Polynomial and algebraic computation
Polynomial and algebraic computation is a research topic within Computational Theory and Mathematics. Science Explorer counts 20k research works in it since 1950. 13.3% of them reached the world's top 10% most cited for their field and year.
This cluster of papers covers topics in symbolic computing, including efficient algorithms for solving polynomial systems, Gröbner bases computation, tropical geometry, and applications in cryptography such as cryptanalysis of various cryptosystems. It also explores numerical methods for algebraic geometry and the use of max-plus algebra in certain computational problems.
- Symbolic Computing
- Gröbner Bases
- Tropical Geometry
- Polynomial Systems
- Cryptanalysis
- Algebraic Varieties
- Numerical Algebraic Geometry
- Multivariate Polynomials
- Homotopy Continuation
- Max-Plus Algebra
- Research works
- 20k fractional, since 1950
- In the world top 10%
- 2.6k per year above
- Top-10% rate
- 13.3% share of its works in the world top 10%
- Growth, 2013–17 → 2018–22
- -2% the tick is no change
Which countries lead Polynomial and algebraic computation research?
By volume, the United States and China publish the most (432 and 239 works in 2022–2025).
By volume, 2022–2025
- 1 United States 432 works
- 2 China 239 works
- 3 Germany 201 works
- 4 India 194 works
- 5 France 173 works
- 6 Japan 130 works
- 7 Russia 118 works
- 8 Italy 104 works
- 9 United Kingdom 101 works
- 10 Spain 81 works
How concentrated that is
The same countries as shares of everything the list above accounts for. A node where two countries do two thirds of the work and one spread evenly across twelve read alike as a ranking and not at all alike here.
Shares of the rows listed above, not of the whole node.
Which institutions lead Polynomial and algebraic computation research?
By volume in 2022–2025, Indian Institute of Technology Kharagpur publishes the most Polynomial and algebraic computation research, followed by Centre National de la Recherche Scientifique and Lomonosov Moscow State University.
By volume, 2022–2025
- 1 Indian Institute of Technology Kharagpur India 45 works
- 2 Centre National de la Recherche Scientifique France 27 works
- 3 Lomonosov Moscow State University Russia 14 works
- 4 Johannes Kepler University of Linz Austria 14 works
- 5 University of California San Diego United States 12 works
- 6 University of Trento Italy 11 works
- 7 University of Oxford United Kingdom 11 works
- 8 University of Waterloo Canada 11 works
- 9 Peking University China 10 works
- 10 National Research University Higher School of Economics Russia 10 works
Who are the leading researchers in Polynomial and algebraic computation?
The most-cited researchers publishing on Polynomial and algebraic computation include Lei Zhang and Thomas J.R. Hughes.
- 1 Lei Zhang 5.3k citations
- 2 Thomas J.R. Hughes 3.7k citations
Ranked by citations received across their whole record, among researchers with at least three works on this topic.
Where is Polynomial and algebraic computation research done?
The largest centres of Polynomial and algebraic computation research in 2022–2025 are Moscow (Russia), Beijing (China), Paris (France) and Tokyo (Japan). Among places with at least 20 works in it, it is an unusually large share of all research in Kharagpur.
Largest cities, 2022–2025
Where it is the local speciality
- KharagpurIN · 45.1 works35×
Location quotient: how much more of its research is in Polynomial and algebraic computation than the world average.
Where is the best place to study Polynomial and algebraic computation?
Among universities, judged by research, Indian Institute of Technology Kharagpur, National Research University Higher School of Economics and Johannes Kepler University of Linz score highest, combining excellence, specialisation, size, growth and international reach. Research strength is one signal when choosing where to study; it does not measure teaching.
One dot per university in the table below. The upper left is the interesting corner: small places doing unusually strong work.
| # | University | Score | Top 10% | Specialisation | Works | Growth |
|---|---|---|---|---|---|---|
| 1 | Indian Institute of Technology Kharagpur India | 54.5 | 3.5% | 35.3× | 45 | — |
| 2 | National Research University Higher School of Economics Russia | 52.0 | 13.5% | 9.7× | 10 | +127.0% |
| 3 | Johannes Kepler University of Linz Austria | 46.5 | 5.6% | 34.4× | 14 | +30.7% |
| 4 | KU Leuven Belgium | 42.5 | 29.6% | 3.9× | 9 | -36.3% |
| 5 | Chennai Mathematical Institute India | 41.1 | 11.4% | 57.4× | 8 | -14.8% |
| 6 | Technical University of Munich Germany | 40.8 | 23.2% | 5.0× | 10 | -10.6% |
| 7 | University of Trento Italy | 40.6 | 6.0% | 17.2× | 11 | -34.2% |
| 8 | Simon Fraser University Canada | 36.3 | 2.7% | 12.1× | 8 | +11.9% |
| 9 | University of Augsburg Germany | 34.2 | 0.0% | 24.7× | 8 | — |
| 10 | Sorbonne Université France | 33.6 | 8.9% | 6.8× | 8 | +9.7% |
Universities only. Score blends excellence (30%), specialisation (25%), size (20%), growth (15%) and international reach (10%), 2015–2022; growth compares 2010–14 with 2015–19.
Is Polynomial and algebraic computation research growing?
Output in 2018–2022 was 2% lower than in 2013–2017, peaking in 2025. The fastest-growing topics are Polynomial and algebraic computation.
The same series as a ribbon — one cell per year, darker for more. The line above answers how much; this answers when.
Which topics inside it are moving
Growth and decline on one axis around a shared zero. Two lists side by side hide the thing that matters: whether the growth dwarfs the decline, or the other way round.