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<short_description>Computes reduced Groebner basis of a D-ideal in Weyl algebra <tt>A_n</tt>.</short_description> ...t a Groebner basis then the output will not be the reduced Groebner basis. In fact, this function reduces a list <tt>GB</tt> of Weyl polynomials using <r

<short_description>Transforms a border basis into a Groebner basis.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Reduced Groebner basis of an ideal <tt>I</tt> in Weyl algebra <tt>A_n</tt>.</short_description> ...ynomials in the list <tt>L</tt> and leading coefficient of each polynomial in <tt>L</tt> is 1.

<short_description>Computing a Groebner Basis of a given ideal intersected with <tt>x^2-x</tt> for all indeterminates <tt ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Transforms a Groebner basis into a border basis.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_2</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>compute reduced Groebner basis</short_description> components form a reduced Groebner basis for M with respect to the

<short_description>calculate a Groebner basis</short_description> components form a Groebner basis for M with respect to the

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_512</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_128</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_4</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computes a Border Basis of a given ideal over <tt>F_2</tt>. </short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_16</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_8</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_32</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner basis of a given ideal in <tt>F_1024</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_2048</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_256</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

...n</tt> in to its reduced Groebner Basis using corresponding implementation in ApCoCoALib.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

...putes the reduced two-sided Groebner basis of a two-sided ideal <tt>I</tt> in the Weyl algebra <tt>A_n</tt> over the field of positive characteristic.</s ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computing a Groebner Basis of a given ideal in <tt>F_64</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

In the first two forms this function computes the syzygy module of a list of polynomials or vectors. In the last form this function returns the

<short_description>compute a Groebner basis with a timeout</short_description> ERROR: Time expired: use $gb.Complete to complete the computation

to be that of I or N, respectively. <tt>Res</tt> only works in the homogeneous context, and the coefficient ring

...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. ...nction does not find any zero. In this case the trivial solution is given. To solve linear systems naive Gaußian elimination is used.

<short_description>Computes the Groebner basis of an ideal <tt>I</tt> in Weyl algebra <tt>A_n</tt>.</short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computes a Border Basis of a given ideal over <tt>F_2</tt>. </short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

<short_description>Computes a Border Basis of a given ideal over <tt>F_2</tt>. </short_description> ...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them.

...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. ...find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound.

= Introduction = ...polynomials, ideals and modules are added to provide an intuitive approach to the algebraic nature of the functions.

...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. ...find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound.

...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. ...n. In sparse case it uses <ref>ApCoCoA-1:Slinalg.SEF|Slinalg.SEF</ref> and in dense case it uses <ref>ApCoCoA-1:LinAlg.EF|LinAlg.EF</ref>.

...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. ...s will be displayed to the screen after reaching the maximum degree bound. In fact Mutant NLA-Algorithm is the NLA-Algorithm with mutant strategy. It use

...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. ...find any zero. In this case a massage for non-uniqueness will be displayed to the screen after reaching the maximum degree bound.

...<em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. ...s will be displayed to the screen after reaching the maximum degree bound. In fact Improved Mutant NLA-Algorithm is the NLA-Algorithm with improved mutan