ExpressionToUnivariatePowerSeries(R, FE)¶

expr2ups.spad line 1 [edit on github]

R: Join(GcdDomain, Comparable, RetractableTo Integer, LinearlyExplicitOver Integer)
FE: Join(AlgebraicallyClosedField, TranscendentalFunctionCategory, FunctionSpace R)

This package provides functions to convert functional expressions to power series.

laurent: (FE, Equation FE) -> Any: laurent(f, x = a) expands the expression f as a Laurent series in powers of (x - a).

laurent: (FE, Equation FE, Integer) -> Any: laurent(f, x = a, n) expands the expression f as a Laurent series in powers of (x - a); terms will be computed up to order at least n.

laurent: (FE, Integer) -> Any: laurent(f, n) returns a Laurent expansion of the expression f. Note: f should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least n.

laurent: FE -> Any: laurent(f) returns a Laurent expansion of the expression f. Note: f should have only one variable; the series will be expanded in powers of that variable.

laurent: Symbol -> Any: laurent(x) returns x viewed as a Laurent series.

puiseux: (FE, Equation FE) -> Any: puiseux(f, x = a) expands the expression f as a Puiseux series in powers of (x - a).

puiseux: (FE, Equation FE, Fraction Integer) -> Any: puiseux(f, x = a, n) expands the expression f as a Puiseux series in powers of (x - a); terms will be computed up to order at least n.

puiseux: (FE, Fraction Integer) -> Any: puiseux(f, n) returns a Puiseux expansion of the expression f. Note: f should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least n.

puiseux: FE -> Any: puiseux(f) returns a Puiseux expansion of the expression f. Note: f should have only one variable; the series will be expanded in powers of that variable.

puiseux: Symbol -> Any: puiseux(x) returns x viewed as a Puiseux series.

series: (FE, Equation FE) -> Any: series(f, x = a) expands the expression f as a series in powers of (x - a).

series: (FE, Equation FE, Fraction Integer) -> Any: series(f, x = a, n) expands the expression f as a series in powers of (x - a); terms will be computed up to order at least n.

series: (FE, Fraction Integer) -> Any: series(f, n) returns a series expansion of the expression f. Note: f should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least n.

series: FE -> Any: series(f) returns a series expansion of the expression f. Note: f should have only one variable; the series will be expanded in powers of that variable.

series: Symbol -> Any: series(x) returns x viewed as a series.

taylor: (FE, Equation FE) -> Any: taylor(f, x = a) expands the expression f as a Taylor series in powers of (x - a).

taylor: (FE, Equation FE, NonNegativeInteger) -> Any: taylor(f, x = a) expands the expression f as a Taylor series in powers of (x - a); terms will be computed up to order at least n.

taylor: (FE, NonNegativeInteger) -> Any: taylor(f, n) returns a Taylor expansion of the expression f. Note: f should have only one variable; the series will be expanded in powers of that variable and terms will be computed up to order at least n.

taylor: FE -> Any: taylor(f) returns a Taylor expansion of the expression f. Note: f should have only one variable; the series will be expanded in powers of that variable.

taylor: Symbol -> Any: taylor(x) returns x viewed as a Taylor series.