Gröbner Bases and Applications in Java - KRUM Server

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Coefficients ● e.g. BigRational, BigInteger ● implement both interfaces ● creation of rational number 2 from long 2: – new BigRational(2) – cfac.fromInteger(2) ● creation of rational number 1/2 from two longs: – new BigRational(1,2) – cfac.parse( 1/2 )
Polynomials ● GenPolynomial ● C is coefficient type in the following ● implements RingElem ● factory is GenPolynomialRing ● implements RingFactory ● factory constructors require coefficient factory parameter
Page 1 and 2: Gröbner Bases and Applications in
Page 3 and 4: Introduction to software ● object
Page 5 and 6: T Monoid , C Ring p : T C t pt =c
Page 7 and 8: Type structure
Page 9 and 10: Ring element functionality ● C is
Page 11: Polynomial types (1)
Page 15 and 16: Class functionality (1)
Page 17 and 18: Polynomial factory functionality
Page 19 and 20: Example BigInteger z = new BigInteg
Page 21 and 22: Chebychev polynomials defined by re
Page 23 and 24: Implementation ● 160 classes and
Page 25 and 26: Polynomial implementation ● are (
Page 27 and 28: Performance ● polynomial arithmet
Page 29 and 30: Overview ● Coefficients and Polyn
Page 31 and 32: Term order implementation ● need
Page 33 and 34: Reduction implementation
Page 35 and 36: Overview ● Coefficients and Polyn
Page 37 and 38: Buchberger algorithm algorithm: G =
Page 39 and 40: Improved Buchberger algorithm ● a
Page 41 and 42: Trinks example in jython r = Ring(
Page 43 and 44: Parallel Gröbner bases ● work qu
Page 45 and 46: Implemented Gröbner Bases
Page 47 and 48: Applications (2) ● extended Gröb
Page 49 and 50: ● residue classes Applications (4
Page 51 and 52: Residue class class
Page 53 and 54: Example (cont.) String[] vars = new
Page 55 and 56: Conclusions ● consistent object o

Gröbner Bases and Applications in Java - KRUM Server

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