diff --git a/math/py-fpylll/Makefile b/math/py-fpylll/Makefile
index 1d86640b7856..39e11da821d7 100644
--- a/math/py-fpylll/Makefile
+++ b/math/py-fpylll/Makefile
@@ -1,51 +1,55 @@
 PORTNAME=	fpylll
-PORTVERSION=	0.5.7
-PORTREVISION=	1
+PORTVERSION=	0.5.9
 CATEGORIES=	math python
 PKGNAMEPREFIX=	${PYTHON_PKGNAMEPREFIX}
 
 MAINTAINER=	thierry@FreeBSD.org
 COMMENT=	Python interface for fplll
 WWW=		https://github.com/fplll/fpylll
 
 LICENSE=	GPLv2
 
 BUILD_DEPENDS=	${PYNUMPY}	\
 		cython:lang/cython	\
+		${PYTHON_PKGNAMEPREFIX}black>0:devel/py-black@${PY_FLAVOR}	\
+		${PYTHON_PKGNAMEPREFIX}pythran>0:devel/py-pythran@${PY_FLAVOR}	\
 		${PYTHON_PKGNAMEPREFIX}cysignals>0:devel/py-cysignals@${PY_FLAVOR}
 LIB_DEPENDS=	libfplll.so:math/fplll	\
 		libgmp.so:math/gmp	\
 		libmpfr.so:math/mpfr	\
 		libpari.so:math/pari	\
 		libqd.so:math/qd
 RUN_DEPENDS=	${PYNUMPY}	\
+		${PYTHON_PKGNAMEPREFIX}black>0:devel/py-black@${PY_FLAVOR}	\
+		${PYTHON_PKGNAMEPREFIX}pythran>0:devel/py-pythran@${PY_FLAVOR}	\
 		${PYTHON_PKGNAMEPREFIX}cysignals>0:devel/py-cysignals@${PY_FLAVOR}
 TEST_DEPENDS=	py.test:devel/py-pytest@${PY_FLAVOR}
 
 USE_GITHUB=	yes
 GH_ACCOUNT=	fplll
 
 USES=		compiler:c++11-lang python:3.6+
 USE_PYTHON=	distutils
 .if !defined(WITH_DEBUG)
 LDFLAGS+=	-s
 .endif
 
-OPTIONS_DEFINE=		DOCS
-DOCS_BUILD_DEPENDS=	${PYTHON_PKGNAMEPREFIX}sphinx>=1.6,1:textproc/py-sphinx@${PY_FLAVOR}
-DOCS_USES=		gmake
-PORTDOCS=		*
+OPTIONS_DEFINE=		TUTO
+TUTO_DESC=		Build the tutorial
+OPTIONS_SUB=		Yes
+TUTO_BUILD_DEPENDS=	${PYTHON_PKGNAMEPREFIX}sphinx>=1.6,1:textproc/py-sphinx@${PY_FLAVOR}
+TUTO_USES=		gmake
 
 PLIST_SUB=	VER=${PORTVERSION:R}
 
-do-build-DOCS-on:
+do-build-TUTO-on:
 	(cd ${WRKSRC}/docs && ${GMAKE} html)
 
-post-build-DOCS-on:
+post-build-TUTO-on:
 	${MKDIR} ${STAGEDIR}${DOCSDIR}
 	${CP} -R ${WRKSRC}/docs/_build/html/* ${STAGEDIR}${DOCSDIR}
 
 do-test: install
 	(cd ${WRKSRC} && PY_IGNORE_IMPORTMISMATCH=1 py.test)
 
 .include <bsd.port.mk>
diff --git a/math/py-fpylll/distinfo b/math/py-fpylll/distinfo
index ddae94527541..eeede8dd8884 100644
--- a/math/py-fpylll/distinfo
+++ b/math/py-fpylll/distinfo
@@ -1,3 +1,3 @@
-TIMESTAMP = 1663516099
-SHA256 (fplll-fpylll-0.5.7_GH0.tar.gz) = 350eff2debd1249ef915add8ea0b19217e8a694285b8a90460c593a718d57be4
-SIZE (fplll-fpylll-0.5.7_GH0.tar.gz) = 126463
+TIMESTAMP = 1680168776
+SHA256 (fplll-fpylll-0.5.9_GH0.tar.gz) = d38f3cfaa3c104bba091933d6c798a4f71cad620e19a30843eb02d935a429eb2
+SIZE (fplll-fpylll-0.5.9_GH0.tar.gz) = 129908
diff --git a/math/py-fpylll/pkg-plist b/math/py-fpylll/pkg-plist
index 910f9c2e840a..629db14fb3e1 100644
--- a/math/py-fpylll/pkg-plist
+++ b/math/py-fpylll/pkg-plist
@@ -1,59 +1,62 @@
 %%PYTHON_SITELIBDIR%%/fpylll/__init__.py
 %%PYTHON_SITELIBDIR%%/fpylll/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__init__.py
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.pyc
+%%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/babai.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
+%%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/babai.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/bkz.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/bkz.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/bkz2.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/bkz2.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/simple_bkz.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/simple_bkz.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/simple_dbkz.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/__pycache__/simple_dbkz.cpython-%%PYTHON_SUFFIX%%.pyc
+%%PYTHON_SITELIBDIR%%/fpylll/algorithms/babai.py
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/bkz.py
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/bkz2.py
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/simple_bkz.py
 %%PYTHON_SITELIBDIR%%/fpylll/algorithms/simple_dbkz.py
 %%PYTHON_SITELIBDIR%%/fpylll/config%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/__init__.py
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/bkz%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/bkz_param%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/enumeration%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/gso%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/integer_matrix%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/lll%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/pruner%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/svpcvp%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/fplll/wrapper%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/gmp/__init__.py
 %%PYTHON_SITELIBDIR%%/fpylll/gmp/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/gmp/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/gmp/pylong%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/io%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/numpy%%PYTHON_EXT_SUFFIX%%.so
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__init__.py
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/__init__.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/benchmark.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/benchmark.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/bkz_plot.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/bkz_plot.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/bkz_simulator.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/bkz_simulator.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/bkz_stats.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/bkz_stats.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/compare.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/compare.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/quality.cpython-%%PYTHON_SUFFIX%%.opt-1.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/__pycache__/quality.cpython-%%PYTHON_SUFFIX%%.pyc
 %%PYTHON_SITELIBDIR%%/fpylll/tools/benchmark.py
 %%PYTHON_SITELIBDIR%%/fpylll/tools/bkz_plot.py
 %%PYTHON_SITELIBDIR%%/fpylll/tools/bkz_simulator.py
 %%PYTHON_SITELIBDIR%%/fpylll/tools/bkz_stats.py
 %%PYTHON_SITELIBDIR%%/fpylll/tools/compare.py
 %%PYTHON_SITELIBDIR%%/fpylll/tools/quality.py
 %%PYTHON_SITELIBDIR%%/fpylll/util%%PYTHON_EXT_SUFFIX%%.so