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D.15.2.24 difformIsHomog
Procedure from library difform.lib (see difform_lib).
- Usage:
- homog(df); df difform
- Return:
- 1, if df is homogeneous - 0, otherwise
- Note:
- - the form 0 is homogeneous
- be careful: difformIsHomog does not cast polynomials to differential
forms. So before applying to a polynomial, a type cast should be done
Example:
| | LIB "difform.lib";
ring R = 0,(x,y,z),ds;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
forms dDx, dDy, dDz, dx, dy, dz are available.
/////////////////
// Homogeneous //
/////////////////
homog(3*dx*dz - x8*dx*dy);
==> 0
homog(12x*dx + dy - (y4-y5)*dz);
==> 0
/////////////////////
// Not homogeneous //
/////////////////////
homog(3 + x8*dy);
==> 0
homog(x*dx+dy*dx);
==> 0
// When applying homog to a polynomial which is considered
// as a differential form, a type cast has to be done first
homog(3x-y2);
==> 0
difform df = 3x-y2;
homog(df);
==> 1
kill Omega_R,dx,dy,dz,df;
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See also:
difformDeg;
difformIsHomogDeg.
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