ore polynomials in sage

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

Recommend

The Greater Sage The Greater Sage-grouse: The Greater Sage The Greater Sage grouse: grouse:

The Greater Sage The Greater Sage-grouse: The Greater Sage The Greater Sage grouse: grouse:

The Greater Sage The Greater Sage-grouse: The Greater Sage The Greater Sage grouse: grouse: grouse: Ecology, ESA Finding, Threats, and Solutions Ecology, ESA Finding, Threats, and Solutions Joint Military Affairs Committee Joint Military

516 views • 33 slides
Sage Department Update July 18, 2018 2018-2019 Sage Data Elementary 2018-2019 Sage Data

Sage Department Update July 18, 2018 2018-2019 Sage Data Elementary 2018-2019 Sage Data

Sage Department Update July 18, 2018 2018-2019 Sage Data Elementary 2018-2019 Sage Data Secondary 2018-2019 Demographic Sage Data 2018-2019 Demographic Sage Data 2018-2019 Budget--Staffing Elementary Teachers: 4.5 Middle School

346 views • 19 slides
Sage Inventory What is Sage Inventory Advisor? Advisor Sage Inventory Advisor is an affordable

Sage Inventory What is Sage Inventory Advisor? Advisor Sage Inventory Advisor is an affordable

Sage Inventory Advisor PC Retreat 2015 Sage Inventory What is Sage Inventory Advisor? Advisor Sage Inventory Advisor is an affordable Inventory Optimization Cloud-based solution that integrates with Sage ERP systems to help you optimize your

486 views • 4 slides
Greater Sage-Grouse Gunnison Sage-Grouse Kathy Griffin Statewide Grouse Conservation

Greater Sage-Grouse Gunnison Sage-Grouse Kathy Griffin Statewide Grouse Conservation

Sa Sage-Gr Grouse ouse Sta Status tus Greater Sage-Grouse Gunnison Sage-Grouse Kathy Griffin Statewide Grouse Conservation Coordinator Sage-Gr Grouse ouse Dis istrib ributi ution on - CO CO Gu Gunn nnis ison on Sage-Gr Grouse

430 views • 23 slides
Progression & Sage Gateshead Progression & Sage Gateshead A whistle stop introduction to

Progression & Sage Gateshead Progression & Sage Gateshead A whistle stop introduction to

Progression & Sage Gateshead Progression & Sage Gateshead A whistle stop introduction to progression and Sage Gateshead. To be able to progress in an activity you need to be included in the activity. When it comes to music making Sage

276 views • 13 slides
Elliptic Curves in Sage John Cremona University of Warwick, UK Sage Days 10 11 October, 2008

Elliptic Curves in Sage John Cremona University of Warwick, UK Sage Days 10 11 October, 2008

Elliptic Curves in Sage John Cremona University of Warwick, UK Sage Days 10 11 October, 2008 Overview Elliptic Curves have been in Sage since (almost) the beginning. Overview Elliptic Curves have been in Sage since (almost) the

962 views • 65 slides
Elliptic Curves in Sage William Stein Sage Project Functionality William Stein Demo

Elliptic Curves in Sage William Stein Sage Project Functionality William Stein Demo

Elliptic Curves in Sage Elliptic Curves in Sage William Stein Sage Project Functionality William Stein Demo Questions? October 19 at ECC 2010 Lowest (known) conductor elliptic curves of ranks 0,1,2,3,4 Abstract Elliptic Curves in Sage

628 views • 14 slides
Introduction to Sage Sage Days 45: Multiple Dirichlet Series, Combinatorics, and Representation

Introduction to Sage Sage Days 45: Multiple Dirichlet Series, Combinatorics, and Representation

Introduction to Sage 2/11/13 11:48 AM Introduction to Sage Sage Days 45: Multiple Dirichlet Series, Combinatorics, and Representation Theory ICERM, Providence, RI February 11, 2013 Mission Sage Mission: To create a viable, free, open source

