passagemath is open source mathematical software in Python, released under the GNU General Public Licence GPLv2+.

It is a fork of SageMath, which has been developed 2005-2026 under the motto “Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, and MATLAB”.

The passagemath fork uses the motto “Creating a Free Passage Between the Scientific Python Ecosystem and Mathematical Software Communities.” It was created in October 2024 with the following goals:

Moreover, the passagemath project:

  • provides a stable, frequently updated version of the Sage distribution,

  • integrates additional mathematical software, notably Macaulay2, a full set of GAP packages, and the Combinatorial Matrix Recognition library,

  • curates a library of Sage user packages.

Full documentation is available online.

passagemath attempts to support and provides binary wheels suitable for all major Linux distributions and recent versions of macOS.

Binary wheels for native Windows (x86_64, ARM) are are available for a subset of the passagemath distributions. Use of the full functionality of passagemath on Windows currently requires the use of Windows Subsystem for Linux (WSL) or virtualization.

The supported Python versions in the passagemath-10.8.x series are 3.11.x-3.14.x; the passagemath-10.6.x series (EOL 2026-10) still supports Python 3.10.x.

About this pip-installable distribution package

This pip-installable distribution passagemath-polyhedra is a distribution of a part of the Sage Library. It provides a small subset of the modules of the Sage library (“sagelib”, passagemath-standard), sufficient for computations with convex polyhedra in arbitrary dimension (in exact rational arithmetic), and linear and mixed integer linear optimization (in floating point arithmetic).

What is included

Examples

A quick way to try it out interactively:

$ pipx run --spec "passagemath-polyhedra[test]" ipython

In [1]: from passagemath_polyhedra import *

In [2]: P = Polyhedron(ieqs=[[0, 1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0, 1], [0, 0, 1, -1, -1, 1, 0], [0, 0, -1, 1, -1, 1, 0]], eqns=[[-31, 1, 1, 1, 1, 1, 1]]); P
Out[2]: A 5-dimensional polyhedron in QQ^6 defined as the convex hull of 7 vertices

In [3]: P.Vrepresentation()
Out[4]:
(A vertex at (31, 0, 0, 0, 0, 0),
 A vertex at (0, 0, 0, 0, 0, 31),
 A vertex at (0, 0, 0, 0, 31, 0),
 A vertex at (0, 0, 31/2, 0, 31/2, 0),
 A vertex at (0, 31/2, 31/2, 0, 0, 0),
 A vertex at (0, 31/2, 0, 0, 31/2, 0),
 A vertex at (0, 0, 0, 31/2, 31/2, 0))

Available as extras, from other distributions

Additional features

pip install "passagemath-polyhedra[graphs]"

Face lattices, combinatorial polyhedra, graph-theoretic constructions

$ pipx run --spec "passagemath-polyhedra[graphs,test]" ipython

In [1]: from passagemath_polyhedra import *

In [2]: c5_10 = Polyhedron(vertices = [[i, i**2, i**3, i**4, i**5] for i in range(1, 11)]); c5_10
Out[2]: A 5-dimensional polyhedron in ZZ^5 defined as the convex hull of 10 vertices

In [3]: c5_10_fl = c5_10.face_lattice(); [len(x) for x in c5_10_fl.level_sets()]
Out[3]: [1, 10, 45, 100, 105, 42, 1]
pip install "passagemath-polyhedra[graphs,groups]"

Constructing symmetric polyhedra, computing automorphisms, lattice point counting modulo group actions

$ pipx run --spec "passagemath-polyhedra[graphs,groups,test]" ipython

In [1]: from passagemath_polyhedra import *

In [2]: P24 = polytopes.twenty_four_cell(); P24
Out[2]: A 4-dimensional polyhedron in QQ^4 defined as the convex hull of 24 vertices

In [3]: AutP24 = P24.restricted_automorphism_group(); AutP24.order()
Out[3]: 1152
pip install "passagemath-polyhedra[toric]"

Toric varieties

$ pipx run --spec "passagemath-polyhedra[graphs,toric,test]" ipython

In [1]: from passagemath_polyhedra import *

In [2]: TV3 = ToricVariety(NormalFan(lattice_polytope.cross_polytope(3))); TV3
Out[2]: 3-d toric variety covered by 6 affine patches

In [3]: TV3.is_orbifold()
Out[3]: False
pip install "passagemath-polyhedra[latte]"

Installs LattE integrale for lattice point counting and volume computation using generating function techniques.

