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 |
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.
In> 2*Infinity Out> Infinity; In> 2<Infinity Out> True; |
Pi |
This is a "cached constant" which is recalculated only when precision is increased.
In> Sin(3*Pi/2) Out> -1; In> Pi+1 Out> Pi+1; In> N(Pi) Out> 3.14159265358979323846; |
Undefined |
Most functions also return Undefined when evaluated on it.
In> 2*Infinity Out> Infinity; In> 0*Infinity Out> Undefined; In> Sin(Infinity); Out> Undefined; In> Undefined+2*Exp(Undefined); Out> Undefined; |
GoldenRatio |
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).
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; |
Catalan |
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.
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; |
gamma |
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.
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; |