symeval

Write a sympy expression, fill in pint quantities, and get the full derivation, that is (1) formula, (2) substituted values with units, and (3) the result with unit — rendered as LaTeX in your marimo or Jupyter notebook.

• ✨ Crystal-clear — shows the full derivation: formula, values with units, and result
• 🐍 Pure Python — drop into your interactive notebooks and other Python code, no special syntax, no cell magic, no Domain-Specific Language (DSL)
• 📏 Unit-aware — pint quantities carry units through every step and convert to your chosen output unit
• 🧮 Sympy-native — rearrange or simplify your formula symbolically first, then evaluate
• 📊 DataFrame-ready — use quantity_evalf() to compute a new unit-aware column on a DataFrame

pip install symeval

Axial stress under a compressive force

from pint import Quantity
from sympy import Symbol
from symeval import sym_evalf

sigma = sym_evalf(
    expr=Symbol("F") / Symbol("A"),
    subs={Symbol("F"): Quantity(-680, "kN"), Symbol("A"): Quantity(10_580, "mm^2")},
    output_symbol=r"\sigma",
    output_unit="MPa",
    decimals=2,
)

$$\begin{align*} \sigma &= \frac{F}{A} \\ &= \frac{,-680\ \mathrm{kN}}{,10580\ \mathrm{mm}^{2}} \\ \sigma &= -6.43\times 10^{7}\ \mathrm{Pa} = -64.27\ \mathrm{MPa} \end{align*}$$

You can also build the sympy expression first and call .sym_evalf() as a method — useful when you want to do symbolic math before filling in numbers. Pass mode= to choose the rendering style; mode="verbose" adds an extra line showing all values converted to SI base units:

f_sym, a_sym = Symbol("F"), Symbol("A")
sigma_expr = f_sym / a_sym

sigma_expr.sym_evalf(
    subs={f_sym: Quantity(-680, "kN"), a_sym: Quantity(10_580, "mm^2")},
    output_symbol=r"\sigma",
    output_unit="MPa",
    decimals=2,
    mode="verbose",
)

$$\begin{align*} \sigma &= \frac{F}{A} \\ &= \frac{,-680\ \mathrm{kN}}{,10580\ \mathrm{mm}^{2}} \\ &= \frac{,-6.800\times 10^{5}\ \mathrm{N}}{,1.058\times 10^{-2}\ \mathrm{m}^{2}} \\ \sigma &= -6.43\times 10^{7}\ \mathrm{Pa} = -64.27\ \mathrm{MPa} \end{align*}$$

mode="one_line" collapses the derivation onto a single line:

sigma_expr.sym_evalf(
    subs={f_sym: Quantity(-680, "kN"), a_sym: Quantity(10_580, "mm^2")},
    output_symbol=r"\sigma",
    output_unit="MPa",
    decimals=1,
    mode="one_line",
)

$$\sigma = \frac{F}{A} = \frac{,-680\ \mathrm{kN}}{,10580\ \mathrm{mm}^{2}} = -64.3\ \mathrm{MPa}$$

quantity_evalf() on a DataFrame

quantity_evalf is the numeric-only sibling of sym_evalf — same unit-aware evaluation, no LaTeX overhead. It's useful for applying a formula across every row of a DataFrame:

import polars as pl
from pint import Quantity
from sympy import Symbol
from symeval import quantity_evalf

f_sym, a_sym = Symbol("F"), Symbol("A")
sigma_expr = f_sym / a_sym

members = pl.DataFrame({
    "member_type": ["column", "column", "brace", "strut", "tie"],
    "section":     ["W14x90", "HSS8x8x5/8", "HSS6x6x3/8", "L4x4", "C8x11.5"],
    "F_kN":        [-720.0, -680.0, 340.0, -110.0, 250.0],
    "A_mm2":       [17_100.0, 10_580.0, 4_890.0, 1_870.0, 2_168.0],
})

def stress_MPa(row):
    return quantity_evalf(
        sigma_expr,
        subs={f_sym: Quantity(row["F_kN"], "kN"), a_sym: Quantity(row["A_mm2"], "mm^2")},
        output_unit="MPa",
    ).magnitude

