solve a single polynomial for one variable - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : SolveTools : SolveTools/Polynomial

SolveTools[Polynomial] - solve a single polynomial for one variable

Calling Sequence

Polynomial( f, x, ...)

Parameters

f

-

polynomial in x

x

-

variable

options

-

(optional) equation(s) of the form keyword = value

Description

• 

Solve for a polynomial in x.  Polynomial uses factor,  compoly, and explicit root formulae to write the roots explicitly where possible.

• 

If not possible, a list of indexed RootOf will be returned.

• 

The behavior of Polynomial is controlled by the option explicit, or by the environment variable _EnvExplicit.  In all cases the option, if specified, overrides the environment variable. has three possible behaviors depending on the option

• 

By default (if the option explicit not specified and _EnvExplicit is not set) explicit roots are calculated for polynomials of degree 2 and 3 but not for polynomials higher degree (unless they factor or decompose). Implicit roots that do not involve non-numeric symbols are given as indexed RootOfs.

• 

If explicit is specified as an option (or _EnvExplicit=true) then explicit roots are computed when possible.

• 

If explicit=false is specified as an option (or _EnvExplicit=false) then no attempt is made to compute explicit roots, and unspecialized RootOf expressions are returned.

• 

The domain option can be used to restrict the roots returned. Using domain=real or domain=integer will return only real or integer roots respectively.  domain=absolute will return all the roots and domain=rational will return the roots which lie in the same field  as the coefficients of f in the same way as roots; in particular if f is a polynomial with integer coefficients, domain=rational will return only the roots which are rational numbers.  domain=parametric will return a piecewise expression giving a discussion of different cases.

• 

If the option dropmultiplicity is specified, only one copy of each root is returned.

Examples

withSolveTools:

Polynomial0,x

x

(1)

Polynomial1,x

(2)

Polynomialx2,x

0,0

(3)

Polynomialx21,x

1,1

(4)

Polynomialx2+1,x,explicit=false

RootOf_Z2+1,label=_L1

(5)

Polynomialx5+2x+1,x

RootOf_Z5+2_Z+1,index=1,RootOf_Z5+2_Z+1,index=2,RootOf_Z5+2_Z+1,index=3,RootOf_Z5+2_Z+1,index=4,RootOf_Z5+2_Z+1,index=5

(6)

Polynomialx5+2x+1,x,explicit=false

RootOf_Z5+2_Z+1,label=_L2

(7)

f1:=expandx14z4z1z=x3+x|z4z1z=x3+x:

Polynomialf1,x,domain=integer

1,1,1,1

(8)

Polynomialf1,x,domain=integer,dropmultiplicity

1

(9)

Polynomialf1,x,domain=rational

1,1,1,1

(10)

Polynomialf1,x,domain=real

RootOf_Z12+4_Z10+6_Z8+4_Z6+_Z4_Z3_Z1,0.5542396981,RootOf_Z12+4_Z10+6_Z8+4_Z6+_Z4_Z3_Z1,0.7679130647,1,1,1,1

(11)

SolveTools:-Polynomialax2b+ax+b,x

ba,1

(12)

Polynomialax2b+ax+b,x,domain=parametric

{{xb=01otherwisea=01,baotherwise

(13)

See Also

compoly, factor, roots, solve, SolveTools


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam