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<!DOCTYPE html> <html lang="en"> <head> <title>NCAlgebra : Table of Contents</title> <meta content="text/html; charset=utf-8" http-equiv="Content-Type"> <link type="text/css" rel="stylesheet" href="../../../../Macaulay2/Style/doc.css"> <link rel="stylesheet" href="../../../../Macaulay2/Style/katex/katex.min.css"> <script defer="defer" src="../../../../Macaulay2/Style/katex/katex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/auto-render.min.js"></script> <script> var macros = { "\\break": "\\\\", "\\ZZ": "\\mathbb{Z}", "\\NN": "\\mathbb{N}", "\\QQ": "\\mathbb{Q}", "\\RR": "\\mathbb{R}", "\\CC": "\\mathbb{C}", "\\PP": "\\mathbb{P}" }, delimiters = [ { left: "$$", right: "$$", display: true}, { left: "\\[", right: "\\]", display: true}, { left: "$", right: "$", display: false}, { left: "\\(", right: "\\)", display: false} ], ignoredTags = [ "kbd", "var", "samp", "script", "noscript", "style", "textarea", "pre", "code", "option" ]; document.addEventListener("DOMContentLoaded", function() { renderMathInElement(document.body, { delimiters: delimiters, macros: macros, ignoredTags: ignoredTags, trust: true }); }); </script> <style>.katex { font-size: 1em; }</style> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/copy-tex.min.js"></script> <script defer="defer" src="../../../../Macaulay2/Style/katex/contrib/render-a11y-string.min.js"></script> <script src="../../../../Macaulay2/Style/prism.js"></script> <script>var current_version = '1.25.06';</script> <script src="../../../../Macaulay2/Style/version-select.js"></script> <link type="image/x-icon" rel="icon" href="../../../../Macaulay2/Style/icon.gif"> </head> <body> <div id="buttons"> <div> <a href="https://macaulay2.com/">Macaulay2</a> <span id="version-select-container"></span> » <a title="Macaulay2 documentation" href="../../Macaulay2Doc/html/index.html">Documentation </a> <br><a href="../../Macaulay2Doc/html/_packages_spprovided_spwith_sp__Macaulay2.html">Packages</a> » <span><a href="index.html">NCAlgebra</a> :: <a href="toc.html">Table of Contents</a></span> </div> <div class="right"> <form method="get" action="https://www.google.com/search"> <input placeholder="Search" type="text" name="q" value=""> <input type="hidden" name="q" value="site:macaulay2.com/doc"> </form> next | previous | forward | backward | up | <a href="master.html">index</a> | <a href="toc.html">toc</a> </div> </div> <hr> <h1>NCAlgebra : Table of Contents</h1> <ul> <li><span><a href="index.html">NCAlgebra</a></span> <ul> <li><span><a href="___Basic_spoperations_spon_spnoncommutative_spalgebras.html">Basic operations on noncommutative algebras</a></span></li> <li><span><a href="___General_spsetup_spinformation.html">General setup information</a></span></li> <li><span><a href="___Using_spthe_sp__Bergman_spinterface.html">Using the Bergman interface</a></span></li> </ul> </li> <li><span><a title="Negates NCMatrices" href="_-_sp__N__C__Matrix.html">- NCMatrix</a> -- Negates NCMatrices</span></li> <li><span><a title="Ambient ring of an NCQuotientRing" href="_ambient_lp__N__C__Quotient__Ring_rp.html">ambient(NCQuotientRing)</a> -- Ambient ring of an NCQuotientRing</span></li> <li><span><a title="Extends an NCRingMap to the ambient ring of the source." href="_ambient_lp__N__C__Ring__Map_rp.html">ambient(NCRingMap)</a> -- Extends an NCRingMap to the ambient ring of the source.