\brief convert p == 0 into a solved form v == r, such that
v has bounds [lo, oo) iff r has bounds [lo', oo)
v has bounds (oo,hi] iff r has bounds (oo,hi']
The solved form allows the Grobner solver identify more bounds conflicts.
A bad leading term can miss bounds conflicts.
For example for x + y + z == 0 where x, y : [0, oo) and z : (oo,0]
we prefer to solve z == -x - y instead of x == -z - y
because the solution -z - y has neither an upper, nor a lower bound.
The Grobner solver is augmented with a notion of a substitution that is applied before the solver is run.
For Grobner we want to preserve directions of intervals for finding sign conflicts. This means that it makes sense to have external control over linear solutions.
this update integrates inferences to smt.arith.solver=6 related to grobner basis computation and handling of div/mod axioms to reconcile performance with smt.arith.solver=2.
The default of smt.arth.nl.grobner_subs_fixed is changed to 1 to make comparison with solver=2 more direct.
The selection of cluster equalities for solver=6 was reconciled with how it is done for solver=2.
* Subtle bug in kernel computation
Coefficient was being passed by reference and, therefore, was
being changed indirectly.
In the process, updated the code to be more generic to avoid rational
computation in the middle of matrix manipulation.
* sparse_matrix: fixed handling of 0 in add_var() and add()
particularly in add_var(), without the fix the user is responsible for checking
coefficients for 0.
In some cases, Z3_algebraic_get_i() returned 0. For example, in the following
Python snippet, the last assert would fail:
import z3
x = z3.Real('x')
s = z3.Solver()
s.add( (x * x) - 2 == 0, x <= 0)
s.check()
val_x = s.model().get_interp(x)
assert val_x.index() == 1
The problem was that `algebraic_numbers::manager:👿:get_i()` did not
check whether the root index was properly initialized.
This commit fixes this issue by checking whether root index is initialized
the same way various other routines do.
Fixes issue #5807.
Signed-off-by: Jan Vrany <jan.vrany@labware.com>
