diff --git a/docs/source/dev-tools/bench-coverage.csv b/docs/source/dev-tools/bench-coverage.csv index f79b58f2f..1ca89586e 100644 --- a/docs/source/dev-tools/bench-coverage.csv +++ b/docs/source/dev-tools/bench-coverage.csv @@ -1,7 +1,7 @@ -"feature \\ reference" APFEL QCDNUM xspace-bench -projectiles |T| "" |T| -EM |T| |T| |T| -NC |T| |T| |T| -CC |T| "" |T| -scale-variatons |T| |T| "" -target-mass-corrections |T| "" "" +"feature \\ reference" APFEL QCDNUM xspace-bench APFEL++ +projectiles |T| "" |T| |T| +EM |T| |T| |T| |T| +NC |T| |T| |T| |T| +CC |T| "" |T| |T| +scale-variatons |T| |T| "" |T| +target-mass-corrections |T| "" "" |T| diff --git a/docs/source/dev-tools/bench-fns.csv b/docs/source/dev-tools/bench-fns.csv index c2c3e9eef..f598e2508 100644 --- a/docs/source/dev-tools/bench-fns.csv +++ b/docs/source/dev-tools/bench-fns.csv @@ -1,4 +1,4 @@ -"|FNS| \\ reference" APFEL QCDNUM xspace-bench -|FFNS| |T| |T| "|T| [#f1]_" -|ZM-VFNS| |T| |T| |T| -FONLL "|T| [#f2]_" "" "|T| [#f2]_" +"|FNS| \\ reference" APFEL QCDNUM xspace-bench APFEL++ +|FFNS| |T| |T| "|T| [#f1]_" |T| +|ZM-VFNS| |T| |T| |T| |T| +|FFN0| |T| "" |T| |T| diff --git a/docs/source/dev-tools/benchmarks.rst b/docs/source/dev-tools/benchmarks.rst index 4bdd1549a..275923c14 100644 --- a/docs/source/dev-tools/benchmarks.rst +++ b/docs/source/dev-tools/benchmarks.rst @@ -30,7 +30,6 @@ also incoming projectiles, different type of currents, SV and TMC. :align: center .. [#f1] Only for NfFF=3 -.. [#f2] Only for charm threshold (FFNS3 to FFNS4 interpolation) .. csv-table:: Banchmarks coverage :file: ./bench-coverage.csv @@ -131,5 +130,23 @@ In |xspace-bench| |SF| are defined as follows: Given these definitions, benchmarks with `yadism` are possible only in the region :math:`m^2_{charm} < Q^2 < m^2_{bottom}` selecting either |ZM-VFNS| with :math:`F_X^{total}` -or |FFNS| with NfFF=3 and FONLL with NfFF=4. +or |FFNS| with NfFF=3. FONLL is implemented in the so called `scheme A` with and without damping factor. + +APFEL++ +------- + + +|APFEL++| is a C++ rewriting of the Fortran 77 evolution code |APFEL|. However, |APFEL++| is based on a completely new code design and +guarantees a better performance along with a more optimal memory management. +|APFEL++| is suitable for a wide range of tasks: from the solution of the DGLAP evolution equations to the computation of DIS +and single-inclusive-annihilation cross sections. + +|APFEL++| is also currently interfaced to PARTONS, a software dedicated to the phenomenology of Generalised Parton Distributions (GPDs) and TMDs, +and to xFitter. + + +SF in APFEL++ +~~~~~~~~~~~~~ + +The |APFEL++| definitions follow the ones of |APFEL| diff --git a/docs/source/dev-tools/metrics.rst b/docs/source/dev-tools/metrics.rst deleted file mode 100644 index 1732eb60b..000000000 --- a/docs/source/dev-tools/metrics.rst +++ /dev/null @@ -1,31 +0,0 @@ -Insights & Metrics -================== - -CodeCov -------- - -.. image:: https://codecov.io/gh/N3PDF/yadism/branch/master/graph/badge.svg?token=qgCFyUQ6oG - :target: https://codecov.io/gh/N3PDF/yadism - :alt: CodeCov-badge - -Powered by `pytest` coverage reports (in our use case), just display a nice -interface to navigate these reports and compare code coverage across multiple -commits/branches. - -Also able to merge different code coverage reports, even coming from different -tools. - -.. image:: https://codecov.io/gh/N3PDF/yadism/branch/master/graphs/sunburst.svg - :align: center - -CodeFactor ----------- - -.. image:: https://www.codefactor.io/repository/github/n3pdf/yadism/badge - :target: https://www.codefactor.io/repository/github/n3pdf/yadism - :alt: CodeFactor-badge - -Powered by `pylint` static analysis reports (in our use case). - -Also able to merge different code coverage reports, even coming from different -tools. diff --git a/docs/source/implementation/ESF.rst b/docs/source/implementation/ESF.rst index 3559e8d6c..4d87596bd 100644 --- a/docs/source/implementation/ESF.rst +++ b/docs/source/implementation/ESF.rst @@ -20,7 +20,7 @@ belong to a :class:`StructureFunction` instance of the respective kind. The kinds are defined by choosing one option for each of the following classes: -- ``F2`` or ``FL`` +- ``F2``, ``FL``, ``F3``, ``g1``, `gL``, `g4`` - ``light``, ``charm``, ``bottom``, ``top``, or ``total`` Sometimes an instance of a different kind it is needed to complete the diff --git a/docs/source/implementation/input.rst b/docs/source/implementation/input.rst deleted file mode 100644 index f78306e15..000000000 --- a/docs/source/implementation/input.rst +++ /dev/null @@ -1,29 +0,0 @@ -Input layer -=========== - -The input layer parse and validate the user input for launching the actual run, -enforcing: - -- single field constraints -- multiple fields constraints (*cross-constraints*) - -This layer can be used directly, so it is principle independent from anything -else in `yadism`, but it has been developed to be used mainly inside a `Runner` -instance. - -Example -------- - -Theory runcard -~~~~~~~~~~~~~~ - -.. todo:: - - - provide an example of a theory card - -Observables runcard -~~~~~~~~~~~~~~~~~~~ - -.. todo:: - - - provide at least a couple of examples of observables' cards diff --git a/docs/source/implementation/kernels.rst b/docs/source/implementation/kernels.rst index fcc5ab308..9e7467aa2 100644 --- a/docs/source/implementation/kernels.rst +++ b/docs/source/implementation/kernels.rst @@ -16,8 +16,8 @@ The actual physical combination are not as many as flavors, indeed |QCD| is flavor blind (in the massless case, and the only difference in the massive case are the value of the masses themselves). -In particular there are 3 relevant combinations, as described in -:doc:`../theory/coeff-funcs`. +In particular there are 3 relevant combinations, for polarized and +unpolarized |DIS| as described in :doc:`../theory/coeff-funcs`. .. todo:: @@ -37,11 +37,8 @@ In particular there are 3 relevant combinations, as described in (partons, operator, operator-error) by convolutions -Rearrange Singlet & Non-singlet -------------------------------- +Singlet & Non-singlet +--------------------- -.. todo:: - - describe redefinition of the singlet -> pure singlet from Vogt notation - - essentially include the already written note +For the distinction about singlet and non-singlet coefficient function, +see :doc:`../theory/nonsinglet`. \ No newline at end of file diff --git a/docs/source/implementation/runner.rst b/docs/source/implementation/runner.rst index ff0d8ca19..c02c74ab0 100644 --- a/docs/source/implementation/runner.rst +++ b/docs/source/implementation/runner.rst @@ -59,10 +59,6 @@ Some **handlers objects** are used to dispatch some isolated services. They are mostly not defined internally in :mod:`yadism` package, but mainly imported from :mod:`eko`. -Another common trait that characterize these handlers is the presence of a -method :func:`from_dict`, with which the object can be created loading the -required options directly from a suitable dictionary (that in a :class:`Runner` -object is always either `theory` or `observable` dictionary). Interpolator Dispatcher ~~~~~~~~~~~~~~~~~~~~~~~ diff --git a/docs/source/implementation/structure.rst b/docs/source/implementation/structure.rst index 1b7f1fae3..162ff144b 100644 --- a/docs/source/implementation/structure.rst +++ b/docs/source/implementation/structure.rst @@ -29,12 +29,10 @@ Essentially the flow of an execution is the following: 1. (**user** initiated) a :class:`~yadism.runner.Runner` is instantiated and it is passed the theory configuration, and the requested observables to compute (together with related configurations) -2. a check is performed on the user input (by an - :class:`~yadism.input.inspector.Inspector`) -3. the relevant global *service providers* are initialized and stored by the +2. the relevant global *service providers* are initialized and stored by the :class:`~yadism.runner.Runner` (like the :math:`\alpha_s` evolution, or the interpolation dispatcher, or the couplings computer) -4. the requested observables are scanned, and they are assigned to the +3. the requested observables are scanned, and they are assigned to the respective :class:`~yadism.sf.StructureFunction` / :class:`~yadism.xs.CrossSection` (acting as manager and caching storage) according to their kind and heavyness (but multiple kinematics will belong to @@ -42,17 +40,17 @@ Essentially the flow of an execution is the following: :class:`~yadism.xs.CrossSection`) each kinematic point will correspond to an instance of :class:`~yadism.esf.esf.EvaluatedStructureFunction` / :class:`~yadism.esf.exs.EvaluatedCrossSection` -5. (**user** initiated) output is requested -6. the request is propagated to the managers, and then to all the required +4. (**user** initiated) output is requested +5. the request is propagated to the managers, and then to all the required `ESF` objects -7. the `ESF` issues a request to the +6. the `ESF` issues a request to the :class:`~yadism.coefficient_functions.Combiner` for the relevant :class:`~yadism.coefficient_functions.kernels.Kernel` -8. all the :class:`~yadism.coefficient_functions.kernels.Kernel` are numerically +7. all the :class:`~yadism.coefficient_functions.kernels.Kernel` are numerically convoluted with the |PDF| interpolation polynomials -9. all the results are collected in an :class:`~yadism.output.Output` object and +8. all the results are collected in an :class:`~yadism.output.Output` object and returned to the user -10. (**user** initiated) the :class:`~yadism.output.Output` object might be +9. (**user** initiated) the :class:`~yadism.output.Output` object might be dumped on disk in one of the available formats Elements @@ -62,7 +60,6 @@ Elements :maxdepth: 2 runner - input kernels SF ESF diff --git a/docs/source/index.rst b/docs/source/index.rst index 390aabae6..605c3b9b5 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -52,7 +52,7 @@ In particular: :hidden: overview/features.rst - overview/tutorials/index.rst + overview/tutorials/tutorials.rst .. toctree:: :maxdepth: 1 @@ -84,9 +84,8 @@ In particular: :caption: Dev Tools :hidden: - dev-tools/tests.rst + dev-tools/benchmarks.rst dev-tools/yadmark.rst - dev-tools/metrics.rst dev-tools/code-todos.rst .. toctree:: diff --git a/docs/source/overview/features.rst b/docs/source/overview/features.rst index a6ffce436..569bd320a 100644 --- a/docs/source/overview/features.rst +++ b/docs/source/overview/features.rst @@ -28,7 +28,7 @@ according to their :ref:`heavyness ` (e.g. Moreover the following features are all available: -1. :doc:`flavor number schemes <../theory/fns>`: |FFNS|, |ZM-VFNS|, |FONLL| +1. :doc:`flavor number schemes <../theory/fns>`: |FFNS|, |ZM-VFNS|, |FFN0| 2. :doc:`scale variations <../theory/scale-variations>`: independent variations of factorization scale :math:`\mu_F` and renormalization scale :math:`\mu_R` 3. :ref:`target mass corrections ` diff --git a/docs/source/overview/tutorials/.gitignore b/docs/source/overview/tutorials/.gitignore new file mode 100644 index 000000000..819863bc5 --- /dev/null +++ b/docs/source/overview/tutorials/.gitignore @@ -0,0 +1,2 @@ +*.pineappl.lz4 +*.dat diff --git a/docs/source/overview/tutorials/benchmarks.ipynb b/docs/source/overview/tutorials/benchmarks.ipynb deleted file mode 100644 index 6cf61b7b2..000000000 --- a/docs/source/overview/tutorials/benchmarks.ipynb +++ /dev/null @@ -1,53 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "russian-guidance", - "metadata": {}, - "source": [ - "# Running Benchmarks\n", - "A good way of learning something about `yadism` it's running the benchmarks suite provided, and check the output through its `navigator`" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "perceived-aspect", - "metadata": {}, - "outputs": [], - "source": [] - }, - { - "cell_type": "markdown", - "id": "solid-paraguay", - "metadata": {}, - "source": [ - "## Unit tests\n", - "For more specific information about single functions and usage another good idea it's to have a look to how they are used in unit-tests.