</span></li> <li><span><a title="Weights entries of a matrix to make associated map of free modules graded" href="_assign__Degrees.html">assignDegrees</a> -- Weights entries of a matrix to make associated map of free modules graded</span></li> <li><span><a title="Returns the base name of a generator of an NCRing" href="_base__Name_lp__N__C__Ring__Element_rp.html">baseName(NCRingElement)</a> -- Returns the base name of a generator of an NCRing</span></li> <li><span><a title="Returns a basis of an NCIdeal in a particular degree." href="_basis_lp__Z__Z_cm__N__C__Ideal_rp.html">basis(ZZ,NCIdeal)</a> -- Returns a basis of an NCIdeal in a particular degree.</span></li> <li><span><a title="Returns a basis of an NCLeftIdeal in a particular degree." href="_basis_lp__Z__Z_cm__N__C__Left__Ideal_rp.html">basis(ZZ,NCLeftIdeal)</a> -- Returns a basis of an NCLeftIdeal in a particular degree.</span></li> <li><span><a title="Returns a basis of an NCRightIdeal in a particular degree." href="_basis_lp__Z__Z_cm__N__C__Right__Ideal_rp.html">basis(ZZ,NCRightIdeal)</a> -- Returns a basis of an NCRightIdeal in a particular degree.</span></li> <li><span><a title="Returns a basis of an NCRing in a particular degree." href="_basis_lp__Z__Z_cm__N__C__Ring_rp.html">basis(ZZ,NCRing)</a> -- Returns a basis of an NCRing in a particular degree.</span></li> <li><span><a title="Finds central elements in a given degree" href="_central__Elements.html">centralElements</a> -- Finds central elements in a given degree</span></li> <li><span><a title="Returns the base ring of an NCRing" href="_coefficient__Ring_lp__N__C__Ring_rp.html">coefficientRing(NCRing)</a> -- Returns the base ring of an NCRing</span></li> <li><span><a title="Computes coordinates relative to a given basis" href="_coordinates.html">coordinates</a> -- Computes coordinates relative to a given basis</span></li> <li><span><a title="Returns the degree of an NCRingElement" href="_degree_lp__N__C__Ring__Element_rp.html">degree(NCRingElement)</a> -- Returns the degree of an NCRingElement</span></li> <li><span><a title="Methods for creating endomorphism rings of modules over a commutative ring" href="_endomorphism__Ring.html">endomorphismRing</a> -- Methods for creating endomorphism rings of modules over a commutative ring</span></li> <li><span><a title="Returns the entries of the NCMatrix" href="_entries_lp__N__C__Matrix_rp.html">entries(NCMatrix)</a> -- Returns the entries of the NCMatrix</span></li> <li><span><a title="Create the enveloping algebra" href="_enveloping__Algebra.html">envelopingAlgebra</a> -- Create the enveloping algebra</span></li> <li><span><a title="Defines a four-dimensional Sklyanin with given parameters" href="_four__Dim__Sklyanin.html">fourDimSklyanin</a> -- Defines a four-dimensional Sklyanin with given parameters</span></li> <li><span><a title="Define the free product of two algebras" href="_free__Product.html">freeProduct</a> -- Define the free product of two algebras</span></li> <li><span><a title="Read in a NCGroebnerBasis from a Bergman output file." href="_gb__From__Output__File.html">gbFromOutputFile</a> -- Read in a NCGroebnerBasis from a Bergman output file.</span></li> <li><span><a title="Computes a homogeneous generating set of the kernel of a ring map." href="_gdd__Kernel.html">gddKernel</a> -- Computes a homogeneous generating set of the kernel of a ring map.