MaplePrimes - answers and comments on Question, Primary Decomposition over C

By alias

Markiyan Hirnyk — Fri, 03 Feb 2012 22:47:00 Z

It can be done as follows.

> with(PolynomialIdeals):
> J :=<x^2+1>;

>alias(alpha = RootOf(z^2+1));

>PD:=PrimaryDecomposition(J, alpha);

>Simplify(PD);

See ?PolynomialIdeals[PrimaryDecomposition] for more info.

Remark

Markiyan Hirnyk — Sat, 04 Feb 2012 12:21:52 Z

To say exactly, this is the primary decomposition over Q[sqrt(-1)].

for this approach to work, you need to guess/know

DanielR — Mon, 06 Feb 2012 15:42:33 Z

for this approach to work, you need to guess/know alpha=\sqrt(-1) in advance. for more complicated ideals, i can not do that. Is there a way to let maple find the smallest 'decomposition field' necassary?

Another cup of tea

Markiyan Hirnyk — Mon, 06 Feb 2012 16:44:49 Z

@DanielR Firstly, this is another question. Your question is answered. Secondly, your next question is rather a mathematical question than a Maple related question. Have you tried to ask that in http://mathoverflow.net/ ?

Regard, Markiyan Hirnyk

PS. The two cites from Maple Help:

1."By default, ideals are factored over the domain implied by their coefficients - usually the rationals or the integers mod p. Additional field extensions can be specified with an optional second argument k, which can be a single RootOf or radical, or a list or set of RootOfs and radicals"

2. "The algorithms employed by these commands require polynomials over a perfect field. Infinite fields of positive characteristic are not supported. Over finite fields, only zero-dimensional ideals can be handled because the dimension reducing process generates infinite fields"