dimcheck 1.0.2

A physics dimension checker based on sympy

dimcheck: A physics dimension checker based on sympy

• dimcheck: A physics dimension checker based on sympy
  • Description
  • Dependencies
  • Installation
  • Basic usage
  • Convention
  • Advanced Usage
    • Pretty printing
    • Quantity Mode: Simpler format for inputting quantities
    • Customized definition of the quantities
    • Serialization
    • Save and display all quantities or expressions
  • Methods
    • Property
    • Dimension & Units
    • Derive Formula
    • Save, clean and display

Description

Dimcheck is a Python library that provides an interface for users to check, compare and manipulate dimensions of quantities. It is especially useful in scientific computing and physics, where ensuring correct dimensions is crucial.

Dependencies

python3
sympy
numpy

Installation

You can install the package using pip,

pip install dimcheck

Basic usage

You can try the package as follows,

# Import the package, the package requires some time to initialize the global instance "si". You can make the process faster by serialization in the later section.
>>> from dimcheck import si
Starting to parse the quantity definition file: 
/to/your/pip/lib/path/packages/dimcheck/si.json
Successfully parsed!

# Get the dimension of quantity [E]. All quantities are represented by a symbol wrapped with a square bracket.
>>> si.dim("E")   
'M*L**2/T**2'

# Get the dimension of combination quantities [m*v**2] which is same as [E].
>>> si.dim("m*v**2")  
'M*L**2/T**2'

# Get the unit of combination quantities [m*v**2].
>>> si.unit("m*v**2")  
'kg*m**2/s**2'

# Check whether two quantities have the same dimension/unit.
>>> si.is_dc("E","m*v**2")  
True

# Derive the possible quantity of [G*m**2/r**2] which is the formula of Newton's law of universal gravitation. Here [G] is the gravitational Constant, [m] is the mass, [r] is the radius or length. You can replace the operator of the multiplication '*' with a space " ", and replace exponential operator "**" with "^". 
>>> si.quant("G m^2/r^2")   
'F'

# Derive the possible quantity based on the Ohm's law. Here [V] is the voltage, [I] is the current, [R] is the resistance which have the same dimension as the von Klitzing constant [R_K].
>>> si.quant("V/I")
['R', 'R_K']

# Restore the omitted quantity on the rhs. Here [hbar] is the reduced Planck constant, [k] is the wavenumber.
>>> si.omit_quant(lhs="E",rhs="k",omit_quant=["hbar","v"])  
'E = k*hbar*v'

# Derive the formula based on the given parameters. Here, we try to derive the pendulum formula.
>>> si.formula(lhs="t",parameters=["l","g"])   
't = l**(0.5)*g**(-0.5)'

# Display all quantities in the terminal.
>>> si.all_quant()
All Quantities:
B                 magnetic flux density, magnetic induction, B field           kg/(A*s**2)
C                 capacitance                                                  A**2*s**4/(kg*m**2)
D                 displacement field                                           A*s/m**2
...
None

# Save the definition of quantities in a ".csv" format file. By default, it will save to the "./Quantities.csv".
>>> si.save_all_quant()
True

# After switching to the "quantity" mode, one can remove the square brackets around symbols, which makes the whole formula more easy to write. This term is by default set to True.
>>> si.is_quant=True

# After switching to the "pretty" mode, all exponents will show as superscripts. This term is by default set to False.
>>> si.is_pretty=True
>>> si.quant("G m**2/r**2")  
'F'
>>> si.is_dc("E","m*v**2")  
True
>>> si.omit_quant(lhs="E",rhs="k",omit_quant=["hbar","v"])  
'E = k*hbar*v'
>>> si.unit("m*v**2")  
'kg*m²/s²'

# You can save these two modes by invoking si.save() method, then next time they will be the default mode.
>>> si.save()
True

The definition of all quantities and expressions locates in Quantities.csv and Expressions.csv

Convention

1. Unit: The basic units in "si" unit system (which is the only unit system so far) are {"kg", "m", "s", "A", "mol", "cd", "K"}.