</span></li> <li><span><a title="The list of algebra generators of an NCGroebnerBasis" href="_generators_lp__N__C__Groebner__Basis_rp.html">generators(NCGroebnerBasis)</a> -- The list of algebra generators of an NCGroebnerBasis</span></li> <li><span><a title="Returns the generators of an NCIdeal" href="_generators_lp__N__C__Ideal_rp.html">generators(NCIdeal)</a> -- Returns the generators of an NCIdeal</span></li> <li><span><a title="Returns the generators of an NCLeftIdeal" href="_generators_lp__N__C__Left__Ideal_rp.html">generators(NCLeftIdeal)</a> -- Returns the generators of an NCLeftIdeal</span></li> <li><span><a title="Returns the generators of an NCRightIdeal" href="_generators_lp__N__C__Right__Ideal_rp.html">generators(NCRightIdeal)</a> -- Returns the generators of an NCRightIdeal</span></li> <li><span><a title="The list of algebra generators of an NCRing" href="_generators_lp__N__C__Ring_rp.html">generators(NCRing)</a> -- The list of algebra generators of an NCRing</span></li> <li><span><a title="Calls Bergman to compute the Hilbert series of an NCQuotientRing" href="_hilbert__Bergman.html">hilbertBergman</a> -- Calls Bergman to compute the Hilbert series of an NCQuotientRing</span></li> <li><span><a title="Computes the Hilbert series of an NCRing" href="_hilbert__Series_lp__N__C__Ring_rp.html">hilbertSeries(NCRing)</a> -- Computes the Hilbert series of an NCRing</span></li> <li><span><a title="Compute a graded component of Hom(M,N)" href="___Hom_lp__Z__Z_cm__N__C__Matrix_cm__N__C__Matrix_rp.html">Hom(ZZ,NCMatrix,NCMatrix)</a> -- Compute a graded component of Hom(M,N)</span></li> <li><span><a title="Computes the dual of a pure homogeneous ideal" href="_homog__Dual.html">homogDual</a> -- Computes the dual of a pure homogeneous ideal</span></li> <li><span><a title="The defining ideal of an NCPolynomialRing" href="_ideal_lp__N__C__Polynomial__Ring_rp.html">ideal(NCPolynomialRing)</a> -- The defining ideal of an NCPolynomialRing</span></li> <li><span><a title="Defining ideal of an NCQuotientRing in its ambient ring" href="_ideal_lp__N__C__Quotient__Ring_rp.html">ideal(NCQuotientRing)</a> -- Defining ideal of an NCQuotientRing in its ambient ring</span></li> <li><span><a title="Determines if an element is central" href="_is__Central.html">isCentral</a> -- Determines if an element is central</span></li> <li><span><a title="Returns whether an NCRing is commutative" href="_is__Commutative_lp__N__C__Ring_rp.html">isCommutative(NCRing)</a> -- Returns whether an NCRing is commutative</span></li> <li><span><a title="Returns whether the NCRingElement is constant" href="_is__Constant_lp__N__C__Ring__Element_rp.html">isConstant(NCRingElement)</a> -- Returns whether the NCRingElement is constant</span></li> <li><span><a title="Determines whether the input defines a homogeneous object" href="_is__Homogeneous_lp__N__C__Ideal_rp.html">isHomogeneous(NCIdeal)</a> -- Determines whether the input defines a homogeneous object</span></li> <li><span><a title="Determines if an NCRingMap preserves the natural grading" href="_is__Homogeneous_lp__N__C__Ring__Map_rp.html">isHomogeneous(NCRingMap)</a> -- Determines if an NCRingMap preserves the natural grading</span></li> <li><span><a title="Determines if a given (homogeneous) element is regular in a given degree" href="_is__Left__Regular.html">isLeftRegular</a> -- Determines if a given (homogeneous) element is regular in a given degree</span></li> <li><span><a title="Determines if a given NCRingElement is normal" href="_is__Normal_lp__N__C__Ring__Element_rp.html">isNormal(NCRingElement)</a> -- Determines if a given NCRingElement is normal</span></li> <li><span><a title="Determines if an NCRingMap is well-defined." href="_is__Well__Defined_lp__N__C__Ring__Map_rp.html">isWellDefined(NCRingMap)</a> -- Determines if an NCRingMap is well-defined.