hasSymType

Determine whether symbolic object contains specific type

Syntax

TF = hasSymType(symObj,type)

TF = hasSymType(symObj,funType,vars)

Description

TF = hasSymType(symObj,type) returns logical 1 (true) if the symbolic object symObj contains a subobject of type type, and logical 0 (false) otherwise. The input type must be a case-sensitive string scalar or character vector, and it can include a logical expression.

TF = hasSymType(symObj,funType,vars) checks whether symObj contains an unassigned symbolic function that depends on the variables vars.

You can set the function type funType to 'symfunOf' or 'symfunDependingOn'. For example, syms f(x); hasSymType(f,'symfunOf',x) returns logical 1.

Examples

Symbolic Variable, Constant, or Number

Determine whether a symbolic expression contains a symbolic variable, constant, or number of a specific type.

Create a symbolic expression.

syms x;
expr = sym('1/2') + 2*pi + x

expr = 
$$x+2\hspace{0.17em}\pi +\frac{1}{2}$$

Check whether expr contains a symbolic variable of type 'variable'.

TF = hasSymType(expr,'variable')

TF = logical
   1

Check whether expr contains a symbolic constant of type 'constant'.

TF = hasSymType(expr,'constant')

TF = logical
   1

Check whether expr contains a symbolic number of type 'integer'.

TF = hasSymType(expr,'integer')

TF = logical
   1

Check whether expr contains a symbolic number of type 'integer | real'.

TF = hasSymType(expr,'integer | real')

TF = logical
   1

Check whether expr contains a symbolic number of type 'complex'.

TF = hasSymType(expr,'complex')

TF = logical
   0

Symbolic Function or Operator

Determine whether a symbolic equation contains a symbolic function or operator of a specific type.

Create a symbolic equation.

syms f(x) n
eq = f(x^n) + int(f(x),x) + vpa(2.7) == 1i

eq = 
$$f\left(x^n\right)+\int f\left(x\right)\mathrm{d}x+2.7=\mathrm{i}$$

Check whether eq contains the symbolic function 'f'.

TF = hasSymType(eq,'f')

TF = logical
   1

Check whether eq contains an unassigned symbolic function of type 'symfun'.

TF = hasSymType(eq,'symfun')

TF = logical
   1

Check whether eq contains a symbolic math function of type 'int'.

TF = hasSymType(eq,'int')

TF = logical
   1

Check whether eq contains an operator of type 'power'.

TF = hasSymType(eq,'power')

TF = logical
   1

Function of Multiple Variables

Create a symbolic function of multiple variables using syms.

syms f(x,y,z)
g = f + x*y + pi

g(x, y, z) = $$\pi +x\hspace{0.17em}y+f\left(x,y,z\right)$$

Check whether g depends on the exact variable x using 'symfunOf'.

TF = hasSymType(g,'symfunOf',x)

TF = logical
   0

Check whether g depends on the exact sequence of variables [x y z] using 'symfunOf'.

TF = hasSymType(g,'symfunOf',[x y z])

TF = logical
   1

Check whether g has any dependency on the variables [y x] using 'symfunDependingOn'.

TF = hasSymType(g,'symfunDependingOn',[y x])

TF = logical
   1

Input Arguments

symObj — Symbolic objects

symbolic expressions | symbolic functions | symbolic variables | symbolic numbers | symbolic units

Symbolic objects, specified as symbolic expressions, symbolic functions, symbolic variables, symbolic numbers, or symbolic units.

type — Symbolic types

scalar string | character vector

Symbolic types, specified as a case-sensitive scalar string or character vector. The input type can contain a logical expression. The value options follow.

Symbolic Type Category	String Values	Examples Returning Logical 1
numbers	'integer' — integer numbers 'rational' — rational numbers 'vpareal' — variable-precision floating-point real numbers 'complex' — complex numbers 'real' — real numbers, including 'integer', 'rational', and 'vpareal' 'number' — numbers, including 'integer', 'rational', 'vpareal', 'complex', and 'real'	hasSymType(sym(2),'integer') hasSymType(sym(1/2),'rational') hasSymType(vpa(0.5),'vpareal') hasSymType(vpa(1i),'complex') hasSymType([sym(1/2) vpa(0.5)],'real') hasSymType([vpa(1i) sym(1/2)],'number')
constants	'constant' — symbolic mathematical constants, including 'number'	hasSymType([sym(pi) vpa(1i)],'constant')
symbolic math functions	'vpa', 'sin', 'exp', and so on — symbolic math functions in symbolic expressions	hasSymType(vpa(sym(pi)),'vpa')
unassigned symbolic functions	'F', 'g', and so on — function name of an unassigned symbolic function 'symfun' — unassigned symbolic functions	syms F(x); hasSymType(F(x+2),'F') syms g(x); hasSymType(g(x),'symfun')
arithmetic operators	'plus' — addition operator + and subtraction operator - 'times' — multiplication operator * and division operator / 'power' — power or exponentiation operator ^ and square root operator sqrt	syms x y; hasSymType(2*x + y,'plus') syms x y; hasSymType(x*y,'times') syms x y; hasSymType(x^(y+2),'power')
variables	'variable' — symbolic variables	hasSymType(sym('x'),'variable')
units	'units' — symbolic units	hasSymType(symunit('m'),'units')
expressions	'expression' — symbolic expressions, including all of the preceding symbolic types	hasSymType(sym('x')+1,'expression')
logical expressions	'or' — logical OR operator | 'and' — logical AND operator & 'not' — logical NOT operator ~ 'xor' — logical exclusive-OR operator xor 'logicalconstant' — symbolic logical constants symtrue and symfalse 'logicalexpression' — logical expressions, including 'or', 'and', 'not', 'xor', symtrue and symfalse	syms x y; hasSymType(x|y,'or') syms x y; hasSymType(x&y,'and') syms x; hasSymType(~x,'not') syms x y; hasSymType(xor(x,y),'xor') hasSymType(symtrue,'logicalconstant') syms x y; hasSymType(~x|y,'logicalexpression')
equations and inequalities	'eq' — equality operator == 'ne' — inequality operator ~= 'lt' — less-than operator < or greater-than operator > 'le' — less-than-or-equal-to operator <= or greater-than-or-equal-to operator >= 'equation' — symbolic equations and inequalities, including 'eq', 'ne', 'lt', and 'le'	syms x; hasSymType(x==2,'eq') syms x; hasSymType(x~=1,'ne') syms x; hasSymType(x>0,'lt') syms x; hasSymType(x<=2,'le') syms x; hasSymType([x>0 x~=1],'equation')
unsupported symbolic types	'unsupported' — unsupported symbolic types

funType — Function type

'symfunOf' | 'symfunDependingOn'

Function type, specified as 'symfunOf' or 'symfunDependingOn'.

• 'symfunOf' checks whether symObj contains an unassigned symbolic function that depends on the exact sequence of variables specified by the array vars. For example, syms f(x,y); hasSymType(f,'symfunOf',[x y]) returns logical 1.

• 'symfunDependingOn' checks whether symObj contains an unassigned symbolic function that has a dependency on the variables specified by the array vars. For example, syms f(x,y); hasSymType(f,'symfunDependingOn',[y x]) returns logical 1.

vars — Input variables

symbolic variables | symbolic array

Input variables, specified as symbolic variables or a symbolic array.

Tips

• To check whether a symbolic expression contains a particular subexpression, use the has function.