gbv > _E[h > Mac > wK > ZEw

# Monomie

2ϐ̈ʑ􉽊wIvZ

## \tgڍא

2ϐ̈ʑ􉽊wIvZ\tg

@In recent years there has been much interest in the study of degenerations of algebraic curves.@When curves are rational or elliptic, Kodaira [K] completes the classification of degenerations.@When general fibers have a larger genus, classification problem is so hard to solve.@Matsumoto and Montesinos [MM] show that classification of degenerations is equivalent to classification of pseudo-periodic homeomorphisms.@It follows that we have a topological solution for this problem.

@\monomie ('Monomii-kun' in Japanese) is a computer software which runs on only Macintosh.@It was planned to observe classification of singular fibers and their monodromies for any given fibrations.@The latest version is \monoversion and in this version we can know topological data of given algebraic curves in ${\bf C}^2$ even if they have singularities.

@We mention approximating problem of roots of algebraic equations.@The most important parts of the program of \monomie is those about this problem.@In other words, \monomie is a software to 'get roots' of an equation with 2 variables.@It is not so easy to calculate multiple roots precisely in case of algebraic equations, and in \monomie we can not avoid the difficulty.@Because in the prime step, \monomie gets an equation $F_t(x)=0$ of $x$ with one parameter $t$ and computes parameters such that the equation has multiple roots.@Even if we obtain such a parameter $t\sim t_0$ approximately, $F_{t_0}(x)=0$ may has no multiple solutions because $t_0$ is not a explicit value.@In easy (less than 10 degree) case \monomie overcomes this trouble and gives us topological data.

@finally, we have an application of \monomie to complex singularities.@Suppose that an algebraic curve in $\cc^2$ has a discrete singular point $p$.@Around $p$ there happens a cone of a link generally.@\monomie can calculate the link type of this cone if the curve is given by a polynomial.

## 

\tgF Monomie MacOS Mac t[\tg u

[U[̕](0l)F0
RgF0

ŗDG_E[h\tg
Cɓ̃\tgɓ[悤I

## uZEwvJeS[̐lCLO

1. GeoFlair ZEwɊւ鏑ނȒP쐬AȒPȑΘb^pRec̍쐬܂([U[]F0)
2. Vf2 C^NeBuȊ􉽁EV~[VƃvO~Oł([U[]F0)
3. fN ȒfČʂ\ ő񐔁Aŏ{߂@\([U[]F0)
4. GAUSS ~̌vZvO([U[]F0)
5. 20wIsbN12ǂ񐶐(Macp) 2020wIsbN\I12̗ǂ𐶐([U[]F0)

̑̃Rec

R~bN