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PolynomialIdeals[UnivariatePolynomial] - compute the smallest univariate polynomial in an ideal
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Calling Sequence
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UnivariatePolynomial(v, J, X)
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Parameters
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v
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variable name
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J
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polynomial ideal or a list or set of generator polynomials
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X
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(optional) set of variable names
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Description
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The UnivariatePolynomial command computes a univariate polynomial in v of least degree that is contained in the ideal J. If no such polynomial exists, then zero is returned. A zero-dimensional ideal contains a univariate polynomial in every variable.
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The first argument must be the variable in which a univariate polynomial is to be computed. The second argument must be a polynomial ideal. An optional third argument overrides the default ring variables.
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Examples
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![POLYNOMIALIDEAL(y-x, x^3-y^2, variables = {x, y}, characteristic = 0, known_groebner_bases = (table( [ ] )))](/support/helpjp/helpview.aspx?si=8506/file02598/math85.png)
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![POLYNOMIALIDEAL(y^2+2, x^3-y^3+1, 12*z*t^2-2*t^3+1, variables = {t, x, y, z}, characteristic = 0, known_groebner_bases = (table( [ ] )))](/support/helpjp/helpview.aspx?si=8506/file02598/math99.png)
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![POLYNOMIALIDEAL(-2*y^2+2*x^2*y^2-3*y*alpha^3, 6*x^2*beta+7*y^2*alpha+3*x^4, variables = {x, y}, characteristic = 0, known_groebner_bases = (table( [ ] )))](/support/helpjp/helpview.aspx?si=8506/file02598/math141.png)
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