## File: const.chapt.txt

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yacas 1.3.6-2
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234` `````` Yacas-specific 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> x-x^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 --- end-of-file 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 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 \$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)}. *E.G. 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 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 low-level 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 low-level 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 ``````