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gfun

  

algfuntoalgeq

  

find a polynomial equation satisfied by an algebraic function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

algfuntoalgeq(expr, y(z), ini, typ)

Parameters

expr

-

algebraic or radical function in z

y

-

name; holonomic function name

z

-

name; variable of the holonomic function y

ini

-

(optional) set; specify initial conditions for the resulting polynomial equation

typ

-

(optional) 'algebraic' or 'rational'; specify the type of coefficients for the polynomial equation

Description

• 

The algfuntoalgeq(expr, y(z)) command returns a polynomial in y and z that has expr as a root. The polynomial is not necessarily minimal.

• 

If ini is specified, it is assigned a set of initial conditions for the polynomial to specify which branch is indicated (if possible).

• 

If typ is specified as 'rational', the coefficients of the polynomial are of type rational or type name. This is particularly useful for finding a polynomial for an algebraic number.  The default is 'rational'.

  

If typ is specified as 'algebraic' the coefficients are algebraic numbers. This option can be used with algebraicsubs.

Examples

withgfun:

algfuntoalgeqaRootOf_Z5+1x23,yx

a15x10+y15

(1)

algfuntoalgeqaRootOf_Z5+1x23,yx,'algebraic'

RootOf_Z5+13a3x2y3

(2)

algfuntoalgeq513+3723,yx

y93984y6+5112147y32342039552

(3)

algfuntoalgeq1+RootOf_Z3+1x,yx,ini

x3y3+3y23y+1

(4)

ini

y0=1,Dy0=RootOf_Z3+1,D2y0=0

(5)

See Also

gfun

gfun/parameters

gfun[algebraicsubs]

RootOf

 


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