483 views • 5 slides
THE SOUTH AFRICAN IRON ANd STEEl vAlUE CHAIN KUMBA IRON ORE March 2011 BACKGROUNd TO KUMBA

THE SOUTH AFRICAN IRON ANd STEEl vAlUE CHAIN KUMBA IRON ORE March 2011 BACKGROUNd TO KUMBA

THE SOUTH AFRICAN IRON ANd STEEl vAlUE CHAIN KUMBA IRON ORE March 2011 BACKGROUNd TO KUMBA IRON ORE Kumba Iron Ore Ltd is the fifth largest supplier of seaborne iron ore in the world. Operating through its 74%-held subsidiary Sishen Iron Ore

463 views • 22 slides
Presentation on THRESHOLD VALUE OF IRON ORE P.Ramesh Babu (DGM-Geology) S.Manoj Kumar (SM Ore

Presentation on THRESHOLD VALUE OF IRON ORE P.Ramesh Babu (DGM-Geology) S.Manoj Kumar (SM Ore

Presentation on THRESHOLD VALUE OF IRON ORE P.Ramesh Babu (DGM-Geology) S.Manoj Kumar (SM Ore Dressing) CONTENTS o Iron ore formation and deposits o Distribution and occurrence o SAIL Iron ore mines overview o Captive Mines of Bhilai Steel

651 views • 38 slides
Site Visit to Sishen Mine 14 April 2010 Summary: Kumba Iron Ore Large hematite ore body:

Site Visit to Sishen Mine 14 April 2010 Summary: Kumba Iron Ore Large hematite ore body:

Site Visit to Sishen Mine 14 April 2010 Summary: Kumba Iron Ore Large hematite ore body: 14km x 3.2km x 400m: 2.4bt resource 1.6bt reserve Hard ore: 60:40 lump to fine ratio Mining started in 1953; First ore exported in 1976

145 views • 13 slides
Small-span characteristic polynomials of integer symmetric matrices James McKee (RHUL) ANTS 9,

Small-span characteristic polynomials of integer symmetric matrices James McKee (RHUL) ANTS 9,

Small-span characteristic polynomials of integer symmetric matrices James McKee (RHUL) ANTS 9, July 20, 2010 PLAN ISMs, characteristic polynomials, minimal polynomials 1/1729 PLAN ISMs, characteristic polynomials, minimal polynomials

904 views • 71 slides
School Administration Personnel Training Sage 50 Accounts Workshop June 2018 Sage 50 - Monthly

School Administration Personnel Training Sage 50 Accounts Workshop June 2018 Sage 50 - Monthly

School Administration Personnel Training Sage 50 Accounts Workshop June 2018 Sage 50 - Monthly Reporting & FAQs 1. Objectives of the Sage 50 Training Workshop What is expected at month end - Financial Guideline 2017/2018 09

440 views • 30 slides
Sage CRM and Sage 300 CRE How CRM can help your business Agenda What is CRM? Common business

Sage CRM and Sage 300 CRE How CRM can help your business Agenda What is CRM? Common business

Sage CRM and Sage 300 CRE How CRM can help your business Agenda What is CRM? Common business issues faced by companies today How CRM can help your company What is CRM4CRE and how does it work? Live Demo of Sage CRM and CRM4CRE Q & A

428 views • 20 slides
Impact of New UK GAAP on Sage vendor products Abdullah Wamala 3 June 2015 An Overview of the

Impact of New UK GAAP on Sage vendor products Abdullah Wamala 3 June 2015 An Overview of the

Impact of New UK GAAP on Sage vendor products Abdullah Wamala 3 June 2015 An Overview of the New UK GAAP Introduction Abdullah Wamala Professional Services Consultant exchange@sage.com www.sage-exchange.co.uk Sage presentation 18 June

488 views • 17 slides
Enrolment How Sage can help you and your clients Intrinsic AE Training June/July 2014 Sage -

Enrolment How Sage can help you and your clients Intrinsic AE Training June/July 2014 Sage -

