“rational function”的概念、定义、翻译、参考文献-科学参考

rational function

Mathematics

A rational function is one f of the form f(x) = g(x)/h(x), where g(x) and h(x) are polynomials, usually with coefficients from a field F. The rational functions themselves then make a field denoted F(x). Addition and multiplication are defined as expected by

$\begin{array}{c} \frac{f_{1} (x)}{g_{1} (x)} + \frac{f_{2} (x)}{g_{2} (x)} = \frac{g_{2} (x) f_{1} (x) + f_{2} (x) g_{1} (x)}{g_{1} (x) g_{2} (x)}, \\ (\frac{f_{1} (x)}{g_{1} (x)}) (\frac{f_{2} (x)}{g_{2} (x)}) = \frac{f_{1} (x) f_{2} (x)}{g_{1} (x) g_{2} (x)} . \end{array}$

Compare polynomial ring.

单词	rational function
释义	rational function Mathematics A rational function is one f of the form f(x) = g(x)/h(x), where g(x) and h(x) are polynomials, usually with coefficients from a field F. The rational functions themselves then make a field denoted F(x). Addition and multiplication are defined as expected by $\begin{array}{c} \frac{f_{1} (x)}{g_{1} (x)} + \frac{f_{2} (x)}{g_{2} (x)} = \frac{g_{2} (x) f_{1} (x) + f_{2} (x) g_{1} (x)}{g_{1} (x) g_{2} (x)}, \\ (\frac{f_{1} (x)}{g_{1} (x)}) (\frac{f_{2} (x)}{g_{2} (x)}) = \frac{f_{1} (x) f_{2} (x)}{g_{1} (x) g_{2} (x)} . \end{array}$ Compare polynomial ring.
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