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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/input/fr.input.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/input/fr.input.pamphlet')
-rw-r--r-- | src/input/fr.input.pamphlet | 110 |
1 files changed, 110 insertions, 0 deletions
diff --git a/src/input/fr.input.pamphlet b/src/input/fr.input.pamphlet new file mode 100644 index 00000000..bd276d0b --- /dev/null +++ b/src/input/fr.input.pamphlet @@ -0,0 +1,110 @@ +\documentclass{article} +\usepackage{axiom} +\begin{document} +\title{\$SPAD/src/input fr.input} +\author{The Axiom Team} +\maketitle +\begin{abstract} +\end{abstract} +\eject +\tableofcontents +\eject +\section{License} +<<license>>= +--Copyright The Numerical Algorithms Group Limited 1991. +@ +<<*>>= +<<license>> + +-- Manipulation of factored integers +)clear all + +(x,y,z,w): FR INT +-- automatic coercion of integers to factored integers +x := 2**8 * 78**7 * 111**3 * 74534 +y := 2**4 * 45**3 * 162**6 * 774325 +-- computation of 50! +z1 := factorial 50 +z := z1 :: (FR INT) +-- examine the structure if a factor +nthFactor(z,1) +nthFlag(z,1) +nthExponent(z,1) +-- extract the factors in another form +factorList z +-- construct an object that has the factors to multiplicity one +r:=reduce(*,[(nthFactor(z,i) :: (FR INT)) for i in 1..(numberOfFactors z)]) +-- some arithmetic +exquo(z,r) +x*y +y*x +(x*y = y*x) :: BOOLEAN +gcd(x,z) +x+y +-- this is how you multiply the terms together +expand(x+y) +-- now look at quotients +f := x/y +g := (x ** 9) / y +f * g +(f * g) / (g * primeFactor(2,200)) +(f * g) / (g * primeFactor(2,200)) * z + + +--% Manipulation of factored polynomials +)clear all +)set history on + +(u,v,w): FR POLY INT + +-- coercion to FR POLY INT involves factoring +u := (x**4 - y**4) :: POLY INT +-- primeFactor creates factors that are asserted to be prime +v := primeFactor(x-y,2) * primeFactor(x+y,2) * primeFactor(x**2 + y**2,1) +w := factor(x**2 + 2*x*y + 2*x + 2*y + y**2 + 1) * primeFactor(x-y,2) +unit w +-- some ways of looking at the components of an elements of FR P I +l := factorList u +factorList v +factorList w +l.1.fctr +l.1.xpnt +nthFactor(u,1) +nthFactor(u,2) +nthFactor(u,3) +nthExponent(u,3) +nthFlag(u,3) +nthFactor(u,4) +-- this computes a factored object that is similar to v except that +-- each factor occurs with multiplicity 1 +s:=reduce(*,[(nthFactor(v,i) :: FR POLY INT) for i in 1..(numberOfFactors v)]) +-- some arithmetic +exquo(v,s) +gcd(u,v) +u + v +lcm(v,w) +u * v * w +-- "expand" multiplies the factors together +expand(u * v * w) +-- some quotients +u/w +w/(u*v) +-- %%(-1) is the last result, %%(-2) is the one before that +w/(u*v) * u/w +w/(u*v) + u/w + +differentiate(w,x) +differentiate(w,y) + +associates?(x,-x) + +characteristic()$FR POLY INT + +1$FR POLY INT +0$FR POLY INT +@ +\eject +\begin{thebibliography}{99} +\bibitem{1} nothing +\end{thebibliography} +\end{document} |