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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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<Chapter><Heading> Knots and Links</Heading>

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<Table Align="|l|" >

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<Row>

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<Item>

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<Index>PureCubicalKnot</Index>

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<C>PureCubicalKnot(L)</C>

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<C>PureCubicalKnot(n,i)</C>

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<P/>

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Inputs a list <M>L=[[m1,n1], [m2,n2], ..., [mk,nk]]</M> of pairs of integers

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 describing 

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 a cubical arc presentation of a 

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link with all vertical lines at the front and all horizontal lines at the back. The bottom horizontal line extends from the m1-th column to the n1-th column. 

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The second to bottom horizontal line extends from the m2-th column to the n2-th column. And so on. The link is returned 

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as a 3-dimensional pure cubical complex.

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<P/>

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Alternatively the function inputs two

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integers <M>n</M>, <M>i</M> and returns the <M>i</M>-th prime knot on <M>n</M> crossings.

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</Item>

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</Row>

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<Row>

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<Item>

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<Index>ViewPureCubicalKnot</Index>

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<C>ViewPureCubicalKnot(L)</C>

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<P/>

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Inputs a pure cubical link <M>L</M> and displays it.

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<P/>

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</Item>

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</Row>

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<Row>

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<Item>

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<Index>KnotSum</Index>

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<C>KnotSum(K,L)</C>

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<P/>

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Inputs two pure cubical knots <M>K</M>, <M>L</M> and returns their sum as a pure cubical knot. This function is not defined for links with more than one component.

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<P/>

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</Item>

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</Row>

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<Row>

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<Item>

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<Index>KnotGroup</Index>

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<C>KnotGroup(K)</C>

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<P/>

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Inputs a pure cubical link <M>K</M> and returns the fundamental group of its complement. The group is returned as a finitely presented group.

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<P/>

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</Item>

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</Row>

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<Row>

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<Item>

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<Index>AlexanderMatrix</Index>

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<C>AlexanderMatrix(G)</C>

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<P/>

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Inputs a finitely presented group <M>G</M> whose abelianization is infinite cyclic. It returns the Alexander matrix of the presentation. 

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<P/>

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</Item>

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</Row>

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<Row>

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<Item>

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<Index>AlexanderPolynomial</Index>

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<C>AlexanderPolynomial(K)</C>

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<C>AlexanderPolynomial(G)</C>

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<P/>

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Inputs either a pure cubical knot <M>K</M> or a finitely presented group <M>G</M> whose abelianization is infinite cyclic. The Alexander Polynomial is returned. 

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<P/>

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</Item>

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</Row>

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<Row>

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<Item>

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<Index>ProjectionOfPureCubicalComplex</Index>

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<C>ProjectionOfPureCubicalComplex(K)</C>

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<P/>

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Inputs  an $n$-dimensional

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 pure cubical complex <M>K</M> and returns an n-1-dimensional pure cubical complex K'. The returned complex is obtained by projecting Euclidean n-space onto Euclidean n-1-space. 

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<P/>

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</Item>

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</Row>

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<Row>

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<Item>

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<Index>ReadPDBfileAsPureCubicalComplex</Index>

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<C>ReadPDBfileAsPureCubicalComplex(file)</C>

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<C>ReadPDBfileAsPureCubicalComplex(file,m ,c)</C>

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<P/>

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Inputs  a protein database file describing a protein, and optionally

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 inputs  a positive integer m and character string c. The default values for the optional inputs are m=5 and c="A".  

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 It loads the chain of amino acids labelled by c in the file as a 3-dimensional pure cubical complex of the homotopy type of a circle. 

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<P/>

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It might happen that the function fails to construct a pure cubical complex of the homotopy type of a circle. In this case  retry with a larger integer m.

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</Item>

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</Row>

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</Table>

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</Chapter>

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