Real algebraic numbers

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Functions
unsigned int	SizeOfS (unsigned int n, unsigned int k)
template<class POL>
int	choose (int k, int n, POL &ML)
template<class POL>
POL	HomChoose (int k, int n)
template<class R, class L>
R	macaulay (const L &f, char z='N')
template<class R, class L>
R	macaulay (const L &f, unsigned int nu, unsigned int nv, char z='T')

Function Documentation

template<class POL>

int choose	(	int	k,
		int	n,
		POL &	ML
	)

Return the polynomial, which is the sum of all monomials in n variables of degree k, with coefficient 1. The output is stored in the variable ML.

Definition at line 44 of file macaulay.h.

Referenced by macaulay().

template<class POL>

POL HomChoose	(	int	k,
		int	n
	)

Return the polynomial, which is the sum of all monomials in n variables of degree k, with coefficient 1. The output is stored in the variable ML.

Definition at line 72 of file macaulay.h.

template<class R, class L>

R macaulay	(	const L &	f,
		unsigned int	nu,
		unsigned int	nv,
		char	z = `'T'`
	)

Construction of the matrix of all multiples of degree nu of all the polynomials f[0], f[1], , f[n]. The argument nv is the number of variables. The order choosed to sort the monomials indexing the rows of the matrix is the {reverse} order associated to the polynomials of the sequence f. The second template argument specifies the type of the output matrix. For instance, macaulay<Mat>(f); will output a Mat. The usual Macaulay matrix is a submatrix of this one, for $\nu= \sum_{i=0}^{n} \deg(f_{i}) -n +1$ .

Definition at line 223 of file macaulay.h.

References matrixof::assigncoeff(), and matrixof::reserve().

template<class R, class L>

R macaulay	(	const L &	f,
		char	z = `'N'`
	)

Construction of the Macaulay matrix, for the projective resultant of $n+1$ polynomials in n variables. It will be of minimal degree in the coefficients of f[0], that is the product of the degree of f[1], $\dots$ , f[n]. The order choosed to sort the monomials indexing the rows of the matrix is the {reverse} of the order associated to the polynomials of the sequence f. L is the type of a sequence of polynomials. R specifies the type of the output matrix. For instance, macaulay<Mat>(f); will output a matrix of type VAL<Mat*>. It should have a constructor Mat(m,n) which allocates the necessary place to store a $n\times m$ matrix and the method Mat::operator()(size_type i, size_type j). If z is 'T', the transposed matrix is constructed.

Definition at line 111 of file macaulay.h.

References matrixof::assigncoeff(), choose(), degree(), MPOLDST::degree(), matrixof::reserve(), and SizeOfS().

synaps/mpol/macaulay.h File Reference

Detailed Description

Functions

Function Documentation