\n", - "\n", - "But the main option will always be the trivial one: **read the docs**." - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.6" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/docs/source/overview/tutorials/compare_data.ipynb b/docs/source/overview/tutorials/compare_data.ipynb new file mode 100644 index 000000000..0f7eef127 --- /dev/null +++ b/docs/source/overview/tutorials/compare_data.ipynb @@ -0,0 +1,607 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "nominated-inspection", + "metadata": {}, + "source": [ + "# Compare to Experimental Data\n", + "\n", + "We show how to compare `yadism` predictions to an HERA measurement (see [here](https://www.desy.de/h1zeus/herapdf20) for an overview),\n", + "specifically [this dataset](https://www.hepdata.net/record/ins1377206?version=1&table=Table%205).\n", + "\n", + "## Preparing the dataset\n", + "\n", + "Our dataset can be downloaded from the NNPDF server:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "2fada138-79b8-44c7-ad32-8ececc9979f3", + "metadata": {}, + "outputs": [], + "source": [ + "!wget -q -N https://data.nnpdf.science/yadism/HERA12B2_NCem.dat" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "1baa9ce5-ee95-46f9-a2e6-9682d5e295f7", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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" + ], + "text/plain": [ + " x Q2 Sigma\n", + "0 0.0008 60.0 1.483100\n", + "1 0.0013 90.0 1.466000\n", + "2 0.0015 90.0 1.421900\n", + "3 0.0020 90.0 1.270000\n", + "4 0.0016 120.0 1.438800\n", + ".. ... ... ...\n", + "154 0.4000 20000.0 0.205990\n", + "155 0.6500 20000.0 0.017364\n", + "156 0.4000 30000.0 0.230730\n", + "157 0.6500 30000.0 0.044179\n", + "158 0.6500 50000.0 0.082210\n", + "\n", + "[159 rows x 3 columns]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import pandas as pd\n", + "\n", + "# Load the experimental data via pandas\n", + "data = pd.read_csv(\"HERA12B2_NCem.dat\", sep=\"\\s+\")\n", + "\n", + "data[[\"x\", \"Q2\", \"Sigma\"]]" + ] + }, + { + "cell_type": "markdown", + "id": "60da4349-dddc-406e-a3f8-2e81c7e1c767", + "metadata": {}, + "source": [ + "## Computing the yadism predictions\n", + "\n", + "We are now going to compute the `yadism` predictions at the same kinematic points as provided by the experimental measurements. First, we need to prepare the theory and observable cards." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "9849edb4-ae32-49b2-ba6d-a96bf2cdb6f4", + "metadata": {}, + "outputs": [], + "source": [ + "import warnings\n", + "import yadism\n", + "from eko import interpolation\n", + "from yadbox.export import dump_pineappl_to_file" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "5920d43e-b8b4-496a-97c8-98b5c2325716", + "metadata": {}, + "outputs": [], + "source": [ + "theory_card = {\n", + " \"PTO\": 2,\n", + " \"FNS\": \"ZM-VFNS\",\n", + " \"DAMP\": 0,\n", + " \"IC\": 1,\n", + " \"IB\": 0,\n", + " \"ModEv\": \"TRN\",\n", + " \"ModSV\": \"unvaried\",\n", + " \"XIR\": 1.0,\n", + " \"XIF\": 1.0,\n", + " \"NfFF\": 5,\n", + " \"MaxNfAs\": 5,\n", + " \"MaxNfPdf\": 5,\n", + " \"Q0\": 1.65,\n", + " \"alphas\": 0.118,\n", + " \"Qref\": 91.2,\n", + " \"nf0\": 4,\n", + " \"nfref\": 5,\n", + " \"QED\": 0,\n", + " \"alphaqed\": 0.007496252,\n", + " \"Qedref\": 1.777,\n", + " \"SxRes\": 0,\n", + " \"SxOrd\": \"LL\",\n", + " \"HQ\": \"POLE\",\n", + " \"mc\": 1.51,\n", + " \"Qmc\": 1.51,\n", + " \"kcThr\": 1.0,\n", + " \"mb\": 4.92,\n", + " \"Qmb\": 4.92,\n", + " \"kbThr\": 4.0,\n", + " \"mt\": 172.5,\n", + " \"Qmt\": 172.5,\n", + " \"ktThr\": 1.0,\n", + " \"CKM\": \"0.97428 0.22530 0.003470 0.22520 0.97345 0.041000 0.00862 0.04030 0.999152\",\n", + " \"MZ\": 91.1876,\n", + " \"MW\": 80.398,\n", + " \"GF\": 1.1663787e-05,\n", + " \"SIN2TW\": 0.23126,\n", + " \"TMC\": 1,\n", + " \"MP\": 0.938,\n", + " \"global_nx\": 0,\n", + " \"EScaleVar\": 1,\n", + " \"kDIScThr\": 1.0,\n", + " \"kDISbThr\": 1.0,\n", + " \"kDIStThr\": 1.0,\n", + " \"n3lo_cf_variation\": 0,\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "ff60baae-65ee-4544-af2d-3c7a23a5734d", + "metadata": {}, + "outputs": [], + "source": [ + "observables_card = {\n", + " \"PolarizationDIS\": 0.0,\n", + " \"ProjectileDIS\": \"electron\",\n", + " \"PropagatorCorrection\": 0.0,\n", + " \"TargetDIS\": \"proton\",\n", + " \"interpolation_is_log\": True,\n", + " \"interpolation_polynomial_degree\": 4,\n", + " \"interpolation_xgrid\": interpolation.lambertgrid(60).tolist(),\n", + " \"observables\": {\"XSHERANC_total\": []},\n", + " \"prDIS\": \"NC\",\n", + " \"NCPositivityCharge\": None,\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "6e68559d-2f4e-4a0c-a372-8dc836bd1f8a", + "metadata": {}, + "outputs": [], + "source": [ + "def compute_predicionts() -> None:\n", + " \"\"\"Compute yadism prediction for all experimental bins.\"\"\"\n", + " # prepare the kinematics for all the datapoints\n", + " curobs = data.apply(\n", + " lambda dat: {\"x\": dat[\"x\"], \"Q2\": dat[\"Q2\"], \"y\": dat[\"y\"]},\n", + " axis=1,\n", + " )\n", + "\n", + " # Update the observable & kinematics in the `observable_card`\n", + " obs_def = {\n", + " \"observables\" : {\"XSHERANC_total\": list(curobs.to_dict().values())}\n", + " } # As we saw in the previous tutorial, it has to be a dict[dict[list]]\n", + " observables_card.update(obs_def)\n", + "\n", + " with warnings.catch_warnings():\n", + " warnings.simplefilter(\"ignore\") # suppress noisy warnings\n", + " out = yadism.run_yadism(theory_card, observables_card)\n", + "\n", + " # Dump computations as a pineappl grid for later use\n", + " dump_pineappl_to_file(\n", + " out, \"HERA_NC_318GEV_EM_SIGMARED.pineappl.lz4\", \"XSHERANC_total\"\n", + " )" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "006952bf-d2aa-46c0-a1a5-53f19af94068", + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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+       " • XSHERANC_total at 159 pts                                                                                       \n",
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\n" + ], + "text/plain": [ + "\n", + "\u001b[1;33m • \u001b[0mXSHERANC_total at 159 pts \n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
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+       "                                                    Calculation                                                    \n",
+       "
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yadism took off! please stay tuned ...\n",
+       "
\n" + ], + "text/plain": [ + "yadism took off! please stay tuned \u001b[33m...\u001b[0m\n" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "
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+      ],
+      "text/plain": [
+       "\u001b[?25l"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "b913a8eaf91d4163baef0654dc9c0a8f",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Output()"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
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+       "
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+      ],
+      "text/plain": [
+       "\n",
+       "\u001b[?25h\r\u001b[1A\u001b[2K"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
took 86.98 s\n",
+       "
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+      ],
+      "text/plain": [
+       "\u001b[36mtook \u001b[0m\u001b[1;36m86.98\u001b[0m\u001b[36m s\u001b[0m\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "# Compute the predictions - slightly heavier due to complexity & number of datapoints\n",
+    "compute_predicionts()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "ee0cb707-eb66-4888-8ad8-142c3556e26f",
+   "metadata": {},
+   "source": [
+    "## Loading and comparing to HERA\n",
+    "\n",
+    "Now, that we have our pre-computed predictions in the form of a PineAPPL grid, we can compare the results to the HERA measurements. To do so, we can load the grid and convolute it with a PDF set, specifically the NNLO NNPDF4.0 set."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "8fa0f803-de73-4737-a40a-7ffeebf6de77",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import lhapdf\n",
+    "import pineappl"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "b631e769-d706-4d9a-ac30-006a24dffca8",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "LHAPDF 6.4.0 loading /home/felix/local/share/LHAPDF/NNPDF40_nnlo_as_01180/NNPDF40_nnlo_as_01180_0000.dat\n",
+      "NNPDF40_nnlo_as_01180 PDF set, member #0, version 1; LHAPDF ID = 331100\n"
+     ]
+    }
+   ],
+   "source": [
+    "# Load only the central member\n",
+    "pdf = lhapdf.mkPDF(\"NNPDF40_nnlo_as_01180\", 0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "0e0f5c2e-74ce-45ea-9064-749eb3ad47df",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Load the pre-computed grid\n",
+    "grid = pineappl.grid.Grid.read(\"HERA_NC_318GEV_EM_SIGMARED.pineappl.lz4\")\n",
+    "\n",
+    "# Convolute with the PDF\n",
