Constants¶
Yacasspecific constants¶

%
previous result
%
evaluates to the previous result on the command line.%
is a global variable that is bound to the previous result from the command line. Using%
will evaluate the previous result. (This uses the functionality offered by the {SetGlobalLazyVariable} command).Typical examples are
Simplify(%)
andPrettyForm(%)
to simplify and show the result in a nice form respectively. Example
In> Taylor(x,0,5)Sin(x) Out> xx^3/6+x^5/120; In> PrettyForm(%) 3 5 x x x   +  6 120
See also

EndOfFile
¶ endoffile marker
End of file marker when reading from file. If a file contains the expression {EndOfFile;} the operation will stop reading the file at that point.
Mathematical constants¶

True
¶ 
False
¶ boolean constants representing true and false
True
andFalse
are typically a result of boolean expressions such as2 < 3
orTrue And False
.
See also
And()
, Or()
, Not()

Infinity
¶ constant representing mathematical infinity
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. ThusInfinity*2
will returnInfinity
, anda < Infinity
will evaluate toTrue
. Example
In> 2*Infinity Out> Infinity; In> 2<Infinity Out> True;

Pi
¶ mathematical constant, \(\pi\)
The constant represents the number π. It is available symbolically as
Pi
or numerically throughN(Pi)
.This is a cached constant which is recalculated only when precision is increased.
 Example
In> Sin(3*Pi/2) Out> 1; In> Pi+1 Out> Pi+1; In> N(Pi) Out> 3.14159265358979323846;
See also

Undefined
¶ constant signifying an undefined result
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. Example
In> 2*Infinity Out> Infinity; In> 0*Infinity Out> Undefined; In> Sin(Infinity); Out> Undefined; In> Undefined+2*Exp(Undefined); Out> Undefined;
See also

GoldenRatio
¶ the golden ratio
The constant represents the golden ratio
\[\phi := \frac{1+\sqrt{5}}{2} = 1.6180339887\ldots\]It is available symbolically as
GoldenRatio
or numerically throughN(GoldenRatio)
.This is a cached constant which is recalculated only when precision is increased.
 Example
In> x:=GoldenRatio  1 Out> GoldenRatio1; 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

Catalan
¶ Catalan’s constant
The constant represents the Catalan’s constant
\[G := \beta(2) = \sum_{n=0}^\infty\frac{1^n}{(2n+1)^2}=0.9159655941\ldots\]It is available symbolically as
Catalan
or numerically throughN(Catalan)
.This is a cached constant which is recalculated only when precision is increased.
 Example
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

gamma
¶ Euler–Mascheroni constant \(\gamma\)
The constant represents the Euler–Mascheroni constant
\[\gamma := \lim_{n\to\infty}\left(\ln(n)+\sum_{k=1}^n\frac{1}{k}\right)=0.5772156649\ldots\]It is available symbolically as
gamma
or numerically throughN(gamma)
.This is a cached constant which is recalculated only when precision is increased.
Note
Euler’s \(\Gamma(x)\) function is the capitalized
Gamma()
in yacas. Example
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