multiloop_sunset_generic_masses.sage

# Sagemath code for computing the holomorphic period for all the sunset and it Frobenius deformation
# here t=p2

from sage.all import *
from itertools import product, combinations
var('t x n N rho')
R.<x> = PowerSeriesRing(ZZ)

def initialize_sunset_variables(looporder, coPFoperator,params, values, Nmax):
    """
    Initialize sunset diagram variables for perturbative calculations.
    
    Parameters:
    -----------
    looporder : int
        The loop order for the calculation
    Nmax : int
        Maximum number of terms
    max_log_power : int
        Maximum logarithmic power for symbolic variables
    coPFOperator : list coefficients differential operator
    params : parameters (the masses)
    values : the values of the parameters
    Returns:
    --------
    dict : Dictionary containing all initialized variables
    """
    # Initialize main sunset variables
    if len(params) != len(values):
        raise ValueError("Parameter list and value list must have same length")

    subs_dict = dict(zip(params, values))

    Lsunset=sum(
        OA(coPFoperator[k].subs(subs_dict)) * Dt^k
        for k in sorted(coPFoperator)
    )
    
    max_log_power=looporder

    Persunset = Period(values, Nmax)
    
    Qsunset = Q(values, Nmax)
    
    Rsunset = R(values, Nmax)
    
    # Create symbolic variables for each log power
    var_groups = {}
    for log_pow in range(max_log_power):
        var_name = chr(65 + log_pow)  # A, B, C, D, ...
        var_groups[log_pow] = [SR.var(f'{var_name}_{n}') for n in range(1, Nmax)]
    
    # Return all variables in a dictionary
    return {
        'Lsunset': Lsunset,
        'Persunset': Persunset,
        'Qsunset': Qsunset,
        'Rsunset': Rsunset,
        'var_groups': var_groups
    }

# Example usage:
# sunset_vars = initialize_sunset_variables(looporder=2, Nmax=10)
# Lsunset = sunset_vars['Lsunset']
# var_groups = sunset_vars['var_groups']