Course Handouts
Course handouts will be posted after or
in advance of classes. These will be approximately what are
presented in class, though there will be material presented in
class which is not here and vice versa. As well, there will
be reading assignments from the text.
Script 1: Introduction and basic polynomial arithmetic. script01.mws (Maple worksheet).
- Save the maple worksheet and open it under Maple 12 (available on
student.cs machines)
Script 2: Basic algebraic operations.
PDF.
- Related Maple worksheet. MWS.
- Readings (from text): 2.1-2.4, 3.3-3.4
Script 3: Evaluation, Interpolation and Multiplication of Polynomials.
PDF.
- Readings (from text): 5-5.2,8-8.1
- Code for Patterson & Stockmeyer's algorithm (patstock.mpl) and worksheet to drive it (patstockeval.mw)
Script 4: The Discrete Fourier Transform. PDF.
Script 5: Polynomial division and algebraic Newton interation. PDF.
- Readings (from text): 9-9.1
- Worksheet for division with remainder by polynomial reversion: DivRemRev.mws
- Worksheet for inversion of polynomials modulo x^k by Newton iteration: InversePolyMod.mws
Script 6: Chinese remainder algorithm. PDF.
- Readings (from text): 5.4
Script 7: Fast evaluation and interpolation. PDF.
- Readings (from text): all of 10
Script 8: Integer matrix determinant and nonsingular rational system solving. PDF.
- Readings (from text): 5.5
Script 9: The resultant and a modular gcd algorithm in Z[x]. PDF.
- Readings (from text): 6.1-6.4
Script 10: Factoring polynomials over finite fields. PDF.
- Readings (from text): 14-14.4
- Code for computing powers modulo another polynomial: mypowmod.mpl
- Distinct degree factorization code: DDFactor.mpl
- Equal degree factorization worksheet: EQDegreeFact.mw
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