</span></li> <li><span><a title="Computes a basis of the kernel of a ring map in a specified degree." href="_kernel__Component.html">kernelComponent</a> -- Computes a basis of the kernel of a ring map in a specified degree.</span></li> <li><span><a title="Returns the lead monomial of an NCRingElement" href="_lead__Coefficient_lp__N__C__Ring__Element_rp.html">leadCoefficient(NCRingElement)</a> -- Returns the lead monomial of an NCRingElement</span></li> <li><span><a title="Returns the lead monomial of an NCRingElement" href="_lead__Monomial_lp__N__C__Ring__Element_rp.html">leadMonomial(NCRingElement)</a> -- Returns the lead monomial of an NCRingElement</span></li> <li><span><a title="Returns the lead term of an NCRingElement" href="_lead__Term_lp__N__C__Ring__Element_rp.html">leadTerm(NCRingElement)</a> -- Returns the lead term of an NCRingElement</span></li> <li><span><a title="Computes a matrix for left or right multiplication by a homogeneous element" href="_left__Multiplication__Map.html">leftMultiplicationMap</a> -- Computes a matrix for left or right multiplication by a homogeneous element</span></li> <li><span><a title="Lifts an NCMatrix" href="_lift_lp__N__C__Matrix_rp.html">lift(NCMatrix)</a> -- Lifts an NCMatrix</span></li> <li><span><a title="Scales a list by an NCRingElement on the right" href="___List_sp_st_sp__N__C__Ring__Element.html">List * NCRingElement</a> -- Scales a list by an NCRingElement on the right</span></li> <li><span><a title="Applies an NCRingMap to each element of a list" href="___List_sp_sl_sp__N__C__Ring__Map.html">List / NCRingMap</a> -- Applies an NCRingMap to each element of a list</span></li> <li><span><a title="Product of NCMatrices" href="___Matrix_sp_st_sp__N__C__Matrix.html">Matrix * NCMatrix</a> -- Product of NCMatrices</span></li> <li><span><a title="An NCMatrix associated to an NCRingMap." href="_matrix_lp__N__C__Ring__Map_rp.html">matrix(NCRingMap)</a> -- An NCMatrix associated to an NCRingMap.</span></li> <li><span><a title="Minimizes a list of NCRingElements" href="_minimize__Relations.html">minimizeRelations</a> -- Minimizes a list of NCRingElements</span></li> <li><span><a title="Returns the monomials appearing in the NCRingElement" href="_monomials_lp__N__C__Ring__Element_rp.html">monomials(NCRingElement)</a> -- Returns the monomials appearing in the NCRingElement</span></li> <li><span><a title="Type of a Groebner basis for an NCIdeal in an NCRing." href="___N__C__Groebner__Basis.html">NCGroebnerBasis</a> -- Type of a Groebner basis for an NCIdeal in an NCRing.</span></li> <li><span><a title="Compute a noncommutative Groebner basis." href="_nc__Groebner__Basis.html">ncGroebnerBasis</a> -- Compute a noncommutative Groebner basis.</span></li> <li><span><a title="Type of a two-sided ideal in a noncommutative ring" href="___N__C__Ideal.html">NCIdeal</a> -- Type of a two-sided ideal in a noncommutative ring</span></li> <li><span><a title="Define a two-sided ideal in a noncommutative ring" href="_nc__Ideal.html">ncIdeal</a> -- Define a two-sided ideal in a noncommutative ring</span></li> <li><span><a title="Sum of NCIdeals" href="___N__C__Ideal_sp_pl_sp__N__C__Ideal.html">NCIdeal + NCIdeal</a> -- Sum of NCIdeals</span></li> <li><span><a title="Type of a left ideal in a noncommutative ring" href="___N__C__Left__Ideal.html">NCLeftIdeal</a> -- Type