(directly go to documentation on : Infinity, Pi, Undefined, GoldenRatio, Catalan, gamma. )

26. Mathematical constants

Infinity constant representing mathematical infinity
Pi mathematical constant, pi
Undefined constant signifying an undefined result
GoldenRatio the Golden Ratio
Catalan Catalan's Constant
gamma Euler's constant gamma


Infinity -- constant representing mathematical infinity

Standard library
Calling format:
Infinity

Description:
Infinity represents infinitely large values. It can be the result of certain calculations.

Note that for most analytic functions Yacas understands Infinity as a positive number. Thus Infinity*2 will return Infinity, and a < Infinity will evaluate to True.

Examples:
In> 2*Infinity
Out> Infinity;
In> 2<Infinity
Out> True;


Pi -- mathematical constant, pi

Standard library
Calling format:
Pi

Description:
Pi symbolically represents the exact value of pi. When the N() function is used, Pi evaluates to a numerical value according to the current precision. It is better to use Pi than N(Pi) except in numerical calculations, because exact simplification will be possible.

This is a "cached constant" which is recalculated only when precision is increased.

Examples:
In> Sin(3*Pi/2)
Out> -1;
In> Pi+1
Out> Pi+1;
In> N(Pi)
Out> 3.14159265358979323846;

See also:
Sin , Cos , N , CachedConstant .


Undefined -- constant signifying an undefined result

Standard library
Calling format:
Undefined

Description:
Undefined is a token that can be returned by a function when it considers its input to be invalid or when no meaningful answer can be given. The result is then "undefined".

Most functions also return Undefined when evaluated on it.

Examples:
In> 2*Infinity
Out> Infinity;
In> 0*Infinity
Out> Undefined;
In> Sin(Infinity);
Out> Undefined;
In> Undefined+2*Exp(Undefined);
Out> Undefined;

See also:
Infinity .


GoldenRatio -- the Golden Ratio

Standard library
Calling format:
GoldenRatio

Description:
These functions compute the "golden ratio"

phi<=>1.6180339887<=>(1+Sqrt(5))/2.

The ancient Greeks defined the "golden ratio" as follows: If one divides a length 1 into two pieces x and 1-x, such that the ratio of 1 to x is the same as the ratio of x to 1-x, then 1/x<=>1.618... is the "golden ratio".

The constant is available symbolically as GoldenRatio or numerically through N(GoldenRatio). This is a "cached constant" which is recalculated only when precision is increased. The numerical value of the constant can also be obtained as N(GoldenRatio).

Examples:
In> x:=GoldenRatio - 1
Out> GoldenRatio-1;
In> N(x)
Out> 0.6180339887;
In> N(1/GoldenRatio)
Out> 0.6180339887;
In> V(N(GoldenRatio,20));

CachedConstant: Info: constant GoldenRatio is
being recalculated at precision 20 
Out> 1.6180339887498948482;

See also:
N , CachedConstant .


Catalan -- Catalan's Constant

Standard library
Calling format:
Catalan

Description:
These functions compute Catalan's Constant Catalan<=>0.9159655941.

The constant is available symbolically as Catalan or numerically through N(Catalan) with N(...) the usual operator used to try to coerce an expression in to a numeric approximation of that expression. This is a "cached constant" which is recalculated only when precision is increased. The numerical value of the constant can also be obtained as N(Catalan). The low-level numerical computations are performed by the routine CatalanConstNum.

Examples:
In> N(Catalan)
Out> 0.9159655941;
In> DirichletBeta(2)
Out> Catalan;
In> V(N(Catalan,20))

CachedConstant: Info: constant Catalan is
being recalculated at precision 20
Out> 0.91596559417721901505;

See also:
N , CachedConstant .


gamma -- Euler's constant gamma

Standard library
Calling format:
gamma

Description:
These functions compute Euler's constant gamma<=>0.57722...

The constant is available symbolically as gamma or numerically through using the usual function N(...) to get a numeric result, N(gamma). This is a "cached constant" which is recalculated only when precision is increased. The numerical value of the constant can also be obtained as N(gamma). The low-level numerical computations are performed by the routine GammaConstNum.

Note that Euler's Gamma function Gamma(x) is the capitalized Gamma in Yacas.

Examples:
In> gamma+Pi
Out> gamma+Pi;
In> N(gamma+Pi)
Out> 3.7188083184;
In> V(N(gamma,20))

CachedConstant: Info: constant gamma is being
  recalculated at precision 20 
GammaConstNum: Info: used 56 iterations at
  working precision 24 
Out> 0.57721566490153286061;

See also:
Gamma , N , CachedConstant .