 RegularChains[ChainTools] - Maple Programming Help

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RegularChains[ChainTools]

 NumberOfSolutions
 number of solutions of a regular chain

 Calling Sequence NumberOfSolutions(rc, R)

Parameters

 rc - regular chain of R R - polynomial ring

Description

 • The command NumberOfSolutions(rc, R) returns the number of complex solutions of rc.
 • If rc has a positive dimension, then infinity is returned.
 • If rc has dimension zero, the number of roots is returned.
 • This command is part of the RegularChains[ChainTools] package, so it can be used in the form NumberOfSolutions(..) only after executing the command with(RegularChains[ChainTools]). However, it can always be accessed through the long form of the command by using RegularChains[ChainTools][NumberOfSolutions](..).

Examples

 > with(RegularChains):
 > with(ChainTools):
 > R := PolynomialRing([x, a], {b, c});
 ${R}{≔}{\mathrm{polynomial_ring}}$ (1)
 > sys := [a*x^2+b*x+c];
 ${\mathrm{sys}}{≔}\left[{a}{}{{x}}^{{2}}{+}{b}{}{x}{+}{c}\right]$ (2)
 > dec := Triangularize(sys, R, output=lazard);
 ${\mathrm{dec}}{≔}\left[{\mathrm{regular_chain}}{,}{\mathrm{regular_chain}}\right]$ (3)
 > map(Equations, dec, R);
 $\left[\left[{a}{}{{x}}^{{2}}{+}{b}{}{x}{+}{c}\right]{,}\left[{b}{}{x}{+}{c}{,}{a}\right]\right]$ (4)
 > map(Dimension, dec, R);
 $\left[{1}{,}{0}\right]$ (5)
 > map(NumberOfSolutions, dec, R);
 $\left[{\mathrm{\infty }}{,}{1}\right]$ (6)

 See Also