2. Quantity: In the package, this term is a combination of the number 1 and units , e.g. [v] is the unit velocity whose unit is "m/s".

3. Expression: The combination of basic units e.g. "kg*m**2/s**2" or dimensions "M*L**2/T**2".

4. In the package, it will follow the same convention to represent a quantity as Ref. "Fly by Night Physics". For a quantity or a combination of quantities, they should be wrapped with square brackets. However, by default, the si.is_quant=True, so you do not need to worry about the square bracket when you are using those methods.

>>> si.unit("F")
'kg*m/s**2'
>>> si.quant("e**2/hbar")
['conductance', 'sigma_2D']

5. You can replace ** with ^ to represent the exponent. Also, the multiplication * can be simply replaced with a space ,

>>> si.quant("m v^2")
'E'

There is also a few reserved keywords like sqrt and cbrt for convenience,

>>> si.quant("sqrt(hbar e B v^2)")
'E'

6. You can write quantities without a square bracket as the following term is set to True,

>>> si.is_quant=True

After that all quantities can be simply write as

>>> si.unit("m v^2")
'kg*m**2/s**2'

The reason we introduce the square brackets is to distinguish quantities and base units. Since [m] represents the mass as the a quantity, m represents the base unit of length. So, if you only want to focus on the operation between quantities, and won't involve the base units in the formula, then we recommend you use the quantity mode as it is more convenient to write. Even though, the quantity mode work in the terminal, it is still required to wrap quantities when defining other quantities in the Customized definition of the quantities section.

Advanced Usage

Pretty printing

In the terminal mode, Dimcheck class (si is the instance of it) provides is_pretty property to make the results more easy to read.

# Before setting "is_pretty" mode.
>>> si.is_pretty=False
>>> si.unit("m a")
'kg*m/s**2'

# After setting "is_pretty" mode.
>>> si.is_pretty=True
>>> si.unit("m a")
'kg*m/s²'

# Other methods
>>> si.is_dc("sqrt(hbar e B v**2)","E",is_print=True)
DC!
sqrt(hbar e B v²) == E (kg*m²/s²)
True

# Noted that "kg**(1/3)" will be shown as "kg¹ʴ³" since there is no other more proper symbol found in the Unicode for the division that appears at the exponent.
>>> si.unit("m**(1/3)")
'kg¹ʴ³'

Quantity Mode: Simpler format for inputting quantities

In the terminal mode, Dimcheck class (si is an instance of it) provides is_quant property to make the quantities more easy to input.

>>> si.is_quant=True
>>> si.quant("G m**2/r**2")  
'F'
>>> si.is_dc("E","m*v**2")  
True
>>> si.omit_quant(lhs="E",rhs="k",omit_quant="hbar","v")  
'E = k*hbar*v'
>>> si.unit("m*v**2")  
'kg*m**2/s**2'

Customized definition of the quantities

In dimcheck, you can define your own quantities and symbols by simply manipulate the si.json file in the package directory. Here are some steps to define your own unit system.

1. Find the position of the package:

>>> from dimcheck import si
Starting to parse the quantity definition file: 
/to/your/pip/lib/path/packages/dimcheck/si.json
Successfully parsed!

>>> si.quant_def_file
'/to/your/pip/lib/path/packages/dimcheck/si.json'

2. Add, delete or change the definition of symbols in the file. You need to be careful since the quantities should always be wrapped with a pair of square bracket []. In the following example, the quantity [epsilon_0] is defined by the rhs [Q]**2/([F]*[l]**2). Meanwhile, you can also give multiple aliases to the same quantity. Discription can be used to indicate the meaning of the quantity.

{
    "quantity":"[epsilon_0]",
    "rhs":"[Q]**2/([F]*[l]**2)",
    "alias":["[eps_0]"],
    "discription":"vacuum dielectric constant"
}

3. After doing so, you can then import your definition by simply invoking

# Import customized quantity definition.
>>> from dimcheck import si
Starting to parse the quantity definition file: 
/to/your/pip/lib/path/packages/dimcheck/si.json
Successfully parsed!

