diff options
Diffstat (limited to 'doc')
| -rw-r--r-- | doc/sphinx/addendum/micromega.rst | 4 |
1 files changed, 2 insertions, 2 deletions
diff --git a/doc/sphinx/addendum/micromega.rst b/doc/sphinx/addendum/micromega.rst index c01e6a5aa6..070e899c9d 100644 --- a/doc/sphinx/addendum/micromega.rst +++ b/doc/sphinx/addendum/micromega.rst @@ -159,7 +159,7 @@ High level view of `lia` Over :math:`\mathbb{R}`, *positivstellensatz* refutations are a complete proof principle [#mayfail]_. However, this is not the case over :math:`\mathbb{Z}`. Actually, *positivstellensatz* refutations are not even sufficient to decide -linear *integer* arithmetic. The canonical example is :math:`2 * x = 1 -> \mathtt{False}` +linear *integer* arithmetic. The canonical example is :math:`2 * x = 1 \to \mathtt{False}` which is a theorem of :math:`\mathbb{Z}` but not a theorem of :math:`{\mathbb{R}}`. To remedy this weakness, the :tacn:`lia` tactic is using recursively a combination of: @@ -180,7 +180,7 @@ are a way to take into account the discreteness of :math:`\mathbb{Z}` by roundin Let :math:`p` be an integer and :math:`c` a rational constant. Then :math:`p \ge c \rightarrow p \ge \lceil{c}\rceil`. -For instance, from 2 x = 1 we can deduce +For instance, from :math:`2 x = 1` we can deduce + :math:`x \ge 1/2` whose cut plane is :math:`x \ge \lceil{1/2}\rceil = 1`; + :math:`x \le 1/2` whose cut plane is :math:`x \le \lfloor{1/2}\rfloor = 0`. |