poly_degree
-----------

poly_degree(F)
     : It returns the degree of F with respect to the given weight vector.

poly_degree(F | WEIGHT=key0,V=key1)
     : This function allows optional variables WEIGHT, V

The weight is given by the optional variable weight w. It returns

Example:

      poly_degree(x^2+y^2-4 |weight=[100,1],v=[x,y]);

poly_elimination_ideal
----------------------

poly_elimination_ideal(I,VV)
     : It computes the ideal intersection of I and the monomial ideal generated by VV.

poly_elimination_ideal(I,VV | GROBNER_BASIS=key0,V=key1)
     : This function allows optional variables GROBNER_BASIS, V

If grobner_basis is "yes", I is assumed to be a Grobner basis. The optional variable v is a list of variables which defines the ring of polynomials.

Example 0:

      poly_elimination_ideal([x^2+y^2-4,x*y-1],[x]);

Example 1:

      A = poly_grobner_basis([x^2+y^2-4,x*y-1]|order=2,v=[y,x]);
               poly_elimination_ideal(A,[x]|grobner_basis="yes");

References
     gr , hgr , gr_mod , dp_*

poly_factor
-----------

poly_factor(F)
     : It factorizes the polynomial F.

Example:

      poly_factor(x^10-y^10);

poly_gcd
--------

poly_gcd(F,G)
     : It computes the polynomial GCD of F and G.

Example:

      poly_gcd(x^10-y^10,x^25-y^25);

poly_grobner_basis
------------------

poly_grobner_basis(I)
     : It returns the Grobner basis of I.

poly_grobner_basis(I | ORDER=key0,V=key1)
     : This function allows optional variables ORDER, V

The optional variable v is a list of variables which defines the ring of polynomials.

Example:

      A = poly_grobner_basis([x^2+y^2-4,x*y-1]|order=2,v=[y,x]);

poly_hilbert_polynomial
-----------------------

poly_hilbert_polynomial(I)
     : It returns the Hilbert polynomial of the ideal I.

poly_hilbert_polynomial(I | S=key0,V=key1)
     : This function allows optional variables S, V

The optional variable v is a list of variables.

Example:

      poly_hilbert_polynomial([x1*y1,x1*y2,x2*y1,x2*y2]|s=k,v=[x1,x2,y1,y2]);

poly_initial
------------

poly_initial(I)
     : It returns the initial ideal of I with respect to the given order.

poly_initial(I | ORDER=key0,V=key1)
     : This function allows optional variables ORDER, V

The optional variable v is a list of variables. This function computes

Example:

      poly_initial([x^2+y^2-4,x*y-1]|order=0,v=[x,y]);

poly_initial_coefficients
-------------------------

poly_initial_coefficients(I)
     : It computes the coefficients of the initial ideal of I with respect to the given order.

poly_initial_coefficients(I | ORDER=key0,V=key1)
     : This function allows optional variables ORDER, V

The optional variable v is a list of variables. The order is specified by the optional variable order

Example:

      poly_initial_coefficients([x^2+y^2-4,x*y-1]|order=0,v=[x,y]);

poly_initial_term
-----------------

poly_initial_term(F)
     : It returns the initial term of a polynomial F with respect to the given weight vector.

poly_initial_term(F | WEIGHT=key0,ORDER=key1,V=key2)
     : This function allows optional variables WEIGHT, ORDER, V

The weight is given by the optional variable weight w. It returns

Example:

      poly_initial_term( x^2+y^2-4 |weight=[100,1],v=[x,y]);

poly_solve_linear
-----------------

poly_solve_linear(EQS,V)
     : It solves the system of linear equations EQS with respect to the set of variables V.

Example:

      poly_solve_linear([2*x+3*y-z-2, x+y+z-1], [x,y,z]);