From 8f7bd54d1341e6634fe4b67b32c3db470f6a5b2d Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Thu, 12 Oct 2023 18:12:12 +0200 Subject: [PATCH 1/2] import from https://github.com/NNPDF/eko_fhmv_private/pull/2 --- doc/source/refs.bib | 11 ++ doc/source/theory/N3LO_ad.rst | 42 +++--- extras/n3lo_bench/plot_msht.py | 4 +- .../unpolarized/space_like/as4/ggg.py | 131 ++++++++++-------- .../unpolarized/space_like/as4/ggq.py | 107 ++++++-------- .../unpolarized/space_like/test_as4.py | 6 +- 6 files changed, 155 insertions(+), 146 deletions(-) diff --git a/doc/source/refs.bib b/doc/source/refs.bib index e6796d738..16a662451 100644 --- a/doc/source/refs.bib +++ b/doc/source/refs.bib @@ -1021,3 +1021,14 @@ @article{Falcioni:2023tzp month = "10", year = "2023" } + +@article{Moch:2023tdj, + author = "Moch, S. and Ruijl, B. and Ueda, T. and Vermaseren, J. and Vogt, A.", + title = "{Additional moments and x-space approximations of four-loop splitting functions in QCD}", + eprint = "2310.05744", + archivePrefix = "arXiv", + primaryClass = "hep-ph", + reportNumber = "DESY-23-150, Nikhef 23-016, LTH 1354", + month = "10", + year = "2023" +} diff --git a/doc/source/theory/N3LO_ad.rst b/doc/source/theory/N3LO_ad.rst index 6cee0e11a..34030f7e7 100644 --- a/doc/source/theory/N3LO_ad.rst +++ b/doc/source/theory/N3LO_ad.rst @@ -90,16 +90,16 @@ In |EKO| they are implemented as follows: - The large-N limit :cite:`Moch:2017uml`, which reads (Eq. 2.17): .. math :: - \gamma_{ns} \approx A^{(f)}_4 S_1(N) - B_4 + C_4 \frac{S_1(N)}{N} - D_4 \frac{1}{N} + \gamma_{ns} \approx A^{(f)}_4 S_1(N) - B^{(f)}_4 + C^{(f)}_4 \frac{S_1(N)}{N} - D^{(f)}_4 \frac{1}{N} This limit is common for all :math:`\gamma_{ns,+}^{(3)},\gamma_{ns,-}^{(3)},\gamma_{ns,v}^{(3)}`. The coefficient :math:`A^{(f)}_4`, being related to the twist-2 spin-N operators, can be obtained from the |QCD| cusp calculation - :cite:`Henn:2019swt`, while the :math:`B_4` is fixed by the integral of the 4-loop splitting function + :cite:`Henn:2019swt`, while the :math:`B^{(f)}_4` is fixed by the integral of the 4-loop splitting function and has been firstly computed in :cite:`Moch:2017uml` in the large :math:`n_c` limit. More recently :cite:`Duhr:2022cob`, it has been determined in the full color expansion by computing various |N3LO| cross sections in the soft limit. - :math:`C_4,D_4` instead can be computed directly from lower order splitting functions. + :math:`C^{(f)}_4,D^{(f)}_4` instead can be computed directly from lower order splitting functions. From large-x resummation :cite:`Davies:2016jie`, it is possible to infer further constrains on sub-leading terms :math:`\frac{\ln^k(N)}{N^2}`, since the non-singlet splitting functions contain only terms :math:`(1-x)^a\ln^k(1-x)` with :math:`a \ge 1`. @@ -234,11 +234,11 @@ The other parts are approximated using some known limits: It is known that :cite:`Albino:2000cp,Moch:2021qrk` the diagonal terms diverge in N-space as: .. math :: - \gamma_{kk} \approx A^{(r)}_4 S_1(N) + B^{(r)}_4 + C^{(r)}_4 \frac{S_1(N)}{N} + \mathcal{O}(\frac{1}{N}) + \gamma_{kk} \approx A^{(r)}_4 S_1(N) + B^{(r)}_4 + C^{(r)}_4 \frac{S_1(N)}{N} - D^{(r)}_4 \frac{1}{N} Where again the coefficient :math:`A^{(r)}_4` is the |QCD| cusp anomalous dimension for the adjoint or fundamental representation, the coefficient :math:`B^{(r)}_4` has been extracted from soft anomalous dimensions :cite:`Duhr:2022cob`. - and :math:`C^{(r)}_4`can be estimate from lower orders :cite:`Dokshitzer:2005bf`. + and :math:`C^{(r)}_4,D^{(r)}_4`can be estimate from lower orders :cite:`Dokshitzer:2005bf`. However, :math:`\gamma_{qq,ps}^{(3)}` do not constrain any divergence at large-x or constant term so its expansion starts as :math:`\mathcal{O}(\frac{1}{N^2})`. The off-diagonal do not contain any +-distributions or delta distributions but can include divergent logarithms @@ -257,14 +257,14 @@ The other parts are approximated using some known limits: \gamma_{qq,ps} \approx (1-x)[c_{4} \ln^4(1-x) + c_{3} \ln^3(1-x)] + \mathcal{O}((1-x)\ln^2(1-x)) - * The 4 lowest even N moments provided in :cite:`Moch:2021qrk`, where we can use momentum conservation - to fix: + * The 5 lowest even N moments provided in :cite:`Moch:2021qrk,Moch:2023tdj`, + where momentum conservation fixes: .. math :: & \gamma_{qg}(2) + \gamma_{gg}(2) = 0 \\ & \gamma_{qq}(2) + \gamma_{gq}(2) = 0 \\ - For :math:`\gamma_{qq,ps}, \gamma_{qg}` other 6 additional moments are available :cite:`Falcioni:2023luc,Falcioni:2023vqq`. + For :math:`\gamma_{qq,ps}, \gamma_{qg}` other 5 additional moments are available :cite:`Falcioni:2023luc,Falcioni:2023vqq`. making the parametrization of this splitting function much more accurate. The difference between the known moments and the known limits is parametrized @@ -281,9 +281,9 @@ we need to account for a possible source of uncertainties arising during the app This uncertainty is neglected in the non-singlet case. The procedure is performed in two steps for each different anomalous dimension separately. -First, we solve the system associated to the 4 known moments, +First, we solve the system associated to the 5 (10) known moments, minus the known limits, using different functional bases. -Any possible candidate contains 4 elements and is obtained with the following prescription: +Any possible candidate contains 5 elements and is obtained with the following prescription: 1. one function is leading small-N unknown contribution, which correspond to the highest power unknown for the pole at :math:`N=1`, @@ -317,29 +317,29 @@ final reduced sets of candidates. :align: center * - :math:`f_1(N)` - - :math:`\frac{S_2(N-2)}{N}` + - :math:`\frac{1}{(N-1)^2}` * - :math:`f_2(N)` - - :math:`\frac{1}{N}` + - :math:`\mathcal{M}[(1-x)\ln^3(1-x)]` * - :math:`f_3(N)` - - :math:`\frac{1}{N-1},\ \frac{S_1(N)}{N^2}` + - :math:`\frac{1}{N-1},` * - :math:`f_4(N)` - - :math:`\frac{1}{N-1},\ \frac{1}{N^4},\ \frac{1}{N^3},\ \frac{1}{N^2},\ \frac{1}{(N+1)^3},\ \frac{1}{(N+1)^2},\ \frac{1}{N+1},\ \frac{1}{N+2},\ \mathcal{M}[(1-x)\ln(1-x)],\ \frac{S_1(N)}{N^2}, \ \mathcal{M}[(1-x)^2\ln(1-x)],` + - :math:`\frac{1}{N^4},\ \frac{1}{N^3},\ \frac{1}{N^2},\ \frac{1}{(N+1)},\ \frac{1}{(N+2)},\ \mathcal{M}[(1-x)\ln^2(1-x)],\ \mathcal{M}[(1-x)\ln(1-x)]` .. list-table:: :math:`\gamma_{gq}^{(3)}` parametrization basis :align: center * - :math:`f_1(N)` - - :math:`\frac{S_2(N-2)}{N}` + - :math:`\frac{1}{(N-1)^2}` * - :math:`f_2(N)` - - :math:`\frac{S_1^3(N)}{N}` + - :math:`\mathcal{M}[\ln^3(1-x)]` * - :math:`f_3(N)` - - :math:`\frac{1}{N-1},\ \frac{1}{N^4}` + - :math:`\frac{1}{N-1}` * - :math:`f_4(N)` - - :math:`\frac{1}{N-1},\ \frac{1}{N^4},\ \frac{1}{N^3},\ \frac{1}{N^2},\ \frac{1}{N},\ \frac{1}{(N+1)^3},\ \frac{1}{(N+1)^2},\ \frac{1}{N+1},\ \frac{1}{N+2},\ \frac{S_1(N-2)}{N},\ \mathcal{M}[\ln^3(1-x)],\ \mathcal{M}[\ln^2(1-x)], \frac{S_1(N)}{N},\ \frac{S_1^2(N)}{N}` + - :math:`\frac{1}{N^4},\ \frac{1}{N^3},\ \frac{1}{N^2},\ \frac{1}{(N+1)},\ \frac{1}{(N+2)},\ \mathcal{M}[\ln^2(1-x)],\ \mathcal{M}[\ln(1-x)]` - Note that this table refers only to the :math:`n_f^0` part where we assume no violation of the scaling with :math:`\gamma_{gg}` - also for the |NLL| term, to help the convergence. We expect that any possible deviation can be parametrized as a shift in the |NNLL| terms - and in the |NLL| :math:`n_f^1` which are free to vary independently. + Following :cite:`Moch:2023tdj` we have assumed no violation of the scaling with :math:`\gamma_{gg}` + also for the |NLL| small-x term, to help the convergence. We expect that any possible deviation can be parametrized as a shift in the |NNLL| terms + which are free to vary independently. Slightly different choices are performed for :math:`\gamma_{gq}^{(3)}` and :math:`\gamma_{qq,ps}^{(3)}` where 10 moments are known. In this case we can select a larger number of functions in group 3 diff --git a/extras/n3lo_bench/plot_msht.py b/extras/n3lo_bench/plot_msht.py index 54aa8fcfa..c922c1c03 100644 --- a/extras/n3lo_bench/plot_msht.py +++ b/extras/n3lo_bench/plot_msht.py @@ -14,8 +14,8 @@ n3lo_vars_dict = { - "gg": 17, - "gq": 24, + "gg": 19, + "gq": 21, "qg": 15, "qq": 6, } diff --git a/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggg.py b/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggg.py index 6c8b9f0d5..88eee5b88 100644 --- a/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggg.py +++ b/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggg.py @@ -5,7 +5,7 @@ import numpy as np from .....harmonics import cache as c -from .....harmonics.log_functions import lm11, lm11m1, lm11m2 +from .....harmonics.log_functions import lm11, lm11m1, lm12m1, lm13m1 @nb.njit(cache=True) @@ -161,43 +161,48 @@ def gamma_gg_nf1(n, cache, variation): """ S1 = c.get(c.S1, cache, n) S2 = c.get(c.S2, cache, n) - common = 18143.980574437464 + 1992.766087237516/np.power(-1. + n,3) + 20005.925925925927/np.power(n,7) - 19449.679012345678/np.power(n,6) + 80274.123066115/np.power(n,5) - 11714.245609287387*S1 + 13880.514502193577*lm11(n,S1) + S3 = c.get(c.S3, cache, n) + common = 18143.980574437464 + 1992.766087237516/np.power(-1. + n,3) + 20005.925925925927/np.power(n,7) - 19449.679012345678/np.power(n,6) + 80274.123066115/np.power(n,5) + 4341.13370266389/n - 11714.245609287387*S1 + 13880.514502193577*lm11(n,S1) if variation == 1: - fit = 51906.450933224565/n - 55794.44458990475/(1. + n) - (3244.182054400047*S1)/np.power(n,2) + (5896.657744251454*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -10270.11416182055/np.power(-1. + n,2) + 18731.17968740991/(-1. + n) + 297.3210929571657/(1. + n) - 23244.924485271466/(2. + n) - 4050.833138545348*lm13m1(n,S1,S2,S3) elif variation == 2: - fit = 143243.25209661626/n - 140219.52798151976/(2. + n) - (81141.96014226894*S1)/np.power(n,2) + (4359.928069421606*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -11082.13131236475/np.power(-1. + n,2) + 21010.979258355084/(-1. + n) - 21217.46135836648/(1. + n) + 8541.603641080774*lm12m1(n,S1,S2) + 1299.6826595628106*lm13m1(n,S1,S2,S3) elif variation == 3: - fit = -4846.510890091015/n + 73944.02374603187/np.power(1. + n,3) + (15528.258395929412*S1)/np.power(n,2) + (5875.765469829209*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -2710.665352609663/np.power(-1. + n,2) + 22945.993521464054/(-1. + n) - 126229.56225118619/np.power(n,4) - 34046.95702168874/(1. + n) - 9872.686392323958*lm13m1(n,S1,S2,S3) elif variation == 4: - fit = 3769.9068671191385/n - (15787.280088316747*S1)/np.power(n,2) + (3319.747916876306*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n - 209289.30375366632*lm11m2(n,S1) + fit = -11295.981203099282/np.power(-1. + n,2) + 29362.42506506866/(-1. + n) - 31878.254277368906/np.power(n,3) - 35458.54478982031/(1. + n) - 5668.488002948361*lm13m1(n,S1,S2,S3) elif variation == 5: - fit = -4404.650816024677/n + (32166.525125055265*S1)/np.power(n,2) + (5984.665222488821*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 26795.61010300351*lm11m1(n,S1) + fit = -10686.93631688797/np.power(-1. + n,2) + 19906.339608012637/(-1. + n) - 22367.39965022059/(1. + n) - 11221.684701529948*lm11m1(n,S1) - 2145.948106277924*lm13m1(n,S1,S2,S3) elif variation == 6: - fit = 18002.20882549217/(-1. + n) - 34510.86180174593/n + (14377.94953322174*S1)/np.power(n,2) + (12777.152485988116*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -10281.335740623817/np.power(-1. + n,2) + 18762.685118697587/(-1. + n) - 22923.693890952152/(2. + n) + 118.0397215654495*lm12m1(n,S1,S2) - 3976.892293061728*lm13m1(n,S1,S2,S3) elif variation == 7: - fit = 32712.59210667494/np.power(n,3) - 10863.21459339799/n + (19949.446087845266*S1)/np.power(n,2) + (9104.304296741177*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -10204.671424181955/np.power(-1. + n,2) + 18767.66765933924/(-1. + n) - 1092.779160652895/np.power(n,4) - 23043.691361939706/(2. + n) - 4101.2333760090105*lm13m1(n,S1,S2,S3) elif variation == 8: - fit = 23133.58893729803/np.power(n,2) - 6436.943948938613/n + (9529.55663925907*S1)/np.power(n,2) + (6913.820202625404*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -10278.644563822769/np.power(-1. + n,2) + 