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.

``fff'`- Univariate factorizer over large finite fields (See section Finite fields)
``gr'`- Groebner basis package. (See section Groebner basis computation)
``sp'`- Operations over algebraic numbers and factorization, Splitting fields. (See section Algebraic numbers)
``alpi'```bgk'```cyclic'```katsura'```kimura'`-
Example polynomial sets for benchmarks of Groebner basis computation.
(See section
`katsura`

,`hkatsura`

,`cyclic`

,`hcyclic`

) ``defs.h'`- Macro definitions. (See section preprocessor)
``fctrtest'`-
Test program of factorization of integral polynomials.
It includes
``factor.tst'`of REDUCE and several examples for large multiplicity factors. If this file is`load()`

'ed, computation will begin immediately. You may use it as a first test whether**Asir**at you hand runs correctly. ``fctrdata'`-
This contains example polynomials for factorization. It includes
polynomials used in
``fctrtest'`. Polynomials contained in vector`Alg[]`

is for the algebraic factorization`af()`

(See section`asq`

,`af`

).[45] load("sp")$ [84] load("fctrdata")$ [175] cputime(1)$ 0msec [176] Alg[5]; x^9-15*x^6-87*x^3-125 0msec [177] af(Alg[5],[newalg(Alg[5])]); [[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

``ifplot'`-
Examples for plotting (See section
`ifplot`

,`conplot`

,`plot`

,`plotover`

). Vector`IS[]`

contains several famous algebraic curves. Variables`H, D, C, S`

contains something like the suits (Heart, Diamond, Club, and Spade) of cards. ``num'`- Examples of simple operations on numbers.
``mat'`- Examples of simple operations on matrices.
``ratint'`-
Indefinite integration of rational functions. For this,
files
``sp'`and``gr'`is necessary. A function`ratint()`

is defined. Its returns a rather complex result.[0] load("gr")$ [45] load("sp")$ [84] load("ratint")$ [102] 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`[root*log(poly),defpoly]`

. This pair should be interpreted to sum up the expression`root*log(poly)`

through all**root**'s`root`

's of the`defpoly`

. Here,`poly`

contains`root`

, and substitution for`root`

is equally applied to`poly`

. 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. ``primdec'`-
Primary ideal decomposition of polynomial ideals and prime compotision
of radicals (see section
`primadec`

,`primedec`

).

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