Introduction to Computer Algebra

Schedule

Classes on Wednesdays, 10:30-12:00 & 13:30-15:00, Fields Institute, usually room 210.

(Download the worksheets and open them with maple, depending on your browser you may have to modify the extension to .mws for double clicking.)

• 11/ Wednesday, Dec. 2, 2015 - Last lectures:
  • Automatic differentiation part II
    worksheet: 11-diff.mws
  • Elimination of divisions
    worksheet: 11-w-divisions.mws
  • Matrix determinant and characteristic polynomial
  • Linear system solution, Dixon's algorithm
    worksheet: 11-dixon.mws

• 10/ Wednesday, Nov. 25, 2015:
  • Sparse linear algebra, Wiedemann's algorithm
    worksheet: 10-sparse.mws
  • Automatic differentiation part I

• 9/ Wednesday, Nov. 18, 2015:
  • Introduction to exact linear algebra
  • Preconditioning for black box linear algebra
  • Worksheet: 9-linalg-intro.mws

• 8/ Wednesday, Nov. 11, 2015:
  • Reduced polynomial matrices
  • Fast Padé approximation
    worksheet: 8-linrec-B.mws
  • Links with the extended Euclidean algorithm, the Berlekamp-Massey algorithm, and Toeplitz equations
    worksheet: 8-minpoly.mws

• 7/Wednesday, Oct. 28, 2015:
  • Linearly recurrent sequences, part II

• 6/ Wednesday, Oct. 21, 2015:
  • The transposition principle
  • Middle product à la Karatsuba, multi-point evaluation versus interpolation
  • Worksheet: 6-transp.mws
  • Linearly recurrent sequences, part I
    worksheet: 6-linrec-A.mws

• 5/ Wednesday, Oct. 14, 2015:
  • Evaluation and interpolation
  • Chinese remaindering, mixed radix representation
  • Cabay's recursive test for linear system solution
  • Worksheet: 5-eval.mws

• 4/ Wednesday, Oct. 7, 2015:
  • Newton's iteration: power series inversion and polynomial division
    worksheet: 4-div.mws
  • Modular composition
    worksheet: 4-comp.mws

• 3/ Wednesday, Sept. 30, 2015:
  • FFT based polynomial multiplication algorithms
  • Schönhage and Strassen's polynomial multiplication algorithm
  • Example: integer multiplication
    worksheet: 3-prod-B.mws

• 2/ Wednesday, Sept. 23, 2015:
  • Basic representations (end)
    worksheet: 2-cost-rep.mws
  • Karatsuba's and FFT based multiplication algorithms, part I
    worksheet: 2-prod-A.mws

• 1/ Wednesday, Sept. 16, 2015:
  • Introduction to computer algebra
  • Basic representations
  • Worksheet: 1-intro.mws

• Monday, Sept. 16, 2015:
  • Graduate students orientation session