members_with_stress = members.with_columns(
    pl.struct(["F_kN", "A_mm2"])
    .map_elements(stress_MPa, return_dtype=pl.Float64)
    .alias("sigma_MPa")
)

member_type	section	F_kN	A_mm2	sigma_MPa
column	W14x90	-720.00	17100.00	-42.11
column	HSS8x8x5/8	-680.00	10580.00	-64.27
brace	HSS6x6x3/8	340.00	4890.00	69.53
strut	L4x4	-110.00	1870.00	-58.82
tie	C8x11.5	250.00	2168.00	115.31

Then use sym_evalf to show the full derivation for any row you want to inspect:

sigma_expr.sym_evalf(
    subs={f_sym: Quantity(-680, "kN"), a_sym: Quantity(10_580, "mm^2")},
    output_symbol=r"\sigma",
    output_unit="MPa",
    decimals=1,
)

$$\begin{align*} \sigma &= \frac{F}{A} \\ &= \frac{,-680\ \mathrm{kN}}{,10580\ \mathrm{mm}^{2}} \\ \sigma &= -6.4\times 10^{7}\ \mathrm{Pa} = -64.3\ \mathrm{MPa} \end{align*}$$

Axial resistance of a steel HSS member

A worked example from CSA S16-17. Each sym_evalf result feeds into the next — F_e into $\lambda$, $\lambda$ into $C_r$, $C_r$ into $DCR$ — so the LaTeX rendering captures the full audit trail of a multi-step engineering check:

$$F_{e} = \frac{\pi^{2} E r_{y}^{2}}{L^{2} k^{2}} = \frac{\pi^{2} ,200\ \mathrm{GPa} ,\left(76.1\ \mathrm{mm}\right)^{2}}{,\left(6.5\ \mathrm{m}\right)^{2} ,1^{2}} = 0.271\ \mathrm{GPa}$$

$$\lambda = \left(\frac{F_{y}}{F_{e}}\right)^{n} = \left(\frac{,400\ \mathrm{MPa}}{,0.2706\ \mathrm{GPa}}\right)^{,1.34} = 1.689$$

$$C_{r} = A F_{y} \phi_{s} \left(\lambda + 1\right)^{- \frac{1}{n}} = ,10580\ \mathrm{mm}^{2} ,400\ \mathrm{MPa} ,0.85 \left(,1.6886 + 1\right)^{- \frac{1}{,1.34}} = 1.720\ \mathrm{MN}$$

$$DCR = \frac{C_{f}}{C_{r}} = \frac{,680\ \mathrm{kN}}{,1.7196\ \mathrm{MN}} = 0.395$$

See symeval_mo.py for the full reactive marimo notebook with input UIs.

Ideal Gas Law: symbolic rearrangement

Starting from $PV = nRT$, sympy.solve rearranges the equation symbolically for any variable, then the resulting expression feeds straight into sym_evalf:

$$\begin{align*} P &= \frac{R T n}{V} \\ &= \frac{,8.314\ \frac{\mathrm{J}}{\left(\mathrm{K} \cdot \mathrm{mol}\right)} ,273.15\ \mathrm{K} ,1\ \mathrm{mol}}{,22.4\ \mathrm{l}} \\ P &= 1.01\times 10^{5}\ \mathrm{Pa} = 101.39\ \mathrm{kPa} \end{align*}$$

See symeval_mo.py for the full reactive marimo notebook with input UIs.

Author

Built and maintained by Joost Gevaert at Bedrock.

Feedback & contributing

Found a bug or have a feature request? Open an issue — pull requests are welcome too. The package is a single marimo notebook (symeval_mo.py) with ## EXPORT-marked cells extracted into src/symeval/ via mobuild; see CLAUDE.md for the project layout and RELEASING.md for the release workflow.

Inspiration

• handcalcs — renders Python calculation code as LaTeX in Jupyter
• CalcPad — engineering calculations DSL with symbolic/numeric workflow
• Bret Victor's Explorable Explanations

License

Apache License 2.0 — see LICENSE.