of a left ideal in a noncommutative ring</span></li> <li><span><a title="Define a left ideal in a noncommutative ring" href="_nc__Left__Ideal.html">ncLeftIdeal</a> -- Define a left ideal in a noncommutative ring</span></li> <li><span><a title="Sum of NCLeftIdeals" href="___N__C__Left__Ideal_sp_pl_sp__N__C__Left__Ideal.html">NCLeftIdeal + NCLeftIdeal</a> -- Sum of NCLeftIdeals</span></li> <li><span><a title="Make a map to or from an NCRing" href="_nc__Map.html">ncMap</a> -- Make a map to or from an NCRing</span></li> <li><span><a title="Type of a matrix over a noncommutative ring" href="___N__C__Matrix.html">NCMatrix</a> -- Type of a matrix over a noncommutative ring</span></li> <li><span><a title="Create an NCMatrix" href="_nc__Matrix.html">ncMatrix</a> -- Create an NCMatrix</span></li> <li><span><a title="Reduces the entries of an NCMatrix with respect to an NCGroebnerBasis" href="___N__C__Matrix_sp_pc_sp__N__C__Groebner__Basis.html">NCMatrix % NCGroebnerBasis</a> -- Reduces the entries of an NCMatrix with respect to an NCGroebnerBasis</span></li> <li><span><a title="Product of NCMatrices" href="___N__C__Matrix_sp_st_sp__Matrix.html">NCMatrix * Matrix</a> -- Product of NCMatrices</span></li> <li><span><a title="Product of NCMatrices" href="___N__C__Matrix_sp_st_sp__N__C__Matrix.html">NCMatrix * NCMatrix</a> -- Product of NCMatrices</span></li> <li><span><a title="Product of NCMatrices" href="___N__C__Matrix_sp_st_sp__N__C__Ring__Element.html">NCMatrix * NCRingElement</a> -- Product of NCMatrices</span></li> <li><span><a title="Product of NCMatrices" href="___N__C__Matrix_sp_st_sp__Q__Q.html">NCMatrix * QQ</a> -- Product of NCMatrices</span></li> <li><span><a title="Product of NCMatrices" href="___N__C__Matrix_sp_st_sp__Ring__Element.html">NCMatrix * RingElement</a> -- Product of NCMatrices</span></li> <li><span><a title="Product of NCMatrices" href="___N__C__Matrix_sp_st_sp__Z__Z.html">NCMatrix * ZZ</a> -- Product of NCMatrices</span></li> <li><span><a title="Add NCMatrices" href="___N__C__Matrix_sp_pl_sp__N__C__Matrix.html">NCMatrix + NCMatrix</a> -- Add NCMatrices</span></li> <li><span><a title="Subtract NCMatrices" href="___N__C__Matrix_sp-_sp__N__C__Matrix.html">NCMatrix - NCMatrix</a> -- Subtract NCMatrices</span></li> <li><span><a title="Factor one map through another" href="___N__C__Matrix_sp_sl_sl_sp__N__C__Matrix.html">NCMatrix // NCMatrix</a> -- Factor one map through another</span></li> <li><span><a title="Test equality of matrices" href="___N__C__Matrix_sp_eq_eq_sp__N__C__Matrix.html">NCMatrix == NCMatrix</a> -- Test equality of matrices</span></li> <li><span><a title="Select some rows of an NCMatrix" href="___N__C__Matrix_sp%5E_sp__List.html">NCMatrix ^ List</a> -- Select some rows of an NCMatrix</span></li> <li><span><a title="Exponentiate an NCMatrix" href="___N__C__Matrix_sp%5E_sp__Z__Z.html">NCMatrix ^ ZZ</a> -- Exponentiate an NCMatrix</span></li> <li><span><a title="Select some columns of an NCMatrix" href="___N__C__Matrix_sp_us_sp__List.html">NCMatrix _ List</a> -- Select some columns of an NCMatrix</span></li> <li><span><a title="Induced map in homogeneous degree n" href="___N__C__Matrix_sp_us_sp__Z__Z.html">NCMatrix _ ZZ</a> -- Induced map in homogeneous degree n</span></li> <li><span><a title="Join NCMatrices horizontally" href="___N__C__Matrix_sp_vb_sp__N__C__Matrix.html">NCMatrix | NCMatrix</a> -- Join NCMatrices horizontally</span></li> <li><span><a title="Join NCMatrices vertically" href="___N__C__Matrix_sp_vb_vb_sp__N__C__Matrix.html">NCMatrix || NCMatrix</a> -- Join NCMatrices vertically</span></li> <li><span><a title="Graded shift of an NCMatrix." href="___N__C__Matrix_sp__Array.html">NCMatrix Array</a> -- Graded shift of an NCMatrix.