Sector creation

[s-merchant]

Hi! I'm trying to perform sector decomposition using the iterative_decomposition method from pySecDec.decomposition.iterative on the exponentiated forms of U and F from LoopIntegralFromPropagators.

I combined the two polynomials into a Product. When I try to use this Product to create a Sector, I get the error

AssertionError: The first factor of every Product must be a monomial

This issue only arises upon trying to use the Product object as input for creating the Sector, not when creating the Product to begin with.

Here's what I've got:

 from pySecDec.decomposition import Sector
 from pySecDec.decomposition.iterative import iterative_decomposition
 from pySecDec.algebra import Polynomial
 from pySecDec.algebra import Product
  
 propagators = ['k**2','(k+r)**2','(k+s)**2','(k+t)**2']
 loop_momenta = ['k']
  
 one_loop_box = LoopIntegralFromPropagators(propagators,loop_momenta,dimensionality='3-2*eps')
 
 print(one_loop_box)
 
 combined_poly = Product(one_loop_box.exponentiated_U,one_loop_box.exponentiated_F)
 print(type(one_loop_box.exponentiated_U))
 
 print("\n")
 print("printing polynomial:")
 print(combined_poly)
 
 print(combined_poly.factors[0].coeffs)
 print(len(combined_poly.factors[0].coeffs))
 
 initial_sector = Sector([combined_poly])
 
 print(initial_sector)

Thanks so much to anyone who has any suggestions! I'm sure I've just overlooked something small.

[spj101]

Hi @s-merchant, thanks for trying our code.

Firstly, it's not super obvious what your goal is with this code. If you just want to obtain a result for this integral using sector decomposition then there is no need to understand or use the low-level algebra/decomposition functions. See the examples (e.g. elliptic2L_physical).

If you really do not want to compute this integral but instead examine some of the internal functions available within pySecDec (for example if you are following some examples in our documentation), then perhaps I can still help. The issue here is that Sector does not like products that do not have a monomial as the first factor, as the error message says. Admittedly the documentation is not clear about this point, we should probably improve it.

However, you can pass a list of Polynomial or ExponentiatedPolynomial, which is what we actually do in our code.

Perhaps the following example is close to what you wanted:

from pySecDec.decomposition import Sector
from pySecDec.decomposition.iterative import iterative_decomposition
from pySecDec import LoopIntegralFromPropagators

if __name__ == '__main__':
    propagators = ['k**2','(k+r)**2','(k+s)**2','(k+t)**2']
    loop_momenta = ['k']

    one_loop_box = LoopIntegralFromPropagators(propagators,loop_momenta,dimensionality='3-2*eps')

    #print('exponentiated_U', one_loop_box.exponentiated_U)
    #print('exponentiated_F', one_loop_box.exponentiated_F)

    initial_sector = Sector([one_loop_box.exponentiated_U, one_loop_box.exponentiated_F])

    decomposed_sectors = iterative_decomposition(initial_sector)

    for sector in decomposed_sectors:
        print(sector)
        print('\n')

You can then take the product of the Jacobian and cast polynomials in each Sector.

Hope this helps.