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poly_degree
: It returns the degree of F with respect to the given weight vector.
: This function allows optional variables weight, v
Description:
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]); |
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poly_elimination_ideal
: It computes the ideal intersection of I and the monomial ideal generated by VV.
: This function allows optional variables grobner_basis, v
Description:
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_*
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poly_expand
: This is an alias of poly_sort.
References:
poly_sort
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poly_factor
: It factorizes the polynomial F.
Example:
poly_factor(x^10-y^10); |
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poly_gcd
: It computes the polynomial GCD of F and G.
Example:
poly_gcd(x^10-y^10,x^25-y^25); |
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poly_grobner_basis
: It returns the Grobner basis of I.
: This function allows optional variables order, v
Description:
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]); |
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poly_hilbert_polynomial
: It returns the Hilbert polynomial of the ideal I.
: This function allows optional variables s, v
Description:
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]); |
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poly_initial
: It returns the initial ideal of I with respect to the given order.
: This function allows optional variables order, v
Description:
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]); |
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poly_initial_coefficients
: It computes the coefficients of the initial ideal of I with respect to the given order.
: This function allows optional variables order, v
Description:
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]); |
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poly_initial_term
: It returns the initial term of a polynomial F with respect to the given weight vector.
: This function allows optional variables weight, order, v
Description:
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]); |
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poly_solve_linear
: 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]); |
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poly_sort
: It expands F with a given variables v=V and a given weight w=W. It returns a quote object. If trucate option is set, the expansion is truncated at the given degree.
: This function allows optional variables v, w, truncate
Example:
poly_sort((x-y-a)^3 | v=[x,y], w=[-1,-1]) returns a series expansion in terms of x and y. |
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This document was generated by Nobuki Takayama on January, 28 2008 using texi2html 1.76.