+    "yadism_data = grid.convolute_with_one(2212, pdf.xfxQ2, pdf.alphasQ2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "5995d40f-2e53-4d1d-8d5e-84798e127647",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# Combine the exp measurements and Yadism preds into one table\n",
+    "data_vs_yadism_df = pd.concat(\n",
+    "    [\n",
+    "        data[\"Q2\"],\n",
+    "        data[\"x\"],\n",
+    "        data[\"Sigma\"],\n",
+    "        pd.DataFrame([yadism_data], index=[\"yadism\"]).T,\n",
+    "    ],\n",
+    "    axis=1,\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "16e935e5",
+   "metadata": {},
+   "source": [
+    "Finally, we can compare our theory predictions and the experimental data graphically."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "a9ca7478-6101-458a-8f79-ec039111f640",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "def plot_comparisons_q2(df: pd.DataFrame, q2_value: float = 300) -> None:\n",
+    "    fig, ax = plt.subplots(figsize=(5, 3.75), layout=\"tight\")\n",
+    "\n",
+    "    # Select corresponding Q2 values\n",
+    "    df_q2 = df[df.Q2 == q2_value]\n",
+    "\n",
+    "    # Plot measurements and yadism preds\n",
+    "    ax.plot(df_q2.x, df_q2[\"Sigma\"], \"o\", label=\"EXP\")\n",
+    "    ax.plot(df_q2.x, df_q2[\"yadism\"], \"rs\", label=\"Yadism\")\n",
+    "\n",
+    "    ax.set_xlabel(\"x\")\n",
+    "    ax.set_ylabel(\"xsec\")\n",
+    "    ax.legend()\n",
+    "    ax.set_xscale(\"log\")\n",
+    "    ax.set_title(f\"HERA: $Q^2 = {q2_value}~ \\\\mathrm{{GeV}}^2$\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "cde1c144-2195-48d2-ac9c-05b09cb2b088",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "image/png": 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",
+      "text/plain": [
+       "
"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "plot_comparisons_q2(data_vs_yadism_df)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "6eeb13ce",
+   "metadata": {},
+   "source": [
+    "Note that we are using the ZM-VFNS here, so we don't expect perfect agreement as heavy quark effects are only entering through the PDF evolution."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "yadism-QljnF84o-py3.10",
+   "language": "python",
+   "name": "yadism-qljnf84o-py3.10"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/source/overview/tutorials/getting_started.ipynb b/docs/source/overview/tutorials/getting_started.ipynb
new file mode 100644
index 000000000..581990ef8
--- /dev/null
+++ b/docs/source/overview/tutorials/getting_started.ipynb
@@ -0,0 +1,679 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "bfff8f0c-740e-4177-a642-13e9d0a0cc63",
+   "metadata": {},
+   "source": [
+    "# Getting Started\n",
+    "\n",
+    "## Installation \n",
+    "\n",
+    "In order to start using `yadism`, one first needs to install it and some of its extra-dependencies. The easiest way to install the latest stable version of `yadism` is via `pip` using the following command:\n",
+    "\n",
+    "```sh\n",
+    "pip install 'yadism[mark, box]'\n",
+    "```\n",
+    "\n",
+    "In addition to installing the main `yadism` package, the above command also installs `yadmark` and `yadbox`. `yadmark` is package that provides APIs to perform the benchmark of `yadism` to other DIS codes (e.g. `APFEL`, `APFEL++`, `QCDNUM`). `yadbox` instead provides an interface to `PineAPPL` to store predictions in the form of fast-interpolation grids.\n",
+    "\n",
+    "In order to check that `yadism` was installed properly, one can check the version:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "id": "ded2fb96-9fe9-4503-8418-bfcfb6d53998",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'0.0.0'"
+      ]
+     },
+     "execution_count": 1,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "import yadism\n",
+    "yadism.__version__"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "valuable-theater",
+   "metadata": {},
+   "source": [
+    "## Preparing the run cards\n",
+    "\n",
+    "Yadism takes as inputs **two runcards** whose representations are given in terms of python dictionaries. That is, one needs:\n",
+    "- an **observable card** which contains the details on the observable to be computed\n",
+    "- a **theory card** which contains the various theory settings to compute the observable in question\n",
+    "\n",
+    "Below is an example of an observable card in which the meaning of each key is also specified:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "announced-petite",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "observable_card = {\n",
+    "    # Process type: \"EM\", \"NC\", \"CC\"\n",
+    "    \"prDIS\": \"NC\",\n",
+    "    # Projectile: \"electron\", \"positron\", \"neutrino\", \"antineutrino\"\n",
+    "    \"ProjectileDIS\": \"electron\",\n",
+    "    # Scattering target: \"proton\", \"neutron\", \"isoscalar\", \"lead\", \"iron\", \"neon\" or \"marble\"\n",
+    "    \"TargetDIS\": \"proton\",\n",
+    "    # Interpolation: if True use log interpolation\n",
+    "    \"interpolation_is_log\": True,\n",
+    "    # Interpolation: polynomial degree, 1 = linear, ...\n",
+    "    \"interpolation_polynomial_degree\": 4,\n",
+    "    # Interpolation: xgrid values\n",
+    "    # Note: for illustrative purposes the grid is chosen very small here\n",
+    "    \"interpolation_xgrid\": [1e-7, 1e-6, 1e-5, 1e-4, 1e-3, 1e-2, 1e-1, 1.0],\n",
+    "    # Observables configurations\n",
+    "    \"observables\": {\n",
+    "        \"XSHERANCAVG_charm\": [\n",
+    "            {\n",
+    "                \"y\": 0.8240707777909629,\n",
+    "                \"x\": 3e-05,\n",
+    "                \"Q2\": 2.5,\n",
+    "            },\n",
+    "            {\n",
+    "                \"y\": 0.3531731904818413,\n",
+    "                \"x\": 7e-05,\n",
+    "                \"Q2\": 2.5,\n",
+    "            },\n",
+    "            # Add here the kinematics of other datapoints\n",
+    "        ],\n",
+    "        # Potentially include observables other than XSHERANCAVG_charm,\n",
+    "        # each of them has to be: TYPE_heaviness, where heaviness can take:\n",
+    "        # \"charm\", \"bottom\", \"top\", \"total\" or \"light\".\n",
+    "    },\n",
+    "    # Projectile polarization faction, float from 0 to 1.\n",
+    "    \"PolarizationDIS\": 0.0,\n",
+    "    # Exchanged boson propagator correction\n",
+    "    \"PropagatorCorrection\": 0.0,\n",
+    "    # Restrict boson coupling to a single parton ? Monte Carlo PID or None for all partons\n",
+    "    \"NCPositivityCharge\": None,\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "dc1b79fa-7d14-4ed6-a8ae-0a588ebe5582",
+   "metadata": {},
+   "source": [
+    "The `observables` key in the `observable_card` (which is also a dictionary) can contain multiple elements whose keys must represent structure functions or cross-sections. For the list of available observables, refer to the following [part](https://yadism.readthedocs.io/en/latest/theory/intro.html#) of the documentation.\n",
+    "\n",
+    "Similarly, below is an example of a `theory card` defining the theory parameters:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "90df79a9-31cb-40db-ac95-0b88469c1723",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "theory_card = {\n",
+    "    # QCD perturbative order\n",
+    "    \"PTO\": 2,  # perturbative order in alpha_s: 0 = LO (alpha_s^0), 1 = NLO (alpha_s^1) ...\n",
+    "\n",
+    "    # SM parameters and masses\n",
+    "    \"CKM\": \"0.97428 0.22530 0.003470 0.22520 0.97345 0.041000 0.00862 0.04030 0.999152\",  # CKM matrix elements\n",
+    "    \"GF\": 1.1663787e-05,  # [GeV^-2] Fermi coupling constant\n",
+    "    \"MP\": 0.938,  # [GeV] proton mass\n",
+    "    \"MW\": 80.398,  # [GeV] W boson mass\n",
+    "    \"MZ\": 91.1876,  # [GeV] Z boson mass\n",
+    "    \"alphaqed\": 0.007496252,  # alpha_em value\n",
+    "    \"kcThr\": 1.0,  # ratio of the charm matching scale over the charm mass\n",
+    "    \"kbThr\": 1.0,  # ratio of the bottom matching scale over the bottom mass\n",
+    "    \"ktThr\": 1.0,  # ratio of the top matching scale over the top mass\n",
+    "    \"mc\": 1.51,  # [GeV] charm mass\n",
+    "    \"mb\": 4.92,  # [GeV] bottom mass\n",
+    "    \"mt\": 172.5,  # [GeV] top mass\n",
+    "\n",
+    "    # Flavor number scheme settings\n",
+    "    \"FNS\": \"FFNS\",  # Flavour Number Scheme, options: \"FFNS\", \"FFN0\", \"ZM-VFNS\"\n",
+    "    \"NfFF\": 4,  # (fixed) number of running flavors, only for FFNS or FFN0 schemes\n",
+    "    \"Q0\": 1.65,  # [GeV] reference scale for the flavor patch determination\n",
+    "    \"nf0\": 4,  # number of active flavors at the Q0 reference scale\n",
+    "\n",
+    "    # Alphas settings and boundary conditions\n",
+    "    \"Qref\": 91.2,  # [GeV] reference scale for the alphas value\n",
+    "    \"nfref\": 5,  # number of active flavors at the reference scale Qref\n",
+    "    \"alphas\": 0.118,  # alphas value at the reference scale\n",
+    "    \"MaxNfAs\": 5,  # maximum number of flavors in running of strong coupling\n",
+    "    \"QED\": 0,  # QED correction to running of strong coupling: 0 = disabled, 1 = allowed\n",
+    "\n",
+    "    # Scale Variations\n",
+    "    \"XIF\": 1.0,  # ratio of factorization scale over the hard scattering scale\n",
+    "    \"XIR\": 1.0,  # ratio of renormalization scale over the hard scattering scale\n",
+    "\n",
+    "    # Other settings\n",
+    "    \"IC\": 1,  # 0 = perturbative charm only, 1 = intrinsic charm allowed\n",
+    "    \"TMC\": 1,  # include target mass corrections: 0 = disabled, 1 = leading twist, 2 = higher twist approximated, 3 = higher twist exact\n",
+    "    \"n3lo_cf_variation\": 0,  # N3LO coefficient functions variation: -1 = lower bound, 0 = central , 1 = upper bound\n",
+    "\n",
+    "    # Other EKO settings, not relevant for Yadism\n",
+    "    \"HQ\": \"POLE\",  # heavy quark mass scheme (not yet implemented in yadism)\n",
+    "    \"MaxNfPdf\": 5,  # maximum number of flavors in running of PDFs (ignored by yadism)\n",
+    "    \"ModEv\": \"EXA\",  # evolution solver for PDFs (ignored by yadism)\n",
+    "}"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "169b82a0-abdd-4687-9ffe-9df38446a550",
+   "metadata": {},
+   "source": [
