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LF

the leading form of a polynomial or an ideal

Syntax
LF(I: IDEAL): IDEAL
LF(F: RINGELEM): RINGELEM

Description
For a polynomial F this function returns the leading form, i.e. the sum of all summands having highest degree. It throws an error if the argument is zero or if the GradingDim of the polynomial ring is 0 (use DF to allow these cases).

For an ideal I this function returns the ideal of all the LF(f) for f in I . It throws an error if the GradingDim of the polynomial ring is 0.

Example
/**/  Use R ::= QQ[x,y];
/**/  LF(x^2 -x*y +2*x -1);
x^2 -x*y

/**/  Use R ::= QQ[x,y], Lex;  -- GradingDim is 0: everything is homogeneous
-- /**/  LF(x-1); --> !!! ERROR !!! as expected: instead of x-1

/**/ P := NewPolyRing(QQ, IndetSymbols(R), mat([[1,4],[1,0]]), 1);
/**/ Use P;
/**/ LF(x^2 - x*y);
-x*y
/**/  LF(x^4 + x^2 - y);
 x^4 -y

See Also