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Define a power series (as a polynomial). Its constant coefficient is zero, so it is not invertible.
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Define another power series. Its constant coefficient is one, so it is invertible.
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Define a univariate polynomial over power series, . The constant coefficient with respect to its main variable, , is , which is not invertible. Thus, is not invertible.
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Define a univariate polynomial over power series, . The constant coefficient with respect to its main variable, , is , which is invertible. Thus, is invertible. Its inverse is not a polynomial but a power series, so in order to invert , we need to convert it to a power series first.
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| (8) |
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| (10) |
| (11) |