MC++ Toolkit for Construction, Manipulation and Evaluation of Factorable Functions
MC++ provides a collection of classes to support the construction and manipulation of factorable functions and their evaluation using a range of arithmetics. It is primarily written in C++ to promote execution speed, while the module pyMC includes Python binders through pybind11.
Expression trees in MC++ can comprise any finite combination of unary and binary operations from a default library and are described by direct acyclic graphs (DAGs). MC++ also features a mechanism to extend DAGs with external operations, currently including affine and polynomial subexpressions as well as multi-layer perceptrons (MLP) and nested DAGs. Through the library CRONOS, MC++ can also be extended with systems of algebraic and differential equations. Expression trees generated with MC++ can be used by the library CANON for local and global numerical optimization; and the library MAGNUS for the development and analysis of mathematical models.
The present version 5.0 of MC++ has capability for:
- Construction and differentiation of expression trees (both forward and reverse accumulation modes)
- Recursive decomposition of factorable expressions into linear/polynomial subexpressions and transcendental operations
- Specification of nested expression trees to enable tailored bounding strategies
The main bounding components in version 5.0 of MC++ include:
- Interval arithmetic
- Eigenvalue arithmetic
- Ellipsoidal arithmetic
- McCormick relaxations
- Taylor and Chebyshev models
- Polyhedral relaxations
- Superposition relaxations
A range of python scripts and notebooks are provided in notebook subdirectory to illustrate these capabilities.
Setting up MC++
Refer to INSTALL.md for instructions.
Contacts
- Repo owner: Benoit C. Chachuat
- OMEGA Research Group
References
- Bompadre, A., A. Mitsos, Convergence rate of McCormick relaxations, Journal of Global Optimization 52(1), 1-28, 2012
- Bompadre, A., A. Mitsos, B. Chachuat, Convergence analysis of Taylor models and McCormick-Taylor models, Journal of Global Optimization, 57(1), 75-114, 2013
- Bongartz, D., J. Najman, S. Sass, A. Mitsos, MAiNGO – McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization, Technical Report, Process Systems Engineering (AVT.SVT), RWTH Aachen University, 2018
- Chachuat, B, B. Houska, R. Paulen, N. Peric, J. Rajyaguru, M.E. Villanueva, Set-theoretic approaches in analysis, estimation and control of nonlinear systems, IFAC-PapersOnLine, 48(8), 981-995, 2015
- Karia, T., C.S. Adjiman, B. Chachuat, Assessment of a two-step approach for global optimization of mixed-integer polynomial programs using quadratic reformulation, Computers & Chemical Engineering, 165, 107909, 2022
- Mitsos, A., B. Chachuat, P.I. Barton, McCormick-based relaxations of algorithms, SIAM Journal on Optimization, 20(2):573-601, 2009
- Rajyaguru, J., Villanueva M.E., Houska B., Chachuat B., Chebyshev model arithmetic for factorable functions, Journal of Global Optimization, 68, 413-438, 2017
- Tsoukalas, A., A. Mitsos, Multi-variate McCormick relaxations, Journal of Global Optimization, 59(2), 633-662, 2014
- Villanueva, M.E., Set-Theoretic Methods for Analysis, Estimation and Control of Nonlinear Systems, PhD Thesis, Department of Chemical Engineering, Imperial College London, 2016
- Villanueva, M.E., J. Rajyaguru, B. Houska, B. Chachuat, Ellipsoidal arithmetic for multivariate systems, Computer Aided Chemical Engineering, 37, 767-772, 2015
- Wechsung, A., P.I. Barton, Global optimization of bounded factorable functions with discontinuities, Journal of Global Optimization, 58(1), 1-30, 2014
- Y Zha, Y., M.E. Villanueva, B. Houska, B. Chachuat Relaxation via Separable Estimators: Arithmetic and Implementation, arXiv preprint arXiv:2605.10854, 2026
Release files for pymcpp 5.0.2
For a detailed explanation of source distributions (sdists) and built distributions (wheels), please see the package formats documentation.
