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gfun

  

algeqtoseries

  

Puiseux expansions of algebraic functions

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

algeqtoseries(pol, x, y, order, pos_slopes)

Parameters

pol

-

polynomial equation in two variables x and y

x

-

name; variable name

y

-

name; variable name

order

-

positive integer order of the expansions

pos_slopes

-

(optional) only branches tending to 0 are computed

Description

• 

The algeqtoseries(pol, x, y, order) command computes an expansion of all the branches at the origin.  The equation polx,y=0 defines a multivalued function y(x).

• 

If pos_slopes is specified, only those branches tending to 0 are computed. Note that this function is not designed to compute expansions to a large order. In this case, the differential equation should be used.  For more information, see algeqtodiffeq.

Examples

withgfun:

Pyx2x3y2+x6y5

Px6y5x3y2x2+y

(1)

algeqtoseriesP,x,y,4

x2+Ox6,RootOf_Z4+1x32RootOf_Z4+124+Ox

(2)

algeqtoseriesP,x,y,10,true

x2+x7+Ox12

(3)

See Also

gfun

gfun/parameters

RootOf

solve/series