+    "Note that a template observable card is provided by `yadmark` and contains the default `yadism` values. One can thus start from the default card and overwrite the values."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "246f1d7a-e7e3-48ab-9bf2-44c8352adc39",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{\n",
+      "    \"NCPositivityCharge\": null,\n",
+      "    \"PolarizationDIS\": 0,\n",
+      "    \"ProjectileDIS\": \"electron\",\n",
+      "    \"PropagatorCorrection\": 0,\n",
+      "    \"TargetDIS\": \"proton\",\n",
+      "    \"interpolation_is_log\": true,\n",
+      "    \"interpolation_polynomial_degree\": 4,\n",
+      "    \"interpolation_xgrid\": [\n",
+      "        1e-07,\n",
+      "        1.6102620275609392e-07,\n",
+      "        2.592943797404667e-07,\n",
+      "        4.1753189365604003e-07,\n",
+      "        6.723357536499335e-07,\n",
+      "        1.0826367338740541e-06,\n",
+      "        1.7433288221999873e-06,\n",
+      "        2.8072162039411756e-06,\n",
+      "        4.520353656360241e-06,\n",
+      "        7.2789538439831465e-06,\n",
+      "        1.1721022975334793e-05,\n",
+      "        1.8873918221350995e-05,\n",
+      "        3.039195382313195e-05,\n",
+      "        4.893900918477499e-05,\n",
+      "        7.880462815669905e-05,\n",
+      "        0.0001268961003167922,\n",
+      "        0.00020433597178569417,\n",
+      "        0.00032903445623126676,\n",
+      "        0.0005298316906283707,\n",
+      "        0.0008531678524172806,\n",
+      "        0.0013738237958832637,\n",
+      "        0.00221221629107045,\n",
+      "        0.003562247890262444,\n",
+      "        0.005736152510448681,\n",
+      "        0.009236708571873866,\n",
+      "        0.014873521072935119,\n",
+      "        0.02395026619987486,\n",
+      "        0.03856620421163472,\n",
+      "        0.06210169418915616,\n",
+      "        0.1,\n",
+      "        0.1473684210526316,\n",
+      "        0.19473684210526315,\n",
+      "        0.24210526315789474,\n",
+      "        0.2894736842105263,\n",
+      "        0.33684210526315794,\n",
+      "        0.38421052631578945,\n",
+      "        0.43157894736842106,\n",
+      "        0.4789473684210527,\n",
+      "        0.5263157894736842,\n",
+      "        0.5736842105263158,\n",
+      "        0.6210526315789474,\n",
+      "        0.6684210526315789,\n",
+      "        0.7157894736842105,\n",
+      "        0.7631578947368421,\n",
+      "        0.8105263157894737,\n",
+      "        0.8578947368421053,\n",
+      "        0.9052631578947369,\n",
+      "        0.9526315789473684,\n",
+      "        1.0\n",
+      "    ],\n",
+      "    \"observables\": {},\n",
+      "    \"prDIS\": \"EM\"\n",
+      "}\n"
+     ]
+    }
+   ],
+   "source": [
+    "import json # just used for pretty-printing\n",
+    "from yadmark.data.observables import default_card # imports the default yadism observable card\n",
+    "\n",
+    "print(json.dumps(default_card, sort_keys=False, indent=4))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "5083afea-4ac9-483d-93b9-f0473cbc46b0",
+   "metadata": {},
+   "source": [
+    "## Computing predictions\n",
+    "\n",
+    "Now that we have defined our observable and theory, we can now compute the corresponding preditions. This can be easily done by running the following:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 5,
+   "id": "b7d95bf6-4536-41a5-9505-07a8743e5f6e",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "
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+       "                                      │                                    │                                       \n",
+       "                                      │ __     __       _ _                │                                       \n",
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+       "                                      │   \\   / _` |/ _` | / __| '_ ` _ \\  │                                       \n",
+       "                                      │    | | (_| | (_| | \\__ \\ | | | | | │                                       \n",
+       "                                      │    |_|\\__,_|\\__,_|_|___/_| |_| |_| │                                       \n",
+       "                                      │                                    │                                       \n",
+       "                                      └────────────────────────────────────┘                                       \n",
+       "
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+      ],
+      "text/plain": [
+       "                                      \u001b[35m┌────────────────────────────────────┐\u001b[0m                                       \n",
+       "                                      \u001b[35m│\u001b[0m\u001b[35m                                    \u001b[0m\u001b[35m│\u001b[0m                                       \n",
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+       "                                      \u001b[35m│\u001b[0m\u001b[35m \u001b[0m\u001b[35m  \\   / _` |/ _` | / __| '_ ` _ \\\u001b[0m\u001b[35m \u001b[0m\u001b[35m \u001b[0m\u001b[35m│\u001b[0m                                       \n",
+       "                                      \u001b[35m│\u001b[0m\u001b[35m \u001b[0m\u001b[35m   | | (_| | (_| | \\__ \\ | | | | |\u001b[0m\u001b[35m \u001b[0m\u001b[35m│\u001b[0m                                       \n",
+       "                                      \u001b[35m│\u001b[0m\u001b[35m \u001b[0m\u001b[35m   |_|\\__,_|\\__,_|_|___/_| |_| |_|\u001b[0m\u001b[35m \u001b[0m\u001b[35m│\u001b[0m                                       \n",
+       "                                      \u001b[35m│\u001b[0m\u001b[35m                                    \u001b[0m\u001b[35m│\u001b[0m                                       \n",
+       "                                      \u001b[35m└────────────────────────────────────┘\u001b[0m                                       \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n",
+       "                                                       Plan                                                        \n",
+       "
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+      ],
+      "text/plain": [
+       "\n",
+       "                                                       \u001b[1;4mPlan\u001b[0m                                                        \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n",
+       " • XSHERANCAVG_charm at 2 pts                                                                                      \n",
+       "
\n"
+      ],
+      "text/plain": [
+       "\n",
+       "\u001b[1;33m • \u001b[0mXSHERANCAVG_charm at 2 pts                                                                                      \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
\n",
+       "                                                    Calculation                                                    \n",
+       "
\n"
+      ],
+      "text/plain": [
+       "\n",
+       "                                                    \u001b[1;4mCalculation\u001b[0m                                                    \n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
yadism took off! please stay tuned ...\n",
+       "
\n"
+      ],
+      "text/plain": [
+       "yadism took off! please stay tuned \u001b[33m...\u001b[0m\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
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+      ],
+      "text/plain": [
+       "\u001b[?25l"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
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+       "\u001b[?25h
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+      ],
+      "text/plain": [
+       "\n",
+       "\u001b[?25h"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
took 0.36 s\n",
+       "
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+      ],
+      "text/plain": [
+       "\u001b[36mtook \u001b[0m\u001b[1;36m0.36\u001b[0m\u001b[36m s\u001b[0m\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "import warnings\n",
+    "\n",
+    "with warnings.catch_warnings():\n",
+    "    warnings.simplefilter(\"ignore\") # skip noisy warnings\n",
+    "    out = yadism.run_yadism(theory_card, observable_card)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "a1d79202-30d1-465f-9ce2-008fc760ebf1",
+   "metadata": {},
+   "source": [
+    "`out` is an object of type `yadism.output.Output` from which one can perform various operations. In our example, we are interested in convoluting it with a PDF set in the [LHAPDF](https://lhapdf.hepforge.org/) format.\n",
+    "\n",
+    "To do so, first we need to import the `lhapdf` package. For this example, we will use the NNLO NNPDF4.0 set: `NNPDF40_nnlo_as_01180`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "bc6f3aac-802b-4073-9e6a-e18e54f3ef85",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "LHAPDF 6.5.0 loading /home/tanjona/miniconda3/envs/yadism/share/LHAPDF/NNPDF40_nnlo_as_01180/NNPDF40_nnlo_as_01180_0000.dat\n",
+      "NNPDF40_nnlo_as_01180 PDF set, member #0, version 1; LHAPDF ID = 331100\n"
+     ]
+    }
+   ],
+   "source": [
+    "import lhapdf\n",
+    "\n",
+    "# load the PDF set\n",
+    "pdf = lhapdf.mkPDF(\"NNPDF40_nnlo_as_01180\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "359f3118-a317-4345-8e73-bc810b92ea92",
+   "metadata": {},
+   "source": [
+    "The convolution can simply be performed as follow:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "9b983dd8-4724-439c-bdab-773879308985",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "
[13:09:24] INFO     Atlas [0.00e+00 - 2.28e+00 - 2.42e+01 - 2.98e+04 - inf], ref=8317.44 @ 5        matchings.py:69\n",
+       "
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+      ],
+      "text/plain": [
+       "\u001b[2;36m[13:09:24]\u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Atlas \u001b[1m[\u001b[0m\u001b[1;36m0.00e+00\u001b[0m - \u001b[1;36m2.28e+00\u001b[0m - \u001b[1;36m2.42e+01\u001b[0m - \u001b[1;36m2.98e+04\u001b[0m - inf\u001b[1m]\u001b[0m, \u001b[33mref\u001b[0m=\u001b[1;36m8317\u001b[0m\u001b[1;36m.44\u001b[0m @ \u001b[1;36m5\u001b[0m        \u001b]8;id=490630;file:///home/tanjona/miniconda3/envs/yadism/lib/python3.10/site-packages/eko/matchings.py\u001b\\\u001b[2mmatchings.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=61240;file:///home/tanjona/miniconda3/envs/yadism/lib/python3.10/site-packages/eko/matchings.py#69\u001b\\\u001b[2m69\u001b[0m\u001b]8;;\u001b\\\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
