tessl/pypi-pylatex

A comprehensive Python library for programmatically creating and compiling LaTeX documents and snippets.

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Mathematical Expressions

Name: tessl/pypi-pylatex
Author: tessl

Mathematical typesetting with equations, matrices, aligned environments, and vector notation. PyLaTeX provides comprehensive support for LaTeX's mathematical capabilities, enabling the creation of complex equations, matrices, and mathematical symbols with proper formatting.

Capabilities

Math Environment

The Math class provides the foundation for mathematical expressions, supporting both inline and display math modes.

class Math(Container):
    def __init__(self, *, inline=False, data=None, escape=None):
        """
        Create a math environment for equations.
        
        Parameters:
        - inline: bool, if True creates inline math ($...$), if False creates display math (\\[...\\])
        - data: list or str, initial mathematical content
        - escape: bool, whether to escape special characters (usually False for math)
        
        Requires:
        - amsmath package (automatically added)
        """

Usage example:

from pylatex import Document, Section
from pylatex.math import Math

doc = Document()

with doc.create(Section('Mathematical Expressions')):
    # Display math (block)
    with doc.create(Math()) as math:
        math.append(r'E = mc^2')
    
    # Inline math
    doc.append('The famous equation ')
    doc.append(Math(data=r'E = mc^2', inline=True))
    doc.append(' was derived by Einstein.')
    
    # Complex expressions
    with doc.create(Math()) as math:
        math.append(r'\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}')

Aligned Equations

The Alignat environment creates aligned multi-line equations with proper spacing and alignment.

class Alignat(Environment):
    def __init__(self, aligns=2, numbering=True, escape=None):
        """
        Create an aligned equation environment.
        
        Parameters:
        - aligns: int, number of alignment points (default 2)
        - numbering: bool, whether to number equations
        - escape: bool, whether to escape special characters
        
        Requires:
        - amsmath package (automatically added)
        """

Usage example:

from pylatex import Document, Section, NoEscape
from pylatex.math import Alignat

doc = Document()

with doc.create(Section('System of Equations')):
    # Basic aligned equations
    with doc.create(Alignat(numbering=True)) as agn:
        agn.append(r'2x + 3y &= 7 \\')
        agn.append(r'x - y &= 1')
    
    # Multiple alignment points
    with doc.create(Alignat(aligns=3)) as agn:
        agn.append(r'f(x) &= (x+a)(x+b) &= x^2 + (a+b)x + ab \\')
        agn.append(r'g(x) &= (x-a)(x-b) &= x^2 - (a+b)x + ab')
    
    # Unnumbered equations
    with doc.create(Alignat(numbering=False)) as agn:
        agn.append(r'\nabla \times \vec{E} &= -\frac{\partial \vec{B}}{\partial t} \\')
        agn.append(r'\nabla \times \vec{B} &= \mu_0\vec{J} + \mu_0\epsilon_0\frac{\partial \vec{E}}{\partial t}')

Matrix Environments

The Matrix class creates various types of mathematical matrices with automatic formatting.

class Matrix(Environment):
    def __init__(self, matrix, *, mtype="p", alignment=None):
        """
        Create a matrix environment.
        
        Parameters:
        - matrix: numpy.ndarray, matrix data as numpy array
        - mtype: str, matrix type:
          - 'p': parentheses ()
          - 'b': brackets []
          - 'B': braces {}
          - 'v': vertical bars ||
          - 'V': double vertical bars ||||
        - alignment: str, column alignment ('c', 'l', 'r')
        
        Requires:
        - amsmath package (automatically added)
        """

Usage example:

import numpy as np
from pylatex import Document, Section, NoEscape
from pylatex.math import Matrix, Math

doc = Document()

with doc.create(Section('Matrices')):
    # Basic matrix with parentheses (requires numpy)
    matrix_data = np.array([[1, 2, 3], 
                           [4, 5, 6], 
                           [7, 8, 9]])
    
    with doc.create(Math()) as math:
        math.append('A = ')
        math.append(Matrix(matrix_data, mtype='p'))
    
    # Matrix with brackets
    identity = [['1', '0', '0'],
                ['0', '1', '0'], 
                ['0', '0', '1']]
    
    with doc.create(Math()) as math:
        math.append('I = ')
        math.append(Matrix(identity, mtype='b'))
    