</span></li> <li><span><a title="Type of a noncommutative polynomial ring" href="___N__C__Polynomial__Ring.html">NCPolynomialRing</a> -- Type of a noncommutative polynomial ring</span></li> <li><span><a title="Construct a NCQuotientRing" href="___N__C__Polynomial__Ring_sp_sl_sp__N__C__Ideal.html">NCPolynomialRing / NCIdeal</a> -- Construct a NCQuotientRing</span></li> <li><span><a title="Type of a noncommutative ring" href="___N__C__Quotient__Ring.html">NCQuotientRing</a> -- Type of a noncommutative ring</span></li> <li><span><a title="Type of a right ideal in a noncommutative ring" href="___N__C__Right__Ideal.html">NCRightIdeal</a> -- Type of a right ideal in a noncommutative ring</span></li> <li><span><a title="Define a right ideal in a noncommutative ring" href="_nc__Right__Ideal.html">ncRightIdeal</a> -- Define a right ideal in a noncommutative ring</span></li> <li><span><a title="Sum of NCRightIdeals" href="___N__C__Right__Ideal_sp_pl_sp__N__C__Right__Ideal.html">NCRightIdeal + NCRightIdeal</a> -- Sum of NCRightIdeals</span></li> <li><span><a title="Type of a noncommutative ring" href="___N__C__Ring.html">NCRing</a> -- Type of a noncommutative ring</span></li> <li><span><a title="Type of an element in a noncommutative ring" href="___N__C__Ring__Element.html">NCRingElement</a> -- Type of an element in a noncommutative ring</span></li> <li><span><a title="Reduces a NCRingElement by a NCGroebnerBasis" href="___N__C__Ring__Element_sp_pc_sp__N__C__Groebner__Basis.html">NCRingElement % NCGroebnerBasis</a> -- Reduces a NCRingElement by a NCGroebnerBasis</span></li> <li><span><a title="Scales a list by an NCRingElement on the left" href="___N__C__Ring__Element_sp_st_sp__List.html">NCRingElement * List</a> -- Scales a list by an NCRingElement on the left</span></li> <li><span><a title="Product of NCMatrices" href="___N__C__Ring__Element_sp_st_sp__N__C__Matrix.html">NCRingElement * NCMatrix</a> -- Product of NCMatrices</span></li> <li><span><a title="Type of a map to or from a noncommutative ring." href="___N__C__Ring__Map.html">NCRingMap</a> -- Type of a map to or from a noncommutative ring.</span></li> <li><span><a title="Basic operations with NCRingMaps" href="___N__C__Ring__Map_sp_pl_sp__N__C__Ring__Map.html">NCRingMap + NCRingMap</a> -- Basic operations with NCRingMaps</span></li> <li><span><a title="Compose two NCRingMaps" href="___N__C__Ring__Map_sp_at_at_sp__N__C__Ring__Map.html">NCRingMap @@ NCRingMap</a> -- Compose two NCRingMaps</span></li> <li><span><a title="Matrix of one homogeneous component of an NCRingMap" href="___N__C__Ring__Map_sp_us_sp__Z__Z.html">NCRingMap _ ZZ</a> -- Matrix of one homogeneous component of an NCRingMap</span></li> <li><span><a title="Apply a ring map to the generators of an ideal" href="___N__C__Ring__Map_sp__N__C__Ideal.html">NCRingMap NCIdeal</a> -- Apply a ring map to the generators of an ideal</span></li> <li><span><a title="Apply an NCRingMap to an element or matrix" href="___N__C__Ring__Map_sp__N__C__Ring__Element.html">NCRingMap NCRingElement</a> -- Apply an NCRingMap to an element or matrix</span></li> <li><span><a title="Computes the automorphism determined by a normal homogeneous element" href="_normal__Automorphism.html">normalAutomorphism</a> -- Computes