           INFO     Strong Coupling: a_s(µ_R^2=8317.440000)^(nf=5)=0.009390=0.118000/(4π)          couplings.py:458\n",
+       "
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+      ],
+      "text/plain": [
+       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Strong Coupling: \u001b[1;35ma_s\u001b[0m\u001b[1m(\u001b[0mµ_R^\u001b[1;36m2\u001b[0m=\u001b[1;36m8317\u001b[0m\u001b[1;36m.440000\u001b[0m\u001b[1m)\u001b[0m^\u001b[1m(\u001b[0m\u001b[33mnf\u001b[0m=\u001b[1;36m5\u001b[0m\u001b[1m)\u001b[0m=\u001b[1;36m0.\u001b[0m\u001b[1;36m009390\u001b[0m=\u001b[1;36m0\u001b[0m\u001b[1;36m.118000\u001b[0m/\u001b[1m(\u001b[0m4π\u001b[1m)\u001b[0m          \u001b]8;id=709662;file:///home/tanjona/miniconda3/envs/yadism/lib/python3.10/site-packages/eko/couplings.py\u001b\\\u001b[2mcouplings.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=838466;file:///home/tanjona/miniconda3/envs/yadism/lib/python3.10/site-packages/eko/couplings.py#458\u001b\\\u001b[2m458\u001b[0m\u001b]8;;\u001b\\\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "text/html": [
+       "
           INFO     Atlas [0.00e+00 - 2.28e+00 - 2.42e+01 - 2.98e+04 - inf], ref=8317.44 @ 5        matchings.py:69\n",
+       "
\n"
+      ],
+      "text/plain": [
+       "\u001b[2;36m          \u001b[0m\u001b[2;36m \u001b[0m\u001b[34mINFO    \u001b[0m Atlas \u001b[1m[\u001b[0m\u001b[1;36m0.00e+00\u001b[0m - \u001b[1;36m2.28e+00\u001b[0m - \u001b[1;36m2.42e+01\u001b[0m - \u001b[1;36m2.98e+04\u001b[0m - inf\u001b[1m]\u001b[0m, \u001b[33mref\u001b[0m=\u001b[1;36m8317\u001b[0m\u001b[1;36m.44\u001b[0m @ \u001b[1;36m5\u001b[0m        \u001b]8;id=369258;file:///home/tanjona/miniconda3/envs/yadism/lib/python3.10/site-packages/eko/matchings.py\u001b\\\u001b[2mmatchings.py\u001b[0m\u001b]8;;\u001b\\\u001b[2m:\u001b[0m\u001b]8;id=408583;file:///home/tanjona/miniconda3/envs/yadism/lib/python3.10/site-packages/eko/matchings.py#69\u001b\\\u001b[2m69\u001b[0m\u001b]8;;\u001b\\\n"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "values = out.apply_pdf(pdf)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "a56aee13-b08b-492f-80d0-3487bea74318",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "{\n",
+      "    \"XSHERANCAVG_charm\": [\n",
+      "        {\n",
+      "            \"x\": 3e-05,\n",
+      "            \"Q2\": 2.5,\n",
+      "            \"result\": -0.9959496128078331,\n",
+      "            \"error\": 1.281070214968848e-08,\n",
+      "            \"y\": 0.8240707777909629\n",
+      "        },\n",
+      "        {\n",
+      "            \"x\": 7e-05,\n",
+      "            \"Q2\": 2.5,\n",
+      "            \"result\": -0.7710853256052412,\n",
+      "            \"error\": 2.3298246570353407e-08,\n",
+      "            \"y\": 0.3531731904818413\n",
+      "        }\n",
+      "    ]\n",
+      "}\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(json.dumps(values, sort_keys=False, indent=4))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "2c0ffc4a-bb6b-4d89-9a01-1d2c93e49995",
+   "metadata": {},
+   "source": [
+    "We can see that `values` is a dictionary containing one element whose key is the name of the observable (as we defined above). If we had defined two observables in the `observable_card`, `values` would also contain two elements."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "519b8537-9c09-4a66-bf44-ff47e1879449",
+   "metadata": {},
+   "source": [
+    "## Dumping predictions into fast-interpolation grids\n",
+    "\n",
+    "We learned from the previous sections how to compute an observable using `yadism` and now we'll see how to tabulate the output of `yadism.run_yadism` into a fast-interpolation table. This has the convenient advantage that one can re-use the same computations without the need to re-run `yadism` (to convolute with different PDF sets for example).\n",
+    "\n",
+    "One of the main advantage of `yadism` is its interface with PineAPPL - a library providing fast interpolation into a unique format suitable for various HEP-related softwares. \n",
+    "\n",
+    "Each observable defined in `observable_card` can be dumped into its own fast-interpolation grid. The steps are as follow:"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "7f914e87-bb05-47c7-a850-11a18e6cfdb5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# import function that dumps the predictions into a Pineappl format\n",
+    "from yadbox.export import dump_pineappl_to_file\n",
+    "\n",
+    "# Extract the names of the different observables (in case there are many)\n",
+    "list_observables = observable_card['observables'].keys()\n",
+    "\n",
+    "# Dump each observable into a PineAPPL grid\n",
+    "for obs in list_observables:\n",
+    "    dump_pineappl_to_file(out, f\"outputgrid_{obs}.pineappl.lz4\", f\"{obs}\")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7dffb5fd-9e84-4982-b9d4-a4f077a573e8",
+   "metadata": {},
+   "source": [
+    "Our PineAPPL grid has now been written on the disk. Note that the extension has to be `pineappl.lz4`."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "703b29ce-9068-44af-b72b-1144bad805e6",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "outputgrid_XSHERANCAVG_charm.pineappl.lz4\n"
+     ]
+    }
+   ],
+   "source": [
+    "!ls outputgrid_*"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "0c887943-be93-4a0f-815b-1317ad04db2c",
+   "metadata": {},
+   "source": [
+    "To load the pre-computed predictions, we need to import the `pineappl` package. Given that `pineappl` is a dependency of `yadism` it was already installed so we don't have to install it again."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "ebf75d0e-965a-46b1-a3a3-e20eeb1d5e15",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "# imports the pineappl package\n",
+    "import pineappl\n",
+    "\n",
+    "# Read the pineappl grid saved earlier\n",
+    "grid = pineappl.grid.Grid.read(\"./outputgrid_XSHERANCAVG_charm.pineappl.lz4\")\n",
+    "\n",
+    "# Convolute the grid with the same PDF as above, 2212 is the PID of the proton\n",
+    "results = grid.convolute_with_one(2212, pdf.xfxQ2, pdf.alphasQ2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "fc268946-3f84-4f63-be98-a899adf9512c",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "[-0.98699882 -0.7640712 ]\n"
+     ]
+    }
+   ],
+   "source": [
+    "print(results)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "c114b40d-9a40-4d73-8609-ab8761fe37a0",
+   "metadata": {},
+   "source": [
+    "As we can see, we get similar results to what we got before. Now, the `results` is just an array of two dimension corresponding to the different kinematic values."
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "yadism",
+   "language": "python",
+   "name": "yadism"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.10.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/docs/source/overview/tutorials/index.rst b/docs/source/overview/tutorials/index.rst
deleted file mode 100644
index d0109f913..000000000
--- a/docs/source/overview/tutorials/index.rst
+++ /dev/null
@@ -1,13 +0,0 @@
-Tutorials
-=========
-
-Instead of bare examples is better to have full tutorials!
-
-If I will have ever the time to write them this section will be populated by
-tutorials on how to use `yadism`, including fully running examples.
-
-.. toctree::
-   :hidden:
-
-   Introduction 
-   Benchmarks 
diff --git a/docs/source/overview/tutorials/introduction.ipynb b/docs/source/overview/tutorials/introduction.ipynb
deleted file mode 100644
index c9861bfd2..000000000
--- a/docs/source/overview/tutorials/introduction.ipynb
+++ /dev/null
@@ -1,81 +0,0 @@
-{
- "cells": [
-  {
-   "cell_type": "markdown",
-   "id": "accredited-amateur",
-   "metadata": {},
-   "source": [
-    "# Introduction\n",
-    "\n",
-    "`yadism` it's wonderful to install and wonderful to use, you just need:\n",
-    "\n",
-    "- `pip`\n",
-    "- a couple of fully specified runcards (but you can download some example ones from [here])"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "nominated-inspection",
-   "metadata": {},
-   "source": [
-    "## Installation\n",
-    "As written in the `README.md` instructions just run:\n",
-    "\n",
-    "```sh\n",
-    "pip install yadism\n",
-    "```"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "valuable-theater",
-   "metadata": {},
-   "source": [
-    "## Basic usage"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 1,
-   "id": "announced-petite",
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "ModuleNotFoundError",
-     "evalue": "No module named 'yadism'",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
-      "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0;32mimport\u001b[0m \u001b[0myadism\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
-      "\u001b[0;31mModuleNotFoundError\u001b[0m: No module named 'yadism'"
-     ]
-    }
-   ],
-   "source": [
-    "import yadism"
-   ]
-  }
- ],
- "metadata": {
-  "kernelspec": {
-   "display_name": "Python 3",
-   "language": "python",
-   "name": "python3"
-  },
-  "language_info": {
-   "codemirror_mode": {
-    "name": "ipython",
-    "version": 3
-   },
-   "file_extension": ".py",
-   "mimetype": "text/x-python",
-   "name": "python",
-   "nbconvert_exporter": "python",
-   "pygments_lexer": "ipython3",
-   "version": "3.8.6"
-  }
- },
- "nbformat": 4,
- "nbformat_minor": 5
-}
diff --git a/docs/source/overview/tutorials/tutorials.rst b/docs/source/overview/tutorials/tutorials.rst
new file mode 100644
index 000000000..fc7bd26a3
--- /dev/null
+++ b/docs/source/overview/tutorials/tutorials.rst
@@ -0,0 +1,15 @@
+Tutorials
+=========
+
+The following tutorials provide a brief introduction on some of the main features of `yadism`.
+These tutorials show how to:
+
+* prepare the observable and theory cards required for any yadism computation
+* compute observables by convoluting yadism predictions with a |PDF|
+* tabulate the yadism predictions into fast-interpolation grids for later use
+
+.. toctree::
+   :hidden:
+
+   Getting Started 
+   Compare to Data 
diff --git a/docs/source/shared/abbreviations.rst b/docs/source/shared/abbreviations.rst
index 2271fb666..2a4e7657c 100644
--- a/docs/source/shared/abbreviations.rst
+++ b/docs/source/shared/abbreviations.rst
@@ -93,6 +93,9 @@
 .. |FFNS| replace::
    :abbr:`FFNS (Fixed Flavor Number Scheme)`
 
