mv util/lp to math/lp

Signed-off-by: Lev Nachmanson <levnach@hotmail.com>

src/math/lp/nla_tangent_lemmas.h

@@ -0,0 +1,83 @@
+/*++
+  Copyright (c) 2017 Microsoft Corporation
+
+  Module Name:
+
+  <name>
+
+  Abstract:
+
+  <abstract>
+
+  Author:
+  Nikolaj Bjorner (nbjorner)
+  Lev Nachmanson (levnach)
+
+  Revision History:
+
+
+  --*/
+#pragma once
+#include "util/rational.h"
+#include "math/lp/factorization.h"
+#include "math/lp/nla_common.h"
+
+namespace nla {
+    class core;
+
+    struct point {
+        rational x;
+        rational y;
+        point(const rational& a, const rational& b): x(a), y(b) {}
+        point() {}
+        inline point& operator*=(rational a) {
+            x *= a;
+            y *= a;
+            return *this;
+        } 
+        inline point operator+(const point& b) const {
+            return point(x + b.x, y + b.y);
+        } 
+
+        inline point operator-(const point& b) const {
+            return point(x - b.x, y - b.y);
+        }
+    };
+
+    inline std::ostream& operator<<(std::ostream& out, point const& a) { return out << "(" << a.x <<  ", " << a.y << ")"; }
+
+
+class tangents : common {   
+public:
+    tangents(core *core);
+    void tangent_lemma();
+private:    
+    lpvar find_binomial_to_refine();
+    void generate_explanations_of_tang_lemma(const monomial& m, const factorization& bf, lp::explanation& exp);
+    void generate_simple_tangent_lemma(const monomial& m, const factorization&);    
+    void tangent_lemma_bf(const monomial& m,const factorization& bf);
+    void generate_tang_plane(const rational & a, const rational& b, const factor& x, const factor& y, bool below, lpvar j);
+    
+    void generate_two_tang_lines(const factorization & bf, const point& xy, lpvar j);
+    // Get two planes tangent to surface z = xy, one at point a,  and another at point b.
+    // One can show that these planes still create a cut.
+    void get_initial_tang_points(point &a, point &b, const point& xy, bool below) const;
+
+    void push_tang_point(point &a, const point& xy, bool below, const rational& correct_val, const rational& val) const;
+    
+    void push_tang_points(point &a, point &b, const point& xy, bool below, const rational& correct_val, const rational& val) const;
+
+    rational tang_plane(const point& a, const point& x) const;
+    void get_tang_points(point &a, point &b, bool below, const rational& val, const point& xy) const;
+    std::ostream& print_point(const point &a, std::ostream& out) const;
+    std::ostream& print_tangent_domain(const point &a, const point &b, std::ostream& out) const;
+    // "below" means that the val is below the surface xy 
+    bool  plane_is_correct_cut(const point& plane,
+                               const point& xy,
+                               const rational & correct_val,                             
+                               const rational & val,
+                               bool below) const;
+    template <typename T> rational val(T const& t) const;
+    template <typename T> lpvar var(T const& t) const { return t.var(); }
+}; // end of tangents
+}