~ubuntu-branches/debian/squeeze/maxima/squeeze

<dd>exponentitates <var>poly</var> by a positive integer <var>number</var>. If <var>number</var> is not a positive integer number an error will be raised.

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<dl>

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<dt>Function: poly_content (<var>poly</var>. <var>varlist</var>)

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</dt>

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<dd><code>poly_content</code> extracts the GCD of its coefficients

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<dl>

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<dt>Function: poly_pseudo_divide (<var>poly</var>, <var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd>Pseudo-divide a polynomial <var>poly</var> by the list of n polynomials <var>polylist</var>. Return

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multiple values. The first value is a list of quotients a. The

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<dl>

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<dt>Function: poly_exact_divide (<var>poly1</var>, <var>poly2</var>, <var>varlist</var>)

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</dt>

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<dd>Divide a polynomial <var>poly1</var> by another polynomial <var>poly2</var>. Assumes that exact

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division with no remainder is possible. Returns the quotient.

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<dl>

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<dt>Function: poly_normal_form (<var>poly</var>, <var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd><code>poly_normal_form</code> finds the normal form of a polynomial <var>poly</var> with respect

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to a set of polynomials <var>polylist</var>.

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<dl>

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<dt>Function: poly_buchberger_criterion (<var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd>Returns <code>true</code> if <var>polylist</var> is a Groebner basis with respect to the current term

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order, by using the Buchberger

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<dl>

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<dt>Function: poly_buchberger (<var>polylist_fl</var> <var>varlist</var>)

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</dt>

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<dd><code>poly_buchberger</code> performs the Buchberger algorithm on a list of

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polynomials and returns the resulting Groebner basis.

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<td valign="middle" align="left">[<a href="maxima_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>

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<td valign="middle" align="left">[<a href="maxima_79.html#SEC329" title="Index">Index</a>]</td>

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<td valign="middle" align="left">[<a href="maxima_79.html#SEC331" title="Index">Index</a>]</td>

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</tr></table>

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<h3 class="subsection"> 54.2.4 Standard postprocessing of Groebner Bases </h3>

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<dl>

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<dt>Function: poly_reduction (<var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd><code>poly_reduction</code> reduces a list of polynomials <var>polylist</var>, so that

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each polynomial is fully reduced with respect to the other polynomials.

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<dl>

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<dt>Function: poly_minimization (<var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd>Returns a sublist of the polynomial list <var>polylist</var> spanning the same

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monomial ideal as <var>polylist</var> but minimal, i.e. no leading monomial

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<dl>

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<dt>Function: poly_normalize_list (<var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd><code>poly_normalize_list</code> applies <code>poly_normalize</code> to each polynomial in the list.

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That means it divides every polynomial in a list <var>polylist</var> by its leading coefficient.

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<dl>

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<dt>Function: poly_grobner (<var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd>Returns a Groebner basis of the ideal span by the polynomials <var>polylist</var>. Affected by the global flags.

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<dl>

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<dt>Function: poly_reduced_grobner (<var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd>Returns a reduced Groebner basis of the ideal span by the polynomials <var>polylist</var>. Affected by the global flags.

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<dl>

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<dt>Function: poly_depends_p (<var>poly</var>, <var>var</var>, <var>varlist</var>)

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</dt>

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<dd><code>poly_depends</code> tests whether a polynomial depends on a variable <var>var</var>.

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<dl>

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<dt>Function: poly_elimination_ideal (<var>polylist</var>, <var>number</var>, <var>varlist</var>)

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</dt>

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<dd><code>poly_elimination_ideal</code> returns the grobner basis of the number-th elimination ideal of an

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ideal specified as a list of generating polynomials (not necessarily Groebner basis).

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<dl>

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<dt>Function: poly_colon_ideal (<var>polylist1</var>, <var>polylist2</var>, <var>varlist</var>)

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</dt>

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<dd>Returns the reduced Groebner basis of the colon ideal

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<dl>

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<dt>Function: poly_ideal_intersection (<var>polylist1</var>, <var>polylist2</var>, <var>varlist</var>)

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</dt>

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<dd><code>poly_ideal_intersection</code> returns the intersection of two ideals.