    # Determinant with vertical bars
    det_matrix = [['a', 'b'], 
                  ['c', 'd']]
    
    with doc.create(Math()) as math:
        math.append(r'\det(M) = ')
        math.append(Matrix(det_matrix, mtype='v'))
        math.append(' = ad - bc')
    
    # Matrix with mathematical expressions
    symbolic_matrix = [[NoEscape(r'\alpha'), NoEscape(r'\beta')], 
                       [NoEscape(r'\gamma'), NoEscape(r'\delta')]]
    
    with doc.create(Math()) as math:
        math.append('Greek = ')
        math.append(Matrix(symbolic_matrix, mtype='B'))

Vector Notation

The VectorName class creates properly formatted vector names using LaTeX's mathbf command.

class VectorName(Command):
    def __init__(self, name):
        """
        Create a bold vector name.
        
        Parameters:
        - name: str, vector name (will be rendered in bold math font)
        """

Usage example:

from pylatex import Document, Section
from pylatex.math import Math, VectorName

doc = Document()

with doc.create(Section('Vector Operations')):
    # Vector definitions
    with doc.create(Math()) as math:
        math.append(VectorName('v'))
        math.append(' = ')
        math.append(VectorName('a'))
        math.append(' + ')
        math.append(VectorName('b'))
    
    # Vector components
    with doc.create(Math()) as math:
        math.append(VectorName('r'))
        math.append(r' = \begin{pmatrix} x \\ y \\ z \end{pmatrix}')
    
    # Cross product
    with doc.create(Math()) as math:
        math.append(VectorName('c'))
        math.append(' = ')
        math.append(VectorName('a'))
        math.append(r' \times ')
        math.append(VectorName('b'))

Advanced Mathematical Constructs

Complex Equations

from pylatex import Document, Section, NoEscape
from pylatex.math import Math, Alignat

doc = Document()

with doc.create(Section('Advanced Mathematics')):
    # Integral equations
    with doc.create(Math()) as math:
        math.append(NoEscape(r'''
            \oint_{\partial S} \vec{F} \cdot d\vec{l} = 
            \iint_S (\nabla \times \vec{F}) \cdot \hat{n} \, dS
        '''))
    
    # Series expansions
    with doc.create(Math()) as math:
        math.append(NoEscape(r'''
            e^x = \sum_{n=0}^{\infty} \frac{x^n}{n!} = 
            1 + x + \frac{x^2}{2!} + \frac{x^3}{3!} + \cdots
        '''))
    
    # Limit definitions
    with doc.create(Math()) as math:
        math.append(NoEscape(r'''
            \lim_{h \to 0} \frac{f(x+h) - f(x)}{h} = f'(x)
        '''))

Matrix Operations

import numpy as np
from pylatex import Document, Section, NoEscape
from pylatex.math import Math, Matrix

doc = Document()

with doc.create(Section('Matrix Operations')):
    # Matrix multiplication (symbolic)
    A = np.array([['a_{11}', 'a_{12}'], 
                  ['a_{21}', 'a_{22}']])
    B = np.array([['b_{11}', 'b_{12}'], 
                  ['b_{21}', 'b_{22}']])
    
    with doc.create(Math()) as math:
        math.append('AB = ')
        math.append(Matrix(A, mtype='b'))
        math.append(Matrix(B, mtype='b'))
        math.append(' = ')
        result = [['a_{11}b_{11} + a_{12}b_{21}', 'a_{11}b_{12} + a_{12}b_{22}'],
                  ['a_{21}b_{11} + a_{22}b_{21}', 'a_{21}b_{12} + a_{22}b_{22}']]
        math.append(Matrix(result, mtype='b'))
    
    # Eigenvalue equation
    with doc.create(Math()) as math:
        math.append('A')
        math.append(VectorName('v'))
        math.append(r' = \lambda ')
        math.append(VectorName('v'))

Systems of Equations

from pylatex import Document, Section, NoEscape
from pylatex.math import Alignat

doc = Document()

with doc.create(Section('Linear Systems')):
    # Augmented matrix representation
    with doc.create(Alignat(aligns=4, numbering=False)) as agn:
        agn.append(r'2x &+ 3y &- z &= 7 \\')
        agn.append(r'x &- y &+ 2z &= 3 \\') 
        agn.append(r'3x &+ 2y &+ z &= 8')
    