Source distribution (sdist)
| File | Size | Uploaded | Provenance | Actions |
|---|---|---|---|---|
| pymcpp-5.0.2.tar.gz | 8.3 MB | With provenance | Details for pymcpp-5.0.2.tar.gz |
Built distributions (wheels)
Total release size: 408.0 MB
Release files / pymcpp-5.0.2.tar.gz
| Download URL | pymcpp-5.0.2.tar.gz |
|---|---|
| Size | 8.3 MB |
| Tags | Source |
|
SHA-256 checksum How to use checksums |
72009825c2f4a6df2a3961816cdd69b69a35df7da1809c199edd5d0162387720
|
|
BLAKE2b-256 checksum How to use checksums |
80a58a95b7a10db6c4864032003ca9267ba43274d2251568afee24083c464379
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp314-cp314-win_amd64.whl
| Download URL | pymcpp-5.0.2-cp314-cp314-win_amd64.whl |
|---|---|
| Size | 17.6 MB |
| Tags | CPython 3.14 Windows x86-64 |
|
SHA-256 checksum How to use checksums |
709b169aeab623a9f39b4b5c7b311a2e340ae65a965d79aef6990f1755d4f6e2
|
|
BLAKE2b-256 checksum How to use checksums |
531d44669d887ab0200342d9679bf046999f5e01da42cd88ff202547a2a9a372
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp314-cp314-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
| Download URL | pymcpp-5.0.2-cp314-cp314-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl |
|---|---|
| Size | 47.1 MB |
| Tags | CPython 3.14 Linux glibc 2.27+ x86-64 Linux glibc 2.28+ x86-64 |
|
SHA-256 checksum How to use checksums |
54111b5919f623b9c014b3c08a6b6510763e8c3fc1120dfee25b09826b1f0b27
|
|
BLAKE2b-256 checksum How to use checksums |
2df4c07994726a522f55cde5ba2b37225f56a70ef05e079f5ae9d3ddbc959281
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp314-cp314-macosx_14_0_arm64.whl
| Download URL | pymcpp-5.0.2-cp314-cp314-macosx_14_0_arm64.whl |
|---|---|
| Size | 15.4 MB |
| Tags | CPython 3.14 macOS 14.0+ ARM64 |
|
SHA-256 checksum How to use checksums |
4e51ad430ca9111edfe49e376b6b80d65c28806a60fdcd4e84de7f2dadb774ed
|
|
BLAKE2b-256 checksum How to use checksums |
69f1cbe69f3fecec9b6250203d27979a712cc2c9cbf65ae1f50428b562b0a9f1
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp313-cp313-win_amd64.whl
| Download URL | pymcpp-5.0.2-cp313-cp313-win_amd64.whl |
|---|---|
| Size | 17.2 MB |
| Tags | CPython 3.13 Windows x86-64 |
|
SHA-256 checksum How to use checksums |
2a4d40d0b7a8cec195e6e2d7b9c2b91b4bba43790d15b6af349c04678e60abb6
|
|
BLAKE2b-256 checksum How to use checksums |
29a943f7690d0e10465602c5dad321da62181563a6fb8091abdd9349c5cb46ea
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp313-cp313-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
| Download URL | pymcpp-5.0.2-cp313-cp313-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl |
|---|---|
| Size | 47.1 MB |
| Tags | CPython 3.13 Linux glibc 2.27+ x86-64 Linux glibc 2.28+ x86-64 |
|
SHA-256 checksum How to use checksums |
11a312281fc6d8fb6672444e0b84efaf25079bffadd89b96400d20a5bb287a06
|
|
BLAKE2b-256 checksum How to use checksums |
e7e69914ea82e87188daa7fbc28f4f509c4f67804f34d551c29fda96a42cb06b
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp313-cp313-macosx_14_0_arm64.whl
| Download URL | pymcpp-5.0.2-cp313-cp313-macosx_14_0_arm64.whl |
|---|---|
| Size | 15.4 MB |
| Tags | CPython 3.13 macOS 14.0+ ARM64 |
|
SHA-256 checksum How to use checksums |
309183bcfb1b75bb4666021996004d96f96081d93a7d43c47abaee140ade17cd
|
|
BLAKE2b-256 checksum How to use checksums |
abff7f956018d907113063bd9d6a26c8deddec1baf67ae1103e9d7b19f100e99
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp312-cp312-win_amd64.whl
| Download URL | pymcpp-5.0.2-cp312-cp312-win_amd64.whl |
|---|---|
| Size | 17.1 MB |
| Tags | CPython 3.12 Windows x86-64 |
|
SHA-256 checksum How to use checksums |
d633a372f756b7bb36d33974f12971324fdc2cd00aea82f85a95ba93ba87e5be
|
|
BLAKE2b-256 checksum How to use checksums |
b6c13731f0a6427fbde35b2722a39924d52331604645efec9c968889f7d7539a
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp312-cp312-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
| Download URL | pymcpp-5.0.2-cp312-cp312-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl |
|---|---|
| Size | 47.1 MB |
| Tags | CPython 3.12 Linux glibc 2.27+ x86-64 Linux glibc 2.28+ x86-64 |
|
SHA-256 checksum How to use checksums |
eca8fc6a23490d917626d97019d77ddbec8595d609a92a46b98082e394594ace
|
|
BLAKE2b-256 checksum How to use checksums |
7f02624717ca0d02174060a2ef9a60a354ccdb388b3f4c87bdf37eb731a0b1ca
