1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234

Yacasspecific constants
*CMD %  previous result
*CORE
*CALL
%
*DESC
{%} 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(%)} and {PrettyForm(%)} to simplify and show the result in a nice
form respectively.
*E.G.
In> Taylor(x,0,5)Sin(x)
Out> xx^3/6+x^5/120;
In> PrettyForm(%)
3 5
x x
x   + 
6 120
*SEE SetGlobalLazyVariable
*CMD True  boolean constant representing true
*CMD False  boolean constant representing false
*CORE
*CALL
True
False
*DESC
{True} and {False} are typically a result
of boolean expressions such as {2 < 3} or {True And False}.
*SEE And, Or, Not
*CMD EndOfFile  endoffile marker
*CORE
*CALL
EndOfFile
*DESC
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
*CMD Infinity  constant representing mathematical infinity
*STD
*CALL
Infinity
*DESC
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}.
*E.G.
In> 2*Infinity
Out> Infinity;
In> 2<Infinity
Out> True;
*CMD Pi  mathematical constant, $pi$
*STD
*CALL
Pi
*DESC
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.
*E.G.
In> Sin(3*Pi/2)
Out> 1;
In> Pi+1
Out> Pi+1;
In> N(Pi)
Out> 3.14159265358979323846;
*SEE Sin, Cos, N, CachedConstant
*CMD Undefined  constant signifying an undefined result
*STD
*CALL
Undefined
*DESC
{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.
*E.G.
In> 2*Infinity
Out> Infinity;
In> 0*Infinity
Out> Undefined;
In> Sin(Infinity);
Out> Undefined;
In> Undefined+2*Exp(Undefined);
Out> Undefined;
*SEE Infinity
*CMD GoldenRatio  the Golden Ratio
*STD
*CALL
GoldenRatio
*DESC
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 $1x$, such that the ratio of 1 to $x$ is the same as the ratio of $x$ to $1x$, 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)}.
*E.G.
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 N, CachedConstant
*CMD Catalan  Catalan's Constant
*STD
*CALL
Catalan
*DESC
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 lowlevel numerical computations are performed by the routine {CatalanConstNum}.
*E.G.
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 N, CachedConstant
*CMD gamma  Euler's constant $gamma$
*STD
*CALL
gamma
*DESC
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 lowlevel numerical computations are performed by the routine {GammaConstNum}.
Note that Euler's Gamma function $Gamma(x)$ is the capitalized {Gamma} in Yacas.
*E.G.
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 Gamma, N, CachedConstant
