touch.h File Reference

Routines that check the emptyness of the intersection of several sets. More...

Go to the source code of this file.

Functions
MPS_BEGIN_DECLS mps_boolean	mps_ftouchnwt (mps_context *s, double *frad, int n, int i, int j)
	Check if the i-th and the j-th discs are newton-isolated. More...
mps_boolean	mps_dtouchnwt (mps_context *s, rdpe_t *drad, int n, int i, int j)
	Check if the i-th and the j-th discs are newton-isolated. More...
mps_boolean	mps_mtouchnwt (mps_context *s, rdpe_t *drad, int n, int i, int j)
	Check if the i-th and the j-th discs are newton-isolated. More...
mps_boolean	mps_ftouchreal (mps_context *s, int n, int i)
	Return true if the disk intersects the real axis, false otherwise (floating point version). More...
mps_boolean	mps_dtouchreal (mps_context *s, int n, int i)
	Return true if the disk intersects the real axis, false otherwise (DPE version). More...
mps_boolean	mps_mtouchreal (mps_context *s, int n, int i)
	Return true if the disk intersects the real axis, false otherwise (MP version). More...
mps_boolean	mps_ftouchimag (mps_context *s, int n, int i)
	Return true if the disk intersects the imaginary axis, false otherwise (floating point version). More...
mps_boolean	mps_dtouchimag (mps_context *s, int n, int i)
	Return true if the disk intersects the imaginary axis, false otherwise (DPE version). More...
mps_boolean	mps_mtouchimag (mps_context *s, int n, int i)
	Return true if the disk intersects the imaginary axis, false otherwise (MP version). More...
mps_boolean	mps_ftouchunit (mps_context *s, int n, int i)
	Return true if the disk intersects the unitary circle, false otherwise (floating point version). More...
mps_boolean	mps_dtouchunit (mps_context *s, int n, int i)
	Return true if the disk intersects the unitary circle, false otherwise (DPE version). More...
mps_boolean	mps_mtouchunit (mps_context *s, int n, int i)
	Return true if the disk intersects the unitary circle, false otherwise (MP version). More...
void	mps_validate_inclusions (mps_context *ctx)
	This function can be called to validate the inclusion radii and cluster analysis for a limited precision polynomial. More...

Detailed Description

Routines that check the emptyness of the intersection of several sets.

Function Documentation

mps_dtouchimag()

mps_boolean mps_dtouchimag	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the imaginary axis, false otherwise (DPE version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_dtouchnwt()

mps_boolean mps_dtouchnwt	(	mps_context *	s,
		rdpe_t *	drad,
		int	n,
		int	i,
		int	j
	)

Check if the i-th and the j-th discs are newton-isolated.

More precisely, given a parameter n, check if the roots i and j are separated with circles whose radius is less than their distance divided for n.

If this condition correspond to isolation, if where is the degree of the polynomial then it correspond to newton isolation.

Parameters

s	mps_context struct.
drad	The inclusion radii that should be used to perform cluster analysis.
n	See above.
i	the first root.
j	the second root.

Returns

false if the disc i and j are newton-isolated.

mps_dtouchreal()

mps_boolean mps_dtouchreal	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the real axis, false otherwise (DPE version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_dtouchunit()

mps_boolean mps_dtouchunit	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the unitary circle, false otherwise (DPE version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_ftouchimag()

mps_boolean mps_ftouchimag	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the imaginary axis, false otherwise (floating point version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_ftouchnwt()

MPS_BEGIN_DECLS mps_boolean mps_ftouchnwt	(	mps_context *	s,
		double *	frad,
		int	n,
		int	i,
		int	j
	)

Check if the i-th and the j-th discs are newton-isolated.

More precisely, given a parameter n, check if the roots i and j are separated with circles whose radius is less than their distance divided for n.

If this condition correspond to isolation, if where is the degree of the polynomial then it correspond to newton isolation.

Parameters

s	mps_context struct.
n	See above.
i	the first root.
j	the second root.
frad	The inclusion radii precomputed by some other routines.

Returns

false if the disc i and j are newton-isolated.

mps_ftouchreal()

mps_boolean mps_ftouchreal	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the real axis, false otherwise (floating point version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_ftouchunit()

mps_boolean mps_ftouchunit	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the unitary circle, false otherwise (floating point version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_mtouchimag()

mps_boolean mps_mtouchimag	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the imaginary axis, false otherwise (MP version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_mtouchnwt()

mps_boolean mps_mtouchnwt	(	mps_context *	s,
		rdpe_t *	drad,
		int	n,
		int	i,
		int	j
	)

Check if the i-th and the j-th discs are newton-isolated.

More precisely, given a parameter n, check if the roots i and j are separated with circles whose radius is less than their distance divided for n.

If this condition correspond to isolation, if where is the degree of the polynomial then it correspond to newton isolation.

Parameters

s	mps_context struct.
drad	The inclusion radii that should be used to perform cluster analysis.
n	See above.
i	the first root.
j	the second root.

Returns

false if the disc i and j are newton-isolated.

mps_mtouchreal()

mps_boolean mps_mtouchreal	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the real axis, false otherwise (MP version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_mtouchunit()

mps_boolean mps_mtouchunit	(	mps_context *	s,
		int	n,
		int	i
	)

Return true if the disk intersects the unitary circle, false otherwise (MP version).

Parameters

s	A pointer to the current mps_context.
n	The degree of the polynomial.
i	The index of the root to check

mps_validate_inclusions()

void mps_validate_inclusions

(

mps_context *

ctx

)

This function can be called to validate the inclusion radii and cluster analysis for a limited precision polynomial.

In the current implementation MPSolve treat a limited precision polynomial as an infinite one, and then gives a poteriori bounds to the approximations using this function.

Parameters

ctx	The current mps_context