+.. |FFN0| replace::
+   :abbr:`FFN0 (Asymptotic Fixed Flavor Number Scheme)`
+
 .. |VFNS| replace::
    :abbr:`VFNS (Variable Flavor Number Scheme)`
 
@@ -138,6 +141,10 @@
 
    eko
 
+.. |pineko| raw:: html
+
+   pineko
+
 .. |banana| raw:: html
 
    banana
diff --git a/docs/source/theory/fns.rst b/docs/source/theory/fns.rst
index 9ff3c9cff..14ac5c58f 100644
--- a/docs/source/theory/fns.rst
+++ b/docs/source/theory/fns.rst
@@ -28,6 +28,7 @@ unpolarized :ref:`kinds`).
 
 FFNS
 ----
+
 As the name |FFNS| suggests we are considering a fixed number of flavors
 :math:`n_f=n_l+1` with :math:`n_l` light flavors and **1 (and only 1) heavy
 flavor** with a finite mass :math:`m`. The number of light quarks :math:`n_l` is
@@ -119,12 +120,26 @@ This scheme is adequate for :math:`Q^2\gg m^2`.
 patches in which :math:`n_f` is constant (and they are of course different from
 the quark masses, that are always considered to be zero or infinite).
 
+FFN0
+----
+
+This is the high-virtuality limit :math:`Q^2 \gg m^2` of the |FFNS|, where only the
+collinear logs :math:`\log(Q^2/m^2)` are retained, but all power-like heavy quark mass
+corrections are neglected. These collinear logs are the finite expansion of the
+|DGLAP| evolution if the heavy quark would be considered massless. Thus these
+terms are the overlap between the |FFNS| using :math:`n_l` light quarks and one
+heavy quark and |FFNS| using :math:`n_l+1` light quarks.
+These terms are needed in the construction of the FONLL scheme :cite:`forte-fonll`.
+
+
 FONLL
 -----
-| FONLL :cite:`forte-fonll` is a |GM-VFNS| that includes parts of the |DGLAP| equations into the
-  matching conditions.
-| That is: two different schemes are considered, and they are matched at a given
-  scale, accounting for the resummation of collinear logarithms.
+
+FONLL :cite:`forte-fonll` is a |GM-VFNS| that includes parts of the |DGLAP| equations into the
+matching conditions, i.e., two different schemes are considered, and they are matched at a given
+scale, accounting for the resummation of collinear logarithms.
+Hence, FONLL relies on both coefficient functions and evolution kernels, so yadism is not
+solely responsible for the scheme, but also |eko| and |pineko|.
 
 In the original paper the prescription is only presented for the charm
 contributions, but we extend it here to an arbitrary quark.
diff --git a/docs/source/theory/scale-variations.rst b/docs/source/theory/scale-variations.rst
index 88ff09325..eb017be1c 100644
--- a/docs/source/theory/scale-variations.rst
+++ b/docs/source/theory/scale-variations.rst
@@ -146,10 +146,3 @@ Procedures
 - **scheme C**: varying the scales in the context of |PDF| determination only in
   the coefficient functions corresponds to scheme C in
   :cite:`AbdulKhalek:2019ihb`.
-
-Sector Isolated
----------------
-
-.. todo::
-
-   Independent singlet/non-singlet scale variations
diff --git a/poetry.lock b/poetry.lock
index 558472187..f1d73330a 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,4 +1,4 @@
-# This file is automatically @generated by Poetry 1.7.1 and should not be changed by hand.
+# This file is automatically @generated by Poetry 1.6.1 and should not be changed by hand.
 
 [[package]]
 name = "adani"
@@ -113,31 +113,32 @@ hg = ["python-hglib (>=1.5)"]
 
 [[package]]
 name = "attrs"
-version = "23.1.0"
+version = "23.2.0"
 description = "Classes Without Boilerplate"
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "attrs-23.1.0-py3-none-any.whl", hash = "sha256:1f28b4522cdc2fb4256ac1a020c78acf9cba2c6b461ccd2c126f3aa8e8335d04"},
-    {file = "attrs-23.1.0.tar.gz", hash = "sha256:6279836d581513a26f1bf235f9acd333bc9115683f14f7e8fae46c98fc50e015"},
+    {file = "attrs-23.2.0-py3-none-any.whl", hash = "sha256:99b87a485a5820b23b879f04c2305b44b951b502fd64be915879d77a7e8fc6f1"},
+    {file = "attrs-23.2.0.tar.gz", hash = "sha256:935dc3b529c262f6cf76e50877d35a4bd3c1de194fd41f47a2b7ae8f19971f30"},
 ]
 
 [package.extras]
 cov = ["attrs[tests]", "coverage[toml] (>=5.3)"]
-dev = ["attrs[docs,tests]", "pre-commit"]
+dev = ["attrs[tests]", "pre-commit"]
 docs = ["furo", "myst-parser", "sphinx", "sphinx-notfound-page", "sphinxcontrib-towncrier", "towncrier", "zope-interface"]
 tests = ["attrs[tests-no-zope]", "zope-interface"]
-tests-no-zope = ["cloudpickle", "hypothesis", "mypy (>=1.1.1)", "pympler", "pytest (>=4.3.0)", "pytest-mypy-plugins", "pytest-xdist[psutil]"]
+tests-mypy = ["mypy (>=1.6)", "pytest-mypy-plugins"]
+tests-no-zope = ["attrs[tests-mypy]", "cloudpickle", "hypothesis", "pympler", "pytest (>=4.3.0)", "pytest-xdist[psutil]"]
 
 [[package]]
 name = "babel"
-version = "2.13.1"
+version = "2.14.0"
 description = "Internationalization utilities"
 optional = false
 python-versions = ">=3.7"
 files = [
-    {file = "Babel-2.13.1-py3-none-any.whl", hash = "sha256:7077a4984b02b6727ac10f1f7294484f737443d7e2e66c5e4380e41a3ae0b4ed"},
-    {file = "Babel-2.13.1.tar.gz", hash = "sha256:33e0952d7dd6374af8dbf6768cc4ddf3ccfefc244f9986d4074704f2fbd18900"},
+    {file = "Babel-2.14.0-py3-none-any.whl", hash = "sha256:efb1a25b7118e67ce3a259bed20545c29cb68be8ad2c784c83689981b7a57287"},
+    {file = "Babel-2.14.0.tar.gz", hash = "sha256:6919867db036398ba21eb5c7a0f6b28ab8cbc3ae7a73a44ebe34ae74a4e7d363"},
 ]
 
 [package.dependencies]
@@ -159,13 +160,13 @@ files = [
 
 [[package]]
 name = "banana-hep"
-version = "0.6.11"
+version = "0.6.12"
 description = "Benchmark QCD physics"
 optional = true
 python-versions = ">=3.8.0,<3.12"
 files = [
-    {file = "banana_hep-0.6.11-py3-none-any.whl", hash = "sha256:5eed795c5e9b2cdcb93a49df1180832a43cabfa7a4703e7dcb7ed26c3a897e4f"},
-    {file = "banana_hep-0.6.11.tar.gz", hash = "sha256:e1e7f4af2f64ca17c9992ab3a4fc857fb43fbb316a3e781156d465f1ddea452d"},
+    {file = "banana_hep-0.6.12-py3-none-any.whl", hash = "sha256:3cb065926a774689f6dee606dde0453e4e856dc1372c99e12f6b54aca26c41dd"},
+    {file = "banana_hep-0.6.12.tar.gz", hash = "sha256:0cf4a78f5affa5e1afe138ae6c9df5414deb9785901b585fcbdf6bbf531a1b9b"},
 ]
 
 [package.dependencies]
@@ -182,19 +183,22 @@ SQLAlchemy = ">=1.4.29,<2.0.0"
 
 [[package]]
 name = "beautifulsoup4"
-version = "4.12.2"
+version = "4.12.3"
 description = "Screen-scraping library"
 optional = false
 python-versions = ">=3.6.0"
 files = [
-    {file = "beautifulsoup4-4.12.2-py3-none-any.whl", hash = "sha256:bd2520ca0d9d7d12694a53d44ac482d181b4ec1888909b035a3dbf40d0f57d4a"},
-    {file = "beautifulsoup4-4.12.2.tar.gz", hash = "sha256:492bbc69dca35d12daac71c4db1bfff0c876c00ef4a2ffacce226d4638eb72da"},
+    {file = "beautifulsoup4-4.12.3-py3-none-any.whl", hash = "sha256:b80878c9f40111313e55da8ba20bdba06d8fa3969fc68304167741bbf9e082ed"},
+    {file = "beautifulsoup4-4.12.3.tar.gz", hash = "sha256:74e3d1928edc070d21748185c46e3fb33490f22f52a3addee9aee0f4f7781051"},
 ]
 
 [package.dependencies]
 soupsieve = ">1.2"
 
 [package.extras]
+cchardet = ["cchardet"]
+chardet = ["chardet"]
+charset-normalizer = ["charset-normalizer"]
 html5lib = ["html5lib"]
 lxml = ["lxml"]
 
@@ -218,13 +222,13 @@ css = ["tinycss2 (>=1.1.0,<1.3)"]
 
 [[package]]
 name = "certifi"
-version = "2023.7.22"
+version = "2023.11.17"
 description = "Python package for providing Mozilla's CA Bundle."
 optional = false
 python-versions = ">=3.6"
 files = [
-    {file = "certifi-2023.7.22-py3-none-any.whl", hash = "sha256:92d6037539857d8206b8f6ae472e8b77db8058fec5937a1ef3f54304089edbb9"},
-    {file = "certifi-2023.7.22.tar.gz", hash = "sha256:539cc1d13202e33ca466e88b2807e29f4c13049d6d87031a3c110744495cb082"},
+    {file = "certifi-2023.11.17-py3-none-any.whl", hash = "sha256:e036ab49d5b79556f99cfc2d9320b34cfbe5be05c5871b51de9329f0603b0474"},
+    {file = "certifi-2023.11.17.tar.gz", hash = "sha256:9b469f3a900bf28dc19b8cfbf8019bf47f7fdd1a65a1d4ffb98fc14166beb4d1"},
 ]
 
 [[package]]
@@ -415,6 +419,23 @@ files = [
     {file = "colorama-0.4.6.tar.gz", hash = "sha256:08695f5cb7ed6e0531a20572697297273c47b8cae5a63ffc6d6ed5c201be6e44"},
 ]
 
