On differential rational invariants of patches with respect to motion groups
This paper can be considered as a research on Algebraic Differential Geometry. It is about differential rational invariants of subgroups of the Affine group over the constant fields of partial differential fields (characteristic zero). The obtained results can be formulated in terms of Differentia...
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
American Institute of Physics
2015
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| Online Access: | http://irep.iium.edu.my/47300/ http://irep.iium.edu.my/47300/ http://irep.iium.edu.my/47300/ http://irep.iium.edu.my/47300/4/47300-new.pdf |
| Summary: | This paper can be considered as a research on Algebraic Differential Geometry. It is about differential
rational invariants of subgroups of the Affine group over the constant fields of partial differential fields (characteristic
zero). The obtained results can be formulated in terms of Differential Geometry as follows: 1. For any motion group
represented by a subgroup H of the Affine group it is shown that systems of generators of a field of H-invariant (not
differential) rational functions can be used to construct systems of generators for the differential field of H-invariant
differential rational functions of parameterized surface (patch). 2. For some classic motion groups H the generating
systems of the field of H-invariant differential functions are presented. 3. For motion groups, including all classical
subgroups of the Affine group, separating systems of invariants, uniqueness and existence theorems are offered.
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