v-1.62

PackageInfo.g

@@ -8,8 +8,8 @@ SetPackageInfo( rec(
 
   PackageName := "HAP",
   Subtitle  := "Homological Algebra Programming",
-  Version := "1.61",
-  Date    := "02/01/2024",
+  Version := "1.62",
+  Date    := "01/02/2024",
   License := "GPL-2.0-or-later",
 
   SourceRepository := rec(
@@ -107,8 +107,8 @@ AvailabilityTest := ReturnTrue,
 BannerString     := Concatenation( "Loading HAP ",
                             String( ~.Version ), " ...\n" ),
 
-#TestFile :=  "tst/testquick.g",
-TestFile :=  "tst/testall.g",
+TestFile :=  "tst/testquick.g",
+#TestFile :=  "tst/testall.g",
 
 Keywords := [ "homology", "cohomology", "resolution", "homotopy group", 
 "module of identities", "CW complex", "simplicial complex", "cubical complex", "permutahedral complex", "knots", "nonabelian tensor", "nonabelian exterior", "covering space" ]

README.md

@@ -32,12 +32,12 @@ Please send your bug reports to graham.ellis(at)nuigalway.ie .
 On a Linux machine with GAP (and optionally Polymake) installed, the HAP
 library can be loaded as follows:
 
-* First download the file hap1.61.tar.gz to the subdirectory "pkg/" of GAP. (If
+* First download the file hap1.62.tar.gz to the subdirectory "pkg/" of GAP. (If
 you don't have access to this, then create a directory "pkg" in your home
 directory and download the file there.)
 
-* Change to directory "pkg/" and type "gunzip hap1.61.tar.gz" followed by
-"tar -xvf hap1.61.tar" .
+* Change to directory "pkg/" and type "gunzip hap1.62.tar.gz" followed by
+"tar -xvf hap1.62.tar" .
 
 * Start GAP. (If you have created "pkg" in your home directory then start GAP
 with the command "gap -l 'path/homedir;' "   where path/homedir is the path to
@@ -46,12 +46,12 @@ your home directory.)
 * In GAP type " LoadPackage("HAP"); " .
 
 * Help on HAP can be found on the HAP home page (a version of which is
-included in directory "pkg/Hap1.61/www" of this distribution).
+included in directory "pkg/Hap1.62/www" of this distribution).
 
 * Performance can be significantly improved by using a compiled version of the
 HAP library. A compiled version can be created by the following steps.
 
-1. Change to the directory "pkg/Hap1.61/" .
+1. Change to the directory "pkg/Hap1.62/" .
 2. Edit the file "compile" so that: PKGDIR is equal to the path to the
 directory "pkg" where your GAP packages are stored; GACDIR is equal to the
 path to the directory where the GAP compiler "gac" is stored.
@@ -60,4 +60,4 @@ path to the directory where the GAP compiler "gac" is stored.
 The next time HAP is loaded a compiled version will be loaded.
 
 * Should you want to return to an uncompiled version, change to the directory
-"pkg/Hap1.61/" and type "./uncompile".
+"pkg/Hap1.62/" and type "./uncompile".

date

@@ -1 +1 @@
-02 Jan 2024 
+01 Feb 2024 

doc/Test.xml

@@ -509,6 +509,7 @@
 <C>IndeterminateDegrees</C><Br/>
 <C>IndeterminatesOfGradedAlgebraPresentation</C><Br/>
 <C>IndeterminatesOfPolynomial</C><Br/>
+<C>InitialObject</C><Br/>
 <C>InnerAutomorphismGroupQuandle</C><Br/>
 <C>InnerAutomorphismGroupQuandleAsPerm</C><Br/>
 <C>InverseRingHomomorphism</C><Br/>
@@ -535,6 +536,7 @@
 <C>SourcePolynomialRing</C><Br/>
 <C>SourceRelations</C><Br/>
 <C>StarGraph</C><Br/>
+<C>TerminalObject</C><Br/>
 <C>TermsOfPolynomial</C><Br/>
 <C>UnivariateMonomialsOfMonomial</C><Br/>
 <C>CoefficientsRing</C><Br/>