18819.581783601687/(-1. + n) - 265.07755215895946/np.power(n,3) - 23051.635742762955/(2. + n) - 4064.284439480962*lm13m1(n,S1,S2,S3) elif variation == 9: - fit = 3314.1531443520435/(-1. + n) + 35997.28048068957/n - 45522.85315535845/(1. + n) + (7163.336378194301*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -10347.501508088137/np.power(-1. + n,2) + 19058.23126571671/(-1. + n) - 572.2668461573236/np.power(n,2) - 23256.742273946194/(2. + n) - 4035.759520905052*lm13m1(n,S1,S2,S3) elif variation == 10: - fit = 15292.461183783358/(-1. + n) - 7754.767835203314/n - 21106.273066417427/(2. + n) + (11510.166071508424*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -10275.582132070176/np.power(-1. + n,2) + 18746.595709341593/(-1. + n) - 22939.992144309395/(2. + n) - 147.20867721931182*lm11m1(n,S1) - 4025.8444124078146*lm13m1(n,S1,S2,S3) elif variation == 11: - fit = 18943.68531934485/(-1. + n) - 34231.50197430196/n + 38795.17200645132/np.power(1. + n,2) + (12574.453319273369*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -24926.888750623133/np.power(-1. + n,2) + 17810.84642127126/(-1. + n) + 208758.85768476047/np.power(n,4) + 22667.73532614404*lm12m1(n,S1,S2) + 19776.5826765651*lm13m1(n,S1,S2,S3) elif variation == 12: - fit = 243015.55817041075/(-1. + n) - 405291.74871837825/n - 924241.7199143948/np.power(1. + n,3) + (99039.0230533651*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -10763.5212982461/np.power(-1. + n,2) + 8568.352997277027/(-1. + n) + 47494.674935205614/np.power(n,3) + 21267.541668576003*lm12m1(n,S1,S2) + 11681.399225017101*lm13m1(n,S1,S2,S3) elif variation == 13: - fit = 9421.639301348665/(-1. + n) - 16264.723220366097/n + (8269.376900788462*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n - 99755.61548732712*lm11m2(n,S1) + fit = -5727.151193148642/np.power(-1. + n,2) - 1579.7328323989361/(-1. + n) + 39389.08181155469/np.power(n,2) + 8242.704431969565*lm12m1(n,S1,S2) + 74.93434922328093*lm13m1(n,S1,S2,S3) elif variation == 14: - fit = 32552.831422747156/(-1. + n) - 58844.770942175055/n + (18267.307590060325*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n - 21658.053945007472*lm11m1(n,S1) + fit = -18373.856968226213/np.power(-1. + n,2) + 41392.63735393215/(-1. + n) + 207050.815868518*lm11m1(n,S1) + 166142.36054620336*lm12m1(n,S1,S2) + 64874.865907564*lm13m1(n,S1,S2,S3) elif variation == 15: - fit = 26670.108040113628/(-1. + n) - 192284.97382369108/np.power(n,4) - 17027.576353111184/n - (2060.8605568773337*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = 5243.900655452294/np.power(-1. + n,2) - 12659.834824913609/(-1. + n) - 119288.31030415706/np.power(n,4) + 61896.66336205812/np.power(n,2) - 11182.917725840534*lm13m1(n,S1,S2,S3) elif variation == 16: - fit = 64459.179128132346/(-1. + n) - 84418.96962498086/np.power(n,3) - 95536.59785086475/n + (22255.40045589177*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -25962.210430671832/np.power(-1. + n,2) + 14085.129803728569/(-1. + n) + 241740.93047797284/np.power(n,4) - 32712.217132272293*lm11m1(n,S1) + 12651.448553539236*lm13m1(n,S1,S2,S3) elif variation == 17: - fit = -35383.49147569926/(-1. + n) + 68602.85078732096/np.power(n,2) + 48742.57555689275/n - (4610.608264940457*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -2539.909047069818/np.power(-1. + n,2) - 8001.899230702169/(-1. + n) - 30056.772339779138/np.power(n,3) + 64316.26925516245/np.power(n,2) - 7270.160083308018*lm13m1(n,S1,S2,S3) + elif variation == 18: + fit = -9646.328315869272/np.power(-1. + n,2) + 3749.766574153606/(-1. + n) + 54466.866417785626/np.power(n,3) - 30394.942945299434*lm11m1(n,S1) + 3872.6283293477754*lm13m1(n,S1,S2,S3) + elif variation == 19: + fit = -5066.965729118176/np.power(-1. + n,2) - 3822.9837355590003/(-1. + n) + 41445.27729170122/np.power(n,2) - 10808.501548399454*lm11m1(n,S1) - 3307.7625874988926*lm13m1(n,S1,S2,S3) else: - fit = 23311.07841529563/(-1. + n) - 11310.8808131583/np.power(n,4) - 3041.5516187238777/np.power(n,3) + 5396.261160271705/np.power(n,2) - 24256.141353532745/n - 50017.51153931546/np.power(1. + n,3) + 2282.06894155596/np.power(1. + n,2) - 5959.841043839012/(1. + n) - 9489.753002819834/(2. + n) - (507.1580296279411*S1)/np.power(n,2) + (13331.74331502859*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 302.2091857644728*lm11m1(n,S1) - 18179.112896529026*lm11m2(n,S1) + fit = -10273.4997259521/np.power(-1. + n,2) + 13981.787431778737/(-1. + n) + 10731.007181407218/np.power(n,4) + 2092.707220193907/np.power(n,3) + 10867.106572332586/np.power(n,2) - 5936.475880375734/(1. + n) - 7287.404205220098/(2. + n) + 6408.750571778819*lm11m1(n,S1) + 11946.315017659957*lm12m1(n,S1,S2) + 2659.4069274848257*lm13m1(n,S1,S2,S3) return common + fit @@ -223,43 +228,48 @@ def gamma_gg_nf2(n, cache, variation): """ S1 = c.get(c.S1, cache, n) S2 = c.get(c.S2, cache, n) - common = -423.811346198137 - 568.8888888888889/np.power(n,7) + 1725.6296296296296/np.power(n,6) - 2196.543209876543/np.power(n,5) + 440.0487580115612*S1 - 135.11111111111114*lm11(n,S1) + S3 = c.get(c.S3, cache, n) + common = -423.811346198137 - 568.8888888888889/np.power(n,7) + 1725.6296296296296/np.power(n,6) - 2196.543209876543/np.power(n,5) + 21.333333333333336/n + 440.0487580115612*S1 - 135.11111111111114*lm11(n,S1) if variation == 1: - fit = -2376.754718471023/n + 1986.9752104021475/(1. + n) - (29.413328132453657*S1)/np.power(n,2) + (243.6914020341996*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -16.959956452231857/np.power(-1. + n,2) - 629.5045317989062/(-1. + n) - 682.6697400582308/(1. + n) + 1217.639625778457/(2. + n) - 72.64979891934051*lm13m1(n,S1,S2,S3) elif variation == 2: - fit = -5629.479269151885/n + 4993.556762890926/(2. + n) + (2744.7150845388774*S1)/np.power(n,2) + (298.41806508138217*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = 25.57596402110471/np.power(-1. + n,2) - 748.9273459351353/(-1. + n) + 444.33979999567083/(1. + n) - 447.4350978280687*lm12m1(n,S1,S2) - 352.92603979329243*lm13m1(n,S1,S2,S3) elif variation == 3: - fit = -355.6443895005434/n - 2633.32565133846/np.power(1. + n,3) - (697.9453672577569*S1)/np.power(n,2) + (244.43542649166247*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -412.9468061824264/np.power(-1. + n,2) - 850.2892602188854/(-1. + n) + 6612.287213025851/np.power(n,4) + 1116.3876833223574/(1. + n) + 232.31652703107594*lm13m1(n,S1,S2,S3) elif variation == 4: - fit = -662.4958800366925/n + (417.27675074971785*S1)/np.power(n,2) + (335.4613978477791*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 7453.298646800853*lm11m2(n,S1) + fit = 36.77806971484529/np.power(-1. + n,2) - 1186.401399819004/(-1. + n) + 1669.8796175207788/np.power(n,3) + 1190.3309307108536/(1. + n) + 12.087867790598803*lm13m1(n,S1,S2,S3) elif variation == 5: - fit = -371.3800961661366/n - (1290.4743148587395*S1)/np.power(n,2) + (240.55724273082328*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n - 954.2565288285368*lm11m1(n,S1) + fit = 4.874451882150377/np.power(-1. + n,2) - 691.0629716579465/(-1. + n) + 504.5770544662291/(1. + n) + 587.8258700832249*lm11m1(n,S1) - 172.43345273623754*lm13m1(n,S1,S2,S3) elif variation == 6: - fit = -641.1022267836108/(-1. + n) + 700.7749426995084/n - (656.9800845794034*S1)/np.power(n,2) - (1.339668489438944*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = 8.805562596792123/np.power(-1. + n,2) - 701.843175427027/(-1. + n) + 480.0720211823408/(2. + n) - 271.02734366604454*lm12m1(n,S1,S2) - 242.4230809561374*lm13m1(n,S1,S2,S3) elif variation == 7: - fit = -1164.9745787725433/np.power(n,3) - 141.37500847741444/n - (855.3945615089527*S1)/np.power(n,2) + (129.45934487552083*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -167.2209966272019/np.power(-1. + n,2) - 713.2834324613012/(-1. + n) + 2509.096338027503/np.power(n,4) + 755.5944925816235/(2. + n) + 43.07262314317838*lm13m1(n,S1,S2,S3) elif variation == 8: - fit = -823.8430919763521/np.power(n,2) - 299.005218970897/n - (484.3170791242564*S1)/np.power(n,2) + (207.4677850666592*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = 2.6264350142567814/np.power(-1. + n,2) - 832.4818430533794/(-1. + n) + 608.6363460583859/np.power(n,3) + 773.8353390059995/(2. + n) - 41.76468402930814*lm13m1(n,S1,S2,S3) elif variation == 9: - fit = 30.047719973994777/(-1. + n) - 2520.994974716468/n + 2080.1024406993206/(1. + n) + (255.17572494624633*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = 160.72672912659135/np.power(-1. + n,2) - 1380.437517169532/(-1. + n) + 1313.9641564742117/np.power(n,2) + 1244.7740838194043/(2. + n) - 107.25986487346194*lm13m1(n,S1,S2,S3) elif variation == 10: - fit = -517.28413779068/(-1. + n) - 521.8069586029795/n + 964.421319764148/(2. + n) + (56.55348517779473*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -4.4051195549716065/np.power(-1. + n,2) - 664.9007816190623/(-1. + n) + 517.4939352213107/(2. + n) + 338.0012780657685*lm11m1(n,S1) - 130.02563798413794*lm13m1(n,S1,S2,S3) elif variation == 11: - fit = -684.1216646478402/(-1. + n) + 688.0099901838175/n - 1772.6905583568107/np.power(1. + n,2) + (7.922383473211929*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = 315.51530441621395/np.power(-1. + n,2) - 681.9096023524954/(-1. + n) - 4371.86464036536/np.power(n,4) - 743.2670270884392*lm12m1(n,S1,S2) - 739.8725231366963*lm13m1(n,S1,S2,S3) elif variation == 12: - fit = -10922.769229617297/(-1. + n) + 17643.083571901912/n + 42231.91922591065/np.power(1. + n,3) - (3942.953936253496*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = 18.90357718091744/np.power(-1. + n,2) - 488.3516827637743/(-1. + n) - 994.6418190719808/np.power(n,3) - 713.9439257405169*lm12m1(n,S1,S2) - 570.3417703743911*lm13m1(n,S1,S2,S3) elif variation == 13: - fit = -249.02522869092658/(-1. + n) - 132.95657379723917/n + (204.6367663552972*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 4558.191872124068*lm11m2(n,S1) + fit = -86.56896957695098/np.power(-1. + n,2) - 275.828688059755/(-1. + n) - 824.8930651290783/np.power(n,2) - 441.1754981260873*lm12m1(n,S1,S2) - 327.27714570223736*lm13m1(n,S1,S2,S3) elif variation == 14: - fit = -1305.9723629973262/(-1. + n) + 1812.678531475261/n - (252.20454712133116*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 989.6341672183413*lm11m1(n,S1) + fit = 178.2805625979371/np.power(-1. + n,2) - 1175.763607295771/(-1. + n) - 4336.094528843359*lm11m1(n,S1) - 3747.9378120594934*lm12m1(n,S1,S2) - 1684.3286865084197*lm13m1(n,S1,S2,S3) elif variation == 15: - fit = -1037.169631665525/(-1. + n) + 8786.190136094137/np.power(n,4) - 98.09907798298099/n + (676.6623679879976*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -673.7742132225945/np.power(-1. + n,2) + 317.2132626956936/(-1. + n) + 6384.686015786331/np.power(n,4) - 2029.5697078635478/np.power(n,2) + 275.27854922027643*lm13m1(n,S1,S2,S3) elif variation == 16: - fit = -2763.8878304060045/(-1. + n) + 3857.4055136430484/np.power(n,3) + 3489.2597080989826/n - (434.43481453536947*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = 349.4631362634346/np.power(-1. + n,2) - 559.7446717031943/(-1. + n) - 5453.335146329048/np.power(n,4) + 1072.6220342502565*lm11m1(n,S1) - 506.2418943583583*lm13m1(n,S1,S2,S3) elif variation == 17: - fit = 1798.2819022378217/(-1. + n) - 3134.710315160434/np.power(n,2) - 3103.373221197692/n + (793.169486129463*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -257.1602061122679/np.power(-1. + n,2) + 67.90588148648591/(-1. + n) + 1608.7331067743435/np.power(n,3) - 2159.0746347923864/np.power(n,2) + 65.85543860914298*lm13m1(n,S1,S2,S3) + elif variation == 18: + fit = -18.600199987013553/np.power(-1. + n,2) - 326.59342404939514/(-1. + n) - 1228.6958454214596/np.power(n,3) + 1020.3475901067098*lm11m1(n,S1) - 308.20406610462027*lm13m1(n,S1,S2,S3) + elif variation == 19: + fit = -121.90417458800518/np.power(-1. + n,2) - 155.76283554846327/(-1. + n) - 934.9471223483207/np.power(n,2) + 578.5050396951302*lm11m1(n,S1) - 146.22455326916472*lm13m1(n,S1,S2,S3) else: - fit = -958.4119229639646/(-1. + n) + 516.8347138878904/np.power(n,4) + 158.3782902865003/np.power(n,3) - 