the automorphism determined by a normal homogeneous element</span></li> <li><span><a title="Finds normal elements" href="_normal__Elements.html">normalElements</a> -- Finds normal elements</span></li> <li><span><a title="Finds elements normalized by a ring map" href="_normal__Elements_lp__N__C__Ring__Map_cm__Z__Z_rp.html">normalElements(NCRingMap,ZZ)</a> -- Finds elements normalized by a ring map</span></li> <li><span><a title="Calls Bergman for a normal form calculation" href="_normal__Form__Bergman.html">normalFormBergman</a> -- Calls Bergman for a normal form calculation</span></li> <li><span><a title="The number of algebra generators of an NCRing" href="_numgens_lp__N__C__Ring_rp.html">numgens(NCRing)</a> -- The number of algebra generators of an NCRing</span></li> <li><span><a title="Creates the opposite ring of a noncommutative ring" href="_opposite__Ring.html">oppositeRing</a> -- Creates the opposite ring of a noncommutative ring</span></li> <li><span><a title="Creates an Ore extension of a noncommutative ring" href="_ore__Extension.html">oreExtension</a> -- Creates an Ore extension of a noncommutative ring</span></li> <li><span><a title="Creates the defining ideal of an Ore extension of a noncommutative ring" href="_ore__Ideal.html">oreIdeal</a> -- Creates the defining ideal of an Ore extension of a noncommutative ring</span></li> <li><span><a title="Product of NCMatrices" href="___Q__Q_sp_st_sp__N__C__Matrix.html">QQ * NCMatrix</a> -- Product of NCMatrices</span></li> <li><span><a title="Define the (q-)commuting tensor product" href="_q__Tensor__Product.html">qTensorProduct</a> -- Define the (q-)commuting tensor product</span></li> <li><span><a title="Creates the subideal generated by quadratic elements of a given ideal" href="_quadratic__Closure.html">quadraticClosure</a> -- Creates the subideal generated by quadratic elements of a given ideal</span></li> <li><span><a title="Compute the resolution of coker M as a map of free right modules" href="_resolution_lp__N__C__Matrix_rp.html">resolution(NCMatrix)</a> -- Compute the resolution of coker M as a map of free right modules</span></li> <li><span><a title="Method for computing kernels of matrices over noncommutative rings in a given degree without using Bergman" href="_right__Kernel.html">rightKernel</a> -- Method for computing kernels of matrices over noncommutative rings in a given degree without using Bergman</span></li> <li><span><a title="Methods for computing kernels of matrices over noncommutative rings using Bergman" href="_right__Kernel__Bergman.html">rightKernelBergman</a> -- Methods for computing kernels of matrices over noncommutative rings using Bergman</span></li> <li><span><a title="Returns the ring of an NCIdeal or NCGroebnerBasis" href="_ring_lp__N__C__Ideal_rp.html">ring(NCIdeal)</a> -- Returns the ring of an NCIdeal or NCGroebnerBasis</span></li> <li><span><a title="Returns the ring of an NCLeftIdeal" href="_ring_lp__N__C__Left__Ideal_rp.html">ring(NCLeftIdeal)</a> -- Returns the ring of an NCLeftIdeal</span></li> <li><span><a title="Gives the ring of the NCMatrix" href="_ring_lp__N__C__Matrix_rp.html">ring(NCMatrix)</a> -- Gives the ring of the NCMatrix</span></li> <li><span><a title="Returns the ring of an NCRightIdeal" href="_ring_lp__N__C__Right__Ideal_rp.html">ring(NCRightIdeal)</a> -- Returns the ring of an NCRightIdeal</span></li> <li><span><a title="Returns the NCRing of an NCRingElement" href="_ring_lp__N__C__Ring__Element_rp.html">ring(NCRingElement)</a> -- Returns the NCRing of an NCRingElement</span></li> <li><span><a title="Product of NCMatrices" href="___Ring__Element_sp_st_sp__N__C__Matrix.html">RingElement * NCMatrix</a> -- Product of NCMatrices</span></li> <li><span><a title="Set a nonstandard grading for a NCRing." href="_set__Weights.html">setWeights</a> -- Set a nonstandard grading for a NCRing.