On birational monomial transformations of plane
We study birational monomial transformations of the form φ(x:y:z)=(ϵ1xα1yβ1zγ1:ϵ2xα2yβ2zγ2:xα3yβ3zγ3), where ϵ1,ϵ2∈{−1,1}. These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation φ, we prove a formula, which represents the tr...
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Hindawi Limited
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204306514 |
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doaj-d8f271232b6c4cd5a7a8864eda7cd5d52020-11-24T23:30:41ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004321671167710.1155/S0161171204306514On birational monomial transformations of planeAnatoly B. Korchagin0Department of Mathematics and Statistics, Texas Tech University, Lubbock 79409-1042, TX, USAWe study birational monomial transformations of the form φ(x:y:z)=(ϵ1xα1yβ1zγ1:ϵ2xα2yβ2zγ2:xα3yβ3zγ3), where ϵ1,ϵ2∈{−1,1}. These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation φ, we prove a formula, which represents the transformation φ as a product of generators of the group. To prove this formula, we use birationally equivalent polynomials Ax+By+C and Axp+Byq+Cxrys. If φ is the transformation which carries one polynomial onto another, then the integral powers of generators in the product, which represents the transformation φ, can be calculated by the expansion of p/q in the continued fraction.http://dx.doi.org/10.1155/S0161171204306514 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Anatoly B. Korchagin |
| spellingShingle |
Anatoly B. Korchagin On birational monomial transformations of plane International Journal of Mathematics and Mathematical Sciences |
| author_facet |
Anatoly B. Korchagin |
| author_sort |
Anatoly B. Korchagin |
| title |
On birational monomial transformations of plane |
| title_short |
On birational monomial transformations of plane |
| title_full |
On birational monomial transformations of plane |
| title_fullStr |
On birational monomial transformations of plane |
| title_full_unstemmed |
On birational monomial transformations of plane |
| title_sort |
on birational monomial transformations of plane |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2004-01-01 |
| description |
We study birational monomial transformations of the form φ(x:y:z)=(ϵ1xα1yβ1zγ1:ϵ2xα2yβ2zγ2:xα3yβ3zγ3), where ϵ1,ϵ2∈{−1,1}. These transformations form a group. We describe this group in terms of generators and relations and, for every such transformation φ, we prove a formula, which represents the transformation φ as a product of generators of the group. To prove this formula, we use birationally equivalent polynomials Ax+By+C and Axp+Byq+Cxrys. If φ is the transformation which carries one polynomial onto another, then the integral powers of generators in the product, which represents the transformation φ, can be calculated by the expansion of p/q in the continued fraction. |
| url |
http://dx.doi.org/10.1155/S0161171204306514 |
| work_keys_str_mv |
AT anatolybkorchagin onbirationalmonomialtransformationsofplane |
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