232.85608277275213/np.power(n,2) + 477.6730210169136/n + 2329.329033798364/np.power(1. + n,3) - 104.27591519745945/np.power(1. + n,2) + 239.23986182949812/(1. + n) + 350.46929897971023/(2. + n) - (50.14899412782161*S1)/np.power(n,2) - (55.13659342362342*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 2.0810375523414395*lm11m1(n,S1) + 706.5582658191131*lm11m2(n,S1) + fit = -34.631097341548454/np.power(-1. + n,2) - 614.62987509215/(-1. + n) + 298.9931463234356/np.power(n,4) + 87.57428451895092/np.power(n,3) - 243.92212492942747/np.power(n,2) + 135.41924886509895/(1. + n) + 262.60049987311237/(2. + n) - 38.88382719169835*lm11m1(n,S1) - 334.9887739215079*lm12m1(n,S1,S2) - 251.2295891027122*lm13m1(n,S1,S2,S3) return common + fit @@ -284,43 +294,48 @@ def gamma_gg_nf0(n, cache, variation): """ S1 = c.get(c.S1, cache, n) S2 = c.get(c.S2, cache, n) - common = -68587.9129845144 - 49851.703887834694/np.power(-1. + n,4) + 213823.9810748423/np.power(-1. + n,3) - 103680./np.power(n,7) - 17280./np.power(n,6) - 627978.8224813186/np.power(n,5) + 40880.33011934297*S1 - 85814.12027987762*lm11(n,S1) + S3 = c.get(c.S3, cache, n) + common = -68587.9129845144 - 49851.703887834694/np.power(-1. + n,4) + 213823.9810748423/np.power(-1. + n,3) - 103680./np.power(n,7) - 17280./np.power(n,6) - 627978.8224813186/np.power(n,5) - 54482.80778086425/n + 40880.33011934297*S1 - 85814.12027987762*lm11(n,S1) if variation == 1: - fit = 657693.1275908262/n - 1.1706414373839432e6/(1. + n) - (370650.30059459625*S1)/np.power(n,2) + (287643.02359540213*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -295448.0379235009/np.power(-1. + n,2) + 224578.11757296775/(-1. + n) - 526757.6738519811/(1. + n) + 296021.5646034255/(2. + n) + 2224.0922337045213*lm13m1(n,S1,S2,S3) elif variation == 2: - fit = 2.5740603391615152e6/n - 2.941991644365525e6/(2. + n) - (2.0050489863420033e6*S1)/np.power(n,2) + (255400.3971361596*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -285107.088545888/np.power(-1. + n,2) + 195545.1200082606/(-1. + n) - 252769.2783475656/(1. + n) - 108776.38581520668*lm12m1(n,S1,S2) - 65914.13979179235*lm13m1(n,S1,S2,S3) elif variation == 3: - fit = -533059.2724548094/n + 1.5514436765207502e6/np.power(1. + n,3) + (23220.39448094448*S1)/np.power(n,2) + (287204.67597244744*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -391716.7896443467/np.power(-1. + n,2) + 170902.9255344149/(-1. + n) + 1.607519634683242e6/np.power(n,4) - 89387.05777989682/(1. + n) + 76364.75507676331*lm13m1(n,S1,S2,S3) elif variation == 4: - fit = -352275.4015418936/n - (633821.1309449758*S1)/np.power(n,2) + (233576.03813655287*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n - 4.3911671345781535e6*lm11m2(n,S1) + fit = -282383.73363518645/np.power(-1. + n,2) + 89190.37336362494/(-1. + n) + 405966.0728943653/np.power(n,3) - 71410.64232788606/(1. + n) + 22824.74956225227*lm13m1(n,S1,S2,S3) elif variation == 5: - fit = -523788.46214332484/n + (372313.29472429893*S1)/np.power(n,2) + (289489.537196911*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 562207.434039533*lm11m1(n,S1) + fit = -290139.8534816189/np.power(-1. + n,2) + 209612.58483575174/(-1. + n) - 238124.94028671857/(1. + n) + 142906.92425938678*lm11m1(n,S1) - 22034.409788754692*lm13m1(n,S1,S2,S3) elif variation == 6: - fit = 377710.2141700686/(-1. + n) - 1.1554566929419546e6/n - (914.6109012422813*S1)/np.power(n,2) + (432004.92760893324*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -275566.9972336391/np.power(-1. + n,2) + 168760.59203878703/(-1. + n) - 273096.0817605587/(2. + n) - 209128.55034080063*lm12m1(n,S1,S2) - 128775.38508377109*lm13m1(n,S1,S2,S3) elif variation == 7: - fit = 686353.5630791902/np.power(n,3) - 659297.6949952773/n + (115982.7752636412*S1)/np.power(n,2) + (354943.7019770036*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -411391.59210307786/np.power(-1. + n,2) + 159933.1271168039/(-1. + n) + 1.9360543948787057e6/np.power(n,4) - 60499.02697383511/(2. + n) + 91517.15779852161*lm13m1(n,S1,S2,S3) elif variation == 8: - fit = 485373.3737194109/np.power(n,2) - 566428.6671276395/n - (102640.3233464204*S1)/np.power(n,2) + (308984.44084716233*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -280334.89989693864/np.power(-1. + n,2) + 67957.93940012196/(-1. + n) + 469632.45484412194/np.power(n,3) - 46424.130625098995/(2. + n) + 26055.48583672462*lm13m1(n,S1,S2,S3) elif variation == 9: - fit = 378644.55156064907/(-1. + n) - 1.1599418606928566e6/n + 2895.802190713511/(1. + n) + (432362.03398212773*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -158342.46596423967/np.power(-1. + n,2) - 354852.44655132474/(-1. + n) + 1.0138734178112751e6/np.power(n,2) + 316958.89807541796/(2. + n) - 24481.5265510284*lm13m1(n,S1,S2,S3) elif variation == 10: - fit = 377882.58678340475/(-1. + n) - 1.1571587030349977e6/n + 1342.6133808775278/(2. + n) + (432085.52321715665*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -285760.5473383797/np.power(-1. + n,2) + 197265.86814370425/(-1. + n) - 244220.80103026525/(2. + n) + 260806.5899887168*lm11m1(n,S1) - 42047.920641263154*lm13m1(n,S1,S2,S3) elif variation == 11: - fit = 377650.3249167252/(-1. + n) - 1.1554744635946492e6/n - 2467.8405744727033/np.power(1. + n,2) + (432017.82171933743*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -450043.3779284024/np.power(-1. + n,2) + 157421.08366934053/(-1. + n) + 2.4869999720694227e6/np.power(n,4) + 59511.9900450049*lm12m1(n,S1,S2) + 154206.10006698*lm13m1(n,S1,S2,S3) elif variation == 12: - fit = 363396.65285306936/(-1. + n) - 1.1318705591614237e6/n + 58792.91414672283/np.power(1. + n,3) + (426517.6328449669*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -281311.4024370307/np.power(-1. + n,2) + 47312.79345234101/(-1. + n) + 565816.73490305/np.power(n,3) + 42831.109406509524*lm12m1(n,S1,S2) + 57766.0196738513*lm13m1(n,S1,S2,S3) elif variation == 13: - fit = 378256.0418217043/(-1. + n) - 1.1566173672939881e6/n + (432291.67647271376*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 6345.659593752382*lm11m2(n,S1) + fit = -221311.7815844328/np.power(-1. + n,2) - 73584.06072125914/(-1. + n) + 469252.6413087417/np.power(n,2) - 112337.25184482028*lm12m1(n,S1,S2) - 80504.89319687682*lm13m1(n,S1,S2,S3) elif variation == 14: - fit = 376784.61918064323/(-1. + n) - 1.1539087630012901e6/n + (431655.6875663606*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 1377.713295886333*lm11m1(n,S1) + fit = -371975.3618425755/np.power(-1. + n,2) + 438357.2510794566/(-1. + n) + 2.4666516141772955e6*lm11m1(n,S1) + 1.7687634818009005e6*lm12m1(n,S1,S2) + 691473.981199157*lm13m1(n,S1,S2,S3) elif variation == 15: - fit = 377158.8312978629/(-1. + n) + 12231.642128156545/np.power(n,4) - 1.1565688406394941e6/n + (432948.8040951983*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -370832.83073654736/np.power(-1. + n,2) + 77423.19888297348/(-1. + n) + 1.6257432335929913e6/np.power(n,4) + 162503.82143718746/np.power(n,2) + 72924.86692930982*lm13m1(n,S1,S2,S3) elif variation == 16: - fit = 374754.9908692327/(-1. + n) + 5370.064049746925/np.power(n,3) - 1.1515747205286513e6/n + (431401.9967878436*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -452761.5168438991/np.power(-1. + n,2) + 147639.56791297536/(-1. + n) + 2.573591277265509e6/np.power(n,4) - 85882.82474255121*lm11m1(n,S1) + 135499.7359376153*lm13m1(n,S1,S2,S3) elif variation == 17: - fit = 381106.18821765727/(-1. + n) - 4363.968245037315/np.power(n,2) - 1.1607526150905455e6/n + (433110.99878386786*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + fit = -264749.7122550716/np.power(-1. + n,2) + 13941.645196000183/(-1. + n) + 409634.3902470049/np.power(n,3) + 129527.76620894097/np.power(n,2) + 19599.111490094336*lm13m1(n,S1,S2,S3) + elif variation == 18: + fit = -279061.4660973225/np.power(-1. + n,2) + 37608.549986420694/(-1. + n) + 579858.1648363634/np.power(n,3) - 61212.957613155806*lm11m1(n,S1) + 42039.78644131242*lm13m1(n,S1,S2,S3) + elif variation == 19: + fit = -230309.24368551886/np.power(-1. + n,2) - 43011.492732260434/(-1. + n) + 441229.3934290683/np.power(n,2) + 147305.70173040565*lm11m1(n,S1) - 34403.17005106444*lm13m1(n,S1,S2,S3) else: - fit = 221373.2353924128/(-1. + n) + 719.5083604797968/np.power(n,4) + 40689.6251252316/np.power(n,3) + 28294.67091025727/np.power(n,2) - 643671.8010288504/n + 94719.79945102782/np.power(1. + n,3) - 145.16709261604137/np.power(1. + n,2) - 68690.9197172488/(1. + n) - 172979.3547638028/(2. + n) - (153032.87574472665*S1)/np.power(n,2) + (372566.99517294974*((-1. + 2.*n - 2.*np.power(n,2))/(np.power(-1. + n,2)*np.power(n,2)) + S2))/n + 33152.06749031878*lm11m1(n,S1) - 257930.6749990824*lm11m2(n,S1) + fit = -309397.2999567167/np.power(-1. + n,2) + 101684.3546415316/(-1. + n) + 538416.2374994669/np.power(n,4) + 127942.51672236343/np.power(n,3) + 116651.94948395861/np.power(n,2) - 62023.66276810779/(1. + n) - 592.6093532060254/(2. + n) + 151082.8972526367*lm11m1(n,S1) + 75834.96806587302*lm12m1(n,S1,S2) + 52333.389323249234*lm13m1(n,S1,S2,S3) return common + fit diff --git a/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggq.py b/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggq.py index 688472289..129a3c702 100644 --- a/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggq.py +++ b/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggq.py @@ -92,59 +92,51 @@ def gamma_gq_nf0(n, cache, variation): S3 = c.get(c.S3, cache, n) S4 = c.get(c.S4, cache, n) S5 = c.get(c.S5, cache, n) - S2m2 = ((-1 + 2 * n - 2 * n**2)/((-1 + n)**2 * n**2) + S2)/n - S1m2 = ((1 - 2 * n)/((-1 + n) * n) + S1)/n common = -22156.31283903764/np.power(-1. + n,4) + 95032.88047770769/np.power(-1. + n,3) - 37609.87654320987/np.power(n,7) - 35065.67901234568/np.power(n,6) - 175454.58483973087/np.power(n,5) - 375.3983146907502*lm14(n,S1,S2,S3,S4) - 13.443072702331962*lm15(n,S1,S2,S3,S4,S5) if variation == 1: - fit = 54395.612515252/(-1. + n) - 2.1646239683351885e6/np.power(n,4) + (2855.303350475541*np.power(S1,3))/n - 60918.73535555526*S2m2 + fit = -134611.31548520518/np.power(-1. + n,2) + 105578.6478973615/(-1. + n) - 271004.1457372756/(1. + n) + 135827.42962246042/(2. + n) - 1659.6381024386487*lm13(n,S1,S2,S3) elif variation == 2: - fit = -226090.67195519924/(-1. + n) + 1.1897625270895162e6/np.power(n,3) + (767.5822028088761*np.power(S1,3))/n + 166822.85829328437*S2m2 + fit = -129784.96381286802/np.power(-1. + n,2) + 92404.11351667382/(-1. + n) - 166871.00811514194/(1. + n) + 8603.419512104943*lm12(n,S1,S2) - 333.06211910306587*lm13(n,S1,S2,S3) elif variation == 3: - fit = -156969.41163838003/(-1. + n) + 308065.6508918336/np.power(n,2) + (2298.0372229048253*np.power(S1,3))/n + 79897.51027543494*S2m2 + fit = -130354.69780717866/np.power(-1. + n,2) + 93906.9798287439/(-1. + n) - 206720.3072485826/(1. + n) - 30775.363703337393*lm11(n,S1) - 1101.8494545818282*lm13(n,S1,S2,S3) elif variation == 4: - fit = 166341.6709608748/(-1. + n) - 491341.2274352182/n + (1928.2261659049982*np.power(S1,3))/n + 192393.6054838923*S2m2 + fit = -156517.8307292757/np.power(-1. + n,2) + 89433.22729993386/(-1. + n) + 384766.5696200253/np.power(n,4) - 128852.37353471664/(1. + n) - 1762.2085163661038*lm13(n,S1,S2,S3) elif variation == 5: - fit = -2910.286549470067/(-1. + n) - 231374.96742185086/(1. + n) + (2346.7938301139043*np.power(S1,3))/n + 124908.19081096651*S2m2 + fit = -129351.9314649959/np.power(-1. + n,2) + 54671.293834508826/(-1. + n) + 148449.9518256113/np.power(n,3) - 88593.14563810707/(1. + n) - 1703.1788616091594*lm13(n,S1,S2,S3) elif variation == 6: - fit = -31627.458190721398/(-1. + n) - 195967.18171506765/(2. + n) + (2692.8548253146964*np.power(S1,3))/n + 109472.35691430997*S2m2 + fit = -289524.23824347754/np.power(-1. + n,2) + 762852.3222214412/(-1. + n) - 1.1600176710948618e6/np.power(n,2) - 809182.8193866021/(1. + n) - 1836.245183321374*lm13(n,S1,S2,S3) elif variation == 7: - fit = -162008.96605774807/(-1. + n) + 720879.4649423409/np.power(1. + n,2) + (3458.480965363866*np.power(S1,3))/n + 46219.18000891417*S2m2 + fit = -122050.84394025133/np.power(-1. + n,2) + 71292.218842658/(-1. + n) - 217660.39733703827/(2. + n) + 