Configuration and Types

def set_printoptions(**kwargs):
    """
    Set global print options for field arrays.
    
    Parameters:
    - coeffs (str, optional): Coefficient display format
      - "int": Display as integers (default)
      - "poly": Display as polynomial representation
      - "power": Display as powers of primitive element
    - details (bool, optional): Show detailed field information, default True  
    - precision (int, optional): Precision for floating point display
    - threshold (int, optional): Array size threshold for summarization
    - edgeitems (int, optional): Number of edge items in summarized arrays
    - linewidth (int, optional): Character width for line wrapping
    - suppress (bool, optional): Suppress small floating point values
    """

def get_printoptions():
    """
    Get current global print options.
    
    Returns:
    dict: Current print option settings
    """

def printoptions(**kwargs):
    """
    Context manager for temporary print option changes.
    
    Parameters: Same as set_printoptions()
    
    Returns:
    Context manager that temporarily modifies print options
    
    Example:
    with galois.printoptions(coeffs="poly"):
        print(field_array)  # Uses polynomial representation
    # Reverts to previous settings after context
    """

# Import the typing module
import galois.typing

# Core type aliases for field elements and arrays
ElementLike = Union[int, np.integer, FieldArray]
"""Type alias for objects that can be coerced to field elements."""

IterableLike = Union[Iterable[ElementLike], Iterable[Iterable[ElementLike]]]
"""Type alias for iterable objects that can be coerced to field arrays."""

ArrayLike = Union[FieldArray, IterableLike, ElementLike]
"""Type alias for objects that can be coerced to field arrays."""

ShapeLike = Union[int, Sequence[int]]
"""Type alias for objects that can be coerced to array shapes."""

DTypeLike = Union[np.dtype, type, str]
"""Type alias for objects that can be coerced to NumPy dtypes."""

PolyLike = Union[Poly, ArrayLike, str, int]
"""Type alias for objects that can be coerced to polynomials."""

import galois
import numpy as np

# Create a finite field
GF = galois.GF(2**4)
x = GF([1, 2, 3, 4, 5])

# Default integer representation
print("Default (int) representation:")
print(x)

# Change to polynomial representation
galois.set_printoptions(coeffs="poly")
print("\nPolynomial representation:")
print(x)

# Change to power representation  
galois.set_printoptions(coeffs="power")
print("\nPower representation:")
print(x)

# Reset to default
galois.set_printoptions(coeffs="int")
print("\nBack to integer representation:")
print(x)

import galois

GF = galois.GF(3**3)
poly = galois.Poly([1, 2, 0, 1], field=GF)
array = GF([5, 10, 15, 20])

print("Default settings:")
print(f"Polynomial: {poly}")
print(f"Array: {array}")

# Temporary change to polynomial representation
with galois.printoptions(coeffs="poly"):
    print("\nInside context (poly representation):")
    print(f"Polynomial: {poly}")
    print(f"Array: {array}")

print("\nAfter context (back to default):")
print(f"Polynomial: {poly}")
print(f"Array: {array}")

# Multiple temporary changes
with galois.printoptions(coeffs="power", details=False):
    print("\nPower representation without details:")
    print(f"Array: {array}")

import galois
from galois.typing import ElementLike, ArrayLike, PolyLike
from typing import Union
import numpy as np

def create_field_array(data: ArrayLike, field_order: int) -> galois.FieldArray:
    """
    Create field array with proper type hints.
    
    Args:
        data: Input data coercible to field array
        field_order: Order of the finite field
        
    Returns:
        Field array over GF(field_order)
    """
    GF = galois.GF(field_order)
    return GF(data)

def polynomial_from_input(coeffs: PolyLike, field: type = None) -> galois.Poly:
    """
    Create polynomial from various input types.
    
