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Polynomials
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246
Table of contents
246
1. Generating functions
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Polynomials
10
1.1. Betti number
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Generating functions
1.2. Cyclic sieving
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Generating functions
1.3. Factorial moment generating function
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Generating functions
1.4. Generating function
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Generating functions
1.5. Generating function transformation
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Generating functions
1.6. Matsushima's formula
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Generating functions
1.7. Moment-generating function
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Generating functions
1.8. Probability-generating function
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Generating functions
1.9. Tau function (integrable systems)
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Generating functions
1.10. Weisner's method
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Generating functions
2. Homogeneous polynomials
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Polynomials
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2.1. Quadratic forms
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Homogeneous polynomials
2.2. Complete homogeneous symmetric polynomial
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Homogeneous polynomials
2.3. Diagonal form
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Homogeneous polynomials
2.4. Elementary symmetric polynomial
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Homogeneous polynomials
2.5. Polynomial SOS
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Homogeneous polynomials
2.6. Power sum symmetric polynomial
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Homogeneous polynomials
2.7. SOS-convexity
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Homogeneous polynomials
2.8. Schur polynomial
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Homogeneous polynomials
3. Orthogonal polynomials
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Polynomials
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3.1. Affine q-Krawtchouk polynomials
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Orthogonal polynomials
3.2. Affine root system
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Orthogonal polynomials
3.3. Al-Salam–Carlitz polynomials
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Orthogonal polynomials
3.4. Al-Salam–Chihara polynomials
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Orthogonal polynomials
3.5. Askey scheme
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Orthogonal polynomials
3.6. Askey–Gasper inequality
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Orthogonal polynomials
3.7. Associated Legendre polynomials
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Orthogonal polynomials
3.8. Bateman polynomials
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Orthogonal polynomials
3.9. Bessel polynomials
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Orthogonal polynomials
3.10. Big q-Laguerre polynomials
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Orthogonal polynomials
3.11. Biorthogonal polynomial
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Orthogonal polynomials
3.12. Christoffel–Darboux formula
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Orthogonal polynomials
3.13. Classical orthogonal polynomials
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Orthogonal polynomials
3.14. Continuous Hahn polynomials
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Orthogonal polynomials
3.15. Continuous big q-Hermite polynomials
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Orthogonal polynomials
3.16. Continuous dual Hahn polynomials
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Orthogonal polynomials
3.17. Continuous dual q-Hahn polynomials
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Orthogonal polynomials
3.18. Continuous q-Hahn polynomials
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Orthogonal polynomials
3.19. Continuous q-Hermite polynomials
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Orthogonal polynomials
3.20. Continuous q-Jacobi polynomials
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Orthogonal polynomials
3.21. Continuous q-Laguerre polynomials
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Orthogonal polynomials
3.22. Discrete Chebyshev polynomials
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Orthogonal polynomials
3.23. Discrete orthogonal polynomials
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Orthogonal polynomials
3.24. Discrete q-Hermite polynomials
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Orthogonal polynomials
3.25. Dual Hahn polynomials
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Orthogonal polynomials
3.26. Dual q-Hahn polynomials
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Orthogonal polynomials
3.27. Favard's theorem
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Orthogonal polynomials
3.28. Gegenbauer polynomials
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Orthogonal polynomials
3.29. Hahn polynomials
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Orthogonal polynomials
3.30. Hall–Littlewood polynomials
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Orthogonal polynomials
3.31. Heckman–Opdam polynomials
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Orthogonal polynomials
3.32. Jack function
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Orthogonal polynomials
3.33. Jacobi polynomials
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Orthogonal polynomials
3.34. Koornwinder polynomials
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Orthogonal polynomials
3.35. Kravchuk polynomials
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Orthogonal polynomials
3.36. Little q-Jacobi polynomials
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Orthogonal polynomials
3.37. Little q-Laguerre polynomials
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Orthogonal polynomials
3.38. Macdonald polynomials
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Orthogonal polynomials
3.39. Mehler kernel
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Orthogonal polynomials
3.40. Mehler–Heine formula
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Orthogonal polynomials
3.41. Meixner polynomials
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Orthogonal polynomials
3.42. Meixner–Pollaczek polynomials
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Orthogonal polynomials
3.43. Multiple orthogonal polynomials
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Orthogonal polynomials
3.44. Orthogonal polynomials on the unit circle
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Orthogonal polynomials
3.45. Plancherel–Rotach asymptotics
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Orthogonal polynomials
3.46. Pseudo-Zernike polynomials
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Orthogonal polynomials
3.47. Pseudo Jacobi polynomials
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Orthogonal polynomials
3.48. Q-Bessel polynomials
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Orthogonal polynomials
3.49. Q-Charlier polynomials
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Orthogonal polynomials
3.50. Q-Hahn polynomials
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Orthogonal polynomials
3.51. Q-Krawtchouk polynomials
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Orthogonal polynomials
3.52. Q-Laguerre polynomials
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Orthogonal polynomials
3.53. Q-Meixner polynomials
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Orthogonal polynomials
3.54. Q-Meixner–Pollaczek polynomials
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Orthogonal polynomials
3.55. Q-Racah polynomials