+[[package]]
+name = "comm"
+version = "0.2.1"
+description = "Jupyter Python Comm implementation, for usage in ipykernel, xeus-python etc."
+optional = false
+python-versions = ">=3.8"
+files = [
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 [[package]]
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 version = "0.9.1"
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 docs = ["ipython", "matplotlib", "numpydoc", "sphinx"]
 tests = ["pytest", "pytest-cov", "pytest-xdist"]
 
+[[package]]
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 name = "decorator"
 version = "5.1.1"
@@ -631,13 +679,13 @@ files = [
 
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+version = "0.14.1"
 description = "Evolution Kernel Operators"
 optional = false
 python-versions = ">=3.8,<3.12"
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 [package.dependencies]
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 [[package]]
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 description = "Backport of PEP 654 (exception groups)"
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 [package.extras]
@@ -696,13 +744,13 @@ pyrepl = ">=0.8.2"
 
 [[package]]
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+version = "2.19.1"
 description = "Fastest Python implementation of JSON schema"
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 python-versions = "*"
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 [package.extras]
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 [[package]]
 name = "fonttools"
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 test = ["objgraph", "psutil"]
 
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+attrs = ">=22.2.0"
 exceptiongroup = {version = ">=1.0.0", markers = "python_version < \"3.11\""}
 sortedcontainers = ">=2.1.0,<3.0.0"
 
 [package.extras]
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 codemods = ["libcst (>=0.3.16)"]
 dateutil = ["python-dateutil (>=1.4)"]
@@ -873,17 +922,17 @@ pandas = ["pandas (>=1.1)"]
 pytest = ["pytest (>=4.6)"]
 pytz = ["pytz (>=2014.1)"]
 redis = ["redis (>=3.0.0)"]
-zoneinfo = ["backports.zoneinfo (>=0.2.1)", "tzdata (>=2023.3)"]
+zoneinfo = ["backports.zoneinfo (>=0.2.1)", "tzdata (>=2023.4)"]
 
 [[package]]
 name = "idna"
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+version = "3.6"
 description = "Internationalized Domain Names in Applications (IDNA)"
 optional = false
 python-versions = ">=3.5"
 files = [
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 ]
 
 [[package]]
@@ -899,20 +948,20 @@ files = [
 
 [[package]]
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+version = "7.0.1"
 description = "Read metadata from Python packages"
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 python-versions = ">=3.8"
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 [package.dependencies]
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 [package.extras]
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+docs = ["furo", "jaraco.packaging (>=9.3)", "jaraco.tidelift (>=1.4)", "rst.linker (>=1.9)", "sphinx (<7.2.5)", "sphinx (>=3.5)", "sphinx-lint"]
 perf = ["ipython"]
 testing = ["flufl.flake8", "importlib-resources (>=1.3)", "packaging", "pyfakefs", "pytest (>=6)", "pytest-black (>=0.3.7)", "pytest-checkdocs (>=2.4)", "pytest-cov", "pytest-enabler (>=2.2)", "pytest-mypy (>=0.9.1)", "pytest-perf (>=0.9.2)", "pytest-ruff"]
 
@@ -945,6 +994,39 @@ files = [
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 ]
 
+[[package]]
+name = "ipykernel"
+version = "6.29.0"
+description = "IPython Kernel for Jupyter"
+optional = false
+python-versions = ">=3.8"
+files = [
+    {file = "ipykernel-6.29.0-py3-none-any.whl", hash = "sha256:076663ca68492576f051e4af7720d33f34383e655f2be0d544c8b1c9de915b2f"},
+    {file = "ipykernel-6.29.0.tar.gz", hash = "sha256:b5dd3013cab7b330df712891c96cd1ab868c27a7159e606f762015e9bf8ceb3f"},
+]
+
+[package.dependencies]
+appnope = {version = "*", markers = "platform_system == \"Darwin\""}
+comm = ">=0.1.1"
+debugpy = ">=1.6.5"
+ipython = ">=7.23.1"
+jupyter-client = ">=6.1.12"
+jupyter-core = ">=4.12,<5.0.dev0 || >=5.1.dev0"
+matplotlib-inline = ">=0.1"
+nest-asyncio = "*"
+packaging = "*"
+psutil = "*"
+pyzmq = ">=24"
+tornado = ">=6.1"
+traitlets = ">=5.4.0"
+
+[package.extras]
+cov = ["coverage[toml]", "curio", "matplotlib", "pytest-cov", "trio"]
+docs = ["myst-parser", "pydata-sphinx-theme", "sphinx", "sphinx-autodoc-typehints", "sphinxcontrib-github-alt", "sphinxcontrib-spelling", "trio"]
+pyqt5 = ["pyqt5"]
+pyside6 = ["pyside6"]
+test = ["flaky", "ipyparallel", "pre-commit", "pytest (>=7.0)", "pytest-asyncio (==0.23.2)", "pytest-cov", "pytest-timeout"]
+
 [[package]]
 name = "ipython"
 version = "8.12.3"
@@ -986,20 +1068,17 @@ test-extra = ["curio", "matplotlib (!=3.2.0)", "nbformat", "numpy (>=1.21)", "pa
 
 [[package]]
 name = "isort"
-version = "5.12.0"
+version = "5.13.2"
 description = "A Python utility / library to sort Python imports."
 optional = false
 python-versions = ">=3.8.0"
 files = [
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+    {file = "isort-5.13.2-py3-none-any.whl", hash = "sha256:8ca5e72a8d85860d5a3fa69b8745237f2939afe12dbf656afbcb47fe72d947a6"},
+    {file = "isort-5.13.2.tar.gz", hash = "sha256:48fdfcb9face5d58a4f6dde2e72a1fb8dcaf8ab26f95ab49fab84c2ddefb0109"},
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 [package.extras]
-colors = ["colorama (>=0.4.3)"]
-pipfile-deprecated-finder = ["pip-shims (>=0.5.2)", "pipreqs", "requirementslib"]
-plugins = ["setuptools"]
-requirements-deprecated-finder = ["pip-api", "pipreqs"]
+colors = ["colorama (>=0.4.6)"]
 
 [[package]]
 name = "jedi"
@@ -1039,13 +1118,13 @@ i18n = ["Babel (>=2.7)"]
 
 [[package]]
 name = "jsonschema"
-version = "4.19.2"
+version = "4.21.0"
 description = "An implementation of JSON Schema validation for Python"
 optional = false
 python-versions = ">=3.8"
 files = [
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+    {file = "jsonschema-4.21.0-py3-none-any.whl", hash = "sha256:70a09719d375c0a2874571b363c8a24be7df8071b80c9aa76bc4551e7297c63c"},
+    {file = "jsonschema-4.21.0.tar.gz", hash = "sha256:3ba18e27f7491ea4a1b22edce00fb820eec968d397feb3f9cb61d5894bb38167"},
 ]
 
 [package.dependencies]
@@ -1062,18 +1141,18 @@ format-nongpl = ["fqdn", "idna", "isoduration", "jsonpointer (>1.13)", "rfc3339-
 
 [[package]]
 name = "jsonschema-specifications"
-version = "2023.7.1"
+version = "2023.12.1"
 description = "The JSON Schema meta-schemas and vocabularies, exposed as a Registry"
 optional = false
 python-versions = ">=3.8"
 files = [
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+    {file = "jsonschema_specifications-2023.12.1.tar.gz", hash = "sha256:48a76787b3e70f5ed53f1160d2b81f586e4ca6d1548c5de7085d1682674764cc"},
 ]
 
 [package.dependencies]
 importlib-resources = {version = ">=1.4.0", markers = "python_version < \"3.9\""}
-referencing = ">=0.28.0"
+referencing = ">=0.31.0"
 
 [[package]]
 name = "jupyter-client"
@@ -1100,13 +1179,13 @@ test = ["coverage", "ipykernel (>=6.14)", "mypy", "paramiko", "pre-commit", "pyt
 
 [[package]]
 name = "jupyter-core"
-version = "5.5.0"
+version = "5.7.1"
 description = "Jupyter core package. A base package on which Jupyter projects rely."
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -1120,13 +1199,13 @@ test = ["ipykernel", "pre-commit", "pytest", "pytest-cov", "pytest-timeout"]
 
 [[package]]
 name = "jupyterlab-pygments"
-version = "0.2.2"
+version = "0.3.0"
 description = "Pygments theme using JupyterLab CSS variables"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
 files = [
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 ]
 
 [[package]]
@@ -1258,47 +1337,48 @@ six = ">=1.4.1"
 
 [[package]]
 name = "lazy-object-proxy"
-version = "1.9.0"
+version = "1.10.0"
 description = "A fast and thorough lazy object proxy."
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.8"
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 ]
 
 [package.dependencies]
@@ -1534,7 +1605,6 @@ packaging = ">=20.0"
 pillow = ">=6.2.0"
 pyparsing = ">=2.3.1"
 python-dateutil = ">=2.7"
-setuptools_scm = ">=7"
 
 [[package]]
 name = "matplotlib-inline"
@@ -1596,13 +1666,13 @@ test = ["flaky", "ipykernel (>=6.19.3)", "ipython", "ipywidgets", "nbconvert (>=
 
 [[package]]
 name = "nbconvert"
-version = "7.11.0"
+version = "7.14.2"
 description = "Converting Jupyter Notebooks"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [package.dependencies]
@@ -1629,7 +1699,7 @@ docs = ["ipykernel", "ipython", "myst-parser", "nbsphinx (>=0.2.12)", "pydata-sp
 qtpdf = ["nbconvert[qtpng]"]
 qtpng = ["pyqtwebengine (>=5.15)"]
 serve = ["tornado (>=6.1)"]
-test = ["flaky", "ipykernel", "ipywidgets (>=7)", "pytest"]
+test = ["flaky", "ipykernel", "ipywidgets (>=7.5)", "pytest"]
 webpdf = ["playwright"]
 
 [[package]]
@@ -1672,6 +1742,17 @@ nbformat = "*"
 sphinx = ">=1.8"
 traitlets = ">=5"
 
+[[package]]
+name = "nest-asyncio"
+version = "1.5.9"
+description = "Patch asyncio to allow nested event loops"
+optional = false
+python-versions = ">=3.5"
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+
 [[package]]
 name = "numba"
 version = "0.57.1"
@@ -1808,13 +1889,13 @@ test = ["hypothesis (>=5.5.3)", "pytest (>=6.0)", "pytest-xdist (>=1.31)"]
 
 [[package]]
 name = "pandocfilters"
-version = "1.5.0"
+version = "1.5.1"
 description = "Utilities for writing pandoc filters in python"
 optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 files = [
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 ]
 
 [[package]]
@@ -1888,13 +1969,13 @@ pytzdata = ">=2020.1"
 
