in

Express Condition on Symbolic Variable or Expression

The syntax in(x,type) expresses the condition that x is of the specified type. Express the condition that x is of type Real.

syms x
cond = in(x,'real')

cond =
in(x, 'real')

Evaluate the condition using isAlways. Because isAlways cannot determine the condition, it issues a warning and returns logical 0 (false).

isAlways(cond)

Warning: Unable to prove 'in(x, 'real')'.

ans =
  logical
     0

Assume the condition cond is true using assume, and evaluate the condition again. The isAlways function returns logical 1 (true) indicating that the condition is true.

assume(cond)
isAlways(cond)

ans =
  logical
     1

To use x in further computations, clear its assumption recreating it using syms.

syms x

Express Conditions in Output

Functions such as solve use in in output to express conditions.

Solve the equation sin(x) == 0 using solve. Set the option ReturnConditions to true to return conditions on the solution. The solve function uses in to express the conditions.

syms x
[solx, params, conds] = solve(sin(x) == 0,'ReturnConditions',true)

solx =
pi*k

params =
k

conds =
in(k, 'integer')

The solution is pi*k with parameter k under the condition in(k,'integer'). You can use this condition to set an assumption for further computations. Under the assumption, solve returns only integer values of k.

assume(conds)
k = solve(solx > 0, solx < 5*pi, params)

k =
 1
 2
 3
 4

To find the solutions corresponding to these values of k, use subs to substitute for k in solx.

subs(solx,k)

ans =
   pi
 2*pi
 3*pi
 4*pi

Clear the assumption on k to use it in further computations.

assume(params, 'clear')

Test if Elements of Symbolic Matrix Are Rational

Create symbolic matrix M.

syms x y z
M = sym([1.22 i x; sin(y) 3*x 0; Inf sqrt(3) sym(22/7)])

M =
[  61/50,      1i,    x]
[ sin(y),     3*x,    0]
[    Inf, 3^(1/2), 22/7]

Use isAlways to test if the elements of M are rational numbers. The in function acts on M element-by-element. Note that isAlways returns logical 0 (false) for statements that cannot be decided and issues a warning for those statements.

in(M,'rational')

ans =
[  in(61/50, 'rational'),      in(1i, 'rational'),    in(x, 'rational')]
[ in(sin(y), 'rational'),     in(3*x, 'rational'),    in(0, 'rational')]
[    in(Inf, 'rational'), in(3^(1/2), 'rational'), in(22/7, 'rational')]

isAlways(in(M,'rational'))

Warning: Unable to prove 'in(sin(y), 'rational')'.
Warning: Unable to prove 'in(3*x, 'rational')'.
Warning: Unable to prove 'in(x, 'rational')'.
ans =
  3×3 logical array
   1   0   0
   0   0   1
   0   0   1