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algcurves

  

homogeneous

  

Make a polynomial in two variables homogeneous in three variables.

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

homogeneous(f, x, y, z)

Parameters

f

-

polynomial in x and y

x, y, z

-

variables

Description

• 

Algebraic curves are often represented using a polynomial in two variables, or as a homogeneous polynomial in three variables. This command converts a polynomial to the homogeneous representation.

• 

If f is a polynomial in x and y of degree d, and f can be written as i,jci,jxiyj for some coefficients ci,j, then the output of this command is i,jci,jxiyjzdij.

Examples

withalgcurves:

fy2x3

f:=x3+y2

(1)

homogeneousf,x,y,z

x3+y2z

(2)

Now one can convert back as follows:

subsz=1,

x3+y2

(3)

See Also

algcurves

 


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