Automatic Enrolment How Sage can help you and your clients Intrinsic AE Training June/July 2014 Sage - Intrinsic AE Training 1 Agenda 1.0 Introduction to Sage 1.1 About Us 2.0 Customer insight 2.1 Research findings 2.2 Customer burdens

613 views • 26 slides
SAGE: the Scalable Adaptive Graphics Environment Middleware for Visualization Streaming and

SAGE: the Scalable Adaptive Graphics Environment Middleware for Visualization Streaming and

SAGE: the Scalable Adaptive Graphics Environment Middleware for Visualization Streaming and Collaboration in Scalable Display Environments Jason Leigh, Luc Renambot Electronic Visualization Laboratory University of Illinois at Chicago Erik

440 views • 27 slides
Revitalization Tax Credit Application Workshop for 2020-21 Your Presenter Brad Harrington

Revitalization Tax Credit Application Workshop for 2020-21 Your Presenter Brad Harrington

New Jerseys Neighborhood Revitalization Tax Credit Application Workshop for 2020-21 Your Presenter Brad Harrington Supervisor, NRTC Program Today Handouts (2), while webinar is active Slides Q&A via Questions For

711 views • 43 slides
Differential geometry with SageMath ric Gourgoulhon Laboratoire Univers et Thories (LUTH)

Differential geometry with SageMath ric Gourgoulhon Laboratoire Univers et Thories (LUTH)

Differential geometry with SageMath ric Gourgoulhon Laboratoire Univers et Thories (LUTH) CNRS / Observatoire de Paris / Universit Paris Diderot Paris Sciences et Lettres Research University 92190 Meudon, France

808 views • 63 slides
DD-finite functions in Sage 2 Using the package Computing beyond holonomic functions 3 Computing

DD-finite functions in Sage 2 Using the package Computing beyond holonomic functions 3 Computing

Installation and usage Computing and proving Conclusions Installation and usage Computing and proving Conclusions Outline 1 Installing the package DD-finite functions in Sage 2 Using the package Computing beyond holonomic functions 3

367 views • 3 slides
Toward Continuous SAGE How to Interrupt and Migrate Dynamic Test Generation Mehdi

Toward Continuous SAGE How to Interrupt and Migrate Dynamic Test Generation Mehdi

Toward Continuous SAGE How to Interrupt and Migrate Dynamic Test Generation Mehdi Bouazizs End -of-Internship talk Joint work with Ella Bounimova (mentor), Patrice Godefroid (MSR), David Molnar (MSR) and Eric Jarvi (Office) Security is

428 views • 20 slides
Translation Protg Knowledge for Executing Clinical Guidelines Jeong Ah Kim, BinGu Shim,

Translation Protg Knowledge for Executing Clinical Guidelines Jeong Ah Kim, BinGu Shim,

Translation Protg Knowledge for Executing Clinical Guidelines Jeong Ah Kim, BinGu Shim, SunTae Kim , JaeHoon Lee, InSook Cho, Yoon Kim Agenda 1. Motivation 1. Motivation 2. How to translate 2. How to translate 3. Implementation and Case

659 views • 26 slides
Financial Year 2018 Samantha Jameson Founder, Soapsmith #SageResults Safe harbour The

Financial Year 2018 Samantha Jameson Founder, Soapsmith #SageResults Safe harbour The

Year-end results Financial Year 2018 Samantha Jameson Founder, Soapsmith #SageResults Safe harbour The following presentation is being made only to, and is only directed at, persons to among others: Inherent difficulty in predicting customer

569 views • 45 slides
A subfield lattice attack on overstretched NTRU assumptions Cryptanalysis of some FHE and Graded

A subfield lattice attack on overstretched NTRU assumptions Cryptanalysis of some FHE and Graded

A subfield lattice attack on overstretched NTRU assumptions Cryptanalysis of some FHE and Graded Encoding Schemes Martin R. Albrecht , Shi Bai and Lo Ducas London-ish Lattice Coding and Cryptography Meeting, Star Wars Day, 2016 Outline

1.35k views • 66 slides

More recommend