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KASH^{3} Reference Manual | |||||||||||||

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## KeywordFinite and Infinite Maximal Orders
## DescriptionOne can define elements of orders by calling 'Element'. Since the orders have bases, it is enough to specify coefficients of linear combinations of the basis elements (see example). Afterwards one can perform the operations with these elements as usual. Usually one wants to work with the maximal orders since only these are Dedekind rings. For convenience there is a function which expects the defining polynomial and which first checks for irreducibility and separability and defines then the algebraic function field 'F' and the maximal orders 'o' and 'oi' (see example below). ## Examplesff := FiniteField(5);
fx := FunctionField(ff);
fxy := PolynomialAlgebra(fx);
F := FunctionField(fxy.1^3+fx.1^4+1);
o:=MaximalOrderFinite(F);
oi:=MaximalOrderInfinite(F);
a:=Element(o,[0,1,0]); b:=Element(oi,[0,1/fx.1,1/fx.1^2+1]);
a^3+fx.1^4+1;
a+b;
Coerce(o,a);
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Mon Nov 14 21:12:39 UTC 2005 on mackThe KANT Group |