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