22390.205543958295*lm12(n,S1,S2) + 1792.7460216611355*lm13(n,S1,S2,S3) elif variation == 8: - fit = -127936.1111804959/(-1. + n) + 1.317743273735378e6/np.power(1. + n,3) + (1810.811048345219*np.power(S1,3))/n + 80332.05372142064*S2m2 + fit = -116666.509065989/np.power(-1. + n,2) + 56373.894282328176/(-1. + n) - 436786.1136556859/(2. + n) - 129741.02583569557*lm11(n,S1) + 691.8555166149675*lm13(n,S1,S2,S3) elif variation == 9: - fit = -31133.856975192168/(-1. + n) + (4363.35894123817*np.power(S1,3))/n + 108577.87074947657*S2m2 + 69739.16311988933*lm11(n,S1) + fit = -176374.82189677586/np.power(-1. + n,2) + 74798.33577898303/(-1. + n) + 733535.2482241682/np.power(n,4) - 123119.72215889738/(2. + n) - 1855.182674086565*lm13(n,S1,S2,S3) elif variation == 10: - fit = -43609.29566283978/(-1. + n) + (7720.209697473076*np.power(S1,3))/n + 101242.36850860748*S2m2 - 25996.353887666173*lm12(n,S1,S2) + fit = -126797.5604335579/np.power(-1. + n,2) + 29946.67399201152/(-1. + n) + 220548.93815270695/np.power(n,3) - 65968.49558222751/(2. + n) - 1724.3256828880108*lm13(n,S1,S2,S3) elif variation == 11: - fit = -36336.05360209993/(-1. + n) + (16069.407610813529*np.power(S1,3))/n + 106190.63289422497*S2m2 + 11885.534727629803*lm13(n,S1,S2,S3) + fit = -56603.682794921304/np.power(-1. + n,2) - 225396.73137215254/(-1. + n) + 584136.1120157596/np.power(n,2) + 204224.41065290783/(2. + n) - 1570.7062041132795*lm13(n,S1,S2,S3) elif variation == 12: - fit = -56096.82600570976/(-1. + n) - (30904.014914347616*np.power(S1,2))/n + (8763.722478566568*np.power(S1,3))/n + 94447.37306501447*S2m2 + fit = -127399.17314512776/np.power(-1. + n,2) + 86110.78284306003/(-1. + n) + 128873.43260633861*lm11(n,S1) + 44630.68519659024*lm12(n,S1,S2) + 2886.2747447077363*lm13(n,S1,S2,S3) elif variation == 13: - fit = -1.744831439637831e6/np.power(n,4) + 230734.49573806854/np.power(n,3) + (2450.4248345695696*np.power(S1,3))/n - 16752.071359429487*S2m2 + fit = -247120.59412629303/np.power(-1. + n,2) + 79364.32964611659/(-1. + n) + 1.6888135534086183e6/np.power(n,4) - 29158.622788111865*lm12(n,S1,S2) - 6605.8570968113345*lm13(n,S1,S2,S3) elif variation == 14: - fit = -1.607549555980178e6/np.power(n,4) + 79281.89558453669/np.power(n,2) + (2711.8887412487193*np.power(S1,3))/n - 24679.125874904974*S2m2 + fit = -128861.83507443611/np.power(-1. + n,2) + 11966.126835094941/(-1. + n) + 316462.3091625236/np.power(n,3) - 9737.159060072763*lm12(n,S1,S2) - 3253.8465506459015*lm13(n,S1,S2,S3) elif variation == 15: - fit = -3.2164345301161744e6/np.power(n,4) + 238747.19120481954/n + (3305.7786240482187*np.power(S1,3))/n - 184005.5159797561*S2m2 + fit = -88285.0983393474/np.power(-1. + n,2) - 81776.66054398555/(-1. + n) + 301369.70052571065/np.power(n,2) + 10838.566464150015*lm12(n,S1,S2) + 57.46109548925452*lm13(n,S1,S2,S3) elif variation == 16: - fit = -109930.67245290388/np.power(n,4) - 219624.56359674424/(1. + n) + (2372.618543477443*np.power(S1,3))/n + 115470.94939990941*S2m2 + fit = -199811.41276401555/np.power(-1. + n,2) + 82030.26173438856/(-1. + n) + 1.021461077715438e6/np.power(n,4) + 50925.69521801989*lm11(n,S1) - 2854.941152739061*lm13(n,S1,S2,S3) elif variation == 17: - fit = -795851.0838465183/np.power(n,4) - 123917.39558697924/(2. + n) + (2752.5810580044063*np.power(S1,3))/n + 46825.94005648564*S2m2 + fit = -128599.87560093393/np.power(-1. + n,2) + 25245.26855710262/(-1. + n) + 259784.61882981652/np.power(n,3) + 23080.94295557716*lm11(n,S1) - 2154.164587558643*lm13(n,S1,S2,S3) elif variation == 18: - fit = -1.6205225107818602e6/np.power(n,4) + 181200.78744997882/np.power(1. + n,2) + (3006.918515153242*np.power(S1,3))/n - 33988.47090234153*S2m2 + fit = -75739.554722418/np.power(-1. + n,2) - 135625.28803179998/(-1. + n) + 398031.7522689792/np.power(n,2) - 41335.178649992326*lm11(n,S1) - 849.8594840371891*lm13(n,S1,S2,S3) elif variation == 19: - fit = -1.5188447027408783e6/np.power(n,4) + 393126.6104427561/np.power(1. + n,3) + (2543.6965856722713*np.power(S1,3))/n - 18778.930858748437*S2m2 + fit = -69571.53835633998/np.power(-1. + n,2) - 21824.684729051125/(-1. + n) - 846704.7809898313/np.power(n,4) + 475124.08069442277/np.power(n,3) - 1573.2801259880794*lm13(n,S1,S2,S3) elif variation == 20: - fit = -787951.7251390232/np.power(n,4) + (3814.406780618335*np.power(S1,3))/n + 46878.866608639015*S2m2 + 44353.186297165696*lm11(n,S1) + fit = -131326.8497758187/np.power(-1. + n,2) - 38110.15884910321/(-1. + n) + 457640.10637686535/np.power(n,4) + 219703.5737179606/np.power(n,2) - 1748.1862124636395*lm13(n,S1,S2,S3) elif variation == 21: - fit = -963193.8684382912/np.power(n,4) + (5555.469755339871*np.power(S1,3))/n + 29085.456626461673*S2m2 - 14428.742592292887*lm12(n,S1,S2) - elif variation == 22: - fit = -866884.6931575488/np.power(n,4) + (10777.447027986002*np.power(S1,3))/n + 39266.975234472426*S2m2 + 7125.637269182096*lm13(n,S1,S2,S3) - elif variation == 23: - fit = -1.0989759638298883e6/np.power(n,4) - (15214.098294404646*np.power(S1,2))/n + (5764.027981513135*np.power(S1,3))/n + 15568.25999702346*S2m2 - elif variation == 24: - fit = -1.30410210442889e6/np.power(n,4) + (3218.5602518731034*np.power(S1,3))/n - 20261.445878695344*S1m2 + 8032.736655052195*S2m2 + fit = -109659.49203855239/np.power(-1. + n,2) - 32396.266625595177/(-1. + n) + 166701.1822848159/np.power(n,3) + 142618.77212791165/np.power(n,2) - 1686.818976852953*lm13(n,S1,S2,S3) else: - fit = -27249.23559757206/(-1. + n) - 741654.0341202153/np.power(n,4) + 59187.37595114936/np.power(n,3) + 16139.481103182095/np.power(n,2) - 10524.751509599944/n + 71286.24517408892/np.power(1. + n,3) + 37586.67718301332/np.power(1. + n,2) - 18791.647125774794/(1. + n) - 13328.524054251953/(2. + n) - (1921.5880503646777*np.power(S1,2))/n + (4306.191959951149*np.power(S1,3))/n - 844.2269116123059*S1m2 + 48854.5972905356*S2m2 + 4753.847892377293*lm11(n,S1) - 1684.379019998294*lm12(n,S1,S2) + 792.1321665338291*lm13(n,S1,S2,S3) + fit = -136905.419981799/np.power(-1. + n,2) + 56230.69937898662/(-1. + n) + 163786.27496929924/np.power(n,4) + 75574.81337856653/np.power(n,3) + 23135.3447410219/np.power(n,2) - 79582.08569811552/(1. + n) - 23975.375640880044/(2. + n) + 48.97631385287552*lm11(n,S1) + 2265.099755648517*lm12(n,S1,S2) - 1373.5720765300828*lm13(n,S1,S2,S3) return common + fit @@ -172,60 +164,51 @@ def gamma_gq_nf1(n, cache, variation): S3 = c.get(c.S3, cache, n) S4 = c.get(c.S4, cache, n) S5 = c.get(c.S5, cache, n) - S3m2 = (-(((-1 + 2 * n) * (1 - n + n**2))/((-1 + n)**3 * n**3)) + S3)/n - S2m2 = ((-1 + 2 * n - 2 * n**2)/((-1 + n)**2 * n**2) + S2)/n - S1m2 = ((1 - 2 * n)/((-1 + n) * n) + S1)/n - common = 5309.62962962963/np.power(n,7) + 221.23456790123456/np.power(n,6) + 9092.91243376357/np.power(n,5) + 34.49474165523548*lm14(n,S1,S2,S3,S4) + 0.5486968449931413*lm15(n,S1,S2,S3,S4,S5) + common = 885.6738165500071/np.power(-1. + n,3) + 5309.62962962963/np.power(n,7) + 221.23456790123456/np.power(n,6) + 9092.91243376357/np.power(n,5) + 34.49474165523548*lm14(n,S1,S2,S3,S4) + 0.5486968449931413*lm15(n,S1,S2,S3,S4,S5) if variation == 1: - fit = 61414.641491730144/np.power(n,4) - (275.8821081210985*np.power(S1,3))/n - 1723.0775384248207*S2m2 + 5359.279437479722*S3m2 + fit = -4488.023094730909/np.power(-1. + n,2) + 11415.451852682689/(-1. + n) - 22278.11557093013/(1. + n) + 16857.05748831136/(2. + n) + 218.39366882799368*lm13(n,S1,S2,S3) elif variation == 2: - fit = 30628.764498540346/np.power(n,3) - (270.06312683778754*np.power(S1,3))/n + 1773.2287929788677*S2m2 + 579.1073675469371*S3m2 + fit = -3889.0418151355752/np.power(-1. + n,2) + 9780.407413909863/(-1. + n) - 9354.523537908572/(1. + n) + 1067.7396878871195*lm12(n,S1,S2) + 383.03027923765*lm13(n,S1,S2,S3) elif variation == 3: - fit = 14964.683461563509/np.power(n,2) - (218.2558990293935*np.power(S1,3))/n + 1752.1522405673672*S2m2 - 1437.7646853596411*S3m2 + fit = -3959.7494676460906/np.power(-1. + n,2) + 9966.92278779446/(-1. + n) - 14300.077821225603/(1. + n) - 3819.420544236109*lm11(n,S1) + 287.618827026041*lm13(n,S1,S2,S3) elif variation == 4: - fit = 7580.473213968261/n - (247.331894047618*np.power(S1,3))/n - 6197.2716578690515*S2m2 + 4215.915142027546*S3m2 + fit = -7206.762511830159/np.power(-1. + n,2) + 9411.701329387806/(-1. + n) + 47752.005627238184/np.power(n,4) - 4636.1664981662325/(1. + n) + 205.6640208549657*lm13(n,S1,S2,S3) elif variation == 5: - fit = 11506.23542429956/(1. + n) - (274.1023835976748*np.power(S1,3))/n - 10030.195812335383*S2m2 + 7245.875500079163*S3m2 + fit = -3835.299716042018/np.power(-1. + n,2) + 5097.521841045809/(-1. + n) + 18423.593665995402/np.power(n,3) + 360.2625808084624/(1. + n) + 212.9899806152177*lm13(n,S1,S2,S3) elif variation == 6: - fit = 15648.586212999671/(2. + n) - (319.57482516808324*np.power(S1,3))/n - 13077.961868048167*S2m2 + 9906.744899797963*S3m2 + fit = -23713.713015219728/np.power(-1. + n,2) + 92987.34159859698/(-1. + n) - 143965.65276583107/np.power(n,2) - 89069.54986300123/(1. + n) + 196.47559437456405*lm13(n,S1,S2,S3) elif variation == 7: - fit = 32890.76649300865/np.power(1. + n,2) - (166.9129330699367*np.power(S1,3))/n - 70.8880877568522*S2m2 - 1177.148738100283*S3m2 + fit = -3455.4793454735536/np.power(-1. + n,2) + 8596.908147688335/(-1. + n) - 12201.695987567426/(2. + n) + 1840.6050040604714*lm12(n,S1,S2) + 502.1997054577737*lm13(n,S1,S2,S3) elif variation == 8: - fit = 102016.12308266855/np.power(1. + n,3) - (240.30275153122795*np.power(S1,3))/n + 4585.802226607708*S2m2 - 3985.368690549865*S3m2 + fit = -3012.8557307127066/np.power(-1. + n,2) + 7370.535179202942/(-1. + n) - 30215.103197366938/(2. + n) - 10665.466242204988*lm11(n,S1) + 411.70010872417294*lm13(n,S1,S2,S3) elif variation == 9: - fit = (-450.823181671801*np.power(S1,3))/n - 12903.050719269673*S2m2 + 9834.061598926022*S3m2 - 5511.504206466589*lm11(n,S1) + fit = -7921.226007375836/np.power(-1. + n,2) + 8885.131333721463/(-1. + n) + 60300.859940087874/np.power(n,4) - 4429.9031168628235/(2. + n) + 202.31876873895882*lm13(n,S1,S2,S3) elif variation == 10: - fit = (-882.1406501674703*np.power(S1,3))/n - 15619.249097143265*S2m2 + 12292.391588412715*S3m2 + 2777.986504535076*lm12(n,S1,S2) + fit = -3845.68702415166/np.power(-1. + n,2) + 5198.064104104413/(-1. + n) + 18130.404314827305/np.power(n,3) + 268.2598106136584/(2. + n) + 213.07597381881035*lm13(n,S1,S2,S3) elif variation == 11: - fit = (-1513.783497714283*np.power(S1,3))/n - 13902.310762445584*S2m2 + 10684.561917950059*S3m2 - 1053.755322341623*lm13(n,S1,S2,S3) + fit = 1924.6576108019278/np.power(-1. + n,2) - 15792.64760438993/(-1. + n) + 48019.38279297407/np.power(n,2) + 22479.68678039739/(2. + n) + 225.7043876490835*lm13(n,S1,S2,S3) elif variation == 12: - fit = (5100.183003924889*np.power(S1,2))/n - (1401.3877591921307*np.power(S1,3))/n - 21387.15682013914*S2m2 + 17430.91515626977*S3m2 + fit = -3755.2981815948488/np.power(-1. + n,2) + 9427.613297165519/(-1. + n) + 7224.439837356762*lm11(n,S1) + 3087.370950732838*lm12(n,S1,S2) + 563.5011879300971*lm13(n,S1,S2,S3) elif variation == 13: - fit = 31147.78863209503/np.power(n,4) + 15094.71171421834/np.power(n,3) - (273.0143514100448*np.power(S1,3))/n + 3003.4769582959475*S3m2 + fit = -10466.690790833369/np.power(-1. + n,2) + 9049.417851827156/(-1. + n) + 94672.20408711508/np.power(n,4) - 1049.1403952794576*lm12(n,S1,S2) + 31.387360972561613*lm13(n,S1,S2,S3) elif variation == 14: - fit = 30964.22640709071/np.power(n,4) + 7419.742457931761/np.power(n,2) - (247.31006171693753*np.power(S1,3))/n + 1989.190320913944*S3m2 + fit = -3837.292685015662/np.power(-1. + n,2) + 5271.181705657407/(-1. + n) + 17740.37415701935/np.power(n,3) + 39.59599839782818*lm12(n,S1,S2) + 219.29574546428225*lm13(n,S1,S2,S3) elif variation == 15: - fit = 85066.31740469787/np.power(n,4) - 2919.3510109124736/n - (286.87721277546535*np.power(S1,3))/n + 5799.605736056626*S3m2 + fit = -1562.6253047002033/np.power(-1. + n,2) + 16.11001314684768/(-1. + n) + 16894.306500710383/np.power(n,2) + 1193.038474115512*lm12(n,S1,S2) + 404.9223900617979*lm13(n,S1,S2,S3) elif variation == 16: - fit = 74153.37781346358/np.power(n,4) - 