5.1.46 homog
------------

Syntax:
homog ( ideal_expression )

homog ( module_expression )
Type:
int
Purpose:
tests for homogeneity: returns 1 for homogeneous input, 0 otherwise.
Syntax:

homog ( polynomial_expression, ring_variable )

homog ( vector_expression, ring_variable )

homog ( ideal_expression, ring_variable )

homog ( module_expression, ring_variable )
Type:
same as first argument
Purpose:
homogenizes polynomials, vectors, ideals, or modules by multiplying
each monomial with a suitable power of the given ring variable (which must have
weight 1).
Example:
  ring r=32003,(x,y,z),ds;
  poly s1=x3y2+x5y+3y9;
  poly s2=x2y2z2+3z8;
  poly s3=5x4y2+4xy5+2x2y2z3+y7+11x10;
  ideal i=s1,s2,s3;
  homog(s2,z);
==> x2y2z4+3z8
  homog(i,z);
==> _[1]=3y9+x5yz3+x3y2z4
==> _[2]=x2y2z4+3z8
==> _[3]=11x10+y7z3+5x4y2z4+4xy5z4+2x2y2z6
  homog(i);
==> 0
  homog(homog(i,z));
==> 1
See
ideal;
module;
poly;
vector.
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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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