minimalPrimes I
minprimes I
decompose I
Given an ideal in a polynomial ring, or a quotient of a polynomial ring whose base ring is either QQ or ZZ/p, this function computes the minimal associated primes of the ideal I. Geometrically, it decomposes the algebraic set defined by I.
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Example. The homogenized equations of the affine twisted cubic curve define the union of the projective twisted cubic curve and a line at infinity:
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Note that the ideal is decomposed over the given field of coefficients and not over the extension field where the decomposition into absolutely irreducible factors occurs:
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For monomial ideals, the method used is essentially what is shown in the example.
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It is sometimes useful to compute P instead, where each generator encodes a single minimal prime. This can be obtained directly, as in the following code.
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The object minimalPrimes is a method function with options.