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<!DOCTYPE html> <html lang="en"> <head> <title>Divisor : 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 title="divisors" href="index.html">Divisor</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>Divisor : Table of Contents</h1> <ul> <li><span><a title="divisors" href="index.html">Divisor</a> -- divisors</span></li> <li><span><a title="an option used to tell divisor construction that a particular ambient ring is expected." href="___Ambient__Ring.html">AmbientRing</a> -- an option used to tell divisor construction that a particular ambient ring is expected.</span></li> <li><span><a title="apply a function to the coefficients of a divisor" href="_apply__To__Coefficients.html">applyToCoefficients</a> -- apply a function to the coefficients of a divisor</span></li> <li><span><a title="compute the locus where a graded module (or O(D) of a Weil divisor) is not globally generated" href="_base__Locus.html">baseLocus</a> -- compute the locus where a graded module (or O(D) of a Weil divisor) is not globally generated</span></li> <li><span><a title="the Types of divisors" href="___Basic__Divisor.html">BasicDivisor</a> -- the Types of divisors</span></li> <li><span><a title="add or subtract two divisors, or negate a divisor" href="___Basic__Divisor_sp_pl_sp__Basic__Divisor.html">BasicDivisor + BasicDivisor</a> -- add or subtract two divisors, or negate a divisor</span></li> <li><span><a title="compute a canonical divisor of a ring" href="_canonical__Divisor.html">canonicalDivisor</a> -- compute a canonical divisor of a ring</span></li> <li><span><a title="produce a WeilDivisor whose coefficients are ceilings or floors of the divisor" href="_ceiling_lp__R__Weil__Divisor_rp.html">ceiling(RWeilDivisor)</a> -- produce a WeilDivisor whose coefficients are ceilings or floors of the divisor</span></li> <li><span><a title="removes primes with coefficient zero from a divisor" href="_clean__Support.html">cleanSupport</a> -- removes primes with coefficient zero from a divisor</span></li> <li><span><a title="creates a new divisor with most entries from the cache removed" href="_clear__Cache.html">clearCache</a> -- creates a new divisor with most entries from the cache removed</span></li> <li><span><a title="get the coefficient of an ideal for a fixed divisor" href="_coefficient_lp__Basic__List_cm__Basic__Divisor_rp.html">coefficient(BasicList,BasicDivisor)</a> -- get the coefficient of an ideal for a fixed divisor</span></li> <li><span><a title="get the coefficient of an ideal for a fixed divisor" href="_coefficient_lp__Ideal_cm__Basic__Divisor_rp.html">coefficient(Ideal,BasicDivisor)</a> -- get the coefficient of an ideal for a fixed divisor</span></li> <li><span><a title="get the list of coefficients of a divisor" href="_coefficients_lp__Basic__Divisor_rp.html">coefficients(BasicDivisor)</a> -- get the list of coefficients of a divisor</span></li> <li><span><a title="an option used to tell divisor construction that a particular type of coefficients are expected." href="___Coefficient__Type.html">CoefficientType</a> -- an option used to tell divisor construction that a particular type of coefficients are expected.</span></li> <li><span><a title="constructor for (Weil/Q/R)-divisors" href="_divisor.html">divisor</a> -- constructor for (Weil/Q/R)-divisors</span></li> <li><span><a title="finds an ideal or module isomorphic to Hom(M, R)" href="_dualize.html">dualize</a> -- finds an ideal or module isomorphic to Hom(M, R)</span></li> <li><span><a title="embed a module as an ideal of a ring" href="_embed__As__Ideal.html">embedAsIdeal</a> -- embed a module as an ideal of a ring</span></li> <li><span><a title="find an element of a specified degree" href="_find__Element__Of__Degree.html">findElementOfDegree</a> -- find an element of a specified degree</span></li> <li><span><a title="get the list of Groebner bases corresponding to the height-one primes in the support of a divisor" href="_gbs.html">gbs</a> -- get the list of Groebner bases corresponding to the height-one primes in the support of a divisor</span></li> <li><span><a title="find a solution of the linear Diophantine equation Ax = b" href="_get__Linear__Diophantine__Solution.html">getLinearDiophantineSolution</a> -- find a solution of the linear Diophantine equation Ax = b</span></li> <li><span><a title="get the number of height-one primes in the support of the divisor" href="_get__Prime__Count.html">getPrimeCount</a> -- get the number of height-one primes in the support of the divisor</span></li> <li><span><a title="get the list of prime divisors of a given divisor" href="_get__Prime__Divisors.html">getPrimeDivisors</a> -- get