RegularChains[FastArithmeticTools][BivariateModularTriangularize] - triangular decomposition of a bivariate square system by a modular method
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Calling Sequence
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BivariateModularTriangularize(F, R)
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Parameters
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R
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polynomial ring
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F
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bivariate square system of R
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Description
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The command BivariateModularTriangularize(F, R) returns a triangular decomposition of F in R. See the command Triangularize and the page RegularChains for the concept of a triangular decompostion.
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F consists of two bivariate polynomials f1 and f2 of R. No other assumptions are required.
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R must have only two variables and no parameters.
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The algorithm is deterministic (i.e. non-probabilistic) and uses modular techniques together with asymptotically fast polynomial arithmetic.
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When both Triangularize and BivariateModularTriangularize apply, the latter command is very likely to outperform the former one.
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Examples
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Define a ring of polynomials.
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Define two polynomials of R.
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Compute a triangular decomposition of this system
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Check the number of solutions
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Download Help Document
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