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RegularChains[FastArithmeticTools][NormalizeRegularChainDim0] - normalize a zero-dimensional regular chain
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Calling Sequence
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NormalizeRegularChainDim0(rc, R)
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Parameters
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R
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polynomial ring
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rc
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a regular chain of R
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Description
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Returns a normalized regular chain generating the same ideal as rc.
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rc is a zero-dimensional non-empty regular chain.
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Examples
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![variables := [x, y, z]](/support/helpjp/helpview.aspx?si=6449/file06495/math93.png) 
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We solve a system in 3 variables and 3 unknowns
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![lrc := [regular_chain]](/support/helpjp/helpview.aspx?si=6449/file06495/math114.png)
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Its triangular decomposition consists of only one regular chain
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![rc := lrc[1]](/support/helpjp/helpview.aspx?si=6449/file06495/math120.png)
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Each initial is not equal to 1, hence this regular chain is not normalized
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![[z^12+94127136*z^8+691135635*z^7+676458799*z^4+195425386*z^3+326553470*z^2+574327669, z^12+94127136*z^8+691135635*z^7+676458799*z^4+195425386*z^3+326553470*z^2+574327669, 1]](/support/helpjp/helpview.aspx?si=6449/file06495/math139.png)
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We compute here a regular chain which is normalized and which describes the same solution as the previous one
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We check that it is normalized
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![[1, 1, 1]](/support/helpjp/helpview.aspx?si=6449/file06495/math158.png)
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We check that the two regular chains describe the set of solutions
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