assumingAlso
, _assumingAlso
Add temporary assumption
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calculation
assumingAlsocondition
calculation
assumingAlso (expr
,set
) _assumingAlso(calculation
,condition
) _assumingAlso(calculation
, (expr
,set
))
calculation assumingAlso condition
evaluates calculation
under
all existing assumptions along with the new assumption that condition
is
true for that calculation.
calculation assumingAlso(expr, set)
temporarily
attaches the property set
to the identifier or
expression expr
and evaluates calculation
.
This call takes into account all previous assumptions containing identifiers
used in expr
.
calculation assumingAlso condition
is equivalent
to _assumingAlso(calculation, condition)
.
calculation assumingAlso (expr, set)
is equivalent
to _assumingAlso(calculation, (expr, set))
.
assumingAlso
sets temporary assumptions in
addition to existing permanent assumptions. Here, condition
holds
true only while the argument calculation
is evaluated.
After this evaluation, condition
is removed. Therefore,
it does not affect further computations. condition
is
also removed if the evaluation stops with an error.
If assumptions contain linear equations with one variable, assumingAlso
solves
these equations. Then the command inserts the solutions into calculation
and
evaluates the result. See Example 3.
If expr
is a list, vector, or matrix, use
the syntaxes calculation assumingAlso(expr, set)
and _assumingAlso(calculation,
(expr, set))
. Here, set
is specified
as one of C_
, R_
, Q_
, Z_
, N_
, or an expression
constructed with the set operations, such as union
, intersect
, or minus
. set
also can
be a function of the Type
library, for example, Type::Real
, Type::Integer
, Type::PosInt
, and so
on.
Do not use the syntaxes calculation assumingAlso (expr
in set)
(or its equivalent _assumingAlso(calculation,
expr in set)
) and calculation assumingAlso condition
(or
its equivalent _assumingAlso(calculation, condition)
)
for nonscalar expr
.
Solve this equation without any assumptions on the variable x
:
solve(x^5  x, x)
Suppose your computations deal with real numbers only. In this
case, use the assume
function
to set the permanent assumption that x
is real:
assume(x in R_)
If you solve the same equation now, you will get three real solutions:
solve(x^5  x, x)
To get only nonzero solutions for this particular equation,
use assumingAlso
to temporarily add the corresponding
assumption:
solve(x^5  x, x) assumingAlso x <> 0
After solving this equation, MuPAD^{®} discards the temporary assumption, but keeps the permanent one:
getprop(x)
If you already use a permanent assumption and want to add a
temporary assumption on the same object, do not use assuming
. It temporarily
overwrites the permanent assumption:
assume(x in Z_): solve(x^3  (44*x^2)/3 + (148*x)/3  80/3 = 0, x) assuming x < 5
Instead, use assumingAlso
:
solve(x^3  (44*x^2)/3 + (148*x)/3  80/3 = 0, x) assumingAlso x < 5
If assumptions contain linear equations with one variable, assumingAlso
solves
the equations, inserts the solutions into the expression, and then
evaluates the expression:
a^2 + 1 assumingAlso a  2 = 1;
assume
and assumeAlso
do
not solve equations:
assumeAlso(a  2 = 1) ; a^2 + 1

Any MuPAD command or expression that you want to evaluate under the temporary assumption. 

Equality, inequality, element of relation, or Boolean combination
(with the operators 

Identifier, mathematical expression, list, vector, or matrix containing identifiers. If 

Property representing a set of numbers or a set returned by 
assumingAlso
returns the result of evaluating calculation
.
assume
 assumeAlso
 assuming
 getprop
 is
 property::hasprop
 property::showprops
 unassume