# Test your definition.
>>> si.unit("m v**2")
'kg*m**2/s**2'
>>> si.quant("m v**2")
'E'

In case, the si.json is modified, there is another copy of si.json at data/si.json in the repository.

Serialization

Since sometimes loading "si.json" can be time-consuming, dimcheck provides the serialization to directly save the Dimcheck object (like si).

# Serialize the instance
>>> si.save()
True

# The position of the file of quantity definition
>>> si.quant_def_file
'/to/your/pip/lib/path/packages/dimcheck/si.json'

# The position of the serialized file
>>> si.serialized_file
'/to/your/pip/lib/path/packages/dimcheck/si.pickle'

# Delete the serialized file
>>> si.clean()
True

Save and display all quantities or expressions

dimcheck provides a few method to display and save the table of quantities and expressions. You can simply invoke the method,

# Display all quantities in the terminal.
>>> si.all_quant()
All Quantities:
B                 magnetic flux density, magnetic induction, B field           kg/(A*s**2)
C                 capacitance                                                  A**2*s**4/(kg*m**2)
D                 displacement field                                           A*s/m**2
...

# Display all expressions with their aliases in the terminal.
>>> si.all_expr(is_inc_alias=True, is_sorted=True)
All Expression:
1                   alpha A['alp'] 
1/m                 k nabla A['nbl'] 
1/mol               N_A
...

# Make the output more easy to read
>>> si.is_pretty=True

>>> si.all_quant(is_sorted=False)
All Quantities:
m                  mass                           kg
t                  time                           s
...
rho_m              density of mass                kg/m³
v                  velocity                       m/s
a                  acceleration                   m/s²
g                  acceleration of gravity        m/s²
F                  force                          kg*m/s²

# Save quantities, by default the location will be "./Expressions.csv".
>>> si.save_all_expr()
True

# Save quantities to the path, by default the location will be "./Quantities.csv".
>>> si.save_all_quant(file_path="/path/to/output/Quantities.csv")
True

You can review above results from Quantities.csv and Expressions.csv

Methods

Property

property	Description	Writable	Default
is_pretty	The output is setting to be more easy to read (based on some symbols in UTF-8) or not.	Yes	True
is_quant	Quantity mode	Yes	False
setting_file	Returns the path of the global setting file.	No
unit_system	Returns the unit system.	No
quant_def_file	Returns the path of the file of quantity definition.	No
serialized_file	Returns the path of the serialized file.	No

Dimension & Units

method	Description	Parameters	Return
dim	To get the dimension of a quantity.	s: str	expr: str
dimension	Alias of dim.	s: str	expr: str
is_dc	To check whether two quantities are same.	lhs: str, rhs: str, is_print: bool=False	dc: bool
quant	To print the possible quantity by deriving the combination of quantities.	s: str, is_print=False	quantity: str or quantities: list
unit	To get the unit of a quantity.	s: str	expr: str

Derive Formula

method	Description	Parameters	Return
formula	Print the formula of the target based on the parameters.	lhs : str, parameters : list	expr: str
omit_quant	Restore the units of lhs based on the omitted quantities and rhs.	lhs : str, rhs : str, omit_quant: list	expr: str

Save, clean and display

method	Description	Parameters	Return
all_expr	To display all expressions based on the quantity definition file.	is_inc_alias: bool=False, is_sorted: bool=True
all_quant	To display all quantities based on the quantity definition file.	is_inc_alias: bool=False, is_sorted: bool=True
clean	To clean the binary serialized file of the current object.		success: bool
save	To save the binary serialized file of the current object.		success: bool
save_all_expr	To save all expression in ".csv" format based on the quantity definition file.	file_path='./Expressions.csv', is_sorted: bool=True	success: bool
save_all_quant	To save all quantities in ".csv" format based on the quantity definition file.	file_path='./Quantities.csv', is_sorted: bool=True	success: bool