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type/monomial

check for a monomial

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

type(m, monomial)

type(m, monomial(K))

type(m, monomial(K, v))

Parameters

m

-

any expression

K

-

(optional) type name for the coefficient domain

v

-

(optional) variable(s)

Description

• 

The call type(m, monomial(K, v)) checks to see if m is a monomial in the variable(s) v over the coefficient domain K, where v is either an indeterminate or a list or set of indeterminates.

• 

A monomial is defined to be a polynomial in v which syntactically is the product of powers of indeterminates in v with nonnegative exponents, times a coefficient c free of the indeterminates in v, i.e., it is of the form cx1e1xkek, where v=x1,,xk, e1,,ek, and c does not contain any of the xi. Note that the coefficient c may be a sum. This function returns true if m is such a monomial, and false otherwise.

• 

If v is omitted, it is taken to be the set of all indeterminates appearing in m, that is, it checks if m is a monomial in all of its variables.

• 

The domain specification K should be a type name, such as rational or algebraic.  If K is specified, then this function will check that the coefficients of m come from the domain K.  If the coefficient domain K is omitted, then only coefficients of type constant are allowed.

Examples

typesin1x2,monomial

true

(1)

typesin1x2,monomial

false

(2)

type1+yx2,monomialanything,y

false

(3)

type1+yx2,monomialanything,x

true

(4)

typesinxy,monomialanything,y

true

(5)

The following is not syntactically a monomial.

fx+sqrt2x

fx+2x

(6)

typef,monomialradalgnum

false

(7)

typecollectf,x,monomialradalgnum

true

(8)

typecollectf,x,monomialrational

false

(9)

Any constant is a monomial.

type1+sqrt2,monomial

true

(10)

Compatibility

• 

The type/monomial command was updated in Maple 2020.

See Also

indets

type

type/polynom