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<dl>

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<dt>Function: poly_lcm (<var>poly1</var>, <var>poly2</var>, <var>varlist</var>)

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</dt>

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<dd>Returns the lowest common multiple of <var>poly1</var> and <var>poly2</var>.

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<dt>Function: poly_gcd (<var>poly1</var>, <var>poly2</var>, <var>varlist</var>)

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</dt>

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<dd>Returns the greatest common divisor of <var>poly1</var> and <var>poly2</var>.

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<dl>

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<dt>Function: poly_grobner_equal (<var>polylist1</var>, <var>polylist2</var>, <var>varlist</var>)

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</dt>

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<dd><code>poly_grobner_equal</code> tests whether two Groebner Bases generate the same ideal.

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Returns <code>true</code> if two lists of polynomials <var>polylist1</var> and <var>polylist2</var>, assumed to be Groebner Bases,

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<dl>

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<dt>Function: poly_grobner_subsetp (<var>polylist1</var>, <var>polylist2</var>, <var>varlist</var>)

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</dt>

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<dd><code>poly_grobner_subsetp</code> tests whether an ideal generated by <var>polylist1</var>

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is contained in the ideal generated by <var>polylist2</var>. For this test to always succeed,

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<dl>

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<dt>Function: poly_grobner_member (<var>poly</var>, <var>polylist</var>, <var>varlist</var>)

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</dt>

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<dd>Returns <code>true</code> if a polynomial <var>poly</var> belongs to the ideal generated by the

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polynomial list <var>polylist</var>, which is assumed to be a Groebner basis. Returns <code>false</code> otherwise.

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<dl>

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<dt>Function: poly_ideal_saturation1 (<var>polylist</var>, <var>poly</var>, <var>varlist</var>)

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</dt>

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<dd>Returns the reduced Groebner basis of the saturation of the ideal

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<dl>

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<dt>Function: poly_ideal_saturation (<var>polylist1</var>, <var>polylist2</var>, <var>varlist</var>)

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</dt>

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<dd>Returns the reduced Groebner basis of the saturation of the ideal

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<dl>

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<dt>Function: poly_ideal_polysaturation1 (<var>polylist1</var>, <var>polylist2</var>, <var>varlist</var>)

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</dt>

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<dd><var>polylist2</var> ist a list of n polynomials <code>[poly1,...,polyn]</code>.

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Returns the reduced Groebner basis of the ideal

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<dl>

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<dt>Function: poly_ideal_polysaturation (<var>polylist</var>, <var>polylistlist</var>, <var>varlist</var>)

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</dt>

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<dd><var>polylistlist</var> is a list of n list of polynomials <code>[polylist1,...,polylistn]</code>.

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Returns the reduced Groebner basis of the saturation of the ideal

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<dl>

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<dt>Function: poly_saturation_extension (<var>poly</var>, <var>polylist</var>, <var>varlist1</var>, <var>varlist2</var>)

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</dt>

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<dd><code>poly_saturation_extension</code> implements the famous Rabinowitz trick.

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<dl>

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<dt>Function: poly_polysaturation_extension (<var>poly</var>, <var>polylist</var>, <var>varlist1</var>, <var>varlist2</var>)

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</dt>

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<td valign="middle" align="left">[<a href="maxima_toc.html#SEC_Contents" title="Table of contents">Contents</a>]</td>

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<td valign="middle" align="left">[<a href="maxima_79.html#SEC329" title="Index">Index</a>]</td>

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<td valign="middle" align="left">[<a href="maxima_79.html#SEC331" title="Index">Index</a>]</td>

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</tr></table>

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This document was generated by Robert Dodier on December, 13 2009 using <a href="http://texi2html.cvshome.org/">texi2html 1.76</a>.

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This document was generated by Robert Dodier on April, 24 2010 using <a href="http://texi2html.cvshome.org/">texi2html 1.76</a>.

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