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Resolve
Resolve
[
expr
]
attempts to resolve
expr
into a form that eliminates
ForAll
and
Exists
quantifiers.
Resolve
[
expr
,
dom
]
works over the domain
dom
. Common choices of
dom
are
Complexes
,
Reals
and
Booleans
.
MORE INFORMATION
Resolve
is in effect automatically applied by
Reduce
.
expr
can contain equations, inequalities, domain specifications and quantifiers, in the same form as in
Reduce
.
The result of
Resolve
[
expr
]
always describes exactly the same mathematical set as
expr
, but without quantifiers.
Resolve
[
expr
]
assumes by default that quantities appearing algebraically in inequalities are real, while all other quantities are complex.
When a quantifier such as
ForAll
[
x
,
...
]
is eliminated the result will contain no mention of the localized variable
x
.
Resolve
[
expr
]
can in principle always eliminate quantifiers if
expr
contains only polynomial equations and inequalities over the reals or complexes.
EXAMPLES
CLOSE ALL
Basic Examples
(1)
Prove that the unit disk is nonempty:
In[1]:=
Out[1]=
Find the conditions for a quadratic form over the reals to be positive:
In[2]:=
Out[2]=
Find conditions for a quadratic to have at least two distinct complex roots:
In[3]:=
Out[3]=
Scope
(31)
Options
(4)
Applications
(6)
Properties & Relations
(3)
Possible Issues
(1)
SEE ALSO
Reduce
FindInstance
Exists
ForAll
CylindricalDecomposition
TUTORIALS
Quantifiers
Complex Polynomial Systems
RELATED LINKS
Implementation notes: Algebra and Calculus
MORE ABOUT
Assumptions and Domains
Logic & Boolean Algebra
Polynomial Algebra
Polynomial Systems
New in 5
© 2008 Wolfram Research, Inc.
EXAMPLES
Basic Examples 
Scope 