the list of prime divisors of a given divisor</span></li> <li><span><a title="calculate the corresponding module of a divisor and represent it as an ideal" href="_ideal_lp__R__Weil__Divisor_rp.html">ideal(RWeilDivisor)</a> -- calculate the corresponding module of a divisor and represent it as an ideal</span></li> <li><span><a title="compute the ideal generated by the generators of the ideal raised to a power" href="_ideal__Power.html">idealPower</a> -- compute the ideal generated by the generators of the ideal raised to a power</span></li> <li><span><a title="a symbol used as a key within the divisor cache" href="_ideals.html">ideals</a> -- a symbol used as a key within the divisor cache</span></li> <li><span><a title="a valid value for the Strategy option in dualize or reflexify" href="___Ideal__Strategy.html">IdealStrategy</a> -- a valid value for the Strategy option in dualize or reflexify</span></li> <li><span><a title="whether a Weil divisor is Cartier" href="_is__Cartier.html">isCartier</a> -- whether a Weil divisor is Cartier</span></li> <li><span><a title="whether a ring is a domain" href="_is__Domain.html">isDomain</a> -- whether a ring is a domain</span></li> <li><span><a title="whether a divisor is effective" href="_is__Effective.html">isEffective</a> -- whether a divisor is effective</span></li> <li><span><a title="an option used by numerous functions which tells it to treat the divisors as if we were working on the Proj of the ambient ring." href="___Is__Graded.html">IsGraded</a> -- an option used by numerous functions which tells it to treat the divisors as if we were working on the Proj of the ambient ring.</span></li> <li><span><a title="whether the divisor is graded (homogeneous)" href="_is__Homogeneous_lp__Basic__Divisor_rp.html">isHomogeneous(BasicDivisor)</a> -- whether the divisor is graded (homogeneous)</span></li> <li><span><a title="whether two Weil divisors are linearly equivalent" href="_is__Linear__Equivalent.html">isLinearEquivalent</a> -- whether two Weil divisors are linearly equivalent</span></li> <li><span><a title="whether a divisor is prime" href="_is__Prime_lp__Basic__Divisor_rp.html">isPrime(BasicDivisor)</a> -- whether a divisor is prime</span></li> <li><span><a title="whether a Weil divisor is globally principal" href="_is__Principal.html">isPrincipal</a> -- whether a Weil divisor is globally principal</span></li> <li><span><a title="whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1." href="_is__Q__Cartier.html">isQCartier</a> -- whether m times a divisor is Cartier for any m from 1 to a fixed positive integer n1.</span></li> <li><span><a title="whether two Q-divisors are linearly equivalent" href="_is__Q__Linear__Equivalent.html">isQLinearEquivalent</a> -- whether two Q-divisors are linearly equivalent</span></li> <li><span><a title="whether a divisor is reduced" href="_is__Reduced.html">isReduced</a> -- whether a divisor is reduced</span></li> <li><span><a title="whether an ideal or module is reflexive" href="_is__Reflexive_lp__Ideal_rp.html">isReflexive(Ideal)</a> -- whether an ideal or module is reflexive</span></li> <li><span><a title="whether R mod the ideal is smooth" href="_is__Smooth_lp__Ideal_rp.html">isSmooth(Ideal)</a> -- whether R mod the ideal is smooth</span></li> <li><span><a title="whether the divisor is simple normal crossings" href="_is__S__N__C.html">isSNC</a> -- whether the divisor is simple normal crossings</span></li> <li><span><a title="whether a divisor is very ample." href="_is__Very__Ample_lp__Weil__Divisor_rp.html">isVeryAmple(WeilDivisor)</a> -- whether a divisor is very ample.</span></li> <li><span><a title="whether a rational/real divisor is in actuality a Weil divisor" href="_is__Weil__Divisor.html">isWeilDivisor</a> -- whether a rational/real divisor is in actuality a Weil divisor</span></li> <li><span><a title="whether a divisor is valid" href="_is__Well__Defined_lp__Basic__Divisor_rp.html">isWellDefined(BasicDivisor)</a> -- whether a divisor is valid</span></li> <li><span><a title="whether the divisor is the zero divisor" href="_is__Zero__Divisor.html">isZeroDivisor</a> -- whether the divisor is the zero divisor</span></li> <li><span><a title="an option used to specify to certain functions that we know that the divisor is Cartier" href="___Known__Cartier.html">KnownCartier</a> -- an option used to specify to certain functions that we know that the divisor is Cartier</span></li> <li><span><a title="an option used to specify to certain functions that we know that the ring is a domain" href="___Known__Domain.html">KnownDomain</a> -- an option used to specify to certain functions that we know that the ring is a domain</span></li> <li><span><a title="compute the map to projective space associated with the global sections of a Cartier divisor" href="_map__To__Projective__Space.html">mapToProjectiveSpace</a> -- compute the map to projective space associated with the global sections of a Cartier divisor</span></li> <li><span><a title="an option used by embedAsIdeal how many times to try embedding the module as an ideal in a random way." href="___M__Tries.html">MTries</a> -- an option used by embedAsIdeal how many times to try embedding the module as an ideal in a random way.