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Orthogonal polynomials
3.56. Quantum q-Krawtchouk polynomials
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Orthogonal polynomials
3.57. Rodrigues' formula
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Orthogonal polynomials
3.58. Rogers polynomials
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Orthogonal polynomials
3.59. Sobolev orthogonal polynomials
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Orthogonal polynomials
3.60. Stieltjes–Wigert polynomials
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Orthogonal polynomials
3.61. Turán's inequalities
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Orthogonal polynomials
3.62. Zernike polynomials
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Orthogonal polynomials
4. Polynomial functions
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Polynomials
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4.1. Constant function
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Polynomial functions
4.2. Cubic function
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Polynomial functions
4.3. Linear function
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Polynomial functions
4.4. Linear function (calculus)
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Polynomial functions
4.5. Newton polytope
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Polynomial functions
4.6. Quadratic function
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Polynomial functions
4.7. Quartic function
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Polynomial functions
4.8. Quintic function
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Polynomial functions
4.9. Ring of polynomial functions
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Polynomial functions
5. Polynomials factorization algorithms
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Polynomials
6. Rational functions
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Polynomials
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6.1. Partial fractions
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Rational functions
6.2. Chebyshev rational functions
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Rational functions
6.3. Elliptic rational functions
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Rational functions
6.4. Hartogs–Rosenthal theorem
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Rational functions
6.5. Legendre rational functions
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Rational functions
6.6. Linear fractional transformation
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Rational functions
6.7. Padé approximant
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Rational functions
6.8. Polylogarithm
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Rational functions
6.9. Rational function
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Rational functions
7. Theorems about polynomials
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Polynomials
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7.1. Abel–Ruffini theorem
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Theorems about polynomials
7.2. Bernstein's theorem (polynomials)
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Theorems about polynomials
7.3. Binomial theorem
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Theorems about polynomials
7.4. Cohn's theorem
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Theorems about polynomials
7.5. Complex conjugate root theorem
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Theorems about polynomials
7.6. Descartes' rule of signs
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Theorems about polynomials
7.7. Equioscillation theorem
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Theorems about polynomials
7.8. Factor theorem
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Theorems about polynomials
7.9. Gauss's lemma (polynomials)
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Theorems about polynomials
7.10. Gauss–Lucas theorem
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Theorems about polynomials
7.11. Grace–Walsh–Szegő theorem
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Theorems about polynomials
7.12. Hilbert's irreducibility theorem
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Theorems about polynomials
7.13. Kharitonov's theorem
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Theorems about polynomials
7.14. Lagrange's theorem (number theory)
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Theorems about polynomials
7.15. Marden's theorem
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Theorems about polynomials
7.16. Mason–Stothers theorem
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Theorems about polynomials
7.17. Multi-homogeneous Bézout theorem
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Theorems about polynomials
7.18. Multinomial theorem
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Theorems about polynomials
7.19. Polynomial remainder theorem
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Theorems about polynomials
7.20. Rational root theorem
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Theorems about polynomials
7.21. Routh–Hurwitz theorem
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Theorems about polynomials
8. Additive polynomial
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Polynomials
9. Algebraic equation
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Polynomials
10. Algebraic function
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Polynomials
11. Alternating polynomial
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Polynomials
12. Angelescu polynomials
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Polynomials
13. Appell sequence
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Polynomials
14. Bell polynomials
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Polynomials
15. Bernoulli polynomials
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Polynomials
16. Bernoulli polynomials of the second kind
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Polynomials
17. Bernoulli umbra
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Polynomials
18. Bernstein polynomial
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Polynomials
19. Bernstein–Sato polynomial
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Polynomials
20. Binomial type
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Polynomials
21. Bollobás–Riordan polynomial
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Polynomials
22. Bombieri norm
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Polynomials
23. Bracket polynomial
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Polynomials
24. Bring radical
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Polynomials
25. Cavalieri's quadrature formula
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Polynomials
26. Chebyshev polynomials
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Polynomials
27. Coefficient diagram method
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Polynomials
28. Cohn's irreducibility criterion
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Polynomials
29. Complex quadratic polynomial
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Polynomials
30. Constant term
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Polynomials
31. Cubic equation
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Polynomials
32. Cyclic redundancy check
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Polynomials
33. Degree of a polynomial
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Polynomials
34. Derivation of the Routh array
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Polynomials
35. Dickson polynomial
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Polynomials
36. Difference polynomials
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Polynomials
37. Discriminant
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Polynomials
38. Divided power structure
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Polynomials