</span></li> <li><span><a title="Returns the number of terms of an NCRingElement" href="_size_lp__N__C__Ring__Element_rp.html">size(NCRingElement)</a> -- Returns the number of terms of an NCRingElement</span></li> <li><span><a title="Defines a skew polynomial ring via a skewing matrix" href="_skew__Polynomial__Ring.html">skewPolynomialRing</a> -- Defines a skew polynomial ring via a skewing matrix</span></li> <li><span><a title="Defines a skew polynomial ring via a scaling factor" href="_skew__Polynomial__Ring_lp__Ring_cm__Ring__Element_cm__List_rp.html">skewPolynomialRing(Ring,RingElement,List)</a> -- Defines a skew polynomial ring via a scaling factor</span></li> <li><span><a title="Source of a map" href="_source_lp__N__C__Ring__Map_rp.html">source(NCRingMap)</a> -- Source of a map</span></li> <li><span><a title="Converts ring elements into vectors over the coefficient ring" href="_sparse__Coeffs.html">sparseCoeffs</a> -- Converts ring elements into vectors over the coefficient ring</span></li> <li><span><a title="Returns the variables appearing in the NCRingElement" href="_support_lp__N__C__Ring__Element_rp.html">support(NCRingElement)</a> -- Returns the variables appearing in the NCRingElement</span></li> <li><span><a title="Target of a map" href="_target_lp__N__C__Ring__Map_rp.html">target(NCRingMap)</a> -- Target of a map</span></li> <li><span><a title="Returns the terms of an NCRingElement" href="_terms_lp__N__C__Ring__Element_rp.html">terms(NCRingElement)</a> -- Returns the terms of an NCRingElement</span></li> <li><span><a title="Defines a three-dimensional Sklyanin with given parameters" href="_three__Dim__Sklyanin.html">threeDimSklyanin</a> -- Defines a three-dimensional Sklyanin with given parameters</span></li> <li><span><a title="Compute the abelianization of an NCRing and returns a Ring." href="_to__M2__Ring.html">toM2Ring</a> -- Compute the abelianization of an NCRing and returns a Ring.</span></li> <li><span><a title="Converts a Ring to an NCRing" href="_to__N__C__Ring.html">toNCRing</a> -- Converts a Ring to an NCRing</span></li> <li><span><a title="Converts an NCRingElement to a string" href="_to__String_lp__N__C__Ring__Element_rp.html">toString(NCRingElement)</a> -- Converts an NCRingElement to a string</span></li> <li><span><a title="Transposes an NCMatrix" href="_transpose_lp__N__C__Matrix_rp.html">transpose(NCMatrix)</a> -- Transposes an NCMatrix</span></li> <li><span><a title="Calls Bergman to compute a two sided noncommutative Groebner Basis." href="_two__Sided__N__C__Groebner__Basis__Bergman.html">twoSidedNCGroebnerBasisBergman</a> -- Calls Bergman to compute a two sided noncommutative Groebner Basis.</span></li> <li><span><a title="Brings the variables of a particular NCRing in scope" href="_use_lp__N__C__Ring_rp.html">use(NCRing)</a> -- Brings the variables of a particular NCRing in scope</span></li> <li><span><a title="Product of NCMatrices" href="___Z__Z_sp_st_sp__N__C__Matrix.html">ZZ * NCMatrix</a> -- Product of NCMatrices</span></li> </ul> </body> </html>
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