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singular

find singularities of an expression

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

singular(expr)

singular(expr, vars, range)

Parameters

expr

-

algebraic expression

vars

-

(optional) variable or set of variables

range

-

(optional) a numeric range, to return only the singularities inside it

Description

• 

The function singular outputs an expression sequence representing the singularities  of expr.

• 

If two arguments are given and the second argument, vars, is a name or a set of them, the expression, expr, is considered to be a function in vars. If singular is called with only one argument, then expr is considered as a function in the variables returned by the command indets(expr, name).

• 

If a numeric range is given as second or third argument, only the singularities found within this range, if any, will be returned.

• 

Each singular point is represented by a set of equations, the left-hand side of the equations being the variables.

• 

The singular function will return non-removable as well as removable singularities.  For instance, x2sinx2 will report a singularity at x=2.

• 

The power of singular to find singularities is basically that of solve. For example, some zeros that solve cannot find may result in singularities that singular will not find.

• 

The singular function may return expressions prefixed by _Z or _N, representing the integers and positive integers, respectively.

Examples

singularxy+1xy,x

x=0,x=∞,x=∞

(1)

singularlnxx21

x=1,x=0,x=1

(2)

singularxxy

x=y,y=y

(3)

singulartanx

x=12π+_Z1~π

(4)

singulartanx,1..10

x=12π,x=32π,x=52π

(5)

The range must have endpoints that are of numeric type. Otherwise an error is returned.

singulartanx,1..π

Error, invalid input: singular expects its 2nd argument, vars, to be of type {name, set(name), numeric .. numeric}, but received 1 .. Pi

singulartanx,1..evalfπ

x=12π

(6)

singularΨ1x

x=0,x=∞,x=∞,x=1_N1~1

(7)

See Also

residue

roots

Roots

solve

 


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