2386.6442197774195/(1. + n) - (276.25126180951514*np.power(S1,3))/n + 4967.958260585389*S3m2 + fit = -8764.48511413068/np.power(-1. + n,2) + 9145.339290408388/(-1. + n) + 70660.56110839365/np.power(n,4) + 1832.3294758866361*lm11(n,S1) + 166.3470078948553*lm13(n,S1,S2,S3) elif variation == 17: - fit = 70734.17185530512/np.power(n,4) - 2374.6369076942033/(2. + n) - (269.2518389654746*np.power(S1,3))/n + 4669.21202970862*S3m2 + fit = -3838.357938938717/np.power(-1. + n,2) + 5217.182292574578/(-1. + n) + 17970.85305971273/np.power(n,3) - 93.85827782443143*lm11(n,S1) + 214.8239067092436*lm13(n,S1,S2,S3) elif variation == 18: - fit = -2635.0286245103766/np.power(n,4) + 34301.96273361259/np.power(1. + n,2) - (162.23755129655925*np.power(S1,3))/n - 1457.5977471044935*S3m2 + fit = -181.6939552271119/np.power(-1. + n,2) - 5911.194541729347/(-1. + n) + 27534.232647597233/np.power(n,2) - 4549.9059886744935*lm11(n,S1) + 305.05047772799065*lm13(n,S1,S2,S3) elif variation == 19: - fit = 44641.11065487181/np.power(n,4) + 27862.583657909938/np.power(1. + n,3) - (266.1646951326012*np.power(S1,3))/n + 2807.074625599327*S3m2 + fit = -4078.395708944439/np.power(-1. + n,2) + 5408.59148938392/(-1. + n) + 3443.111172846758/np.power(n,4) + 17095.178652601353/np.power(n,3) + 212.46174952689813*lm13(n,S1,S2,S3) elif variation == 20: - fit = 70879.97629826797/np.power(n,4) - (248.919875787699*np.power(S1,3))/n + 4669.617977026223*S3m2 + 849.4429232949681*lm11(n,S1) + fit = -6300.379658737184/np.power(-1. + n,2) + 4822.632787569217/(-1. + n) + 50374.02833779294/np.power(n,4) + 7905.033644756689/np.power(n,2) + 206.16854967191063*lm13(n,S1,S2,S3) elif variation == 21: - fit = 69029.84607075108/np.power(n,4) - (200.7081314711859*np.power(S1,3))/n + 4499.597346756129*S3m2 - 344.4607838774497*lm12(n,S1,S2) - elif variation == 22: - fit = 70103.38136051684/np.power(n,4) - (100.74792356621695*np.power(S1,3))/n + 4605.876127181845*S3m2 + 149.08180946409476*lm13(n,S1,S2,S3) - elif variation == 23: - fit = 66796.13877765737/np.power(n,4) - (446.9068014839647*np.power(S1,2))/n - (177.25895475872284*np.power(S1,3))/n + 4301.494627873232*S3m2 - elif variation == 24: - fit = 60675.73486178171/np.power(n,4) - (248.51519590078777*np.power(S1,3))/n - 682.8975276953039*S1m2 + 4145.5785035058925*S3m2 + fit = -3915.3786995698256/np.power(-1. + n,2) + 5451.580654627375/(-1. + n) + 18349.375335216806/np.power(n,3) - 579.9569091789359/np.power(n,2) + 212.92345341087133*lm13(n,S1,S2,S3) else: - fit = 30540.48679182162/np.power(n,4) + 1905.1448421982786/np.power(n,3) + 932.6844133123028/np.power(n,2) + 194.21342512732446/n + 5411.6127808574365/np.power(1. + n,3) + 2799.6970511092186/np.power(1. + n,2) + 379.9829668550892/(1. + n) + 553.0812210543945/(2. + n) + (193.88650843503848*np.power(S1,2))/n - (375.74241936415484*np.power(S1,3))/n - 28.454063653970994*S1m2 - 3616.665795969917*S2m2 + 4789.568969203283*S3m2 - 194.2525534654842*lm11(n,S1) + 101.3969050274011*lm12(n,S1,S2) - 37.694729703230344*lm13(n,S1,S2,S3) + fit = -5243.037055009921/np.power(-1. + n,2) + 9562.656801160758/(-1. + n) + 15581.084298736878/np.power(n,4) + 5129.037104065377/np.power(n,3) - 2104.412099474839/np.power(n,2) - 6632.29384335349/(1. + n) - 344.8427724987991/(2. + n) - 479.6134161760297*lm11(n,S1) + 294.2480819006815*lm12(n,S1,S2) + 266.47872117598763*lm13(n,S1,S2,S3) return common + fit diff --git a/tests/ekore/anomalous_dimensions/unpolarized/space_like/test_as4.py b/tests/ekore/anomalous_dimensions/unpolarized/space_like/test_as4.py index ad72659cb..13562cd61 100644 --- a/tests/ekore/anomalous_dimensions/unpolarized/space_like/test_as4.py +++ b/tests/ekore/anomalous_dimensions/unpolarized/space_like/test_as4.py @@ -17,8 +17,8 @@ NF = 5 n3lo_vars_dict = { - "gg": 17, - "gq": 24, + "gg": 19, + "gq": 21, "qg": 15, "qq": 6, } @@ -120,7 +120,7 @@ def test_momentum_conservation(): np.testing.assert_allclose( gnsp.gamma_nsp_nf1(N, sx_cache) + g_ps[:, 0] + g_gq[:, 1], 0, - atol=4e-11, + atol=7e-11, ) np.testing.assert_allclose( g_gg[:, 1] + g_qg[:, 0], From 7586679881ce2337d7023f89f440b5d80f6b5dce Mon Sep 17 00:00:00 2001 From: giacomomagni Date: Mon, 16 Oct 2023 11:20:16 +0200 Subject: [PATCH 2/2] update gg and gq numbers with 5th analytic moment --- .../unpolarized/space_like/as4/ggg.py | 120 +++++++++--------- .../unpolarized/space_like/as4/ggq.py | 88 ++++++------- 2 files changed, 104 insertions(+), 104 deletions(-) diff --git a/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggg.py b/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggg.py index 88eee5b88..6e8c5e65a 100644 --- a/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggg.py +++ b/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggg.py @@ -164,45 +164,45 @@ def gamma_gg_nf1(n, cache, variation): S3 = c.get(c.S3, cache, n) common = 18143.980574437464 + 1992.766087237516/np.power(-1. + n,3) + 20005.925925925927/np.power(n,7) - 19449.679012345678/np.power(n,6) + 80274.123066115/np.power(n,5) + 4341.13370266389/n - 11714.245609287387*S1 + 13880.514502193577*lm11(n,S1) if variation == 1: - fit = -10270.11416182055/np.power(-1. + n,2) + 18731.17968740991/(-1. + n) + 297.3210929571657/(1. + n) - 23244.924485271466/(2. + n) - 4050.833138545348*lm13m1(n,S1,S2,S3) + fit = -10180.036287065168/np.power(-1. + n,2) + 18513.270411873862/(-1. + n) + 1054.0462034864902/(1. + n) - 23202.37636673074/(2. + n) - 3602.060464842473*lm13m1(n,S1,S2,S3) elif variation == 2: - fit = -11082.13131236475/np.power(-1. + n,2) + 21010.979258355084/(-1. + n) - 21217.46135836648/(1. + n) + 8541.603641080774*lm12m1(n,S1,S2) + 1299.6826595628106*lm13m1(n,S1,S2,S3) + fit = -10990.56710015112/np.power(-1. + n,2) + 20788.896977978722/(-1. + n) - 20421.35502658661/(1. + n) + 8525.968866079374*lm12m1(n,S1,S2) + 1738.6616090235632*lm13m1(n,S1,S2,S3) elif variation == 3: - fit = -2710.665352609663/np.power(-1. + n,2) + 22945.993521464054/(-1. + n) - 126229.56225118619/np.power(n,4) - 34046.95702168874/(1. + n) - 9872.686392323958*lm13m1(n,S1,S2,S3) + fit = -2634.4244909317163/np.power(-1. + n,2) + 22720.3693403071/(-1. + n) - 125998.50835459496/np.power(n,4) - 33227.36724506296/(1. + n) - 9413.257245961297*lm13m1(n,S1,S2,S3) elif variation == 4: - fit = -11295.981203099282/np.power(-1. + n,2) + 29362.42506506866/(-1. + n) - 31878.254277368906/np.power(n,3) - 35458.54478982031/(1. + n) - 5668.488002948361*lm13m1(n,S1,S2,S3) + fit = -11204.025554445116/np.power(-1. + n,2) + 29125.056079570935/(-1. + n) - 31819.903485877207/np.power(n,3) - 34636.371205966374/(1. + n) - 5216.754331416846*lm13m1(n,S1,S2,S3) elif variation == 5: - fit = -10686.93631688797/np.power(-1. + n,2) + 19906.339608012637/(-1. + n) - 22367.39965022059/(1. + n) - 11221.684701529948*lm11m1(n,S1) - 2145.948106277924*lm13m1(n,S1,S2,S3) + fit = -10596.095479944803/np.power(-1. + n,2) + 19686.27928898392/(-1. + n) - 21569.188441280912/(1. + n) - 11201.144235965185*lm11m1(n,S1) - 1700.6621840281703*lm13m1(n,S1,S2,S3) elif variation == 6: - fit = -10281.335740623817/np.power(-1. + n,2) + 18762.685118697587/(-1. + n) - 22923.693890952152/(2. + n) + 118.0397215654495*lm12m1(n,S1,S2) - 3976.892293061728*lm13m1(n,S1,S2,S3) + fit = -10219.818404157402/np.power(-1. + n,2) + 18624.961714720896/(-1. + n) - 22063.56752869039/(2. + n) + 418.4678562263162*lm12m1(n,S1,S2) - 3339.9294915689893*lm13m1(n,S1,S2,S3) elif variation == 7: - fit = -10204.671424181955/np.power(-1. + n,2) + 18767.66765933924/(-1. + n) - 1092.779160652895/np.power(n,4) - 23043.691361939706/(2. + n) - 4101.2333760090105*lm13m1(n,S1,S2,S3) + fit = -9948.03233312767/np.power(-1. + n,2) + 18642.625540707515/(-1. + n) - 3874.0599063901927/np.power(n,4) - 22488.97588930172/(2. + n) - 3780.736583727932*lm13m1(n,S1,S2,S3) elif variation == 8: - fit = -10278.644563822769/np.power(-1. + n,2) + 18819.581783601687/(-1. + n) - 265.07755215895946/np.power(n,3) - 23051.635742762955/(2. + n) - 4064.284439480962*lm13m1(n,S1,S2,S3) + fit = -10210.277793833904/np.power(-1. + n,2) + 18826.668606883333/(-1. + n) - 939.7381958313449/np.power(n,3) - 22517.139866390396/(2. + n) - 3649.747268844151*lm13m1(n,S1,S2,S3) elif variation == 9: - fit = -10347.501508088137/np.power(-1. + n,2) + 19058.23126571671/(-1. + n) - 572.2668461573236/np.power(n,2) - 23256.742273946194/(2. + n) - 4035.759520905052*lm13m1(n,S1,S2,S3) + fit = -10454.38560322065/np.power(-1. + n,2) + 19672.71547858848/(-1. + n) - 2028.768596859424/np.power(n,2) - 23244.272133899653/(2. + n) - 3548.6223138853798*lm13m1(n,S1,S2,S3) elif variation == 10: - fit = -10275.582132070176/np.power(-1. + n,2) + 18746.595709341593/(-1. + n) - 22939.992144309395/(2. + n) - 147.20867721931182*lm11m1(n,S1) - 4025.8444124078146*lm13m1(n,S1,S2,S3) + fit = -10199.42103109479/np.power(-1. + n,2) + 18567.922435470675/(-1. + n) - 22121.34719008958/(2. + n) - 521.8760156034384*lm11m1(n,S1) - 3513.4718226546247*lm13m1(n,S1,S2,S3) elif variation == 11: - fit = -24926.888750623133/np.power(-1. + n,2) + 17810.84642127126/(-1. + n) + 208758.85768476047/np.power(n,4) + 22667.73532614404*lm12m1(n,S1,S2) + 19776.5826765651*lm13m1(n,S1,S2,S3) + fit = -24315.85150285657/np.power(-1. + n,2) + 17708.837224620995/(-1. + n) + 200925.95790419917/np.power(n,4) + 22122.069993382116*lm12m1(n,S1,S2) + 19522.28466669723*lm13m1(n,S1,S2,S3) elif variation == 12: - fit = -10763.5212982461/np.power(-1. + n,2) + 8568.352997277027/(-1. + n) + 47494.674935205614/np.power(n,3) + 21267.541668576003*lm12m1(n,S1,S2) + 11681.399225017101*lm13m1(n,S1,S2,S3) + fit = -10683.911741932305/np.power(-1. + n,2) + 8813.133994420503/(-1. + n) + 45712.61388637733/np.power(n,3) + 20774.41339562901*lm12m1(n,S1,S2) + 11730.84286896203*lm13m1(n,S1,S2,S3) elif variation == 13: - fit = -5727.151193148642/np.power(-1. + n,2) - 1579.7328323989361/(-1. + n) + 39389.08181155469/np.power(n,2) + 8242.704431969565*lm12m1(n,S1,S2) + 74.93434922328093*lm13m1(n,S1,S2,S3) + fit = -5836.51269525416/np.power(-1. + n,2) - 954.1826542477216/(-1. + n) + 37911.15300076812/np.power(n,2) + 8238.284738213413*lm12m1(n,S1,S2) + 559.8674243103725*lm13m1(n,S1,S2,S3) elif variation == 14: - fit = -18373.856968226213/np.power(-1. + n,2) + 41392.63735393215/(-1. + n) + 207050.815868518*lm11m1(n,S1) + 166142.36054620336*lm12m1(n,S1,S2) + 64874.865907564*lm13m1(n,S1,S2,S3) + fit = -18008.69786800099/np.power(-1. + n,2) + 40405.809150940426/(-1. + n) + 199282.00400507107*lm11m1(n,S1) + 160213.3434703554*lm12m1(n,S1,S2) + 62928.42253561968*lm13m1(n,S1,S2,S3) elif variation == 15: - fit = 5243.900655452294/np.power(-1. + n,2) - 12659.834824913609/(-1. + n) - 119288.31030415706/np.power(n,4) + 61896.66336205812/np.power(n,2) - 11182.917725840534*lm13m1(n,S1,S2,S3) + fit = 5128.6565343884595/np.power(-1. + n,2) - 12028.343555706011/(-1. + n) - 119224.34855414196/np.power(n,4) + 60406.6661071792/np.power(n,2) - 10691.948251059068*lm13m1(n,S1,S2,S3) elif variation == 16: - fit = -25962.210430671832/np.power(-1. + n,2) + 14085.129803728569/(-1. + n) + 241740.93047797284/np.power(n,4) - 32712.217132272293*lm11m1(n,S1) + 12651.448553539236*lm13m1(n,S1,S2,S3) + fit = -25326.250571944573/np.power(-1. + n,2) + 14072.807307962283/(-1. + n) + 233114.0751714257/np.power(n,4) - 31924.757662241216*lm11m1(n,S1) + 12568.669163696943*lm13m1(n,S1,S2,S3) elif variation == 17: - fit = -2539.909047069818/np.power(-1. + n,2) - 8001.899230702169/(-1. + n) - 30056.772339779138/np.power(n,3) + 64316.26925516245/np.power(n,2) - 7270.160083308018*lm13m1(n,S1,S2,S3) + fit = -2650.979531261116/np.power(-1. + n,2) - 7372.905521491985/(-1. + n) - 30040.6560602065/np.power(n,3) + 62824.974620623434/np.power(n,2) - 6781.2886081167435*lm13m1(n,S1,S2,S3) elif variation == 18: - fit = -9646.328315869272/np.power(-1. + n,2) + 3749.766574153606/(-1. + n) + 54466.866417785626/np.power(n,3) - 30394.942945299434*lm11m1(n,S1) + 3872.6283293477754*lm13m1(n,S1,S2,S3) + fit = -9592.62299684503/np.power(-1. + n,2) + 4106.275632673743/(-1. + n) + 52523.14189143729/np.power(n,3) - 29690.17856987198*lm11m1(n,S1) + 4103.133130507111*lm13m1(n,S1,S2,S3) elif variation == 19: - fit = -5066.965729118176/np.power(-1. + n,2) - 