Next: Functions and Variables for Predicates, Previous: Functions and Variables for Properties, Up: Maxima’s Database [Contents][Index]
Activates the contexts context_1, …, context_n.
The facts in these contexts are then available to
make deductions and retrieve information.
The facts in these contexts are not listed by facts ().
The variable activecontexts is the list
of contexts which are active by way of the activate function.
Default value: []
activecontexts is a list of the contexts which are active
by way of the activate function, as opposed to being active because
they are subcontexts of the current context.
askequal(expr1, expr2) attempts to determine from the
assume database whether expr1 is equal to expr2,
and prompts the user if it cannot tell.
If the user provides the answer,
the answer is stored in the assume database
for the duration of the evaluation of the expression currently in progress.
When the evaluation is completed,
the user-provided answer is removed from the database.
askequal returns yes or no,
whether the answer was determined from the assume database
or provided by the user.
See also equal.
askinteger (expr, integer) attempts to determine from the
assume database whether expr is an integer.
askinteger prompts the user if it cannot tell otherwise,
and attempt to install the information in the database if possible.
askinteger (expr) is equivalent to
askinteger (expr, integer).
askinteger (expr, even) and askinteger (expr, odd)
likewise attempt to determine if expr is an even integer or odd integer,
respectively.
First attempts to determine whether the specified
expression is positive, negative, or zero. If it cannot, it asks the
user the necessary questions to complete its deduction. The user’s
answer is recorded in the data base for the duration of the current
computation. The return value of asksign is one of pos,
neg, or zero.
Adds predicates pred_1, …, pred_n to the current context.
If a predicate is inconsistent or redundant with the predicates in the current
context, it is not added to the context. The context accumulates predicates
from each call to assume.
assume returns a list whose elements are the predicates added to the
context or the atoms redundant or inconsistent where applicable.
The predicates pred_1, …, pred_n can only be expressions
with the relational operators < <= equal notequal >= and >.
Predicates cannot be literal equality = or literal inequality #
expressions, nor can they be predicate functions such as integerp.
Compound predicates of the form pred_1 and ... and pred_n
are recognized, but not pred_1 or ... or pred_n.
not pred_k is recognized if pred_k is a relational predicate.
Expressions of the form not (pred_1 and pred_2)
and not (pred_1 or pred_2) are not recognized.
Maxima’s deduction mechanism is not very strong;
there are many obvious consequences which cannot be determined by is.
This is a known weakness.
assume does not handle predicates with complex numbers. If a predicate
contains a complex number assume returns inconsistent or
redundant.
assume evaluates its arguments.
See also is, facts, forget,
context, and declare.
Examples:
(%i1) assume (xx > 0, yy < -1, zz >= 0); (%o1) [xx > 0, yy < - 1, zz >= 0] (%i2) assume (aa < bb and bb < cc); (%o2) [bb > aa, cc > bb] (%i3) facts (); (%o3) [xx > 0, - 1 > yy, zz >= 0, bb > aa, cc > bb] (%i4) is (xx > yy); (%o4) true (%i5) is (yy < -yy); (%o5) true (%i6) is (sinh (bb - aa) > 0); (%o6) true (%i7) forget (bb > aa); (%o7) [bb > aa] (%i8) prederror : false; (%o8) false (%i9) is (sinh (bb - aa) > 0); (%o9) unknown (%i10) is (bb^2 < cc^2); (%o10) unknown
Default value: true
assumescalar helps govern whether expressions expr
for which nonscalarp (expr) is false
are assumed to behave like scalars for certain transformations.
Let expr represent any expression other than a list or a matrix,
and let [1, 2, 3] represent any list or matrix.
Then expr . [1, 2, 3] yields [expr, 2 expr, 3 expr]
if assumescalar is true, or scalarp (expr) is
true, or constantp (expr) is true.
If assumescalar is true, such
expressions will behave like scalars only for commutative
operators, but not for noncommutative multiplication ..
When assumescalar is false, such
expressions will behave like non-scalars.
When assumescalar is all, such expressions will behave like
scalars for all the operators listed above.
Default value: false
When assume_pos is true and the sign of a parameter x
cannot be determined from the current context
or other considerations,
sign and asksign (x) return true.
This may forestall some automatically-generated asksign queries,
such as may arise from integrate or other computations.
By default, a parameter is x such that symbolp (x)
or subvarp (x).
The class of expressions considered parameters can be modified to some extent
via the variable assume_pos_pred.
sign and asksign attempt to deduce the sign of expressions
from the sign of operands within the expression.
For example, if a and b are both positive,
then a + b is also positive.
However, there is no way to bypass all asksign queries.
In particular, when the asksign argument is a
difference x - y or a logarithm log(x),
asksign always requests an input from the user,
even when assume_pos is true and assume_pos_pred is
a function which returns true for all arguments.
Default value: false
When assume_pos_pred is assigned the name of a function
or a lambda expression of one argument x,
that function is called to determine
whether x is considered a parameter for the purpose of assume_pos.
assume_pos_pred is ignored when assume_pos is false.
The assume_pos_pred function is called by sign and asksign
with an argument x
which is either an atom, a subscripted variable, or a function call expression.
If the assume_pos_pred function returns true,
x is considered a parameter for the purpose of assume_pos.
By default, a parameter is x such that symbolp (x)
or subvarp (x).
See also assume and assume_pos.
