Assertion: curve | /r/DefinedAs | implicit equation
Facets:
Source sentences:
text: For a curve defined by an implicit equation F(x, y) = 0 with partial derivatives denoted F x , F y ,
text: For a curve defined by its implicit equations, above representation of the curve may easily deduced from a Gröbner basis for a block ordering such that the block of the smaller variables is (x 1 , x 2 ).
text: One method is to use implicit differentiation to compute the derivatives of y with respect to x. Alternatively, for a curve defined by the implicit equation F ( x , y ) = 0 {\displaystyle F(x,y)=0} , one can express these formulas directly in terms of the partial derivatives of F {\displaystyle F} .