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp312-cp312-macosx_14_0_arm64.whl
| Download URL | pymcpp-5.0.2-cp312-cp312-macosx_14_0_arm64.whl |
|---|---|
| Size | 15.4 MB |
| Tags | CPython 3.12 macOS 14.0+ ARM64 |
|
SHA-256 checksum How to use checksums |
a9f60be671e711a73c24984756246b7f74b30b47c22c1f1153f5a6f0f6c73ef7
|
|
BLAKE2b-256 checksum How to use checksums |
338fbaead2d7558b1d1ea7e30abe0e06e298159e37b7df2dc4abedb03ae5633a
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp311-cp311-win_amd64.whl
| Download URL | pymcpp-5.0.2-cp311-cp311-win_amd64.whl |
|---|---|
| Size | 17.4 MB |
| Tags | CPython 3.11 Windows x86-64 |
|
SHA-256 checksum How to use checksums |
d616d3dc20611cac3c794610b753d26293260d3216b81d01ef0815a7d6ece8fc
|
|
BLAKE2b-256 checksum How to use checksums |
8493904954b317c68995cd27dadf27dda07e7d99ba13156c998e8bd9c7c57d0e
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp311-cp311-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
| Download URL | pymcpp-5.0.2-cp311-cp311-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl |
|---|---|
| Size | 47.2 MB |
| Tags | CPython 3.11 Linux glibc 2.27+ x86-64 Linux glibc 2.28+ x86-64 |
|
SHA-256 checksum How to use checksums |
c6c8d300b2315758026ac1d99c0d8b57ca6f3f3c93a7f733dfdf91c93e1f750d
|
|
BLAKE2b-256 checksum How to use checksums |
74f336ba1962c37422efcb06c4120ccc2188a4591f5c72d274baf6e910ab0c72
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp311-cp311-macosx_14_0_arm64.whl
| Download URL | pymcpp-5.0.2-cp311-cp311-macosx_14_0_arm64.whl |
|---|---|
| Size | 15.4 MB |
| Tags | CPython 3.11 macOS 14.0+ ARM64 |
|
SHA-256 checksum How to use checksums |
c9944f41782a72b1ea4fbc6a5b4c1c8b82fdd6c5d28c125658001a3c15f53137
|
|
BLAKE2b-256 checksum How to use checksums |
11c6ac3b5067be8fe3671e75db00605bffd240a0d29689b4dcce95ee15819f6c
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp310-cp310-win_amd64.whl
| Download URL | pymcpp-5.0.2-cp310-cp310-win_amd64.whl |
|---|---|
| Size | 17.4 MB |
| Tags | CPython 3.10 Windows x86-64 |
|
SHA-256 checksum How to use checksums |
9e00e5ca9e401689c0dd3b831962c22b89fe2d026a4dce102f2a9208328fb631
|
|
BLAKE2b-256 checksum How to use checksums |
ed499159c07a3089ffa2479134ec9922d1f579cc2d12ff023e0ad254c367c0c5
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp310-cp310-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl
| Download URL | pymcpp-5.0.2-cp310-cp310-manylinux_2_27_x86_64.manylinux_2_28_x86_64.whl |
|---|---|
| Size | 47.2 MB |
| Tags | CPython 3.10 Linux glibc 2.27+ x86-64 Linux glibc 2.28+ x86-64 |
|
SHA-256 checksum How to use checksums |
1faec56210dcd8f94d8217294852649e10d47a76ec6ae6c7d867f7cffeab6102
|
|
BLAKE2b-256 checksum How to use checksums |
1aa05beffc857fb0da4b968224790b41916ca23bba3b5f3a76e805414f39a029
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logRelease files / pymcpp-5.0.2-cp310-cp310-macosx_14_0_arm64.whl
| Download URL | pymcpp-5.0.2-cp310-cp310-macosx_14_0_arm64.whl |
|---|---|
| Size | 15.4 MB |
| Tags | CPython 3.10 macOS 14.0+ ARM64 |
|
SHA-256 checksum How to use checksums |
8966efb9379c2a07641a9a5328790665b3a8e3a3f66e689eeb452d43163e4e31
|
|
BLAKE2b-256 checksum How to use checksums |
767ba67c08078ff0a5e6ab3fbf7e4cd6a89e65255b7c7bee367d15798907632e
|
| Upload date | |
|
Uploaded using Trusted Publishing? What is trusted publishing? |
Yes |
| Uploaded via |
twine/7.0.0 CPython/3.13.14
|
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logSecurity for pymcpp 5.0.2
Provenance
Provenance describes where a file came from. On PyPI, provenance is shared via attestations, which provide a verifiable record of the build or publishing details. View details, limitations and caveats.
Full provenance
All 16 files in this release have been uploaded with provenance metadata.
Attestation for pymcpp-5.0.2.tar.gz
PyPI Publish Attestation
PyPI verified that this artifact, at this checksum, originated from the publisher listed below.
Signed by GitHub Actions, verified by PyPI on Aug 1, 2026.
Transparency logA note on package security
PyPI is a repository for distributing packages, not a service for auditing them. While third-party security researchers and our staff do their best to detect and remove malicious packages, PyPI cannot guarantee the quality, security or suitability of any given package.
To learn more about protecting yourself from malicious actors, visit our package security documentation.
