CoChat
Sign Up
Cited by 655Polynomial and algebraic computationMathematical and Computational MethodsFormal Methods in Verification

The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.

Quantifier elimination for real closed fields by cylindrical algebraic decompostion

Collins, George E.·1975·Lecture Notes in Computer Science
DOI 10.1007/3-540-07407-4_17
Open this paper in CoChat — free account

Overview

Integrity signals

Registry

Crossref · 10.1007/3-540-07407-4_17

Cites

1 of 1 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Verification

Claims the paper makes

We couldn’t retrieve this paper’s full text, so its claims and self-check weren’t run. The registry and citation checks still apply.

Claims other papers make about this one

Each is checked against this paper’s own text: does it say what the citing paper says it does?

Citations

Cites

Show all 1 references

Research works printed but not linked: 19

  1. Brown, W.S., On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors, J. ACM, vol. 18, no. 4 (Oct. 1971) pp. 478–504. · DOI
  2. Brown, W.S., and Traub, J.F., On Euclid's Algorithm and the Theory of Subresultants, J. ACM, vol. 18, no. 4 (Oct. 1971), pp. 505–514. · DOI
  3. Cohen, P.J., Decision Procedures for Real and p-adic Fields, Comm. Pure and Applied Math., vol. XXII, no. 2 (March 1969), pp. 131–151. · DOI
  4. Collins, G.E., Subresultants and Reduced Polynomial Remainder Sequences, J. ACM, vol. 14, no. 1, (Jan. 1967), pp. 128–142. · DOI
  5. Collins, G.E., The Calculation of Multivariate Polynomial Resultants, J. ACM, vol. 18, no. 4 (Oct. 1971), pp. 515–532. · DOI
  6. Collins, G.E., Computer Algebra of Polynomials and Rational Functions, Am. Math. Monthly, vol. 80, no. 7 (Aug.-Sept. 1973), pp. 725–755. · DOI
  7. Collins, G.E., Efficient Quantifier Elimination for Elementary Algebra (abstract), Symposium on Complexity of Sequential and Parallel Numerical Algorithms, Carnegie-Mellon University, May 1973.
  8. Collins, G.E., Quantifier Elimination for Real Closed Fields by Cylindrical Algebraic Decomposition — Preliminary Report, Proceedings of EUROSAM 74, STGSAM Bulletin, Vol. 8, no. 3 (August 1974), pp. 80–90. · DOI
  9. Heindel, L.E., Integer Arithmetic Algorithms for Polynomial Real Zero Determination, J. ACM, vo. 18, no. 4 (Oct. 1971), pp. 533–548. · DOI
  10. Loos, R., G.K., A Constructive Approach to Algebraic Numbers, SIAM Journal on Computing, to appear.
  11. Musser, D.R., Algorithms for Polynomial Factorization (Ph.D. Thesis), Univ. of Wisconsin Computer Sciences Dept. Tech. Report No. 134, Sept. 1971.
  12. Musser, D.R., Multivariate Polynomial Factorization, J.ACM., Vol. 22, No. 2 (April 1975), pp. 291–308. · DOI
  13. Rubald, C.M., Algorithms for Polynomials over a Real Algebraic Number Field (Ph.D. Thesis), Computer Sciences Dept. Tech. Report No. 206, Jan. 1974.
  14. Seidenberg, A., A New Decision Method for Elementary Algebra, Annals of Math., vol. 60, no. 2 (Sept. 1954), pp. 365–374. · DOI
  15. Tarski, A., A Decision Method for Elementary Algebra and Geometry, second ed., rev., Univ. of California Press, Berkeley, 1951. · DOI
  16. Collins, G.E., and E. Horowitz, The Minimum Root Separation of a Polynomial, Math. of Comp., Vol. 28, No. 126, (April 1974), pp. 589–597. · DOI
  17. Mignotte, M., An Inequality About Factors of Polynomials, Math. of Comp., Vol. 28, No. 128 (October 1974), pp. 1153–1157. · DOI
  18. Knuth, D.E., The Art of Computer Programming, Vol. 2: Seminumerical Algorithms, Addison-Wesley, Reading, 1969.
  19. Ferrante, J., and C. Rackoff, A Decision Procedure for the First Order Theory of Real Addition with Order, SIAM Journal on Computing, Vol. 4, No. 1 (March 1975), pp. 69–76. · DOI

Cited by

Sorted by citations

Metadata

Authors
Collins, G. E.
Affiliations
University of Wisconsin–Madison (US)
Corresponding author
Collins, George E.
Venue
Lecture Notes in Computer Science
Publisher
Springer Berlin Heidelberg
Published
1975
Pages
134-183
ISSN
  • 0302-9743 (ISSN-L)
  • 1611-3349
DOI
10.1007/3-540-07407-4_17
OpenAlex
W4229917934
Cited by
655
References
1
Citations by year
2026: 27 · 2025: 32 · 2024: 30 · 2023: 31 · 2022: 25 · 2021: 23 · 2020: 32 · 2019: 25 · 2018: 29 · 2017: 18 · 2016: 23 · 2015: 17 · 2014: 25 · 2013: 20 · 2012: 12
FWCI
2.07
Type
conference paper
Language
en
Open access
closed
Locations
Lecture notes in computer science (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Polynomial and algebraic computation
  • Physical Sciences › Mathematics › Modeling and Simulation › Mathematical and Computational Methods
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Formal Methods in Verification
Keywords
quantifier elimination, real closed fields, cylindrical algebraic decomposition, decision procedures

About these checks

Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.

Statistics and arithmetic are recomputed, not judged.

Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.

What counts as a claim ›How we measure confidence ›How we check this ›

Are you an author, or do you see a problem with this page? Request a review