T. S. Freeman, G. M. Imirzian, E. Kaltofen, L. Yagati, DAGWOOD - A system for manipulating polynomials given by straight-line programs, ACM Transactions on Mathematical Software 14 (3) (1988) 218-240.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....monomials) of the determinant of a general 13 by 13 symmetric Toeplitz matrix in 15 hours and 25 minutes on a single processor of a Sun Ultra 2 computer. The black box representation has evolved from our experience with the straight line program representation [19, 20] and the DAG WOOD system [10]. In the straight line program model the matrix determinant and the factors box would be restricted to so called single assignment straight line code. That model suffers from expression swell, as the length of the produced straight line programs is in many cases proportional to the complexity of ....

....the matrix determinant and the factors box would be restricted to so called single assignment straight line code. That model suffers from expression swell, as the length of the produced straight line programs is in many cases proportional to the complexity of the algorithm that produced them. In [10] an irreducible quadratic factor of a determinant of a 16 by 16 matrix whose entries are chosen from 16 indeterminates, has almost 200,000 assignments. FOXBOX s factor box requires a comparable number of instruction for the evaluation of that factor, but the procedure for doing so is of almost ....

FREEMAN, T. S., IMIRZIAN, G., KALTOFEN, E., AND LAKSHMAN YAGATI. DAGWOOD: A system for manipulating polynomials given by straight-line programs. ACM Trans. Math. Software 14, 3 (1988), 218--240.

....how the threshold and postcheck count parameters improve the success rate for small moduli, in the setting of polynomial interpolation, can be found in [17, 22] The early termination strategy seems to belong to the folklore of computer algebra. We have used early termination in the mid 1980s [12, 19] for purpose of determining the degree of a straight line and black box polynomial. Our algorithms perform Newton interpolation at non random points and test whether the interpolant agrees with the input polynomial at a random point, thus allowing for preconditioning in the interpolation process ....

Freeman, T. S., Imirzian, G., Kaltofen, E., and Lakshman Yagati. Dagwood: A system for manipulating polynomials given by straight-line programs. ACM Trans. Math. Software 14, 3 (1988), 218--240. 143

....how the threshold and postcheck count parameters improve the success rate for small moduli, in the setting of polynomial interpolation, can be found in [17, 22] The early termination strategy seems to belong to the folklore of computer algebra. We have used early termination in the mid 1980s [12, 19] for purpose of determining the degree of a straight line and black box polynomial. Our algorithms perform Newton interpolation at non random points and test whether the interpolant agrees with the input polynomial at a random point, thus allowing for preconditioning in the interpolation process ....

Freeman, T. S., Imirzian, G., Kaltofen, E., and Lakshman Yagati. Dagwood: A system for manipulating polynomials given by straight-line programs. ACM Trans. Math. Software 14, 3 (1988), 218--240. 6

....developing the FoxBox system in C that makes black box methodology available to users of such systems. It is anticipated that factorizations as those of large symmetric Toeplitz determinants will be possible on computers. Earlier implementations based on the straight line program model [FIKL88] could factor 16 Theta 16 group determinants, which represent polynomials of over 300 million terms. 5 Further Information The books [Knu81] DTS88] GCL92] and [Zip93] provide a much broader introduction to the general subject. There are well known libraries and packages of subroutines for ....

T. S. Freeman, G. Imirzian, E. Kaltofen, and Yagati Lakshman. Dagwood: A system for manipulating polynomials given by straight-line programs. ACM Trans. Math. Software, 14(3):218--240, 1988.

....with programs that follow the CORBA protocol is transparent. 3.4 Memory management Storage allocation, especially in a parallel distributed setting, remains a sticky point. In Java garbage collection is automatic, a process that presented itself problematic in our Lisp based Dagwood system [19]: memory was filled up uncontrollably and a full garbage collection took days of computation. Automatic garbage collection provides convenience to the programmer, but it has its price: the virtual machine must determine if an object is still in use, either by a reference count or by an ....

....languages other than Java: Bernardin has extensive Maple experience: his bivariate polynomial factorization algorithm is now part of the standard Maple library. Char is a co designer of Maple and has recently worked on problem solving environments. Kaltofen has built the Lisp based Dagwood system [19] for manipulation of straight line programs and the C based FoxBox system [17] for manipulation of black box symbolic objects. All three authors have experience in parallel computation [6, 12, 16, 31] 4.1 Timings For a first benchmark we chose multiplication of univariate polynomials over a ....

Freeman, T. S., Imirzian, G., Kaltofen, E., and Lakshman Yagati. Dagwood: A system for manipulating polynomials given by straight-line programs. ACM Trans. Math. Software 14, 3 (1988), 218--240.

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T. S. Freeman, G. Imirzian, E. Kaltofen, and Lakshman Yagati. DAGWOOD: A system for manipulating polynomials given by straight-line programs. In Char [-2], pages 169--175. Journal version in [40]. MRK86

....in the Goldwasser Kilian Atkin primality prover [14, 12, 48, 60] 2.5 Symbolic Numeric Computation ffl Stability of roots of polynomials with respect to coefficient perturbations [100, 105] 2. 6 System Design ffl DAGWOOD: a system for manipulating polynomials given by straight line programs [40]. The archive directory of the Lisp program source code is at BASE . software dagwood. ffl DSC: the distributed symbolic manipulation tool [61, 71, 75, 79] The archive directory of the C, C , Lisp, and Maple program source code is at BASE . software dsc. ffl FOXBOX: a plug and play symbolic ....

T. S. Freeman, G. Imirzian, E. Kaltofen, and Lakshman Yagati. DAGWOOD: A system for manipulating polynomials given by straight-line programs. ACM Trans. Math. Software, 14(3):218--240, 1988. Ka88:jacm

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T. S. Freeman, G. M. Imirzian, E. Kaltofen, L. Yagati, DAGWOOD - A system for manipulating polynomials given by straight-line programs, ACM Transactions on Mathematical Software 14 (3) (1988) 218-240.

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Timothy S. Freeman, Gregory M. Imirzian, Erich Kaltofen, and Lakshman Yagati. Dagwood: A system for manipulating polynomials given by straight-line programs. ACM Transactions on Mathematical Software, 14:218--240, 1988.

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