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gfun

  

listtoalgeq

  

find an algebraic equation satisfied by a generating function

  

seriestoalgeq

  

find an algebraic equation satisfied by a series

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

listtoalgeq(l, y(x), [typelist])

seriestoalgeq(s, y(x), [typelist])

Parameters

l

-

list

y

-

name; function name

x

-

name; variable of the function y

typelist

-

(optional) list of generating function types. The default is 'ogf','egf'. For a complete list of types, see gftypes.

s

-

series

Description

• 

The listtoalgeq(l, y(x), [typelist]) command computes a polynomial equation in y and x satisfied by the generating function y(x) of the expressions in l.  The generating function is one of the types specified by typelist, for example, ordinary (ogf) or exponential (egf). For a complete list of available generating function types, see gftypes.

• 

The seriestoalgeq(s, y(x), [typelist]) command computes a polynomial equation in y and x satisfied by the generating function y(x) of the expressions in s.  The generating function is one of the types specified by typelist, for example, ordinary (ogf) or exponential (egf).  For a complete list of available generating function types, see gftypes.

• 

If typelist contains more than one element, these types are considered in the order that they are listed.

• 

If typelist is not specified, the default typelist, 'ogf','egf', is used.  The function returns a list whose first element is the polynomial in y(x) and x that was found.  The second element is the generating function type to which the first element corresponds.

• 

In the implementation, the maximal degree of y is 6 and the maximum degree of the coefficients is 3. You can change these degree specifications by modifying the variables gfun['maxdegeqn'] and gfun['maxdegcoeff'].

• 

If sufficiently many terms are specified and no solution is found, then the generating function does not satisfy any algebraic equation of degree less than or equal to gfun['maxdegeqn'] with coefficients of degree less than or equal to gfun['maxdegcoeff'].

Examples

withgfun:

l1,1,2,5,14,42,132,429,1430,4862,16796,58786:

listtoalgeql,yx

1+yxxyx2,ogf

(1)

sseries114x,x,9

s:=2x+2x2+4x3+10x4+28x5+84x6+264x7+858x8+Ox9

(2)

seriestoalgeqs,yx

4x2yx+yx2,ogf

(3)

See Also

gfun

gfun/gftypes

gfun/parameters

series

 


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