</span></li> <li><span><a title="the non-Cartier locus of a Weil divisor" href="_non__Cartier__Locus.html">nonCartierLocus</a> -- the non-Cartier locus of a Weil divisor</span></li> <li><span><a title="multiply a divisor by a number" href="___Number_sp_st_sp__Basic__Divisor.html">Number * BasicDivisor</a> -- multiply a divisor by a number</span></li> <li><span><a title="calculate module corresponding to divisor" href="___O__O_sp__R__Weil__Divisor.html">OO RWeilDivisor</a> -- calculate module corresponding to divisor</span></li> <li><span><a title="get the effective part or anti-effective part of a divisor" href="_positive__Part.html">positivePart</a> -- get the effective part or anti-effective part of a divisor</span></li> <li><span><a title="a value for the option Strategy for the pullback method" href="___Primes.html">Primes</a> -- a value for the option Strategy for the pullback method</span></li> <li><span><a title="get the list of height-one primes in the support of a divisor" href="_primes.html">primes</a> -- get the list of height-one primes in the support of a divisor</span></li> <li><span><a title="pullback a divisor under a ring map" href="_pullback_lp__Ring__Map_cm__R__Weil__Divisor_rp.html">pullback(RingMap,RWeilDivisor)</a> -- pullback a divisor under a ring map</span></li> <li><span><a title="compute the ramification divisor of a finite inclusion of normal domains or a blowup over a smooth base" href="_ramification__Divisor.html">ramificationDivisor</a> -- compute the ramification divisor of a finite inclusion of normal domains or a blowup over a smooth base</span></li> <li><span><a title="calculate the double dual of an ideal or module Hom(Hom(M, R), R)" href="_reflexify.html">reflexify</a> -- calculate the double dual of an ideal or module Hom(Hom(M, R), R)</span></li> <li><span><a title="computes a reflexive power of an ideal in a normal domain" href="_reflexive__Power.html">reflexivePower</a> -- computes a reflexive power of an ideal in a normal domain</span></li> <li><span><a title="an option for embedAsIdeal" href="___Return__Map.html">ReturnMap</a> -- an option for embedAsIdeal</span></li> <li><span><a title="get the ambient ring of a divisor" href="_ring_lp__Basic__Divisor_rp.html">ring(BasicDivisor)</a> -- get the ambient ring of a divisor</span></li> <li><span><a title="whether two divisors are equal" href="___R__Weil__Divisor_sp_eq_eq_sp__R__Weil__Divisor.html">RWeilDivisor == RWeilDivisor</a> -- whether two divisors are equal</span></li> <li><span><a title="an option used to tell functions whether not to do checks." href="___Safe.html">Safe</a> -- an option used to tell functions whether not to do checks.</span></li> <li><span><a title="an option used in a number of functions" href="___Section.html">Section</a> -- an option used in a number of functions</span></li> <li><span><a title="a value for the option Strategy for the pullback method" href="___Sheaves.html">Sheaves</a> -- a value for the option Strategy for the pullback method</span></li> <li><span><a title="create a Q-Weil divisor from a Weil divisor" href="_to__Q__Weil__Divisor.html">toQWeilDivisor</a> -- create a Q-Weil divisor from a Weil divisor</span></li> <li><span><a title="create the torsion submodule of a module" href="_torsion__Submodule.html">torsionSubmodule</a> -- create the torsion submodule of a module</span></li> <li><span><a title="create a R-divisor from a Q or Weil divisor" href="_to__R__Weil__Divisor.html">toRWeilDivisor</a> -- create a R-divisor from a Q or Weil divisor</span></li> <li><span><a title="create a Weil divisor from a Q or R-divisor" href="_to__Weil__Divisor.html">toWeilDivisor</a> -- create a Weil divisor from a Q or R-divisor</span></li> <li><span><a title="trims the ideals displayed to the user and removes primes with coefficient zero" href="_trim_lp__Basic__Divisor_rp.html">trim(BasicDivisor)</a> -- trims the ideals displayed to the user and removes primes with coefficient zero</span></li> <li><span><a title="constructs the zero Weil divisor for the ring" href="_zero__Divisor.html">zeroDivisor</a> -- constructs the zero Weil divisor for the ring</span></li> </ul> </body> </html>