type/linear - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Programming : Data Types : Type Checking : Types : type/linear

type/linear

check for linear functions

type/quadratic

check for quadratic functions

type/cubic

check for cubic functions

type/quartic

check for quartic functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

type(a, linear(v))

type(a, quadratic(v))

type(a, cubic(v))

type(a, quartic(v))

Parameters

a

-

expression

v

-

indeterminate or list or set of indeterminates

Description

• 

Check if the expression a is linear (quadratic, cubic, or quartic) in the indeterminates v.  If v is not specified, this is equivalent to the call type(a, linear(indets(a))) That is, a must be linear (quadratic, cubic, quartic) in all of its indeterminates.

• 

The definition of linear in the indeterminates v is type(a, polynom(anything, v)) and (degree(a, v) = 1) where degree means ``total degree'' in the case of several variables. The definitions for quadratic, cubic and quartic are analogous with degree(a, v) = 2, 3, and 4 respectively.

• 

Note, if you wish to also determine the coefficients, for example, test if a polynomial is of the form ax+b and pick off the coefficients a and b, it is NOT recommended that you use the type test followed by the coeff function. The coeff function requires that the polynomial is expanded (collected) in x, and the type test is only syntactic.  It may return true and a value for a which is in fact mathematically 0.  The ispoly function should be used instead.

Examples

typexy+z,linearx

true

(1)

typexy+z,linear

false

(2)

typexy+z,quadratic

true

(3)

typex4+y,cubicx

false

(4)

typex4+y,quarticx

true

(5)

typeγx+f1+212,linear

true

(6)

typexz+yg2,linearx,y

true

(7)

fa1+aa2ax2+a1+ax1aa

fa1+aa2ax2+a1+ax1aa

(8)

typef,quadraticx

true

(9)

typef,linearx

false

(10)

ispolyf,quadratic,x,'a0','a1','a2'

false

(11)

ispolyf,linear,x,'a0','a1'

true

(12)

a0,a1

a2+1a,a1+a

(13)

See Also

degree

indets

ispoly

polynom

type

type[polynom]