A Simple Tree Example

# Initialisations
...
from antares.core.settings import settings
from antares.core.unknown import Unknown, BHUnknown
from antares.particles.particles import Particles

oTree = BHUnknown(helconf="pmpmpm", amppart="tree")
oUnknown = Unknown(oTree, load_partial_results=False, silent=True)

Scalings

oUnknown.do_single_collinear_limits()

Finished calculating single scalings. The partial result is:
/⟨1|2⟩[1|2]⟨1|6⟩[1|6]⟨2|3⟩[2|3]⟨3|4⟩[3|4]⟨4|5⟩[4|5]⟨5|6⟩[5|6]s_123s_234s_345

The mass dimension of the unknown is -2.
The phase weights of the unknown are [-2, 2, -2, 2, -2, 2].
The mass dimension of the new unknown is 16.
The phase weights of the new unknown are [-2, 2, -2, 2, -2, 2].

oUnknown.do_double_collinear_limits()

Finished calculating pair scalings. They are:
[⟨1|2⟩, [1|2]]: 1.0, 2  → 2
[⟨1|2⟩, ⟨1|6⟩]: 1.0, 30 → 5
[⟨1|2⟩, [1|6]]: 1.0, 3  → 2
...
[s_123, s_234]: 1.0, 2  → 2
[s_123, s_345]: 1.0, 2  → 2
[s_234, s_345]: 1.0, 2  → 2

Partial Fractioning

invariants = oUnknown.poles_to_be_eliminated
print("Poles to be  eliminated:")
pprint(invariants)
print("")
lTerms = oUnknown.get_partial_fractioned_terms(invariants[0])

Poles to be  eliminated:
[s_123, s_234, s_345, ⟨1|2⟩, [1|2], ⟨1|6⟩, [1|6], ⟨2|3⟩, [2|3], ⟨3|4⟩, [3|4], ⟨4|5⟩, [4|5], ⟨5|6⟩, [5|6]]

Forced:
[]
Forbidden: 
[⟨1|6⟩, [1|6], ⟨3|4⟩, [3|4], s_234, s_345]
Optional: 
[(⟨5|6⟩, ⟨1|(2+3)|4]), ([4|5], ⟨6|(1+2)|3]), (⟨4|5⟩, ⟨3|(1+2)|6]), (⟨1|2⟩, ⟨6|(1+2)|3]), ([2|3], ⟨1|(2+3)|4]), (⟨2|3⟩, ⟨4|(2+3)|1]), ([5|6], ⟨4|(2+3)|1]), ([1|2], ⟨3|(1+2)|6])]

There are 11 symmetries:                 
[(165432, False), (216543, True), (234561, True), (321654, False), (345612, False), (432165, True), (456123, True), (543216, False), (561234, False), (612345, True), (654321, True)]

/⟨1|2⟩⟨2|3⟩[4|5][5|6]⟨1|(2+3)|4]⟨3|(1+2)|6]s_123                                                                                                                 

/[1|2][2|3]⟨4|5⟩⟨5|6⟩⟨4|(2+3)|1]⟨6|(1+2)|3]s_123

...

/⟨1|2⟩[2|3]⟨4|5⟩[5|6]⟨1|(2+3)|4]⟨3|(1+2)|6]⟨4|(2+3)|1]⟨6|(1+2)|3]s_123

/[1|2]⟨2|3⟩[4|5]⟨5|6⟩⟨1|(2+3)|4]⟨3|(1+2)|6]⟨4|(2+3)|1]⟨6|(1+2)|3]s_123

Found at least a result.

Numerator Fitting

oTerms = lTerms[0]
oTerms.fit_numerators()

Starting fit of numerator coefficients for following ansatz:              
/⟨1|2⟩⟨2|3⟩[4|5][5|6]⟨1|(2+3)|4]⟨3|(1+2)|6]s_123

Inversion will proceed in s_123^1.0 collinear limit. No symmetry will be used.
The following symmetries will then be appended to the result [(u'165432', False), (u'216543', True)]. Accuracy set to: -24
Obtained ansatz from Daniel's spinor solve with lM, lPW: [8], [[0, 4, 0, 0, -4, 0]]. Size: 15.
Finished loading augmented column.                                                                            Created new matrix of size 15x16
Time elapsed loading the matrix: 0:00:00. Created new matrix of size 15x16.                                       
Time elapsed in row reduction: 0:00:00. 0 elements of the ansatz were redundant!
Nbr dropped redundant: 0, Nbr dropped zero: 10, Nbr dropped total: 10.

Coeff. of ⟨1|2⟩⟨1|2⟩⟨1|2⟩⟨1|2⟩[1|5][1|5][1|5][1|5]: 1*I
Coeff. of ⟨1|2⟩⟨1|2⟩⟨1|2⟩⟨2|3⟩[1|5][1|5][1|5][3|5]: -4*I
Coeff. of ⟨1|2⟩⟨1|2⟩⟨2|3⟩⟨2|3⟩[1|5][1|5][3|5][3|5]: 6*I
Coeff. of ⟨1|2⟩⟨2|3⟩⟨2|3⟩⟨2|3⟩[1|5][3|5][3|5][3|5]: -4*I
Coeff. of ⟨2|3⟩⟨2|3⟩⟨2|3⟩⟨2|3⟩[3|5][3|5][3|5][3|5]: 1*I
This piece correctly removes the singularity ([0])                                                 

Refining the fit...
Finished calculating single scalings. The partial result is:                                                              
⟨2|(1+3)|5]⁴/⟨1|2⟩⟨2|3⟩[4|5][5|6]⟨1|(2+3)|4]⟨3|(1+2)|6]s_123

The mass dimension of the unknown is -2.
The phase weights of the unknown are [-2, 2, -2, 2, -2, 2].
The mass dimension of the new unknown is 0.
The phase weights of the new unknown are [0, 0, 0, 0, 0, 0].

Starting fit of numerator coefficients for following ansatz:              
⟨2|(1+3)|5]⁴/⟨1|2⟩⟨2|3⟩[4|5][5|6]⟨1|(2+3)|4]⟨3|(1+2)|6]s_123

Inversion will proceed in s_123^1.0 collinear limit. No symmetry will be used.
The following symmetries will then be appended to the result [(u'165432', False), (u'216543', True)]. Accuracy set to: -24
Obtained ansatz from Daniel's spinor solve with lM, lPW: [0], [[0, 0, 0, 0, 0, 0]]. Size: 1.
Finished loading augmented column.                                                                            Created new matrix of size 1x2
Time elapsed loading the matrix: 0:00:00. Created new matrix of size 1x2.                                       
Time elapsed in row reduction: 0:00:00. 0 elements of the ansatz were redundant!
Nbr dropped redundant: 0, Nbr dropped zero: 0, Nbr dropped total: 0.

Coeff. of this whole term is: 1*I
This piece correctly removes the singularity ([0])                                                 

print(oTerms)

+1I⟨2|(1+3)|5]⁴/⟨1|2⟩⟨2|3⟩[4|5][5|6]⟨1|(2+3)|4]⟨3|(1+2)|6]s_123
(u'165432', False)
(u'216543', True)

oParticles = Particles(6)
oParticles.fix_mom_cons()
assert(abs(oTerms(oParticles) - oTree(oParticles)) < 10 ** -280)