 [[package]]
 name = "pexpect"
-version = "4.8.0"
+version = "4.9.0"
 description = "Pexpect allows easy control of interactive console applications."
 optional = false
 python-versions = "*"
 files = [
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 [package.dependencies]
@@ -1998,33 +2079,35 @@ xmp = ["defusedxml"]
 
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 python-versions = ">=3.7"
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 [package.dependencies]
@@ -2047,13 +2130,13 @@ files = [
 
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+version = "4.1.0"
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-python-versions = ">=3.7"
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@@ -2077,18 +2160,46 @@ testing = ["pytest", "pytest-benchmark"]
 
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 python-versions = ">=3.7.0"
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 [package.dependencies]
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+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, !=3.5.*"
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+
+[package.extras]
+test = ["enum34", "ipaddress", "mock", "pywin32", "wmi"]
+
 [[package]]
 name = "ptyprocess"
 version = "0.7.0"
@@ -2161,17 +2272,18 @@ files = [
 
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 name = "pygments"
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 [package.extras]
 plugins = ["importlib-metadata"]
+windows-terminal = ["colorama (>=0.4.6)"]
 
 [[package]]
 name = "pylint"
@@ -2238,13 +2350,13 @@ files = [
 
 [[package]]
 name = "pytest"
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+version = "7.4.4"
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 python-versions = ">=3.7"
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 [package.dependencies]
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 python-versions = ">=3.6"
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 [package.dependencies]
@@ -3049,7 +3119,7 @@ greenlet = {version = "!=0.4.17", markers = "python_version >= \"3\" and (platfo
 
 [package.extras]
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-aiosqlite = ["aiosqlite", "greenlet (!=0.4.17)", "typing-extensions (!=3.10.0.1)"]
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 asyncio = ["greenlet (!=0.4.17)"]
 asyncmy = ["asyncmy (>=0.2.3,!=0.2.4)", "greenlet (!=0.4.17)"]
 mariadb-connector = ["mariadb (>=1.0.1,!=1.1.2)"]
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 mypy = ["mypy (>=0.910)", "sqlalchemy2-stubs"]
 mysql = ["mysqlclient (>=1.4.0)", "mysqlclient (>=1.4.0,<2)"]
 mysql-connector = ["mysql-connector-python"]
-oracle = ["cx-oracle (>=7)", "cx-oracle (>=7,<8)"]
+oracle = ["cx_oracle (>=7)", "cx_oracle (>=7,<8)"]
 postgresql = ["psycopg2 (>=2.7)"]
 postgresql-asyncpg = ["asyncpg", "greenlet (!=0.4.17)"]
 postgresql-pg8000 = ["pg8000 (>=1.16.6,!=1.29.0)"]
 postgresql-psycopg2binary = ["psycopg2-binary"]
 postgresql-psycopg2cffi = ["psycopg2cffi"]
 pymysql = ["pymysql", "pymysql (<1)"]
-sqlcipher = ["sqlcipher3-binary"]
+sqlcipher = ["sqlcipher3_binary"]
 
 [[package]]
 name = "stack-data"
@@ -3118,59 +3188,59 @@ files = [
 
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 description = "Style preserving TOML library"
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 python-versions = ">=3.7"
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 [[package]]
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 python-versions = ">= 3.8"
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 ]
 
 [[package]]
 name = "traitlets"
-version = "5.13.0"
+version = "5.14.1"
 description = "Traitlets Python configuration system"
 optional = false
 python-versions = ">=3.8"
 files = [
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 [package.extras]
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-test = ["argcomplete (>=3.0.3)", "mypy (>=1.6.0)", "pre-commit", "pytest (>=7.0,<7.5)", "pytest-mock", "pytest-mypy-testing"]
+test = ["argcomplete (>=3.0.3)", "mypy (>=1.7.0)", "pre-commit", "pytest (>=7.0,<7.5)", "pytest-mock", "pytest-mypy-testing"]
 
 [[package]]
 name = "typing-extensions"
-version = "4.8.0"
+version = "4.9.0"
 description = "Backported and Experimental Type Hints for Python 3.8+"
 optional = false
 python-versions = ">=3.8"
 files = [
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 ]
 
 [[package]]
@@ -3191,13 +3261,13 @@ zstd = ["zstandard (>=0.18.0)"]
 
 [[package]]
 name = "wcwidth"
-version = "0.2.10"
+version = "0.2.13"
 description = "Measures the displayed width of unicode strings in a terminal"
 optional = false
 python-versions = "*"
 files = [
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 ]
 
 [[package]]
@@ -3329,4 +3399,4 @@ mark = ["banana-hep", "sqlalchemy"]
 [metadata]
 lock-version = "2.0"
 python-versions = ">=3.8,<3.12"
-content-hash = "ad042a74a077766ce436ee2ab3cfbbaa90e57c76071c6b3ea923c7fbbd555bdb"
+content-hash = "bcc0109269c0c850ddc515f83d30306c384d606adaf219f33e1cbaeb1ae68fa5"
diff --git a/pyproject.toml b/pyproject.toml
index c9b996300..e8d7ac505 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -76,6 +76,7 @@ recommonmark = "^0.7.1"
 sphinxcontrib-bibtex = "^2.3.0"
 sphinxcontrib-details-directive = "^0.1.0"
 nbsphinx = "^0.8.6"
+ipykernel = "^6.13.0"
 
 [tool.poetry.extras]
 mark = ["banana-hep", "sqlalchemy"]
@@ -104,6 +105,7 @@ docs-view = { "shell" = "cd docs; make view" }
 docs-server = { "shell" = "cd docs; make server" }
 docs-clean = { "shell" = "cd docs; make clean" }
 docs-cleanall = { "shell" = "cd docs; make cleanall" }
+docs-install-nb = { "shell" = "python -m ipykernel install --user --name=$(basename $(poetry env info -p))" }
 
 [tool.poetry-dynamic-versioning]
 enable = true
diff --git a/src/yadism/coefficient_functions/light/n3lo/common.py b/src/yadism/coefficient_functions/light/n3lo/common.py
index 21c3314e6..fc2e30bd2 100644
--- a/src/yadism/coefficient_functions/light/n3lo/common.py
+++ b/src/yadism/coefficient_functions/light/n3lo/common.py
@@ -1,4 +1,4 @@
-"""Common factors see :ref:`Larin:1996wd` (Table 2)"""
+"""Common factors see :cite:`Larin:1996wd` (Table 2)."""
 import numba as nb
 import numpy as np
 
@@ -10,7 +10,7 @@
 
 
 def nc_color_factor(coupling_constants, nf, channel, skip_heavylight):
-    """Returns the |N3LO| color factor.
+    """Compute a |N3LO| color factor.
 
     Parameters
     ----------
@@ -49,7 +49,7 @@ def nc_color_factor(coupling_constants, nf, channel, skip_heavylight):
 
 @nb.njit("f8(f8[:])", cache=True)
 def fl(nc_weights):
-    """:math:`fl_{11}` Non Singlet as defined in :ref:`Larin:1996wd` (Table 2) and generalized for |NC|"""
+    """:math:`fl_{11}` Non Singlet as defined in :cite:`Larin:1996wd` (Table 2) and generalized for |NC|."""
     # fl = [2.0, 0.5, 0.0, 0.5, 0.2, 0.5]
     avg = np.mean(nc_weights)
     return 3 * avg
@@ -57,7 +57,7 @@ def fl(nc_weights):
 
 @nb.njit("f8(f8[:])", cache=True)
 def fls(nc_weights):
-    """:math:`fl_{11}` pure Singlet as defined in :ref:`Larin:1996wd` (Table 2) and generalized for |NC|"""
+    """:math:`fl_{11}` pure Singlet as defined in :cite:`Larin:1996wd` (Table 2) and generalized for |NC|."""
     avg_2 = np.mean(nc_weights) ** 2
     sum_w2 = np.mean(nc_weights**2)
     # fls = [1.0, 0.1, 0.0, 0.1, 0.01818181818, 0.1]
@@ -66,5 +66,5 @@ def fls(nc_weights):
 
 @nb.njit("f8(f8[:])", cache=True)
 def flg(nc_weights):
-    """:math:`fl_{11}^g` pure Singlet as defined in :ref:`Larin:1996wd` (Table 2) and generalized for |NC|"""
+    """:math:`fl_{11}^g` pure Singlet as defined in :cite:`Larin:1996wd` (Table 2) and generalized for |NC|."""
     return fls(nc_weights)
diff --git a/src/yadism/input/__init__.py b/src/yadism/input/__init__.py
index e774827fd..5267fefea 100644
--- a/src/yadism/input/__init__.py
+++ b/src/yadism/input/__init__.py
@@ -1,15 +1,4 @@
 """
-Goal
-----
-
-These subpackage has the main goal of parsing and validate user input, in
-particular the following three operations are performed:
-
-#. **constraints**: constraints on single fields are enforced, raising an error
-    for each violation
-#. **cross-constraints**: constraints involving multiple fields are enforced,
-    raising an error for each violation
-
 Note
 ----
 
diff --git a/src/yadmark/benchmark/external/apfelpy_utils.py b/src/yadmark/benchmark/external/apfelpy_utils.py
index 43200b93a..b6f8c5fda 100644
--- a/src/yadmark/benchmark/external/apfelpy_utils.py
+++ b/src/yadmark/benchmark/external/apfelpy_utils.py
@@ -62,7 +62,7 @@ def map_apfelpy_sf(init, observables, fns):
         "F2": init.InitializeF2NCObjectsMassive,
         "FL": init.InitializeFLNCObjectsMassive,
     }
-    MAP_FFNS0_NC = {
+    MAP_FFN0_NC = {
         "F2": init.InitializeF2NCObjectsMassiveZero,
         "FL": init.InitializeFLNCObjectsMassiveZero,
     }
@@ -76,8 +76,8 @@ def map_apfelpy_sf(init, observables, fns):
         return MAP_ZM_NC
     if fns == "FFNS":
         return MAP_FFNS_NC
-    if fns == "FFNS0":
-        return MAP_FFNS0_NC
+    if fns == "FFN0":
+        return MAP_FFN0_NC
 
 
 def couplings(ap, pids, proc_type, obs_name):
@@ -100,7 +100,6 @@ def couplings(ap, pids, proc_type, obs_name):
 
     """
 
-    # Effective charges
     def _fBq(Q):
         if proc_type == "EM":
             # For Q=0 we only have electric charges
@@ -300,7 +299,7 @@ def compute_apfelpy_data(theory, observables, pdf):
 
     # Setting the theory
     fns = theory["FNS"]
-    if fns not in ["ZM-VFNS", "FFNS", "FFNS0"]:
+    if fns not in ["ZM-VFNS", "FFNS", "FFN0"]:
         raise ValueError(f"APFEL++ does not contain {fns}.")
 
     # Perturbative Order