Examples:
(%i1) assume_pos: true$
(%i2) assume_pos_pred: symbolp$
(%i3) sign (a);
(%o3) pos
(%i4) sign (a[1]);
(%o4) pnz
(%i5) assume_pos_pred: lambda ([x], display (x), true)$
(%i6) asksign (a);
x = a
(%o6) pos
(%i7) asksign (a[1]);
x = a
1
(%o7) pos
(%i8) asksign (foo (a));
x = foo(a)
(%o8) pos
(%i9) asksign (foo (a) + bar (b));
x = foo(a)
x = bar(b)
(%o9) pos
(%i10) asksign (log (a));
x = a
Is a - 1 positive, negative, or zero?
p;
(%o10) pos
(%i11) asksign (a - b);
x = a
x = b
x = a
x = b
Is b - a positive, negative, or zero?
p;
(%o11) neg
Default value: initial
context names the collection of facts maintained by assume and
forget. assume adds facts to the collection named by
context, while forget removes facts.
Binding context to a name foo changes the current context to
foo. If the specified context foo does not yet exist,
it is created automatically by a call to newcontext.
The specified context is activated automatically.
See contexts for a general description of the context mechanism.
Default value: [initial, global]
contexts is a list of the contexts which
currently exist, including the currently active context.
The context mechanism makes it possible for a user to bind together and name a collection of facts, called a context. Once this is done, the user can have Maxima assume or forget large numbers of facts merely by activating or deactivating their context.
Any symbolic atom can be a context, and the facts contained in that
context will be retained in storage until destroyed one by one
by calling forget or destroyed as a whole by calling kill
to destroy the context to which they belong.
Contexts exist in a hierarchy, with the root always being
the context global, which contains information about Maxima that some
functions need. When in a given context, all the facts in that
context are "active" (meaning that they are used in deductions and
retrievals) as are all the facts in any context which is a subcontext
of the active context.
When a fresh Maxima is started up, the user is in a
context called initial, which has global as a subcontext.
See also facts, newcontext, supcontext,
killcontext, activate, deactivate,
assume, and forget.
Deactivates the specified contexts context_1, …, context_n.
If item is the name of a context, facts (item) returns a
list of the facts in the specified context.
If item is not the name of a context, facts (item) returns a
list of the facts known about item in the current context. Facts that
are active, but in a different context, are not listed.
facts () (i.e., without an argument) lists the current context.
Removes predicates established by assume.
The predicates may be expressions equivalent to (but not necessarily identical
to) those previously assumed.
forget (L), where L is a list of predicates,
forgets each item on the list.
Attempts to determine whether the predicate expr is provable from the
facts in the assume database.
If the predicate is provably true or false, is returns
true or false, respectively. Otherwise, the return value is
governed by the global flag prederror. When prederror is
true, is complains with an error message. Otherwise, is
returns unknown.
ev(expr, pred) (which can be written expr, pred at
the interactive prompt) is equivalent to is(expr).
See also assume, facts, and maybe.
Examples:
is causes evaluation of predicates.
(%i1) %pi > %e; (%o1) %pi > %e (%i2) is (%pi > %e); (%o2) true
is attempts to derive predicates from the assume database.
(%i1) assume (a > b); (%o1) [a > b] (%i2) assume (b > c); (%o2) [b > c] (%i3) is (a < b); (%o3) false (%i4) is (a > c); (%o4) true (%i5) is (equal (a, c)); (%o5) false
If is can neither prove nor disprove a predicate from the assume
database, the global flag prederror governs the behavior of is.
(%i1) assume (a > b); (%o1) [a > b] (%i2) prederror: true$ (%i3) is (a > 0); Maxima was unable to evaluate the predicate: a > 0 -- an error. Quitting. To debug this try debugmode(true); (%i4) prederror: false$ (%i5) is (a > 0); (%o5) unknown
Kills the contexts context_1, …, context_n.
If one of the contexts is the current context, the new current context will
become the first available subcontext of the current context which has not been
killed. If the first available unkilled context is global then
initial is used instead. If the initial context is killed, a
new, empty initial context is created.
killcontext refuses to kill a context which is
currently active, either because it is a subcontext of the current
context, or by use of the function activate.
killcontext evaluates its arguments.
killcontext returns done.
Attempts to determine whether the predicate expr is provable from the
facts in the assume database.
If the predicate is provably true or false, maybe returns
true or false, respectively. Otherwise, maybe returns
unknown.
maybe is functionally equivalent to is with
prederror: false, but the result is computed without actually assigning
a value to prederror.
See also assume, facts, and is.
Examples:
(%i1) maybe (x > 0); (%o1) unknown (%i2) assume (x > 1); (%o2) [x > 1] (%i3) maybe (x > 0); (%o3) true
Creates a new, empty context, called name, which
has global as its only subcontext. The newly-created context
becomes the currently active context.
If name is not specified, a new name is created (via gensym) and returned.
newcontext evaluates its argument.
newcontext returns name (if specified) or the new context name.
Attempts to determine the sign of expr on the basis of the facts in the
current data base. It returns one of the following answers: pos
(positive), neg (negative), zero, pz (positive or zero),
nz (negative or zero), pn (positive or negative), or pnz
(positive, negative, or zero, i.e. nothing known).
See also signum.
Creates a new context, called name, which has context as a subcontext. context must exist.
If context is not specified, the current context is assumed.
If name is not specified, a new name is created (via gensym) and returned.
supcontext evaluates its argument.
supcontext returns name (if specified) or the new context name.
Next: Functions and Variables for Predicates, Previous: Functions and Variables for Properties, Up: Maxima’s Database [Contents][Index]