3822.9837355590003/(-1. + n) + 41445.27729170122/np.power(n,2) - 10808.501548399454*lm11m1(n,S1) - 3307.7625874988926*lm13m1(n,S1,S2,S3) + fit = -5176.681219116345/np.power(-1. + n,2) - 3196.230738347968/(-1. + n) + 39966.24595996931/np.power(n,2) - 10802.706088036985*lm11m1(n,S1) - 2821.015728520721*lm13m1(n,S1,S2,S3) else: - fit = -10273.4997259521/np.power(-1. + n,2) + 13981.787431778737/(-1. + n) + 10731.007181407218/np.power(n,4) + 2092.707220193907/np.power(n,3) + 10867.106572332586/np.power(n,2) - 5936.475880375734/(1. + n) - 7287.404205220098/(2. + n) + 6408.750571778819*lm11m1(n,S1) + 11946.315017659957*lm12m1(n,S1,S2) + 2659.4069274848257*lm13m1(n,S1,S2,S3) + fit = -10163.154508989206/np.power(-1. + n,2) + 14038.103511363668/(-1. + n) + 9733.848224236723/np.power(n,4) + 1865.024107152609/np.power(n,3) + 10477.909004825295/np.power(n,2) - 5726.328195547913/(1. + n) - 7138.825209215919/(2. + n) + 6060.070601755382*lm11m1(n,S1) + 11594.344648415032*lm12m1(n,S1,S2) + 2899.599321273186*lm13m1(n,S1,S2,S3) return common + fit @@ -231,45 +231,45 @@ def gamma_gg_nf2(n, cache, variation): S3 = c.get(c.S3, cache, n) common = -423.811346198137 - 568.8888888888889/np.power(n,7) + 1725.6296296296296/np.power(n,6) - 2196.543209876543/np.power(n,5) + 21.333333333333336/n + 440.0487580115612*S1 - 135.11111111111114*lm11(n,S1) if variation == 1: - fit = -16.959956452231857/np.power(-1. + n,2) - 629.5045317989062/(-1. + n) - 682.6697400582308/(1. + n) + 1217.639625778457/(2. + n) - 72.64979891934051*lm13m1(n,S1,S2,S3) + fit = -28.872079560670887/np.power(-1. + n,2) - 600.687665018851/(-1. + n) - 782.7409584384554/(1. + n) + 1212.0129563274725/(2. + n) - 131.99661800641996*lm13m1(n,S1,S2,S3) elif variation == 2: - fit = 25.57596402110471/np.power(-1. + n,2) - 748.9273459351353/(-1. + n) + 444.33979999567083/(1. + n) - 447.4350978280687*lm12m1(n,S1,S2) - 352.92603979329243*lm13m1(n,S1,S2,S3) + fit = 13.46728393535039/np.power(-1. + n,2) - 719.5586305737447/(-1. + n) + 339.0607105706994/(1. + n) - 445.3675161372763*lm12m1(n,S1,S2) - 410.9777123288363*lm13m1(n,S1,S2,S3) elif variation == 3: - fit = -412.9468061824264/np.power(-1. + n,2) - 850.2892602188854/(-1. + n) + 6612.287213025851/np.power(n,4) + 1116.3876833223574/(1. + n) + 232.31652703107594*lm13m1(n,S1,S2,S3) + fit = -423.0290881266415/np.power(-1. + n,2) - 820.4521550528278/(-1. + n) + 6581.732068732447/np.power(n,4) + 1008.0030845050551/(1. + n) + 171.5604693866337*lm13m1(n,S1,S2,S3) elif variation == 4: - fit = 36.77806971484529/np.power(-1. + n,2) - 1186.401399819004/(-1. + n) + 1669.8796175207788/np.power(n,3) + 1190.3309307108536/(1. + n) + 12.087867790598803*lm13m1(n,S1,S2,S3) + fit = 24.617625096660852/np.power(-1. + n,2) - 1155.0111323969943/(-1. + n) + 1662.163163134959/np.power(n,3) + 1081.6046427740755/(1. + n) - 47.65052104384607*lm13m1(n,S1,S2,S3) elif variation == 5: - fit = 4.874451882150377/np.power(-1. + n,2) - 691.0629716579465/(-1. + n) + 504.5770544662291/(1. + n) + 587.8258700832249*lm11m1(n,S1) - 172.43345273623754*lm13m1(n,S1,S2,S3) + fit = -7.138567251448382/np.power(-1. + n,2) - 661.9616455143912/(-1. + n) + 399.01961082863164/(1. + n) + 585.1095476215276*lm11m1(n,S1) - 231.31917510401414*lm13m1(n,S1,S2,S3) elif variation == 6: - fit = 8.805562596792123/np.power(-1. + n,2) - 701.843175427027/(-1. + n) + 480.0720211823408/(2. + n) - 271.02734366604454*lm12m1(n,S1,S2) - 242.4230809561374*lm13m1(n,S1,S2,S3) + fit = 0.6703563957663715/np.power(-1. + n,2) - 683.6302885496931/(-1. + n) + 366.326763050706/(2. + n) - 310.75671045013235*lm12m1(n,S1,S2) - 326.65663250723026*lm13m1(n,S1,S2,S3) elif variation == 7: - fit = -167.2209966272019/np.power(-1. + n,2) - 713.2834324613012/(-1. + n) + 2509.096338027503/np.power(n,4) + 755.5944925816235/(2. + n) + 43.07262314317838*lm13m1(n,S1,S2,S3) + fit = -201.15959093110155/np.power(-1. + n,2) - 696.7475504266947/(-1. + n) + 2876.8998495153933/np.power(n,4) + 682.2375331931647/(2. + n) + 0.6893269576792295*lm13m1(n,S1,S2,S3) elif variation == 8: - fit = 2.6264350142567814/np.power(-1. + n,2) - 832.4818430533794/(-1. + n) + 608.6363460583859/np.power(n,3) + 773.8353390059995/(2. + n) - 41.76468402930814*lm13m1(n,S1,S2,S3) + fit = -6.414557380878645/np.power(-1. + n,2) - 833.4190222620106/(-1. + n) + 697.8551544024533/np.power(n,3) + 703.1522695219711/(2. + n) - 96.58411469486595*lm13m1(n,S1,S2,S3) elif variation == 9: - fit = 160.72672912659135/np.power(-1. + n,2) - 1380.437517169532/(-1. + n) + 1313.9641564742117/np.power(n,2) + 1244.7740838194043/(2. + n) - 107.25986487346194*lm13m1(n,S1,S2,S3) + fit = 174.86134878770187/np.power(-1. + n,2) - 1461.6984440261558/(-1. + n) + 1506.5755852971279/np.power(n,2) + 1243.1250013579786/(2. + n) - 171.6801056536221*lm13m1(n,S1,S2,S3) elif variation == 10: - fit = -4.4051195549716065/np.power(-1. + n,2) - 664.9007816190623/(-1. + n) + 517.4939352213107/(2. + n) + 338.0012780657685*lm11m1(n,S1) - 130.02563798413794*lm13m1(n,S1,S2,S3) + fit = -14.476853744515829/np.power(-1. + n,2) - 641.2725816829176/(-1. + n) + 409.23428207929186/(2. + n) + 387.5482225476748*lm11m1(n,S1) - 197.7830687973748*lm13m1(n,S1,S2,S3) elif variation == 11: - fit = 315.51530441621395/np.power(-1. + n,2) - 681.9096023524954/(-1. + n) - 4371.86464036536/np.power(n,4) - 743.2670270884392*lm12m1(n,S1,S2) - 739.8725231366963*lm13m1(n,S1,S2,S3) + fit = 234.71021283280834/np.power(-1. + n,2) - 668.4196514406609/(-1. + n) - 3336.0224123418016/np.power(n,4) - 671.1068807980374*lm12m1(n,S1,S2) - 706.2435192552492*lm13m1(n,S1,S2,S3) elif variation == 12: - fit = 18.90357718091744/np.power(-1. + n,2) - 488.3516827637743/(-1. + n) - 994.6418190719808/np.power(n,3) - 713.9439257405169*lm12m1(n,S1,S2) - 570.3417703743911*lm13m1(n,S1,S2,S3) + fit = 8.375810645634878/np.power(-1. + n,2) - 520.7221331157691/(-1. + n) - 758.9776156472786/np.power(n,3) - 648.7314114404783*lm12m1(n,S1,S2) - 576.880321324907*lm13m1(n,S1,S2,S3) elif variation == 13: - fit = -86.56896957695098/np.power(-1. + n,2) - 275.828688059755/(-1. + n) - 824.8930651290783/np.power(n,2) - 441.1754981260873*lm12m1(n,S1,S2) - 327.27714570223736*lm13m1(n,S1,S2,S3) + fit = -72.10673143086429/np.power(-1. + n,2) - 358.5530058001772/(-1. + n) - 629.4480683703055/np.power(n,2) - 440.59102678646576*lm12m1(n,S1,S2) - 391.4059065714235*lm13m1(n,S1,S2,S3) elif variation == 14: - fit = 178.2805625979371/np.power(-1. + n,2) - 1175.763607295771/(-1. + n) - 4336.094528843359*lm11m1(n,S1) - 3747.9378120594934*lm12m1(n,S1,S2) - 1684.3286865084197*lm13m1(n,S1,S2,S3) + fit = 129.9910112750619/np.power(-1. + n,2) - 1045.262981333448/(-1. + n) - 3308.727447025322*lm11m1(n,S1) - 2963.8697874593217*lm12m1(n,S1,S2) - 1426.926154164017*lm13m1(n,S1,S2,S3) elif variation == 15: - fit = -673.7742132225945/np.power(-1. + n,2) + 317.2132626956936/(-1. + n) + 6384.686015786331/np.power(n,4) - 2029.5697078635478/np.power(n,2) + 275.27854922027643*lm13m1(n,S1,S2,S3) + fit = -658.5340428548301/np.power(-1. + n,2) + 233.70328023719887/(-1. + n) + 6376.227554233226/np.power(n,4) - 1832.5287499192084/np.power(n,2) + 210.35151978073395*lm13m1(n,S1,S2,S3) elif variation == 16: - fit = 349.4631362634346/np.power(-1. + n,2) - 559.7446717031943/(-1. + n) - 5453.335146329048/np.power(n,4) + 1072.6220342502565*lm11m1(n,S1) - 506.2418943583583*lm13m1(n,S1,S2,S3) + fit = 265.36221636680716/np.power(-1. + n,2) - 558.115114090075/(-1. + n) - 4312.498256800645/np.power(n,4) + 968.4864274161131*lm11m1(n,S1) - 495.2949411211266*lm13m1(n,S1,S2,S3) elif variation == 17: - fit = -257.1602061122679/np.power(-1. + n,2) + 67.90588148648591/(-1. + n) + 1608.7331067743435/np.power(n,3) - 2159.0746347923864/np.power(n,2) + 65.85543860914298*lm13m1(n,S1,S2,S3) + fit = -242.4719679073227/np.power(-1. + n,2) - 15.273817400740654/(-1. + n) + 1606.6018497165833/np.power(n,3) - 1961.8621081220385/np.power(n,2) + 1.2058538747811829*lm13m1(n,S1,S2,S3) elif variation == 18: - fit = -18.600199987013553/np.power(-1. + n,2) - 326.59342404939514/(-1. + n) - 1228.6958454214596/np.power(n,3) + 1020.3475901067098*lm11m1(n,S1) - 308.20406610462027*lm13m1(n,S1,S2,S3) + fit = -25.702325492667082/np.power(-1. + n,2) - 373.7390722554988/(-1. + n) - 971.6528600084858/np.power(n,3) + 927.147789097384*lm11m1(n,S1) - 338.6865966478428*lm13m1(n,S1,S2,S3) elif variation == 19: - fit = -121.90417458800518/np.power(-1. + n,2) - 155.76283554846327/(-1. + n) - 934.9471223483207/np.power(n,2) + 578.5050396951302*lm11m1(n,S1) - 146.22455326916472*lm13m1(n,S1,S2,S3) + fit = -107.39512419897143/np.power(-1. + n,2) - 238.64621708524552/(-1. + n) - 739.3563254661514/np.power(n,2) + 577.7386335438422*lm11m1(n,S1) - 210.59317344974744*lm13m1(n,S1,S2,S3) else: - fit = -34.631097341548454/np.power(-1. + n,2) - 614.62987509215/(-1. + n) + 298.9931463234356/np.power(n,4) + 87.57428451895092/np.power(n,3) - 243.92212492942747/np.power(n,2) + 135.41924886509895/(1. + n) + 262.60049987311237/(2. + n) - 38.88382719169835*lm11m1(n,S1) - 334.9887739215079*lm12m1(n,S1,S2) - 251.2295891027122*lm13m1(n,S1,S2,S3) + fit = -49.223424397058984/np.power(-1. + n,2) - 622.0772540941418/(-1. + n) + 430.8599370178221/np.power(n,4) + 117.68366797885425/np.power(n,3) - 192.45366666213553/np.power(n,2) + 107.62879422315821/(1. + n) + 242.9520423963465/(2. + n) + 7.226482800064206*lm11m1(n,S1) - 288.44333331956375*lm12m1(n,S1,S2) - 282.9932310879313*lm13m1(n,S1,S2,S3) return common + fit @@ -297,45 +297,45 @@ def gamma_gg_nf0(n, cache, variation): S3 = c.get(c.S3, cache, n) common = -68587.9129845144 - 49851.703887834694/np.power(-1. + n,4) + 213823.9810748423/np.power(-1. + n,3) - 103680./np.power(n,7) - 17280./np.power(n,6) - 627978.8224813186/np.power(n,5) - 54482.80778086425/n + 40880.33011934297*S1 - 85814.12027987762*lm11(n,S1) if variation == 1: - fit = -295448.0379235009/np.power(-1. + n,2) + 224578.11757296775/(-1. + n) - 526757.6738519811/(1. + n) + 296021.5646034255/(2. + n) + 2224.0922337045213*lm13m1(n,S1,S2,S3) + fit = -295597.8343912357/np.power(-1. + n,2) + 224940.49334893477/(-1. + n) - 528016.0821893369/(1. + n) + 295950.8085172776/(2. + n) + 1477.798412728375*lm13m1(n,S1,S2,S3) elif variation == 2: - fit = -285107.088545888/np.power(-1. + n,2) + 195545.1200082606/(-1. + n) - 252769.2783475656/(1. + n) - 108776.38581520668*lm12m1(n,S1,S2) - 65914.13979179235*lm13m1(n,S1,S2,S3) + fit = -285259.35674268805/np.power(-1. + n,2) + 195914.43535053887/(-1. + n) - 254093.176327687/(1. + n) - 108750.38571168127*lm12m1(n,S1,S2) - 66644.14697966084*lm13m1(n,S1,S2,S3) elif variation == 3: - fit = -391716.7896443467/np.power(-1. + n,2) + 170902.9255344149/(-1. + n) + 1.607519634683242e6/np.power(n,4) - 89387.05777989682/(1. + n) + 76364.75507676331*lm13m1(n,S1,S2,S3) + fit = -391843.5756260241/np.power(-1. + n,2) + 171278.1309382666/(-1. + n) + 1.607135399845882e6/np.power(n,4) - 90750.00793688672/(1. + n) + 75600.73990110215*lm13m1(n,S1,S2,S3) elif variation == 4: - fit = -282383.73363518645/np.power(-1. + n,2) + 89190.37336362494/(-1. + n) + 405966.0728943653/np.power(n,3) - 71410.64232788606/(1. + n) + 22824.74956225227*lm13m1(n,S1,S2,S3) + fit = -282536.6527775845/np.power(-1. + n,2) + 89585.10998095598/(-1. + n) + 405869.0374960631/np.power(n,3) - 72777.8892690519/(1. + n) + 22073.53170175139*lm13m1(n,S1,S2,S3) elif variation == 5: - fit = -290139.8534816189/np.power(-1. + n,2) + 209612.58483575174/(-1. + n) - 238124.94028671857/(1. + n) + 142906.92425938678*lm11m1(n,S1) - 22034.409788754692*lm13m1(n,S1,S2,S3) + fit = -290290.91872975003/np.power(-1. + n,2) + 209978.53772452284/(-1. + n) - 239452.33860661855/(1. + n) + 142872.76615791937*lm11m1(n,S1) - 22774.905259686046*lm13m1(n,S1,S2,S3) elif variation == 6: - fit = -275566.9972336391/np.power(-1. + n,2) + 168760.59203878703/(-1. + n) - 273096.0817605587/(2. + n) - 209128.55034080063*lm12m1(n,S1,S2) - 128775.38508377109*lm13m1(n,S1,S2,S3) + fit = -275669.2984894303/np.power(-1. + n,2) + 168989.62141469866/(-1. + n) - 274526.4428921221/(2. + n) - 209628.1521964082*lm12m1(n,S1,S2) - 129834.63274025511*lm13m1(n,S1,S2,S3) elif variation == 7: - fit = -411391.59210307786/np.power(-1. + n,2) + 