    # Solution steps
    with doc.create(Alignat(numbering=False)) as agn:
        agn.append(r'x &= \frac{D_x}{D} \\')
        agn.append(r'y &= \frac{D_y}{D} \\')
        agn.append(r'z &= \frac{D_z}{D}')

Mathematical Symbols and Notation

Common Mathematical Constructs

from pylatex import Document, Section, NoEscape
from pylatex.math import Math

doc = Document()

# Greek letters and symbols
with doc.create(Math()) as math:
    math.append(NoEscape(r'\alpha, \beta, \gamma, \delta, \epsilon'))

# Calculus notation
with doc.create(Math()) as math:
    math.append(NoEscape(r'\frac{d}{dx}f(x), \frac{\partial}{\partial x}f(x,y)'))

# Set theory
with doc.create(Math()) as math:
    math.append(NoEscape(r'A \cup B, A \cap B, A \subset B, x \in A'))

# Logic symbols
with doc.create(Math()) as math:
    math.append(NoEscape(r'\forall x \in \mathbb{R}, \exists y \in \mathbb{N}'))

# Operators
with doc.create(Math()) as math:
    math.append(NoEscape(r'\sum_{i=1}^{n} x_i, \prod_{i=1}^{n} x_i, \int_a^b f(x)dx'))

Custom Mathematical Functions

from pylatex import Document, Command, NoEscape
from pylatex.math import Math

doc = Document()

# Define custom operators
doc.preamble.append(Command('DeclareMathOperator', arguments=[NoEscape(r'\Tr'), 'Tr']))
doc.preamble.append(Command('DeclareMathOperator', arguments=[NoEscape(r'\rank'), 'rank']))

with doc.create(Math()) as math:
    math.append(NoEscape(r'\Tr(A) = \sum_{i} A_{ii}'))

with doc.create(Math()) as math:
    math.append(NoEscape(r'\rank(A) \leq \min(m, n)'))

Equation Numbering and References

Numbered Equations

from pylatex import Document, Section, NoEscape
from pylatex.math import Alignat
from pylatex import Label, Ref

doc = Document()

with doc.create(Section('Referenced Equations')):
    # Numbered alignat environment
    with doc.create(Alignat()) as agn:
        agn.append(NoEscape(r'E &= mc^2'))
        agn.append(Label('einstein'))
        agn.append(NoEscape(r'\\'))
        agn.append(NoEscape(r'F &= ma'))
        agn.append(Label('newton'))
    
    doc.append(NoEscape('Einstein\'s equation '))
    doc.append(Ref('einstein'))
    doc.append(NoEscape(' and Newton\'s law '))
    doc.append(Ref('newton'))
    doc.append(NoEscape(' are fundamental to physics.'))

Package Dependencies

Mathematical environments automatically include necessary packages:

Math, Alignat, Matrix: amsmath package (automatically added)
Additional symbols: May require amssymb, amsfonts
Bold math: bm package for bold mathematical symbols
Custom operators: Use \DeclareMathOperator in preamble

from pylatex import Document, Package

doc = Document()
doc.packages.append(Package('amsmath'))
doc.packages.append(Package('amssymb'))
doc.packages.append(Package('amsfonts'))
doc.packages.append(Package('bm'))

Mathematical Best Practices

Equation Formatting

from pylatex import Document, NoEscape
from pylatex.math import Math, Alignat

# Use proper spacing
with doc.create(Math()) as math:
    math.append(NoEscape(r'a \cdot b \quad \text{not} \quad a.b'))

# Use text in equations
with doc.create(Math()) as math:
    math.append(NoEscape(r'P(\text{event}) = \frac{\text{favorable outcomes}}{\text{total outcomes}}'))

# Break long equations
with doc.create(Alignat(numbering=False)) as agn:
    agn.append(NoEscape(r'f(x) &= a_0 + a_1x + a_2x^2 + a_3x^3 \\'))
    agn.append(NoEscape(r'&\quad + a_4x^4 + a_5x^5 + \cdots'))

Mathematical expressions in PyLaTeX maintain LaTeX's high-quality typesetting while providing programmatic control over equation generation and formatting.

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