$ pipx run --spec "passagemath-polyhedra[latte,test]" ipython

In [1]: from passagemath_polyhedra import *

In [2]: P = polytopes.cube()

In [3]: P.integral_points_count()
Out[3]:
27

In [4]: (1000000000*P).integral_points_count(verbose=True)
This is LattE integrale...
...
Total time:...
Out[4]:
8000000012000000006000000001

Additional backends for polyhedral computations

pip install "passagemath-polyhedra[normaliz]"

Normaliz, via PyNormaliz, provides very fast computations in particular for polyhedra with data in algebraic number fields.

$ pipx run --spec "passagemath-polyhedra[normaliz,test]" ipython

In [1]: from passagemath_polyhedra import *

In [2]: gap_norm = polytopes.grand_antiprism(backend='normaliz'); gap_norm

In [3]: gap_norm.f_vector()
pip install "passagemath-polyhedra[cddlib]"

cddlib provides support for computations with polyhedra in floating-point arithmetic.

$ pipx run --spec "passagemath-polyhedra[cddlib,test]" ipython

In [1]: from passagemath_polyhedra import *

In [2]: P1 = polytopes.regular_polygon(5, exact=False); P1
Out[2]: A 2-dimensional polyhedron in RDF^2 defined as the convex hull of 5 vertices
pip install "passagemath-polyhedra[lrslib]"

lrslib can be used for polytope volume computations and for enumerating Nash equilibria.

$ pipx run --spec "passagemath-polyhedra[flint,lrslib,test]" ipython

In [1]: from passagemath_polyhedra import *

In [2]: A = matrix([[2, 1], [1, 5/2]]); B = matrix([[-1, 3], [2, 1]])

In [3]: g = NormalFormGame([A, B]); g.obtain_nash(algorithm='lrs')
Out[3]: [[(1/5, 4/5), (3/5, 2/5)]]
pip install "passagemath-polyhedra[polymake]"

Polymake, via passagemath-polymake

Optional backends for optimization

pip install "passagemath-polyhedra[cbc]"

COIN/OR CBC Mixed Integer Linear Optimization solver, via passagemath-coin-or-cbc

pip install "passagemath-polyhedra[cplex]"

CPLEX Mixed Integer Optimization solver (proprietary; requires licensed installation), via passagemath-cplex

pip install "passagemath-polyhedra[cvxpy]"

CVXPy as middle-end for various backends

pip install "passagemath-polyhedra[gurobi]"

Gurobi Mixed Integer Optimization solver (proprietary; requires licensed installation), via passagemath-gurobi

pip install "passagemath-polyhedra[highs]"

HiGHS

pip install "passagemath-polyhedra[scip]"

SCIP Mixed Integer Optimization solver, via PySCIPOpt

Development

$ git clone --origin passagemath https://github.com/passagemath/passagemath.git
$ cd passagemath
passagemath $ ./bootstrap
passagemath $ python3 -m venv polyhedra-venv
passagemath $ source polyhedra-venv/bin/activate
(polyhedra-venv) passagemath $ pip install -v -e pkgs/sagemath-polyhedra

Project links

Key dates

PyPI data
Data sourced directly from PyPI's database.
  • Released:
Newer release available (10.8.11)

Owner

PyPI data
Data sourced directly from PyPI's database.

Credits

Author: The Sage Developers

Maintainer: Matthias Köppe, passagemath contributors

License expression

GPL-2.0-or-later
View SPDX License List

Requires

Python <3.15, >=3.11

Provides Extra

conf test flint fpylll linbox pari 4ti2 cddlib latte latte-int normaliz palp polymake ppl topcom cbc cbc-sage coin coin-sage cplex cplex-sage cvxopt cvxopt-sage cvxpy glpk glpk-sage highs gurobi gurobi-sage scip polytopes-db-4d qq zz rdf numberfield databases graphs groups plot standard