159933.1271168039/(-1. + n) + 1.9360543948787057e6/np.power(n,4) - 60499.02697383511/(2. + n) + 91517.15779852161*lm13m1(n,S1,S2,S3) + fit = -411818.37425604276/np.power(-1. + n,2) + 160141.0679428944/(-1. + n) + 1.9406795709568677e6/np.power(n,4) - 61421.50009639418/(2. + n) + 90984.18244209285*lm13m1(n,S1,S2,S3) elif variation == 8: - fit = -280334.89989693864/np.power(-1. + n,2) + 67957.93940012196/(-1. + n) + 469632.45484412194/np.power(n,3) - 46424.130625098995/(2. + n) + 26055.48583672462*lm13m1(n,S1,S2,S3) + fit = -280448.59152967954/np.power(-1. + n,2) + 67946.15425201622/(-1. + n) + 470754.3927408164/np.power(n,3) - 47312.97924099773/(2. + n) + 25366.124502714512*lm13m1(n,S1,S2,S3) elif variation == 9: - fit = -158342.46596423967/np.power(-1. + n,2) - 354852.44655132474/(-1. + n) + 1.0138734178112751e6/np.power(n,2) + 316958.89807541796/(2. + n) - 24481.5265510284*lm13m1(n,S1,S2,S3) + fit = -158164.7213188171/np.power(-1. + n,2) - 355874.3130731763/(-1. + n) + 1.0162955311005719e6/np.power(n,2) + 316938.16065307835/(2. + n) - 25291.619297074456*lm13m1(n,S1,S2,S3) elif variation == 10: - fit = -285760.5473383797/np.power(-1. + n,2) + 197265.86814370425/(-1. + n) - 244220.80103026525/(2. + n) + 260806.5899887168*lm11m1(n,S1) - 42047.920641263154*lm13m1(n,S1,S2,S3) + fit = -285887.2006806783/np.power(-1. + n,2) + 197562.99577218326/(-1. + n) - 245582.1799793595/(2. + n) + 261429.64913634845*lm11m1(n,S1) - 42899.97897764852*lm13m1(n,S1,S2,S3) elif variation == 11: - fit = -450043.3779284024/np.power(-1. + n,2) + 157421.08366934053/(-1. + n) + 2.4869999720694227e6/np.power(n,4) + 59511.9900450049*lm12m1(n,S1,S2) + 154206.10006698*lm13m1(n,S1,S2,S3) + fit = -451059.5122634805/np.power(-1. + n,2) + 157590.7215229884/(-1. + n) + 2.500025820230639e6/np.power(n,4) + 60419.41309017621*lm12m1(n,S1,S2) + 154628.98908088758*lm13m1(n,S1,S2,S3) elif variation == 12: - fit = -281311.4024370307/np.power(-1. + n,2) + 47312.79345234101/(-1. + n) + 565816.73490305/np.power(n,3) + 42831.109406509524*lm12m1(n,S1,S2) + 57766.0196738513*lm13m1(n,S1,S2,S3) + fit = -281443.7904442531/np.power(-1. + n,2) + 46905.73090962251/(-1. + n) + 568780.2423251155/np.power(n,3) + 43651.165093081385*lm12m1(n,S1,S2) + 57683.796561516865*lm13m1(n,S1,S2,S3) elif variation == 13: - fit = -221311.7815844328/np.power(-1. + n,2) - 73584.06072125914/(-1. + n) + 469252.6413087417/np.power(n,2) - 112337.25184482028*lm12m1(n,S1,S2) - 80504.89319687682*lm13m1(n,S1,S2,S3) + fit = -221129.91709477766/np.power(-1. + n,2) - 74624.32957010131/(-1. + n) + 471710.387076172/np.power(n,2) - 112329.90204316098*lm12m1(n,S1,S2) - 81311.32054580169*lm13m1(n,S1,S2,S3) elif variation == 14: - fit = -371975.3618425755/np.power(-1. + n,2) + 438357.2510794566/(-1. + n) + 2.4666516141772955e6*lm11m1(n,S1) + 1.7687634818009005e6*lm12m1(n,S1,S2) + 691473.981199157*lm13m1(n,S1,S2,S3) + fit = -372582.60911082564/np.power(-1. + n,2) + 439998.3130990782/(-1. + n) + 2.479570886293798e6*lm11m1(n,S1) + 1.7786232372348914e6*lm12m1(n,S1,S2) + 694710.8508805855*lm13m1(n,S1,S2,S3) elif variation == 15: - fit = -370832.83073654736/np.power(-1. + n,2) + 77423.19888297348/(-1. + n) + 1.6257432335929913e6/np.power(n,4) + 162503.82143718746/np.power(n,2) + 72924.86692930982*lm13m1(n,S1,S2,S3) + fit = -370641.1836499627/np.power(-1. + n,2) + 76373.05020007766/(-1. + n) + 1.6256368673598904e6/np.power(n,4) + 164981.63662011502/np.power(n,2) + 72108.40125127957*lm13m1(n,S1,S2,S3) elif variation == 16: - fit = -452761.5168438991/np.power(-1. + n,2) + 147639.56791297536/(-1. + n) + 2.573591277265509e6/np.power(n,4) - 85882.82474255121*lm11m1(n,S1) + 135499.7359376153*lm13m1(n,S1,S2,S3) + fit = -453819.096640544/np.power(-1. + n,2) + 147660.05980785593/(-1. + n) + 2.587937446690415e6/np.power(n,4) - 87192.34328327361*lm11m1(n,S1) + 135637.39527110517*lm13m1(n,S1,S2,S3) elif variation == 17: - fit = -264749.7122550716/np.power(-1. + n,2) + 13941.645196000183/(-1. + n) + 409634.3902470049/np.power(n,3) + 129527.76620894097/np.power(n,2) + 19599.111490094336*lm13m1(n,S1,S2,S3) + fit = -264565.00578584545/np.power(-1. + n,2) + 12895.649871143309/(-1. + n) + 409607.5894176158/np.power(n,3) + 132007.7388904974/np.power(n,2) + 18786.134714622272*lm13m1(n,S1,S2,S3) elif variation == 18: - fit = -279061.4660973225/np.power(-1. + n,2) + 37608.549986420694/(-1. + n) + 579858.1648363634/np.power(n,3) - 61212.957613155806*lm11m1(n,S1) + 42039.78644131242*lm13m1(n,S1,S2,S3) + fit = -279150.776231584/np.power(-1. + n,2) + 37015.68744579348/(-1. + n) + 583090.5131692598/np.power(n,3) - 62384.957000475675*lm11m1(n,S1) + 41656.46473103294*lm13m1(n,S1,S2,S3) elif variation == 19: - fit = -230309.24368551886/np.power(-1. + n,2) - 43011.492732260434/(-1. + n) + 441229.3934290683/np.power(n,2) + 147305.70173040565*lm11m1(n,S1) - 34403.17005106444*lm13m1(n,S1,S2,S3) + fit = -230126.7905259369/np.power(-1. + n,2) - 44053.76182863434/(-1. + n) + 443688.97265165334/np.power(n,2) + 147296.0640752822*lm11m1(n,S1) - 35212.61366143017*lm13m1(n,S1,S2,S3) else: - fit = -309397.2999567167/np.power(-1. + n,2) + 101684.3546415316/(-1. + n) + 538416.2374994669/np.power(n,4) + 127942.51672236343/np.power(n,3) + 116651.94948395861/np.power(n,2) - 62023.66276810779/(1. + n) - 592.6093532060254/(2. + n) + 151082.8972526367*lm11m1(n,S1) + 75834.96806587302*lm12m1(n,S1,S2) + 52333.389323249234*lm13m1(n,S1,S2,S3) + fit = -309580.8003310073/np.power(-1. + n,2) + 101590.70290050836/(-1. + n) + 540074.4792149311/np.power(n,4) + 128321.14606046685/np.power(n,3) + 117299.17191257945/np.power(n,2) - 62373.13128050426/(1. + n) - 839.6912125535554/(2. + n) + 151662.74028313678*lm11m1(n,S1) + 76420.28291931044*lm12m1(n,S1,S2) + 51933.95747315065*lm13m1(n,S1,S2,S3) return common + fit diff --git a/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggq.py b/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggq.py index 129a3c702..b5b7eadbc 100644 --- a/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggq.py +++ b/src/ekore/anomalous_dimensions/unpolarized/space_like/as4/ggq.py @@ -94,49 +94,49 @@ def gamma_gq_nf0(n, cache, variation): S5 = c.get(c.S5, cache, n) common = -22156.31283903764/np.power(-1. + n,4) + 95032.88047770769/np.power(-1. + n,3) - 37609.87654320987/np.power(n,7) - 35065.67901234568/np.power(n,6) - 175454.58483973087/np.power(n,5) - 375.3983146907502*lm14(n,S1,S2,S3,S4) - 13.443072702331962*lm15(n,S1,S2,S3,S4,S5) if variation == 1: - fit = -134611.31548520518/np.power(-1. + n,2) + 105578.6478973615/(-1. + n) - 271004.1457372756/(1. + n) + 135827.42962246042/(2. + n) - 1659.6381024386487*lm13(n,S1,S2,S3) + fit = -135325.37409909506/np.power(-1. + n,2) + 107389.69725534944/(-1. + n) - 281247.1594541515/(1. + n) + 145447.60744097419/(2. + n) - 1644.0474725539857*lm13(n,S1,S2,S3) elif variation == 2: - fit = -129784.96381286802/np.power(-1. + n,2) + 92404.11351667382/(-1. + n) - 166871.00811514194/(1. + n) + 8603.419512104943*lm12(n,S1,S2) - 333.06211910306587*lm13(n,S1,S2,S3) + fit = -130157.18895885911/np.power(-1. + n,2) + 93282.05706699888/(-1. + n) - 169738.63893980338/(1. + n) + 9212.769374520116*lm12(n,S1,S2) - 223.51479074632925*lm13(n,S1,S2,S3) elif variation == 3: - fit = -130354.69780717866/np.power(-1. + n,2) + 93906.9798287439/(-1. + n) - 206720.3072485826/(1. + n) - 30775.363703337393*lm11(n,S1) - 1101.8494545818282*lm13(n,S1,S2,S3) + fit = -130767.27520270286/np.power(-1. + n,2) + 94891.36609978844/(-1. + n) - 212410.3233945088/(1. + n) - 32955.07417912945*lm11(n,S1) - 1046.7526219200904*lm13(n,S1,S2,S3) elif variation == 4: - fit = -156517.8307292757/np.power(-1. + n,2) + 89433.22729993386/(-1. + n) + 384766.5696200253/np.power(n,4) - 128852.37353471664/(1. + n) - 1762.2085163661038*lm13(n,S1,S2,S3) + fit = -158783.450560317/np.power(-1. + n,2) + 90100.75345693348/(-1. + n) + 412018.22879229486/np.power(n,4) - 129027.27855213353/(1. + n) - 1753.8825871656047*lm13(n,S1,S2,S3) elif variation == 5: - fit = -129351.9314649959/np.power(-1. + n,2) + 54671.293834508826/(-1. + n) + 148449.9518256113/np.power(n,3) - 88593.14563810707/(1. + n) - 1703.1788616091594*lm13(n,S1,S2,S3) + fit = -129693.48645695807/np.power(-1. + n,2) + 52876.75483885584/(-1. + n) + 158964.13837584556/np.power(n,3) - 85916.6315255873/(1. + n) - 1690.6720701417717*lm13(n,S1,S2,S3) elif variation == 6: - fit = -289524.23824347754/np.power(-1. + n,2) + 762852.3222214412/(-1. + n) - 1.1600176710948618e6/np.power(n,2) - 809182.8193866021/(1. + n) - 1836.245183321374*lm13(n,S1,S2,S3) + fit = -301210.2328458577/np.power(-1. + n,2) + 811215.7479286905/(-1. + n) - 1.242177631711221e6/np.power(n,2) - 857543.1305664484/(1. + n) - 1833.163010136661*lm13(n,S1,S2,S3) elif variation == 7: - fit = -122050.84394025133/np.power(-1. + n,2) + 71292.218842658/(-1. + n) - 217660.39733703827/(2. + n) + 22390.205543958295*lm12(n,S1,S2) + 1792.7460216611355*lm13(n,S1,S2,S3) + fit = -122290.16043542989/np.power(-1. + n,2) + 71807.36048618097/(-1. + n) - 221400.82937350916/(2. + n) + 23236.477404056477*lm12(n,S1,S2) + 1938.8247584430924*lm13(n,S1,S2,S3) elif variation == 8: - fit = -116666.509065989/np.power(-1. + n,2) + 56373.894282328176/(-1. + n) - 436786.1136556859/(2. + n) - 129741.02583569557*lm11(n,S1) + 691.8555166149675*lm13(n,S1,S2,S3) + fit = -116702.31643837337/np.power(-1. + n,2) + 56325.17516760884/(-1. + n) - 448808.73529422894/(2. + n) - 134644.78516249143*lm11(n,S1) + 796.324422989612*lm13(n,S1,S2,S3) elif variation == 9: - fit = -176374.82189677586/np.power(-1. + n,2) + 74798.33577898303/(-1. + n) + 733535.2482241682/np.power(n,4) - 123119.72215889738/(2. + n) - 1855.182674086565*lm13(n,S1,S2,S3) + fit = -178667.39573180894/np.power(-1. + n,2) + 75445.99644274621/(-1. + n) + 761260.3281816904/np.power(n,4) - 123286.8456395018/(2. + n) - 1846.982948588938*lm13(n,S1,S2,S3) elif variation == 10: - fit = -126797.5604335579/np.power(-1. + n,2) + 29946.67399201152/(-1. + n) + 220548.93815270695/np.power(n,3) - 65968.49558222751/(2. + n) - 1724.3256828880108*lm13(n,S1,S2,S3) + fit = -127216.28629540099/np.power(-1. + n,2) + 28899.09790707029/(-1. + n) + 228884.9205878143/np.power(n,3) - 63975.501562926234/(2. + n) - 1711.180018456112*lm13(n,S1,S2,S3) elif variation == 11: - fit = -56603.682794921304/np.power(-1. + n,2) - 225396.73137215254/(-1. + n) + 584136.1120157596/np.power(n,2) + 204224.41065290783/(2. + n) - 1570.7062041132795*lm13(n,S1,S2,S3) + fit = -54369.324330163065/np.power(-1. + n,2) - 236095.39968148115/(-1. + n) + 606214.4244773745/np.power(n,2) + 216429.75635890095/(2. + n) - 1551.7542579210171*lm13(n,S1,S2,S3) elif variation == 12: - fit = -127399.17314512776/np.power(-1. + n,2) + 86110.78284306003/(-1. + n) + 128873.43260633861*lm11(n,S1) + 44630.68519659024*lm12(n,S1,S2) + 2886.2747447077363*lm13(n,S1,S2,S3) + fit = -127730.39915689365/np.power(-1. + n,2) + 86880.5772952685/(-1. + n) + 131088.0859004977*lm11(n,S1) + 45859.153375434624*lm12(n,S1,S2) + 3051.145461650118*lm13(n,S1,S2,S3) elif variation == 13: - fit = -247120.59412629303/np.power(-1. + n,2) + 79364.32964611659/(-1. + n) + 1.6888135534086183e6/np.power(n,4) - 29158.622788111865*lm12(n,S1,S2) - 6605.8570968113345*lm13(n,S1,S2,S3) + fit = -249509.19871481528/np.power(-1. + n,2) + 80018.18821849066/(-1. + n) + 1.7178353341095438e6/np.power(n,4) - 29198.20288498338*lm12(n,S1,S2) - 6604.105966476303*lm13(n,S1,S2,S3) elif variation == 14: - fit = -128861.83507443611/np.power(-1. + n,2) + 11966.126835094941/(-1. + n) + 316462.3091625236/np.power(n,3) - 9737.159060072763*lm12(n,S1,S2) - 3253.8465506459015*lm13(n,S1,S2,S3) + fit = -129218.19651555142/np.power(-1. + n,2) + 11461.766456848798/(-1. + n) + 321900.6239594061/np.power(n,3) - 9442.986825272894*lm12(n,S1,S2) - 3194.4920722194884*lm13(n,S1,S2,S3) elif variation == 15: - fit = -88285.0983393474/np.power(-1. + n,2) - 81776.66054398555/(-1. + n) + 301369.70052571065/np.power(n,2) + 10838.566464150015*lm12(n,S1,S2) + 57.46109548925452*lm13(n,S1,S2,S3) + fit = -87944.16009766924/np.power(-1. + n,2) - 83891.96406756257/(-1. + n) + 306548.65313472337/np.power(n,2) + 11486.326691371696*lm12(n,S1,S2) + 