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There are several files of user defined functions under the standard library directory. (‘/usr/local/lib/asir’ by default.) Here, we explain some of them.
Univariate factorizer over large finite fields (See section Finite fields.)
Groebner basis package. (See section Groebner basis computation.)
Operations over algebraic numbers and factorization, Splitting fields. (See section Algebraic numbers.)
Example polynomial sets for benchmarks of Groebner basis computation.
Macro definitions. (See section preprocessor.)
Test program of factorization of integral polynomials.
It includes ‘factor.tst’ of REDUCE and several examples
for large multiplicity factors. If this file is
computation will begin immediately.
You may use it as a first test whether Asir at you hand runs
This contains example polynomials for factorization. It includes
polynomials used in ‘fctrtest’.
Polynomials contained in vector
Alg is for the algebraic
af(). (See section
 load("sp")$  load("fctrdata")$  cputime(1)$ 0msec  Alg; x^9-15*x^6-87*x^3-125 0msec  af(Alg,[newalg(Alg)]); [[1,1],[75*x^2+(10*#0^7-175*#0^4-470*#0)*x +(3*#0^8-45*#0^5-261*#0^2),1], [75*x^2+(-10*#0^7+175*#0^4+395*#0)*x +(3*#0^8-45*#0^5-261*#0^2),1], [25*x^2+(25*#0)*x+(#0^8-15*#0^5-87*#0^2),1], [x^2+(#0)*x+(#0^2),1],[x+(-#0),1]] 3.600sec + gc : 1.040sec
Examples for plotting. (See section
IS contains several famous algebraic curves.
H, D, C, S contains something like the suits
(Heart, Diamond, Club, and Spade) of cards.
Examples of simple operations on numbers.
Examples of simple operations on matrices.
Indefinite integration of rational functions. For this,
files ‘sp’ and ‘gr’ is necessary. A function
is defined. Its returns a rather complex result.
 load("gr")$  load("sp")$  load("ratint")$  ratint(x^6/(x^5+x+1),x); [1/2*x^2, [[(#2)*log(-140*x+(-2737*#2^2+552*#2-131)), 161*t#2^3-23*t#2^2+15*t#2-1], [(#1)*log(-5*x+(-21*#1-4)),21*t#1^2+3*t#1+1]]]
In this example, indefinite integral of the rational function
x^6/(x^5+x+1) is computed.
The result is a list which comprises two elements:
The first element is the rational part of the integral;
The second part is the logarithmic part of the integral.
The logarithmic part is again a list which comprises finite number of
elements, each of which is of form
This pair should be interpreted to sum up
through all root’s
root’s of the
root, and substitution for
is equally applied to
The logarithmic part in total is obtained by applying such
interpretation to all element pairs in the second element of the
result and then summing them up all.
Primary ideal decomposition of polynomial ideals and prime compotision
of radicals over the rationals (see section
Prime decomposition of radicals of polynomial ideals
over finite fields (see section
Computation of b-function.
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