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5.1.13 FullRed
If FullRed is set to TRUE, then when a normal form is required in any Groebner-type computation, CoCoA will reduce all monomials in a polynomial; if FullRed is FALSE, only the leading terms will be reduced. The default is to have FullRed set to TRUE.

Example
UnSet FullRed;
Use R ::= Q[x,y];
Interreduced([xy^3+y^2+x,x]);
[x, y^2 + x]
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Set FullRed;
Interreduced([xy^3+y^2+x,x]);
[x, y^2]
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