doc/newCW.xml

@@ -9,5 +9,5 @@
 </Description> </ManSection> 
 <ManSection> <Func Name="ChainComplexOfRegularCWComplex" Arg="Y"/> <Description> <P/> Inputs a regular CW-complex <M>Y</M> and returns the cellular chain complex of <M>Y</M>. <P/><B>Examples:</B> <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>2</LinkText></URL>&nbsp;
 </Description> </ManSection> 
-<ManSection> <Func Name="FundamentalGroup" Arg="Y"/> <Func Name="FundamentalGroup" Arg="Y,n"/> <Description> <P/> Inputs a regular CW-complex <M>Y</M> and, optionally, the number of some 0-cell. It returns the fundamental group of <M>Y</M> based at the 0-cell <M>n</M>. The group is returned as a finitely presented group. If <M>n</M> is not specified then it is set <M>n=1</M>. The algorithm requires a discrete vector field on <M>Y</M>. If <M>Y</M> does not initially have a discrete vector field then one is constructed. <P/><B>Examples:</B> <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap2.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap3.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap4.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap5.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLinks.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPeripheral.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRandomComplexes.html</Link><LinkText>11</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutKnots.html</Link><LinkText>12</LinkText></URL>&nbsp;
+<ManSection> <Func Name="FundamentalGroup" Arg="Y"/> <Func Name="FundamentalGroup" Arg="Y,n"/> <Description> <P/> Inputs a regular CW-complex <M>Y</M> and, optionally, the number of some 0-cell. It returns the fundamental group of <M>Y</M> based at the 0-cell <M>n</M>. The group is returned as a finitely presented group. If <M>n</M> is not specified then it is set <M>n=1</M>. The algorithm requires a discrete vector field on <M>Y</M>. If <M>Y</M> does not initially have a discrete vector field then one is constructed. <P/><B>Examples:</B> <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap2.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap3.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap4.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap5.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap11.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLinks.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPeripheral.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutQuandles.html</Link><LinkText>11</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutRandomComplexes.html</Link><LinkText>12</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutKnots.html</Link><LinkText>13</LinkText></URL>&nbsp;
 </Description> </ManSection> </Section> </Chapter>

doc/newCategories.xml

@@ -17,6 +17,10 @@
 </Description> </ManSection> 
 <ManSection> <Func Name="TerminalArrow" Arg="X"/> <Description> <P/> Inputs an object <M>X</M> in some category, and returns the arrow from <M>X</M> to the terminal object in the category. <P/><B>Examples:</B> <URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>1</LinkText></URL>&nbsp;
 </Description> </ManSection> 
+<ManSection> <Func Name="HasInitialObject" Arg="Name"/> <Description> <P/> Inputs the name of a category and returns true or false depending on whether the category has an initial object. <P/><B>Examples:</B> <URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>1</LinkText></URL>&nbsp;
+</Description> </ManSection> 
+<ManSection> <Func Name="HasTerminalObject" Arg="Name"/> <Description> <P/> Inputs the name of a category and returns true or false depending on whether the category has a terminal object. <P/><B>Examples:</B> 
+</Description> </ManSection> 
 <ManSection> <Func Name="Source" Arg="f"/> <Description> <P/> Inputs an arrow <M>f</M> in some category, and returns its source. <P/><B>Examples:</B> <URL><Link>../tutorial/chap2.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap4.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap8.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutNonabelian.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>8</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>9</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutFunctorial.html</Link><LinkText>10</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutLieCovers.html</Link><LinkText>11</LinkText></URL>&nbsp;
 </Description> </ManSection> 
 <ManSection> <Func Name="Target" Arg="f"/> <Description> <P/> Inputs an arrow <M>f</M> in some category, and returns its target. <P/><B>Examples:</B> <URL><Link>../tutorial/chap1.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap2.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap7.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap8.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutAbelianCategories.html</Link><LinkText>5</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoefficientSequence.html</Link><LinkText>6</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoveringSpaces.html</Link><LinkText>7</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCoverinSpaces.html</Link><LinkText>8</LinkText></URL>&nbsp;

