slice.hpp File Reference

Provides the bertini::Slice class – a linear slice of affine or projective space. More...

#include <vector>
#include "bertini2/function_tree.hpp"
#include "bertini2/function_tree/reintern.hpp"
#include "bertini2/num_traits.hpp"
#include "bertini2/eigen_extensions.hpp"
#include "bertini2/system/blocks/linear_forms_block.hpp"

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Classes
class	bertini::Slice
	A linear slice of affine or projective space: a stack of linear forms, M [x ; 1]. More...

Namespaces
namespace	bertini

Functions
std::ostream &	bertini::operator<< (std::ostream &out, Slice const &s)
	Provides output streaming for Slice.

Detailed Description

Provides the bertini::Slice class – a linear slice of affine or projective space.

A Slice is the linear part of a witness set: a stack of linear forms whose common zero set cuts a positive-dimensional component down to isolated witness points. It is backed by a bertini::blocks::LinearFormsBlock (the augmented coefficient matrix M, one row per linear form, the last column carrying each form's constant term), so a Slice evaluates, carries precision, and drops into a System exactly like any other evaluation block. Because that augmented (num_vars+1)-column layout is shared with ProductsOfLinearsBlock, a Slice's rows are also ready-made factors for a product-of-linears block – the composition regeneration needs.

See also

bertini::blocks::LinearFormsBlock

bertini::blocks::ProductsOfLinearsBlock