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Add accessors to get list of roots+coefficients from unipot elements #10

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fingolfin opened this issue Aug 23, 2023 · 0 comments
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@fingolfin
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Suppose you created some elements with unipot:

gap> U_G2 := UnipotChevSubGr("G", 2, Rationals);;
gap> a := Indeterminate( Rationals, "a" );
a
gap> b := Indeterminate( Rationals, "b", [a] );
b
gap> c := Indeterminate( Rationals, "c", [a,b] );
c
gap> x := UnipotChevElemByFC(U_G2, [ [3,1], [1,0], [0,1] ], [a,b,c] );
x_{[ 3, 1 ]}( a ) * x_{[ 1, 0 ]}( b ) * x_{[ 0, 1 ]}( c )
gap> y := CanonicalForm(x);
x_{[ 1, 0 ]}( b ) * x_{[ 0, 1 ]}( c ) * x_{[ 3, 1 ]}( a ) * x_{[ 3, 2 ]}( a*c )

Now you want to do further computations for these: so you need the sequence of roots and coefficients. There seems to be no documented way to do that! We should add one.

In the meantime, users can directly access the innards of those objects:

gap> x!.roots;
[ 5, 1, 2 ]
gap> x!.felems;
[ a, b, c ]
gap> y!.roots;
[ 1, 2, 5, 6 ]
gap> y!.felems;
[ b, c, a, a*c ]
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