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Ore Polynomials in Sage Manuel Kauers joint work with Maximilian - PowerPoint PPT Presentation

May 30, 2023 •510 likes •2.16k views

Ore Polynomials in Sage Manuel Kauers joint work with Maximilian Jaroschek and Fredrik Johansson RISC, JKU. 1 Ore Polynomials in Sage Manuel Kauers joint work with Maximilian Jaroschek and Fredrik Johansson RISC, JKU. 1 Sage Mathematica

  1. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 7 6 5 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  2. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 7 6 5 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  3. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 6 5 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  4. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 6 5 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  5. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 5 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  6. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 5 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  7. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  8. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  9. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 4 3 2 1 deg 0 2000 4000 6000 8000 10 000 3

  10. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 3.5 3.0 2.5 2.0 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  11. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 3.0 2.5 2.0 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  12. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 3.0 2.5 2.0 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  13. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 2.5 2.0 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  14. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 2.5 2.0 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  15. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 2.0 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  16. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 2.0 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  17. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  18. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 1.5 1.0 0.5 deg 0 2000 4000 6000 8000 10 000 3

  19. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 1.4 1.2 1.0 0.8 0.6 0.4 0.2 deg 0 2000 4000 6000 8000 10 000 3

  20. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 1.2 1.0 0.8 0.6 0.4 0.2 deg 0 2000 4000 6000 8000 10 000 3

  21. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 1.0 0.8 0.6 0.4 0.2 deg 0 2000 4000 6000 8000 10 000 3

  22. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 1.0 0.8 0.6 0.4 0.2 deg 0 2000 4000 6000 8000 10 000 3

  23. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.8 0.6 0.4 0.2 deg 0 2000 4000 6000 8000 10 000 3

  24. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.7 0.6 0.5 0.4 0.3 0.2 0.1 deg 0 2000 4000 6000 8000 10 000 3

  25. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.6 0.5 0.4 0.3 0.2 0.1 deg 0 2000 4000 6000 8000 10 000 3

  26. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.5 0.4 0.3 0.2 0.1 deg 0 2000 4000 6000 8000 10 000 3

  27. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.5 0.4 0.3 0.2 0.1 deg 0 2000 4000 6000 8000 10 000 3

  28. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.4 0.3 0.2 0.1 deg 0 2000 4000 6000 8000 10 000 3

  29. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.35 0.30 0.25 0.20 0.15 0.10 0.05 deg 0 2000 4000 6000 8000 10 000 3

  30. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.30 0.25 0.20 0.15 0.10 0.05 deg 0 2000 4000 6000 8000 10 000 3

  31. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.25 0.20 0.15 0.10 0.05 deg 0 2000 4000 6000 8000 10 000 3

  32. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.20 0.15 0.10 0.05 deg 0 2000 4000 6000 8000 10 000 3

  33. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.15 0.10 0.05 deg 0 2000 4000 6000 8000 10 000 3

  34. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.14 0.12 0.10 0.08 0.06 0.04 0.02 deg 0 2000 4000 6000 8000 10 000 3

  35. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.12 0.10 0.08 0.06 0.04 0.02 deg 0 2000 4000 6000 8000 10 000 3

  36. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.10 0.08 0.06 0.04 0.02 deg 0 2000 4000 6000 8000 10 000 3

  37. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.08 0.06 0.04 0.02 deg 0 2000 4000 6000 8000 10 000 3

  38. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.06 0.05 0.04 0.03 0.02 0.01 deg 0 2000 4000 6000 8000 10 000 3

  39. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.05 0.04 0.03 0.02 0.01 deg 0 2000 4000 6000 8000 10 000 3

  40. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.035 0.030 0.025 0.020 0.015 0.010 0.005 deg 0 2000 4000 6000 8000 10 000 3

  41. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.025 0.020 0.015 0.010 0.005 deg 0 2000 4000 6000 8000 10 000 3

  42. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.020 0.015 0.010 0.005 deg 0 2000 4000 6000 8000 10 000 3

  43. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.015 0.010 0.005 deg 0 2000 4000 6000 8000 10 000 3

  44. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.010 0.008 0.006 0.004 0.002 deg 0 2000 4000 6000 8000 10 000 3

  45. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.008 0.006 0.004 0.002 deg 0 2000 4000 6000 8000 10 000 3

  46. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.005 0.004 0.003 0.002 0.001 deg 0 2000 4000 6000 8000 10 000 3

  47. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.0035 0.0030 0.0025 0.0020 0.0015 0.0010 0.0005 deg 0 2000 4000 6000 8000 10 000 3

  48. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.0020 0.0015 0.0010 0.0005 deg 0 2000 4000 6000 8000 10 000 3

  49. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.0014 0.0012 0.0010 0.0008 0.0006 0.0004 0.0002 deg 0 2000 4000 6000 8000 10 000 3

  50. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.0008 0.0006 0.0004 0.0002 deg 0 2000 4000 6000 8000 10 000 3

  51. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.0004 0.0003 0.0002 0.0001 deg 0 2000 4000 6000 8000 10 000 3

  52. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.00025 0.00020 0.00015 0.00010 0.00005 deg 0 2000 4000 6000 8000 10 000 3

  53. A Computation Speed Comparison Multiplication time for dense polynomials with integer coefficients in Mathematica and Sage (Flint) time 0.00015 0.00010 0.00005 deg 0 2000 4000 6000 8000 10 000 3

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