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Goal: Axiom Literate Programming
\index{Corless, Robert M.}
\index{Gianni, Patrizia, M.}
\index{Trager, Barry M.}
\index{Watt, Stephen M.}
\begin{chunk}{axiom.bib}
@inproceedings{Corl95,
author = "Corless, Robert M. and Gianni, Patrizia, M. and Trager, Barry M.
and Watt, Stephen M.",
title = "The Singular Value Decomposition for Polynomial Systems",
booktitle = "ISSAC 95",
year = "1995",
pages = "195-207",
publisher = "ACM",
abstract =
"This paper introduces singular value decomposition (SVD) algorithms
for some standard polynomial computations, in the case where the
coefficients are inexact or imperfectly known. We first give an
algorithm for computing univariate GCD's which gives {\sl exact}
results for interesting {\sl nearby} problems, and give efficient
algorithms for computing precisely how nearby. We generalize this to
multivariate GCD computations. Next, we adapt Lazard's $u$-resultant
algorithm for the solution of overdetermined systems of polynomial
equations to the inexact-coefficent case. We also briefly discuss an
application of the modified Lazard's method to the location of
singular points on approximately known projections of algebraic curves.",
paper = "Corl95.pdf",
keywords = "axiomref",
}
\end{chunk}
\index{Lazard, Daniel}
\begin{chunk}{axiom.bib}
@Article{Laza92,
author = "Lazard, Daniel",
title = "Solving Zero-dimensional Algebraic Systems",
Journal of Symbolic Computation, 1992, 13, 117-131
journal = "J. of Symbolic Computation",
volume = "13",
pages = "117-131",
year = "1992",
abstract =
"It is shown that a good output for a solver of algebraic systems of
dimension zero consists of a family of ``triangular sets of
polynomials''. Such an output is simple, readable, and consists
of all information which may be wanted.
Different algorithms are described for handling triangular systems
and obtaining them from Groebner bases. These algorithms are
practicable, and most of them are polynomial in the number of
solutions",
paper = "Laza92.pdf"
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -1,72 +1,59 @@ | ||
| books/bookvol5 Add chapter Type Inference and Coercion | ||
| books/bookvol10.4 update references | ||
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| Goal: Axiom Literate Programming | ||
|
|
||
| \index{Jenks, Richard D.} | ||
| \index{Corless, Robert M.} | ||
| \index{Gianni, Patrizia, M.} | ||
| \index{Trager, Barry M.} | ||
| \index{Watt, Stephen M.} | ||
| \begin{chunk}{axiom.bib} | ||
| @techreport{Jenk86c, | ||
| author = "Jenks, Richard D.", | ||
| title = "A History of the SCRATCHPAD Project (1977-1986)", | ||
| institution = "IBM Research", | ||
| year = "1986", | ||
| month = "May", | ||
| type = "Scratchpad II Newsletter", | ||
| volume = "1", | ||
| number = "3", | ||
| } | ||
|
|
||
| \end{chunk} | ||
|
|
||
| \index{Liskov, Barbara} | ||
| \index{Atkinson, Russ} | ||
| \index{Bloom, Toby} | ||
| \index{Moss, Eliot} | ||
| \index{Schaffert, Craig} | ||
| \index{Scheifler, Bob} | ||
| \index{Snyder, Alan} | ||
| \begin{chunk}{axiom.bib} | ||
| @techreport{Lisk79, | ||
| author = "Liskov, Barbara and Atkinson, Russ and Bloom, Toby and | ||
| Moss, Eliot and Schaffert, Craig and Scheifler, Bob and | ||
| Snyder, Alan", | ||
| title = "CLU Reference Manual", | ||
| institution = "Massachusetts Institute of Technology", | ||
| year = "1979", | ||
| paper = "Lisk79.pdf" | ||
| @inproceedings{Corl95, | ||
| author = "Corless, Robert M. and Gianni, Patrizia, M. and Trager, Barry M. | ||
| and Watt, Stephen M.", | ||
| title = "The Singular Value Decomposition for Polynomial Systems", | ||
| booktitle = "ISSAC 95", | ||
| year = "1995", | ||
| pages = "195-207", | ||
| publisher = "ACM", | ||
| abstract = | ||
| "This paper introduces singular value decomposition (SVD) algorithms | ||
| for some standard polynomial computations, in the case where the | ||
|
|
||
| coefficients are inexact or imperfectly known. We first give an | ||
| algorithm for computing univariate GCD's which gives {\sl exact} | ||
| results for interesting {\sl nearby} problems, and give efficient | ||
| algorithms for computing precisely how nearby. We generalize this to | ||
| multivariate GCD computations. Next, we adapt Lazard's $u$-resultant | ||
| algorithm for the solution of overdetermined systems of polynomial | ||
| equations to the inexact-coefficent case. We also briefly discuss an | ||
| application of the modified Lazard's method to the location of | ||
| singular points on approximately known projections of algebraic curves.", | ||
| paper = "Corl95.pdf", | ||
| keywords = "axiomref", | ||
| } | ||
|
|
||
| \end{chunk} | ||
|
|
||
| \index{Schaffert, C.} | ||
| \index{Cooper, T.} | ||
| \index{Lazard, Daniel} | ||
| \begin{chunk}{axiom.bib} | ||
| @article{Scha86, | ||
| author = "Schaffert, C. and Cooper, T.", | ||
| title = "An Introduction to Trellis/Owl", | ||
| journal = "SIGPLAN Notices", | ||
| volume = "21", | ||
| number = "11", | ||
| publisher = "ACM", | ||
| year = "1986", | ||
| pages = "9-16" | ||
| @article{Laza92, | ||
| author = "Lazard, Daniel", | ||
| title = "Solving Zero-dimensional Algebraic Systems", | ||
| Journal of Symbolic Computation, 1992, 13, 117-131 | ||
| journal = "J. of Symbolic Computation", | ||
| volume = "13", | ||
| pages = "117-131", | ||
| year = "1992", | ||
| abstract = | ||
| "It is shown that a good output for a solver of algebraic systems of | ||
| dimension zero consists of a family of ``triangular sets of | ||
| polynomials''. Such an output is simple, readable, and consists | ||
| of all information which may be wanted. | ||
|
|
||
| Different algorithms are described for handling triangular systems | ||
| and obtaining them from Groebner bases. These algorithms are | ||
| practicable, and most of them are polynomial in the number of | ||
| solutions", | ||
| paper = "Laza92.pdf" | ||
| } | ||
|
|
||
| \end{chunk} | ||
|
|
||
| \index{Sweedler, Moss E.} | ||
| \begin{chunk}{axiom.bib} | ||
| @techreport{Swee86, | ||
| author = "Sweedler, Moss E.", | ||
| title = "Typing in Scratchpad II", | ||
| institution = "IBM Research", | ||
| year = "1986", | ||
| month = "January", | ||
| type = "Scratchpad II Newsletter", | ||
| volume = "1", | ||
| number = "2", | ||
| } | ||
|
|
||
| \end{chunk} | ||
|
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|
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|
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