    Args:
        coeffs: Polynomial coefficients (various formats accepted)
        field: Finite field class
        
    Returns:
        Polynomial over specified field
    """
    if isinstance(coeffs, str):
        # Handle string representation
        return galois.Poly.Str(coeffs, field=field)
    elif isinstance(coeffs, int):
        # Handle integer representation
        return galois.Poly.Int(coeffs, field=field)
    else:
        # Handle array-like coefficients
        return galois.Poly(coeffs, field=field)

# Usage examples with type checking
GF16 = galois.GF(16)

# These all satisfy ArrayLike
array1 = create_field_array([1, 2, 3], 16)              # List input
array2 = create_field_array(np.array([4, 5, 6]), 16)    # NumPy array input  
array3 = create_field_array(GF16([7, 8, 9]), 16)        # Field array input

# These all satisfy PolyLike
poly1 = polynomial_from_input([1, 0, 1], GF16)          # List coefficients
poly2 = polynomial_from_input("x^2 + 1", GF16)          # String representation
poly3 = polynomial_from_input(5, GF16)                  # Integer representation

print(f"Arrays created: {array1}, {array2}, {array3}")
print(f"Polynomials created: {poly1}, {poly2}, {poly3}")

import galois
import numpy as np

# Create larger field for demonstration
GF = galois.GF(2**8)

# Create large array to test threshold settings
large_array = GF.Random(20)

# Default printing
print("Default printing:")
print(large_array)

# Modify threshold and edge items
galois.set_printoptions(threshold=10, edgeitems=2)
print("\nWith threshold=10, edgeitems=2:")
print(large_array)

# Show field details
galois.set_printoptions(details=True)
print(f"\nWith details=True:")
print(f"Field info: {GF}")

# Polynomial representation with custom formatting
galois.set_printoptions(coeffs="poly", linewidth=50)
poly_array = GF([1, 2, 3, 4, 5, 6, 7, 8])
print(f"\nPolynomial representation with linewidth=50:")
print(poly_array)

# Get current settings
current_options = galois.get_printoptions()
print(f"\nCurrent print options: {current_options}")

# Reset to defaults
galois.set_printoptions(coeffs="int", threshold=1000, edgeitems=3, details=True, linewidth=75)

import galois
from galois.typing import *
from typing import List, Tuple, Optional

def batch_encode_messages(
    messages: List[ArrayLike], 
    field_order: int,
    code_params: Tuple[int, int]
) -> List[galois.FieldArray]:
    """
    Batch encode multiple messages using Reed-Solomon code.
    
    Args:
        messages: List of message arrays
        field_order: Finite field order  
        code_params: (n, k) code parameters
        
    Returns:
        List of encoded codewords
    """
    n, k = code_params
    rs = galois.ReedSolomon(n, k)
    
    encoded = []
    for msg in messages:
        # Convert to proper field array
        field_msg = rs.field(msg)
        codeword = rs.encode(field_msg)
        encoded.append(codeword)
        
    return encoded

def analyze_polynomial(
    poly_input: PolyLike,
    field_class: Optional[type] = None
) -> dict:
    """
    Analyze polynomial properties with flexible input handling.
    
    Args:
        poly_input: Polynomial in various formats
        field_class: Field class for polynomial
        
    Returns:
        Dictionary of analysis results
    """
    # Convert input to polynomial
    if isinstance(poly_input, galois.Poly):
        poly = poly_input
    else:
        poly = galois.Poly(poly_input, field=field_class)
    
    # Perform analysis
    analysis = {
        "degree": poly.degree,
        "is_monic": poly.is_monic(),
        "is_irreducible": poly.is_irreducible(),
        "coefficients": poly.coeffs,
        "field": poly.field.name,
    }
    
    return analysis

# Example usage with proper types
messages = [[1, 2, 3], [4, 5, 6], [7, 8, 9]]
encoded_batch = batch_encode_messages(messages, 16, (15, 9))
print(f"Encoded {len(encoded_batch)} messages")

# Analyze different polynomial inputs
poly_analysis1 = analyze_polynomial([1, 0, 1, 1])  # List coefficients
poly_analysis2 = analyze_polynomial("x^3 + x + 1")  # String format
print(f"Analysis 1: {poly_analysis1}")
print(f"Analysis 2: {poly_analysis2}")