.jl is not loaded, requesting as = :dataframe raises ArgumentError.

Combined workflow

All three extensions compose cleanly:

using Symbolics, SymbolicUncertainties, DynamicQuantities
using Latexify, DataFrames
import Measurements

# Build, propagate, report.
@variables V σV R1 σR1 R2 σR2
Vout = propagate(
    (v, r1, r2) -> v * r2 / (r1 + r2),
    [V ± σV, R1 ± σR1, R2 ± σR2],
)

# Tabular budget.
df = uncertainty_budget(
    Vout,
    [V, R1, R2],
    [σV, σR1, σR2];
    as = :dataframe,
)

# LaTeX for the certificate.
tex = latex(Vout)

# Numeric final result, in volts.
divider = Dict(
    V => 5.0us"V", σV => 0.01us"V",
    R1 => 1_000.0us"Ω", σR1 => 1.0us"Ω",
    R2 => 3_000.0us"Ω", σR2 => 1.0us"Ω",
)
Vout_num = Symbolics.substitute(
    Vout,
    Dict(k => ustrip(v) for (k, v) in divider),
)
meas = Measurements.Measurement(Vout_num) * oneunit(evaluate(Vout, divider).val)

3.75 ± 0.0076 V

API reference

The extensions overload methods on existing functions — no new exports are introduced at the SymbolicUncertainties public surface (REQ-132 audit).

• latex — the extension adds the working method at load time; the fallback keeps its docstring.
• uncertainty_budget — gains the as = :budget | :dataframe keyword.
• Measurements.Measurement(m) — a constructor on Measurements.jl's type, visible to users via the external package's namespace.