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how do we know when to homogenise an equation??? -thnx in advance


9 years ago

SAGAR SINGH - IIT DELHI
879 Points
							Dear student,
The importance of homogeneity is the scale invariance of the  functions. Which implies that the graphs of the functions will be scale  invariant. Indeed, imagine a homogeneous function is used to define a  geometrical object implicitly:

f(x 1,x2,…,xn)=0
meaning all points with coordinates (x1,…,xn  that satisfy this equation will belong to the geometrical figure defined by f. If f is homogeneous, it immediately follows that any multiple of these  coordinates also satisfies the equations. In other words, any point that  satisfies the equation immediately implies the entire ray going through  that point and the origin of the space belong to the geometrical  object.
Homogenizing an implicit polynomial equation means adding an extra variable z and multiply any term by zk with k such that the resulting polynomial is homogeneous. Of course, since any z-multiple  of the polynomial will also be homogeneous, you choose the resulting  homogeneous polynomial with smallest possible degree.

9 years ago
arpan chandrashekhar
5 Points
							i am sorry sagar bhaiyya but i did not understand the starting of what u said..i wntd the conditions n situation when homogenisation is done..

9 years ago
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