39. Division polynomials
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Polynomials
40. Ehrhart polynomial
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Polynomials
41. Exponential polynomial
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Polynomials
42. External ray
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Polynomials
43. Fibonacci polynomials
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Polynomials
44. Geometrical properties of polynomial roots
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Polynomials
45. Graph polynomial
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Polynomials
46. HOMFLY polynomial
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Polynomials
47. Hermite polynomials
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Polynomials
48. Hilbert's Nullstellensatz
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Polynomials
49. Hilbert's thirteenth problem
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Polynomials
50. Hiptmair–Xu preconditioner
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Polynomials
51. Hurwitz polynomial
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Polynomials
52. Integer-valued polynomial
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Polynomials
53. Invariant polynomial
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Polynomials
54. Jacobian conjecture
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Polynomials
55. Jones polynomial
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Polynomials
56. Kazhdan–Lusztig polynomial
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Polynomials
57. Knot polynomial
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Polynomials
58. Lagrange polynomial
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Polynomials
59. Laguerre polynomials
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Polynomials
60. Laurent polynomial
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Polynomials
61. Lebesgue constant
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Polynomials
62. Legendre moment
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Polynomials
63. Legendre polynomials
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Polynomials
64. Lehmer's conjecture
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Polynomials
65. Lill's method
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Polynomials
66. Lindsey–Fox algorithm
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Polynomials
67. Linearised polynomial
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Polynomials
68. List of polynomial topics
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Polynomials
69. Littlewood polynomial
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Polynomials
70. Mahler measure
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Polynomials
71. Maximum length sequence
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Polynomials
72. Minimal polynomial of 2cos(2pi/n)
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Polynomials
73. Mittag-Leffler polynomials
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Polynomials
74. Monic polynomial
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Polynomials
75. Monomial order
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Polynomials
76. Morley–Wang–Xu element
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Polynomials
77. Multilinear polynomial
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Polynomials
78. Multiplicative sequence
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Polynomials
79. Neumann polynomial
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Polynomials
80. Neville's algorithm
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Polynomials
81. Newton polynomial
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Polynomials
82. Order polynomial
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Polynomials
83. P-recursive equation
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Polynomials
84. Permutation polynomial
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Polynomials
85. Perron's irreducibility criterion
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Polynomials
86. Polynomial Wigner–Ville distribution
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Polynomials
87. Polynomial evaluation
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Polynomials
88. Polynomial expansion
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Polynomials
89. Polynomial interpolation
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Polynomials
90. Polynomial matrix spectral factorization
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Polynomials
91. Polynomial ring
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Polynomials
92. Polynomial root-finding algorithms
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Polynomials
93. Polynomial sequence
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Polynomials
94. Polynomial solutions of P-recursive equations
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Polynomials
95. Polynomials calculating sums of powers of arithmetic progressions
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Polynomials
96. Q-difference polynomial
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Polynomials
97. Quartic equation
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Polynomials
98. Quasisymmetric function
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Polynomials
99. Reciprocal polynomial
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Polynomials
100. Remez algorithm
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Polynomials
101. Ring of symmetric functions
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Polynomials
102. Romanovski polynomials
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Polynomials
103. Rook polynomial
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Polynomials
104. Root of unity
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Polynomials
105. Rosenbrock function
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Polynomials
106. Routh–Hurwitz stability criterion
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Polynomials
107. Ruffini's rule
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Polynomials
108. Septic equation
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Polynomials
109. Sextic equation
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Polynomials
110. Shapiro polynomials
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Polynomials
111. Sheffer sequence
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Polynomials
112. Sister Beiter conjecture
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Polynomials
113. Stability radius
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Polynomials
114. Stable polynomial
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Polynomials
115. Stanley symmetric function
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Polynomials
116. Stirling polynomials
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Polynomials
117. Symmetric polynomial
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Polynomials
118. Theory of equations
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Polynomials
119. Thomae's formula
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Polynomials
120. Touchard polynomials
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Polynomials
121. Trigonometric polynomial
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Polynomials
122. Tutte polynomial
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Polynomials
123. Umbral calculus
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Polynomials
124. Vandermonde polynomial
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Polynomials
125. Vieta's formulas
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Polynomials
126. Wilkinson's polynomial
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Polynomials
127. Zolotarev polynomials
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Polynomials
Ancestors
Algebra
Fields of mathematics
Mathematics
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