Description

This package was primarily developed to assist in calculating and writing the estimated standard deviation according to Gaussian error propagation in LaTex. To calculate the uncertainties, the package uses the gaussian error propagation.

Rounding follows the following scheme:

• If the first non-zero digit of the standard deviation is greater than two and is followed by further digits, this digit is rounded up.
• Otherwise, the subsequent digit is rounded up.
• The value is then rounded to the next even number at the same digit.

The package is still in development and will be updated with more features in the future.

Features

Calculation of uncertainties

Core feature of this package is the rounding of the uncertainties to the correct number of significant figures. Suggested by the physical practicals of the TU Berlin is the following rule:

• If the first non zero digit of the uncertainty is 1 or 2, round to 2 significant non zero figures.
• Else round to 1 non zero significant figure.
• The significant figure is alway rounded up.

Get values in LaTeX format

The package also provides a function to get the function to calculate the uncertainty in LaTeX format without and with substitution of the variables with the values.

Installation

To install the package, simply download the newest release from the releases page page and install it with pip:

pip install physpract-{version}-py3-none-any.whl

Usage

To use the package, simply import it and use the functions provided by the package. The package is still in development and will be updated with more features in the future.

Example

Basic usage

To define a value with an uncertainty, simply create a new Value object with the value and the uncertainty as arguments. The value can be accessed with the value attribute and the uncertainty with the uncertainty attribute. The value can be printed with the print function.

from physpract.uncertainties import Value

a = Value(1, 0.1)
b = Value(2, 0.2)

c = a + b

# Print the value
print(c)
# Output: 3.00 ± 0.23
print(c.eq())
# Output: x_0 + x_1 = 3.00 ± 0.23

# Print the value and the uncertainty
print(c.value, c.uncertainty)
# or
print(c.v, c.u)
# Output: 3.00 0.23

# Print the not rounded value and the uncertainty
print(c.value_not_rounded, c.uncertainty_not_rounded)
# or
print(c.vnr, c.unr)
# Output: 3.0 0.223606797749979

Usage with variable names

To use the variable names in the LaTeX output, simply pass the variable names as a string to the Value object.

from physpract.uncertainties import Value

a = Value(1, 0.1, "a")
b = Value(2, 0.2, "b")

c = a + b

print(c)
# Output: 3.00 ± 0.23

print(c.eq())
# Output: a + b = 3.00 ± 0.23

Usage with variable names and units

To use the variable names and units in the LaTeX output, simply pass the variable names and units as a string to the Value object. For the units, sympy.physics.units must be used.

from physpract.uncertainties import Value
from sympy.physics.units import meter, second

a = Value(1, 0.1, "a", meter)
b = Value(2, 0.2, "b", second)

c = a/b

# Print the value
print(c)
# Output: 0.50 ± 0.08 meter/second

print(c.eq())
# Output: a/b = 0.50 ± 0.08 meter/second

Print the LaTeX output

To print the LaTeX output of the equation, use the latex function.

from physpract.uncertainties import Value
from sympy.physics.units import meter, second

a = Value(1, 0.1, "a", meter)
b = Value(2, 0.2, "b", second)

c = a/b

# Print the LaTeX output
print(c.latex())
# Output: \SI{0.50(8)}{\meter\per\second}

# Print the LaTeX output with equation
print(c.latex(equation=True))
# Output: \frac{a}{b}=\SI{0.50(8)}{\meter\per\second}

LaTeX output

$$\frac{a}{b} = \left(0.50 \pm 0.08\right)\frac{\text{m}}{\text{s}}$$

Print the equation

To print the equation to calculate the uncertainty, use the get_equation function of either the Value.value or Value.uncertainty attribute. The equation is returned as a string and can be printed with the print function. To print the equation in LaTeX format, use the latex function of get_equation.

from physpract.uncertainties import Value
from sympy.physics.units import meter, second

a = Value(1, 0.1, "a", meter)
b = Value(2, 0.2, "b", second)

c = a/b

# Print the equation of the value
print(c.value.get_equation())
# Output: a/b

# Print the LaTeX equation of the value
print(c.value.get_equation().latex())
# Output: \frac{a}{b}=\frac{\SI{1.0(0.1)}{\meter}}{\SI{2.0(0.2)}{\second}}

# Print the equation of the uncertainty
print(c.uncertainty.get_equation())
# Output: sqrt(\Delta a**2/b**2 + \Delta b**2*a**2/b**4)

# Print the LaTeX equation of the uncertainty
print(c.uncertainty.get_equation().latex())
# Output: \Delta\left(\frac{a}{b}\right)=\sqrt{\frac{\Delta a^{2}}{b^{2}} + \frac{\Delta b^{2} a^{2}}{b^{4}}}=\sqrt{\frac{\left(\SI{0.1}{\meter}\right)^{2}}{\left(\SI{2.0}{\second}\right)^{2}} + \frac{\left(\SI{0.2}{\second}\right)^{2} \left(\SI{1.0}{\meter}\right)^{2}}{\left(\SI{2.0}{\second}\right)^{4}}}

LaTeX output

Value:

$$\frac{a}{b}=\frac{\left(1.0 \pm 0.1\right)\text{m}}{\left(2.0 \pm 0.2\right)\text{s}}$$

Uncertainty:

$$\Delta\left(\frac{a}{b}\right)=\sqrt{\frac{\Delta a^{2}}{b^{2}} + \frac{\Delta b^{2} a^{2}}{b^{4}}}=\sqrt{\frac{\left(0.1~\text{m}\right)^{2}}{\left(2.0~\text{s}\right)^{2}} + \frac{\left(0.2~\text{s}\right)^{2} \left(1.0~\text{m}\right)^{2}}{\left(2.0~\text{s}\right)^{4}}}$$