doc/newChainComplexes.xml

@@ -3,7 +3,7 @@
 </Description> </ManSection> 
 <ManSection> <Func Name="ChainComplexOfPair" Arg="T,S"/> <Description> <P/> Inputs a pure cubical complex or cubical complex <M>T</M> and contractible subcomplex <M>S</M>. It returns the quotient <M>C(T)/C(S)</M> of cellular chain complexes. <P/><B>Examples:</B> <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>2</LinkText></URL>&nbsp;
 </Description> </ManSection> 
-<ManSection> <Func Name="ChevalleyEilenbergComplex" Arg="X,n"/> <Description> <P/> Inputs either a Lie algebra <M>X=A</M> (over the ring of integers <M>Z</M> or over a field <M>K</M>) or a homomorphism of Lie algebras <M>X=(f:A \longrightarrow B)</M>, together with a positive integer <M>n</M>. It returns either the first <M>n</M> terms of the Chevalley-Eilenberg chain complex <M>C(A)</M>, or the induced map of Chevalley-Eilenberg complexes <M>C(f):C(A) \longrightarrow C(B)</M>. <P/> (The homology of the Chevalley-Eilenberg complex <M>C(A)</M> is by definition the homology of the Lie algebra <M>A</M> with trivial coefficients in <M>Z</M> or <M>K</M>). <P/> This function was written by <B>Pablo Fernandez Ascariz</B> <P/><B>Examples:</B> 
+<ManSection> <Func Name="ChevalleyEilenbergComplex" Arg="X,n"/> <Description> <P/> Inputs either a Lie algebra <M>X=A</M> (over the ring of integers <M>Z</M> or over a field <M>K</M>) or a homomorphism of Lie algebras <M>X=(f:A \longrightarrow B)</M>, together with a positive integer <M>n</M>. It returns either the first <M>n</M> terms of the Chevalley-Eilenberg chain complex <M>C(A)</M>, or the induced map of Chevalley-Eilenberg complexes <M>C(f):C(A) \longrightarrow C(B)</M>. <P/> (The homology of the Chevalley-Eilenberg complex <M>C(A)</M> is by definition the homology of the Lie algebra <M>A</M> with trivial coefficients in <M>Z</M> or <M>K</M>). <P/> This function was written by <B>Pablo Fernandez Ascariz</B> <P/><B>Examples:</B> <URL><Link>../tutorial/chap7.html</Link><LinkText>1</LinkText></URL>&nbsp;
 </Description> </ManSection> 
 <ManSection> <Func Name="LeibnizComplex" Arg="X,n"/> <Description> <P/> Inputs either a Lie or Leibniz algebra <M>X=A</M> (over the ring of integers <M>Z</M> or over a field <M>K</M>) or a homomorphism of Lie or Leibniz algebras <M>X=(f:A \longrightarrow B)</M>, together with a positive integer <M>n</M>. It returns either the first <M>n</M> terms of the Leibniz chain complex <M>C(A)</M>, or the induced map of Leibniz complexes <M>C(f):C(A) \longrightarrow C(B)</M>. <P/> (The Leibniz complex <M>C(A)</M> was defined by J.-L.Loday. Its homology is by definition the Leibniz homology of the algebra <M>A</M>). <P/> This function was written by <B>Pablo Fernandez Ascariz</B> <P/><B>Examples:</B> 
 </Description> </ManSection> 