Classifiers

Report project as malware

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SHA256 3f440527ccabd60b9e58dab456637a654e7daac4a14e8f53c8540430342e41df
MD5 ae5fcafb0e8f9b366543ac3d15c9e1f5
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SHA256 70a1fdd290fd6b4e4f43891cd2b5da3434581f153d932d1b2dd9f293cef1562b
MD5 6e4d3ceb84520f49fb7f208b669b3d89
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SHA256 715295494b11612f7e6b8aef9dd750236ed93629173f82541153ec7eade3842f
MD5 a2ebd31ca13c249091baade6b3dde699
BLAKE2b-256 1f05aa32b22bb44929b33c74cb7bd347bae19736043a8f53932aea7c79387d5f

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SHA256 bf294c9009d5aed6ae3b662caed5d264f893e8f55059f74d5071ff20d3a98acb
MD5 d6f291db7ba02c09b985ae4049750972
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SHA256 c86361358dd54d8d870d685fa95047c176301c3de525c97b9c7ddbd714143e18
MD5 af3f91f36b6b0205a0f118ff0017b158
BLAKE2b-256 84ab61717a3da14a94c8c523959290ad6932f142bd496ef66fac0e7e820d504f

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SHA256 a52e666c87e1963fcc914aeeb974ec298838a25b062276df9b15db54be9ceb7c
MD5 64f0cc18abb3c2c0bfe2053c0fcfb2b6
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SHA256 042cd70585bd0f71204fc18a66e217a0d373f64b6394b45a3484ba100ccdb815
MD5 e4f4aa4a563a6cc2be1fcf1fd8705186
BLAKE2b-256 65fe0cb4cc0745c212e7e3ac5668ba4ac765ce921f0983bf5293bd652858162f

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SHA256 049e9fa0bee7617c65138459778d4dd0ee612ec74cf373aeedce6da1978566dd
MD5 98dd57e725ab813a1bdb6b42e56138e9
BLAKE2b-256 6e994de8f19a918e5d8d3ecbe96ad4f416ed92eeb2557e1b32bb038cf229a523

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SHA256 0f828a876b39e1713b71fbffbb56a1b3db51817d0e7cbb91da43348a83848317
MD5 9c80141a13a3d26506b171b7a79b28db
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SHA256 d1e3b52acdc27c2961e823568540789fcccf53323e1718bd8f9b3689b2a6cae1
MD5 fb589e6992080d5d636595b0f095ce3c
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SHA256 e89cd41072de9fadc345bbef48d0676b50e8387f78d6889ce4fc122284098253
MD5 ed7942c9e466df448078772cbafa6910
BLAKE2b-256 7c52983f561fd5f29add44dc49da7033674dc9580e7f3da5964618d4c8c73d62

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SHA256 b93c1b47221e4945ac82866723316a768ffa8af6364824f004aca31f7e42bfeb
MD5 bd28714f56719cf3804a910b2b82658c
BLAKE2b-256 2cbf6712222415d1c109cde73497793dabf21eb44b1a394852168c69f53ba173

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SHA256 4198f3dc843edffb62f21464e312d44d5a9ef83274ce1c6d72a0301d35e3414c
MD5 7d6131f95fca6986bb0a32c58a2c5418
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SHA256 1cfa88b0a56e2a8c323488a3e2115518566a293fb727170026a3e554b09848a1
MD5 ee9a9e1aaf6b45d5ea3ead039087c59d
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SHA256 b84914b035653bf00b7f18d4787578aca51a7b1357e9dbc8f1958d47f7055c36
MD5 7f042189fbd739f0f531f9db3d51bef7
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SHA256 65d2481fc8e2e7387ac963e59209bc58e58e78dca59af6bff33b8cef9261a65b
MD5 07cd78c4b1c7385446afeae45126b5bd
BLAKE2b-256 87a9b100eddbe0eb73d489c23ebe5b2e9f165fe75a0c54dd52c1e5cc6600a96f

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SHA256 da52ee55b0e9ea30398a7a0ef017b6426e96308a97d1b37ee2f4b2adb77654bf
MD5 7c0f8c70cb1cb36fabc636071382cad8
BLAKE2b-256 e32e95dc3403b1dc6ab3a05df8f0081007dbc269c8b7b84e5600c9aeb54e5d7f

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