Science Explorer Back to mapMap
Discussion
Topic · Computational Theory and Mathematics

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. 10.1% 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%
2k
per year above
Top-10% rate
10.1%
share of its works in the world top 10%
Growth, 2018-21 → 2022-25
+28%
the tick is no change
Largest producer
United States
25% of the 10 largest, 2022-now
Polynomial and algebraic computation

Which countries lead Polynomial and algebraic computation research?

By volume, the United States and China publish the most (533 and 335 works in 2022-now).

By volume, 2022-now

  1. 1 United States 533 works
  2. 2 China 335 works
  3. 3 India 236 works
  4. 4 Germany 233 works
  5. 5 France 199 works
  6. 6 Japan 164 works
  7. 7 Russia 136 works
  8. 8 Italy 124 works
  9. 9 United Kingdom 116 works
  10. 10 Spain 97 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.

United States: 24.5%China: 15.4%India: 10.9%Germany: 10.7%6 others listed: 38.5%25%largest
United States533 · 24.5%China335 · 15.4%India236 · 10.9%Germany233 · 10.7%6 others listed836 · 38.5%

Shares of the rows listed above, not of the whole node.

Which institutions lead Polynomial and algebraic computation research?

By volume in 2022-now, Centre National de la Recherche Scientifique publishes the most Polynomial and algebraic computation research, followed by Indian Institute of Technology Kharagpur and Russian Academy of Sciences.

By volume, 2022-now

  1. 1 Centre National de la Recherche ScientifiqueFrance 94 works
  2. 2 Indian Institute of Technology KharagpurIndia 47 works
  3. 3 Russian Academy of SciencesRussia 34 works
  4. 4 Max Planck SocietyGermany 22 works
  5. 5 Chinese Academy of SciencesChina 20 works
  6. 6 Lomonosov Moscow State UniversityRussia 16 works
  7. 7 Johannes Kepler University of LinzAustria 14 works
  8. 8 Peking UniversityChina 14 works
  9. 9 University of TrentoItaly 13 works
  10. 10 University of OxfordUnited Kingdom 13 works

Who are the leading researchers in Polynomial and algebraic computation?

The most-cited researchers publishing on Polynomial and algebraic computation include Stephen Boyd, Pushmeet Kohli and Hywel C Williams.

  1. 1 Stephen Boyd United States 142k citations
  2. 2 Pushmeet Kohli United Kingdom 129k citations
  3. 3 Hywel C Williams United Kingdom 126k citations

Ranked by citations received across their whole record, among researchers with at least three works on this topic.

What are the most cited papers in Polynomial and algebraic computation?

The most cited paper in Polynomial and algebraic computation is "The Magma Algebra System I: The User Language" (Wieb Bosma, John Cannon, Catherine Playoust, 1997), with 7,465 citations. Next come "Matrix multiplication via arithmetic progressions" (2,313) and "Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus" (2,009).

Most cited papers
#PaperReleasedCitations
1 The Magma Algebra System I: The User Language Wieb Bosma, John Cannon, Catherine Playoust · Journal of Symbolic Computation Open access Sep 1997 7,465
2 Matrix multiplication via arithmetic progressions Don Coppersmith, Shmuel Winograd · Journal of Symbolic Computation Open access Mar 1990 2,313
3 Analysis on Measure Chains — A Unified Approach to Continuous and Discrete Calculus Stefan Hilger · Results in Mathematics Aug 1990 2,009
4 Basic Linear Algebra Subprograms for Fortran Usage Charles L. Lawson, Richard J. Hanson, David R. Kincaid et al. · ACM Transactions on Mathematical Software Open access Sep 1979 1,641
5 Introduction to Algorithms Gerard O’Regan · Texts in computer science Book chapter 2023 1,630
All 99 most cited papers, with filters and sorting

Where is Polynomial and algebraic computation research done?

The largest centres of Polynomial and algebraic computation research in 2022-now 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-now

  1. 1 MoscowRussia 80 works
  2. 2 BeijingChina 78 works
  3. 3 ParisFrance 68 works
  4. 4 TokyoJapan 55 works
  5. 5 KharagpurIndia 47 works
  6. 6 New YorkUnited States 25 works
  7. 7 SeoulSouth Korea 25 works
  8. 8 ShanghaiChina 24 works
  9. 9 WarsawPoland 23 works
  10. 10 ChennaiIndia 22 works

Where it is the local speciality

  1. KharagpurIN · 47.5 works31×
← less than its size predicts1×more →

Location quotient: how much more of its research is in Polynomial and algebraic computation than the world average.

See Polynomial and algebraic computation on the map

Where is the best place to study Polynomial and algebraic computation?

Among universities, judged by research, Indian Institute of Technology Kharagpur, KU Leuven and University of Oxford 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.

0%10%20%mean 14.55%fractional works in this field (log) →share of work in the world top 10% →Indian Institute of …Goethe University Fr…KU LeuvenUniversity of Oxford
above the meannear itbelow it

One dot per university in the first ten of the table below, at the default weights. The upper left is the interesting corner: small places doing unusually strong work.

Excellenceshare of its work in the world top 10%, 2022-now and all time averaged
40%
Specialisationhow much of its work is in this field, counted up to 10× the world share
10%
Sizeits output in this field, on a log scale
30%
Growthoutput growth, counted from -20% to +20%
10%
Internationalshare of its work with a co-author abroad
10%
Each slider sets a weight; the share it gets of the score is beside it.
#UniversityScoreTop 10%SpecialisationWorksGrowth
1Indian Institute of Technology KharagpurIndia 90.020.9%34.4×48 +1834.5%
2KU LeuvenBelgium 69.420.0%4.5×12 +64.1%
3University of OxfordUnited Kingdom 61.115.1%3.3×13 +87.4%
4Goethe University FrankfurtGermany 56.320.1%6.5×8 +211.2%
5Johannes Kepler University of LinzAustria 56.210.5%29.3×14 -10.4%
6University of California San DiegoUnited States 56.211.5%4.7×12 +185.8%
7University of MichiganUnited States 53.916.7%2.7×11 +114.6%
8University of Notre DameUnited States 50.910.7%10.9×9 +39.1%
9Technische Universität BerlinGermany 49.613.1%9.7×9 +19.5%
10Sorbonne UniversitéFrance 48.76.9%5.3×10 +17.4%

Universities only. The score blends excellence (40%), size (30%), specialisation (10%), growth (10%), international reach (10%), 2022-now; growth compares 2018-21 with 2022-25 and counts up to +20%, since a jump from a small base is mostly noise.

Every institution in Polynomial and algebraic computation, country by country

Is Polynomial and algebraic computation research growing?

Output in 2022-2025 was 28% higher than in 2018-2021, peaking in 2025. The fastest-growing topics are Polynomial and algebraic computation.

still counting19801990200020102020
grewheldshrank

The same series as a ribbon: one cell per year, darker for more. The line above answers how much; this answers when.

Its share of all research

Growing output can still be a shrinking share: all of science grows. This is Polynomial and algebraic computation as a percentage of every work published that year, 0.012% in 2024.

still counting0.020%0.040%Polynomial and algebraic computation0.015% in 202519801990200020102020

Fractional works of Polynomial and algebraic computation over all fractional works that year. How the balance of science has shifted.

How much of it reaches the world top 10%

Year by year.

still counting5%10%15%Polynomial and algebraic computation11.8% in 2025200020102020

Of each year's works in it, the share that reached the world's 10% most cited for their field and year. A field is the world for its own topics, so there is no other line to hold it against.

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.

Discussion

Ask a question or share a note about Polynomial and algebraic computation. Posts are plain text and can be reported.