What's New in Maple 14: Output a CTD in piecewise manner
<Text-field style="Heading 1" layout="Heading 1">Description of Feature</Text-field> Comprehensive triangular decomposition (CTD) solves a parametric polynomial system by discussing the "properties" of the solutions depending on the parameters. The underlying algorithm is general and works over any field of coefficients. Its piecewise format is intended to help the user browsing the output.
<Text-field style="Heading 1" layout="Heading 1">Examples </Text-field> Load the RegularChains library. 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H := [x+y-1]; R := PolynomialRing([y, x, s]); NyQsJiomSSJ4RzYiIiIiLCZJInlHRiZGJ0YnRidGJ0YnSSJzR0YmISIiLCYqJkYpRicsJkYlRidGJ0YnRidGJ0YqRis= NyMsKEkieEc2IiIiIkkieUc2IiIiIiIiIiEiIg== STBwb2x5bm9taWFsX3JpbmdHNiI= JSFH Compute CTD of the constructible set 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 LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= ctd := ComprehensiveTriangularize(F, H, 1, R, output=piecewise); 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<Text-field style="Heading 1" layout="Heading 1">Notes for Beta-Testers</Text-field> None.
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<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Descri\303\247\303\243o do recurso</Font></Text-field> A decomposi\303\247\303\243o triangular abrangente (CTD) resolve um sistema polinomial param\303\251trico discutindo as "propriedades" das solu\303\247\303\265es dependendo dos par\303\242metros. O algoritmo subjacente \303\251 geral e funciona em qualquer campo de coeficientes. Seu formato por partes destina-se a ajudar o usu\303\241rio a navegar pela sa\303\255da.
<Text-field style="Heading 1" layout="Heading 1">Exemplos </Text-field> Carregue a biblioteca Cadeias regulares. 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H := [x+y-1]; R := PolynomialRing([y, x, s]); NyQsJiomSSJ4RzYiIiIiLCZJInlHRiZGJ0YnRidGJ0YnSSJzR0YmISIiLCYqJkYpRicsJkYlRidGJ0YnRidGJ0YqRis= NyMsKEkieEc2IiIiIkkieUc2IiIiIiIiIiEiIg== STBwb2x5bm9taWFsX3JpbmdHNiI= LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic= Calcular CTD do conjunto construt\303\255vel 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 JSFHJSFH ctd := ComprehensiveTriangularize(F, H, 1, R, output=piecewise); 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