Difference between revisions of "Principal translation"
From Encyclopedia of Mathematics
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| − | A mapping | + | A mapping $\phi$ of an [[algebraic system]] $\mathbf{A} = (A,\Omega)$ into itself, of the form |
| − | + | $$ | |
| − | + | \phi : x \mapsto F(a_1,\ldots,a_{k-1},x,a_{k+1},\ldots,a_n) | |
| − | + | $$ | |
| − | where | + | where $F$ is the symbol of a basic operation in $\Omega$ and $a_1,\ldots,a_n$ are fixed elements of the set $A$. |
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====Comments==== | ====Comments==== | ||
The term "principal translation" is not used in the Western literature. A function as above would normally be called an algebraic function (of one variable) or a polynomial. | The term "principal translation" is not used in the Western literature. A function as above would normally be called an algebraic function (of one variable) or a polynomial. | ||
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| + | {{TEX|done}} | ||
Revision as of 20:23, 1 September 2017
A mapping $\phi$ of an algebraic system $\mathbf{A} = (A,\Omega)$ into itself, of the form $$ \phi : x \mapsto F(a_1,\ldots,a_{k-1},x,a_{k+1},\ldots,a_n) $$ where $F$ is the symbol of a basic operation in $\Omega$ and $a_1,\ldots,a_n$ are fixed elements of the set $A$.
Comments
The term "principal translation" is not used in the Western literature. A function as above would normally be called an algebraic function (of one variable) or a polynomial.
How to Cite This Entry:
Principal translation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_translation&oldid=13815
Principal translation. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Principal_translation&oldid=13815
This article was adapted from an original article by D.M. Smirnov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article