doc/newCubical.xml

@@ -13,7 +13,7 @@
 </Description> </ManSection> 
 <ManSection> <Func Name="PureCubicalComplexDifference" Arg="S,T"/> <Description> <P/> Inputs two pure cubical complexes with common dimension and array size. It returns the difference S-T. (An entry in the binary array of the difference has value 1 if and only if the corresponding entry in the binary array of S is 1 and the corresponding entry in the binary array of T is 0.) <P/><B>Examples:</B> <URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutKnots.html</Link><LinkText>2</LinkText></URL>&nbsp;
 </Description> </ManSection> 
-<ManSection> <Func Name="ReadImageAsPureCubicalComplex" Arg="str,n"/> <Description> <P/> Reads an image file <M>str</M> (= "file.png", "file.eps", "file.bmp" etc) and an integer <M>n</M> between 0 and 765. It returns a 2-dimensional pure cubical complex based on the black/white version of the image determined by the threshold <M>n</M>. <P/><B>Examples:</B> <URL><Link>../tutorial/chap10.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>4</LinkText></URL>&nbsp;
+<ManSection> <Func Name="ReadImageAsPureCubicalComplex" Arg="str,n"/> <Description> <P/> Reads an image file <M>str</M> (= "file.png", "file.eps", "file.bmp" etc) and an integer <M>n</M> between 0 and 765. It returns a 2-dimensional pure cubical complex based on the black/white version of the image determined by the threshold <M>n</M>. <P/><B>Examples:</B> <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>&nbsp;, <URL><Link>../tutorial/chap10.html</Link><LinkText>2</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutPersistent.html</Link><LinkText>3</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutCubical.html</Link><LinkText>4</LinkText></URL>&nbsp;, <URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>5</LinkText></URL>&nbsp;
 </Description> </ManSection> 
 <ManSection> <Func Name="ReadLinkImageAsPureCubicalComplex" Arg="str"/> <Func Name="ReadLinkImageAsPureCubicalComplex" Arg="str,n"/> <Description> <P/> Reads an image file <M>str</M> (= "file.png", "file.eps", "file.bmp" etc) containing a knot or link diagram, and optionally a positive integer <M>n</M>. The integer <M>n</M> should be a little larger than the line thickness in the link diagram, and if not provided then <M>n</M> is set equal to 10. The function tries to output the corresponding knot or link as a 3-dimensional pure cubical complex. Ideally the link diagram should be produced with line thickness 6 in Xfig, and the under-crossing spaces should not be too large or too small or too near one another. The function does not always succeed: it applies several checks, and if one of these checks fails then the function returns "fail". <P/><B>Examples:</B> <URL><Link>../www/SideLinks/About/aboutLinks.html</Link><LinkText>1</LinkText></URL>&nbsp;
 </Description> </ManSection> 
@@ -67,7 +67,7 @@
 </Description> </ManSection> 
 <ManSection> <Func Name="HomotopyEquivalentMaximalPureCubicalSubcomplex" Arg="T,S"/> <Description> <P/> Inputs a pure cubical complex <M>T</M> together with a pure cubical subcomplex <M>S</M>. It returns a pure cubical subcomplex <M>H</M> of <M>T</M> which contains <M>S</M> and is maximal with respect to the property that it is homotopy equivalent to <M>S</M>. <P/><B>Examples:</B> 
 </Description> </ManSection> 
-<ManSection> <Func Name="HomotopyEquivalentMinimalPureCubicalSubcomplex" Arg="T,S"/> <Description> <P/> Inputs a pure cubical complex <M>T</M> together with a pure cubical subcomplex <M>S</M>. It returns a pure cubical subcomplex <M>H</M> of <M>T</M> which contains <M>S</M> and is minimal with respect to the property that it is homotopy equivalent to <M>T</M>. <P/><B>Examples:</B> 
+<ManSection> <Func Name="HomotopyEquivalentMinimalPureCubicalSubcomplex" Arg="T,S"/> <Description> <P/> Inputs a pure cubical complex <M>T</M> together with a pure cubical subcomplex <M>S</M>. It returns a pure cubical subcomplex <M>H</M> of <M>T</M> which contains <M>S</M> and is minimal with respect to the property that it is homotopy equivalent to <M>T</M>. <P/><B>Examples:</B> <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>&nbsp;
 </Description> </ManSection> 
 <ManSection> <Func Name="BoundaryOfPureCubicalComplex" Arg="T"/> <Description> <P/> Inputs a pure cubical complex <M>T</M> and returns its boundary as a pure cubical complex. The boundary consists of all cubes which have one or more facets that lie in just the one cube. <P/><B>Examples:</B> <URL><Link>../www/SideLinks/About/aboutTDA.html</Link><LinkText>1</LinkText></URL>&nbsp;
 </Description> </ManSection> 
@@ -95,7 +95,7 @@
 </Description> </ManSection> 
 <ManSection> <Func Name="ReadImageAsFilteredPureCubicalComplex" Arg="file,n"/> <Description> <P/> Inputs a string containing the path to an image file, together with a positive integer n. It returns a filtered pure cubical complex of filtration length <M>n</M>. <P/><B>Examples:</B> <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>&nbsp;
 </Description> </ManSection> 
-<ManSection> <Func Name="ComplementOfFilteredPureCubicalComplex" Arg="M"/> <Description> <P/> Inputs a filtered pure cubical complex <M>M</M> and returns the complement as a filtered pure cubical complex. <P/><B>Examples:</B> 
+<ManSection> <Func Name="ComplementOfFilteredPureCubicalComplex" Arg="M"/> <Description> <P/> Inputs a filtered pure cubical complex <M>M</M> and returns the complement as a filtered pure cubical complex. <P/><B>Examples:</B> <URL><Link>../tutorial/chap5.html</Link><LinkText>1</LinkText></URL>&nbsp;
 </Description> </ManSection> 
 <ManSection> <Func Name="PersistentHomologyOfFilteredPureCubicalComplex" Arg="M,n"/> <Description> <P/> Inputs a filtered pure cubical complex <M>M</M> and a non-negative integer <M>n</M>. It returns the degree <M>n</M> persistent homology of <M> M</M> with rational coefficients. <P/><B>Examples:</B> 
 </Description> </ManSection> </Section> </Chapter>