173.71945424342616*lm13(n,S1,S2,S3) elif variation == 16: - fit = -199811.41276401555/np.power(-1. + n,2) + 82030.26173438856/(-1. + n) + 1.021461077715438e6/np.power(n,4) + 50925.69521801989*lm11(n,S1) - 2854.941152739061*lm13(n,S1,S2,S3) + fit = -202135.7995740037/np.power(-1. + n,2) + 82687.73905965324/(-1. + n) + 1.0495769899938635e6/np.power(n,4) + 50994.82207509583*lm11(n,S1) - 2848.098505650866*lm13(n,S1,S2,S3) elif variation == 17: - fit = -128599.87560093393/np.power(-1. + n,2) + 25245.26855710262/(-1. + n) + 259784.61882981652/np.power(n,3) + 23080.94295557716*lm11(n,S1) - 2154.164587558643*lm13(n,S1,S2,S3) + fit = -128964.1511783234/np.power(-1. + n,2) + 24339.728042797506/(-1. + n) + 266935.24034010764/np.power(n,3) + 22383.637660612447*lm11(n,S1) - 2128.032930969243*lm13(n,S1,S2,S3) elif variation == 18: - fit = -75739.554722418/np.power(-1. + n,2) - 135625.28803179998/(-1. + n) + 398031.7522689792/np.power(n,2) - 41335.178649992326*lm11(n,S1) - 849.8594840371891*lm13(n,S1,S2,S3) + fit = -74648.83981878728/np.power(-1. + n,2) - 140958.82150230306/(-1. + n) + 408987.65266967454/np.power(n,2) - 43805.55005962004*lm11(n,S1) - 787.8265790554562*lm13(n,S1,S2,S3) elif variation == 19: - fit = -69571.53835633998/np.power(-1. + n,2) - 21824.684729051125/(-1. + n) - 846704.7809898313/np.power(n,4) + 475124.08069442277/np.power(n,3) - 1573.2801259880794*lm13(n,S1,S2,S3) + fit = -71719.13674652952/np.power(-1. + n,2) - 21308.180757420447/(-1. + n) - 821124.7287279929/np.power(n,4) + 475769.01709201955/np.power(n,3) - 1564.6977442093062*lm13(n,S1,S2,S3) elif variation == 20: - fit = -131326.8497758187/np.power(-1. + n,2) - 38110.15884910321/(-1. + n) + 457640.10637686535/np.power(n,4) + 219703.5737179606/np.power(n,2) - 1748.1862124636395*lm13(n,S1,S2,S3) + fit = -133558.27521182265/np.power(-1. + n,2) - 37615.76088185934/(-1. + n) + 484990.68454355566/np.power(n,4) + 220001.80072250665/np.power(n,2) - 1739.8412493001551*lm13(n,S1,S2,S3) elif variation == 21: - fit = -109659.49203855239/np.power(-1. + n,2) - 32396.266625595177/(-1. + n) + 166701.1822848159/np.power(n,3) + 142618.77212791165/np.power(n,2) - 1686.818976852953*lm13(n,S1,S2,S3) + fit = -110595.9812283641/np.power(-1. + n,2) - 31560.381420415717/(-1. + n) + 176663.97543390834/np.power(n,3) + 138310.07359867013/np.power(n,2) - 1674.8064387740321*lm13(n,S1,S2,S3) else: - fit = -136905.419981799/np.power(-1. + n,2) + 56230.69937898662/(-1. + n) + 163786.27496929924/np.power(n,4) + 75574.81337856653/np.power(n,3) + 23135.3447410219/np.power(n,2) - 79582.08569811552/(1. + n) - 23975.375640880044/(2. + n) + 48.97631385287552*lm11(n,S1) + 2265.099755648517*lm12(n,S1,S2) - 1373.5720765300828*lm13(n,S1,S2,S3) + fit = -138152.69664751078/np.power(-1. + n,2) + 57913.880829154245/(-1. + n) + 171645.5636615693/np.power(n,4) + 77577.04360900483/np.power(n,3) + 20851.665375796576/np.power(n,2) - 82661.10297298252/(1. + n) - 23599.740384299566/(2. + n) - 330.42208404928425*lm11(n,S1) + 2435.882720720316*lm12(n,S1,S2) - 1327.8017698551957*lm13(n,S1,S2,S3) return common + fit @@ -166,49 +166,49 @@ def gamma_gq_nf1(n, cache, variation): S5 = c.get(c.S5, cache, n) common = 885.6738165500071/np.power(-1. + n,3) + 5309.62962962963/np.power(n,7) + 221.23456790123456/np.power(n,6) + 9092.91243376357/np.power(n,5) + 34.49474165523548*lm14(n,S1,S2,S3,S4) + 0.5486968449931413*lm15(n,S1,S2,S3,S4,S5) if variation == 1: - fit = -4488.023094730909/np.power(-1. + n,2) + 11415.451852682689/(-1. + n) - 22278.11557093013/(1. + n) + 16857.05748831136/(2. + n) + 218.39366882799368*lm13(n,S1,S2,S3) + fit = -4154.154695948995/np.power(-1. + n,2) + 10568.669617295407/(-1. + n) - 17488.846844461823/(1. + n) + 12359.004664911017/(2. + n) + 211.10404507107253*lm13(n,S1,S2,S3) elif variation == 2: - fit = -3889.0418151355752/np.power(-1. + n,2) + 9780.407413909863/(-1. + n) - 9354.523537908572/(1. + n) + 1067.7396878871195*lm12(n,S1,S2) + 383.03027923765*lm13(n,S1,S2,S3) + fit = -3715.00258213197/np.power(-1. + n,2) + 9369.912250526479/(-1. + n) - 8013.721406089578/(1. + n) + 782.8293753310119*lm12(n,S1,S2) + 331.8098466308406*lm13(n,S1,S2,S3) elif variation == 3: - fit = -3959.7494676460906/np.power(-1. + n,2) + 9966.92278779446/(-1. + n) - 14300.077821225603/(1. + n) - 3819.420544236109*lm11(n,S1) + 287.618827026041*lm13(n,S1,S2,S3) + fit = -3766.8429586516354/np.power(-1. + n,2) + 9506.658795852165/(-1. + n) - 11639.62874491426/(1. + n) - 2800.265488570204*lm11(n,S1) + 261.8575086390502*lm13(n,S1,S2,S3) elif variation == 4: - fit = -7206.762511830159/np.power(-1. + n,2) + 9411.701329387806/(-1. + n) + 47752.005627238184/np.power(n,4) - 4636.1664981662325/(1. + n) + 205.6640208549657*lm13(n,S1,S2,S3) + fit = -6147.4392986647545/np.power(-1. + n,2) + 9099.589851629416/(-1. + n) + 35010.09952148762/np.power(n,4) - 4554.387135843054/(1. + n) + 201.7711126307286*lm13(n,S1,S2,S3) elif variation == 5: - fit = -3835.299716042018/np.power(-1. + n,2) + 5097.521841045809/(-1. + n) + 18423.593665995402/np.power(n,3) + 360.2625808084624/(1. + n) + 212.9899806152177*lm13(n,S1,S2,S3) + fit = -3675.6007556945196/np.power(-1. + n,2) + 5936.584418528788/(-1. + n) + 13507.53417196719/np.power(n,3) - 891.1801771144223/(1. + n) + 207.1422499668006*lm13(n,S1,S2,S3) elif variation == 6: - fit = -23713.713015219728/np.power(-1. + n,2) + 92987.34159859698/(-1. + n) - 143965.65276583107/np.power(n,2) - 89069.54986300123/(1. + n) + 196.47559437456405*lm13(n,S1,S2,S3) + fit = -18249.757773649242/np.power(-1. + n,2) + 70374.32470231941/(-1. + n) - 105550.57876215602/np.power(n,2) - 66457.98920891003/(1. + n) + 195.03447986946037*lm13(n,S1,S2,S3) elif variation == 7: - fit = -3455.4793454735536/np.power(-1. + n,2) + 8596.908147688335/(-1. + n) - 12201.695987567426/(2. + n) + 1840.6050040604714*lm12(n,S1,S2) + 502.1997054577737*lm13(n,S1,S2,S3) + fit = -3343.5834681677507/np.power(-1. + n,2) + 8356.04624598052/(-1. + n) - 10452.80306687096/(2. + n) + 1444.9183960217892*lm12(n,S1,S2) + 433.89848620522463*lm13(n,S1,S2,S3) elif variation == 8: - fit = -3012.8557307127066/np.power(-1. + n,2) + 7370.535179202942/(-1. + n) - 30215.103197366938/(2. + n) - 10665.466242204988*lm11(n,S1) + 411.70010872417294*lm13(n,S1,S2,S3) + fit = -2996.1134775555597/np.power(-1. + n,2) + 7393.314503624469/(-1. + n) - 24593.753132227568/(2. + n) - 8372.642876397704*lm11(n,S1) + 362.8541655256052*lm13(n,S1,S2,S3) elif variation == 9: - fit = -7921.226007375836/np.power(-1. + n,2) + 8885.131333721463/(-1. + n) + 60300.859940087874/np.power(n,4) - 4429.9031168628235/(2. + n) + 202.31876873895882*lm13(n,S1,S2,S3) + fit = -6849.300061096075/np.power(-1. + n,2) + 8582.308253713018/(-1. + n) + 47337.59912160785/np.power(n,4) - 4351.762124258069/(2. + n) + 198.4848688754035*lm13(n,S1,S2,S3) elif variation == 10: - fit = -3845.68702415166/np.power(-1. + n,2) + 5198.064104104413/(-1. + n) + 18130.404314827305/np.power(n,3) + 268.2598106136584/(2. + n) + 213.07597381881035*lm13(n,S1,S2,S3) + fit = -3649.905711097048/np.power(-1. + n,2) + 5687.873404469671/(-1. + n) + 14232.795555815104/np.power(n,3) - 663.5932741012635/(2. + n) + 206.92952890585326*lm13(n,S1,S2,S3) elif variation == 11: - fit = 1924.6576108019278/np.power(-1. + n,2) - 15792.64760438993/(-1. + n) + 48019.38279297407/np.power(n,2) + 22479.68678039739/(2. + n) + 225.7043876490835*lm13(n,S1,S2,S3) + fit = 879.9511001376588/np.power(-1. + n,2) - 10790.331004577562/(-1. + n) + 37696.34952104189/np.power(n,2) + 16772.9014435428/(2. + n) + 216.84313199599924*lm13(n,S1,S2,S3) elif variation == 12: - fit = -3755.2981815948488/np.power(-1. + n,2) + 9427.613297165519/(-1. + n) + 7224.439837356762*lm11(n,S1) + 3087.370950732838*lm12(n,S1,S2) + 563.5011879300971*lm13(n,S1,S2,S3) + fit = -3600.42868484152/np.power(-1. + n,2) + 9067.684803683303/(-1. + n) + 6188.946763244337*lm11(n,S1) + 2512.9829441244183*lm12(n,S1,S2) + 486.41350744844374*lm13(n,S1,S2,S3) elif variation == 13: - fit = -10466.690790833369/np.power(-1. + n,2) + 9049.417851827156/(-1. + n) + 94672.20408711508/np.power(n,4) - 1049.1403952794576*lm12(n,S1,S2) + 31.387360972561613*lm13(n,S1,S2,S3) + fit = -9349.864281360744/np.power(-1. + n,2) + 8743.696850292556/(-1. + n) + 81102.65214258479/np.power(n,4) - 1030.6341504008299*lm12(n,S1,S2) + 30.568594740114495*lm13(n,S1,S2,S3) elif variation == 14: - fit = -3837.292685015662/np.power(-1. + n,2) + 5271.181705657407/(-1. + n) + 17740.37415701935/np.power(n,3) + 39.59599839782818*lm12(n,S1,S2) + 219.29574546428225*lm13(n,S1,S2,S3) + fit = -3670.6707559192682/np.power(-1. + n,2) + 5507.002671361118/(-1. + n) + 15197.611675043092/np.power(n,3) - 97.9484707672736*lm12(n,S1,S2) + 191.54370342235256*lm13(n,S1,S2,S3) elif variation == 15: - fit = -1562.6253047002033/np.power(-1. + n,2) + 16.11001314684768/(-1. + n) + 16894.306500710383/np.power(n,2) + 1193.038474115512*lm12(n,S1,S2) + 404.9223900617979*lm13(n,S1,S2,S3) + fit = -1722.0358945603757/np.power(-1. + n,2) + 1005.1506697978073/(-1. + n) + 14472.81254861761/np.power(n,2) + 890.1688417705905*lm12(n,S1,S2) + 350.5641184465057*lm13(n,S1,S2,S3) elif variation == 16: - fit = -8764.48511413068/np.power(-1. + n,2) + 9145.339290408388/(-1. + n) + 70660.56110839365/np.power(n,4) + 1832.3294758866361*lm11(n,S1) + 166.3470078948553*lm13(n,S1,S2,S3) + fit = -7677.684552786546/np.power(-1. + n,2) + 8837.926288795223/(-1. + n) + 57514.561003940005/np.power(n,4) + 1800.00821732893*lm11(n,S1) + 163.14762960523643*lm13(n,S1,S2,S3) elif variation == 17: - fit = -3838.357938938717/np.power(-1. + n,2) + 5217.182292574578/(-1. + n) + 17970.85305971273/np.power(n,3) - 93.85827782443143*lm11(n,S1) + 214.8239067092436*lm13(n,S1,S2,S3) + fit = -3668.0356413358095/np.power(-1. + n,2) + 5640.580814304368/(-1. + n) + 14627.476889260639/np.power(n,3) + 232.17686518512448*lm11(n,S1) + 202.60567395706914*lm13(n,S1,S2,S3) elif variation == 18: - fit = -181.6939552271119/np.power(-1. + n,2) - 5911.194541729347/(-1. + n) + 27534.232647597233/np.power(n,2) - 4549.9059886744935*lm11(n,S1) + 305.05047772799065*lm13(n,S1,S2,S3) + fit = -691.6734321623419/np.power(-1. + n,2) - 3417.4240793927916/(-1. + n) + 22411.6434750231/np.power(n,2) - 3394.848223236357*lm11(n,S1) + 276.04609873762405*lm13(n,S1,S2,S3) elif variation == 19: - fit = -4078.395708944439/np.power(-1. + n,2) + 5408.59148938392/(-1. + n) + 3443.111172846758/np.power(n,4) + 17095.178652601353/np.power(n,3) + 212.46174952689813*lm13(n,S1,S2,S3) + fit = -3074.255121846279/np.power(-1. + n,2) + 5167.092611529961/(-1. + n) - 8517.21102404984/np.power(n,4) + 16793.629342505785/np.power(n,3) + 208.44893320267045*lm13(n,S1,S2,S3) elif variation == 20: - fit = -6300.379658737184/np.power(-1. + n,2) + 4822.632787569217/(-1. + n) + 50374.02833779294/np.power(n,4) + 7905.033644756689/np.power(n,2) + 206.16854967191063*lm13(n,S1,S2,S3) + fit = -5257.044527918616/np.power(-1. + n,2) + 4591.469890746334/(-1. + n) + 37585.871230195466/np.power(n,4) + 7765.593309542773/np.power(n,2) + 202.2667418438865*lm13(n,S1,S2,S3) elif variation == 21: - fit = -3915.3786995698256/np.power(-1. + n,2) + 5451.580654627375/(-1. + n) + 18349.375335216806/np.power(n,3) - 579.9569091789359/np.power(n,2) + 212.92345341087133*lm13(n,S1,S2,S3) + fit = -3477.5096784512552/np.power(-1. + n,2) + 5060.750476829951/(-1. + n) + 13691.12777479692/np.power(n,3) + 1434.6372023383353/np.power(n,2) + 207.3068180594*lm13(n,S1,S2,S3) else: - fit = -5243.037055009921/np.power(-1. + n,2) + 9562.656801160758/(-1. + n) + 15581.084298736878/np.power(n,4) + 5129.037104065377/np.power(n,3) - 2104.412099474839/np.power(n,2) - 6632.29384335349/(1. + n) - 344.8427724987991/(2. + n) - 479.6134161760297*lm11(n,S1) + 294.2480819006815*lm12(n,S1,S2) + 266.47872117598763*lm13(n,S1,S2,S3) + fit = -4659.8548692239365/np.power(-1. + n,2) + 8775.661049395696/(-1. + n) + 11906.360571226945/np.power(n,4) + 4192.865495685177/np.power(n,3) - 1036.6448907424908/np.power(n,2) - 5192.654929396816/(1. + n) - 520.4764518573357/(2. + n) - 302.22022583075585*lm11(n,S1) + 214.3960445752241*lm12(n,S1,S2) + 245.07815446568293*lm13(n,S1,S2,S3) return common + fit