GNU-Darwin Web

## Files of user defined functions

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, af_noalg.)
[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, polarplot, 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.