# EvalBuilt-in functions

This document applies to Eval, Eval Graph, Plottron, and Eval for Windows.

### For Input of Complex and Real Numbers

 {inverse} sine, cosine, tangent sin(x), cos(x), tan(x), { asin(x), acos(x), atan(x) } hyperbolic {inverse} sine, cosine, tangent sinh(x), cosh(x), tanh(x), { asinh(x), acosh(x), atanh(x) } square root sqrt(x) or √(x) logarithms: natural, base 10 ln(x), log(x) exponential exp(x) absolute value, magnitude abs(x) store expression sto(expr,var) e.g.: `sto(1+1,X)` var must be a user-defined variable.

### For Input of Complex Numbers Only

 polar angle angle(x) complex conjugate conj(x) imaginary part imag(x) real part real(x)

### For Input of Real Numbers Only

#### any root

Syntax: yyroot(x) or nⁿ√(x)
3ⁿ√(-27) = -3
2yroot(64) = 8

#### any logarithm

Syntax: logx(x,y)
logx(2,64) = 6

• x Base (Cannot be 0, negative, or 1)
• y Number (Cannot be 0, negative)

#### random

Syntax: random
Returns positive pseudo-random number less than 1.

#### factorial, gamma

Syntax: x!
170! = 7.25741561538004×10306
3.5! = 11.631728396567476
x must be positive and less than or equal to 170.
If x is not an integer, returns gamma function for x + 1.

#### numerical derivative (symmetric difference quotient)

Syntax: diffq(expr,var,tolerance)
deriv(expr,var,tolerance) (Older versions)
diffq(X^2,X,.01) = 9.999999999999787 (X is 5)
Returns an approximative derivative using the symmetric difference quotient.

• expr The expression to evaluate.
• var The variable to change.
• tolerance Default is 1E-3, specify 0 for default.

#### numerical derivative

Syntax: nderiv(expr,var)
nderiv(X^2,X) = 10 (X is 5)
Returns the numerical value of the derivative of a function at the value of var.

• expr The expression to evaluate.
• var The variable to change.

#### numerical integral

Syntax: integ(expr,var,min,max)
integ(X^2,X,0,1) = 0.333333333333333

Returns an approximative numerical integral (Legendre-Gauss method).

• expr The expression to evaluate.
• var The variable to change.
• min Lower limit
• max Upper limit

#### function maximization, minimization

Syntax: max(expr,left,right); min(expr,left,right)
max(1/sin(x),-15.64,-12.69) = -14.1371669410663

Returns the value of x where the local extremum occurs between left and right. Assumes function changes with respect to x.

• expr The expression to evaluate.
• left Lower limit
• right Upper limit

#### zero/root finder

Syntax: zero(expr,var,left,right)
zero((x-π/2)(x+3),x,1,3 = 1.5707963267949

Returns the value of var where the root of expr occurs between left and right.

• expr The expression to evaluate.
• var The variable to change.
• left Lower limit
• right Upper limit
Probability Distribution Functions
PDF: Probability Distribution Function
CDF: Cumulative ~
prob: Probability of success prob, 0 ≤ prob ≤ 1 must be true.

#### binomial PDF, CDF

binpdf(trials,prob,x); bincdf(trials,prob,x)
binpdf(6,1/6,2) = 0.2009387600823062
bincdf(23,1/3,10) = 0.8931235700291735

• trials Number of trials (Integer)
• x Position {PDF}, Upper limit {CDF} (Integer less than trials)

#### chi-square PDF, CDF

chipdf(x,df); chicdf(x,df)
chipdf(7.2,9) = 0.10397390837927548
chicdf(18.1,9) = 0.9659690712671236

• x Position {PDF}, Upper limit {CDF}
• df Degrees of freedom (Integer > 0)

#### Gaussian PDF, CDF

normpdf(x,mean,dev); normcdf(lo,hi,mean,dev)
normpdf(.7,.9,.5) = 0.73654028066467
normcdf(0,12,11.5,1) = 0.6914624830813982

• lo, hi {CDF} Lower limit, Upper limit
• x Position {PDF}
• mean Mean (Default 0)
• dev Standard Deviation (Default 1)

#### inverse Gaussian CDF

invnorm(area,mean,dev)
invnorm(.6914624830813982,11.5,1) = 12.000000061941217

• area Area under distribution curve

#### geometric PDF, CDF

geompdf(prob,x); geomcdf(prob,x)
geompdf(.5,2) = 0.25
geomcdf(.5,7) = 0.9921875

• x Position {PDF}, Upper limit {CDF}

#### Poisson PDF, CDF

poispdf(mean,x); poiscdf(mean,x)
poispdf(7.2,10) = 0.07702676555986275
poiscdf(7.2,10) = 0.886676646816657

• mean  Real number > 0

#### Student-t PDF, CDF

studpdf(x,df); studcdf(x,df)
studpdf(7.2,10) = 1.7301686669799527×10-5
studcdf(2,1.4) = 0.3824221618651978

• df Degrees of freedom (Real number > 0)

### For Input of Integers Only

#### binomial coefficient

Syntax: nCr(r)
Example: 64Cr(3) = 41664

#### permutations

Syntax: nPr(r)
Example: 10Pr(3) = 720

#### greatest common divisor

Syntax: gcd(x,y)
Example: gcd(189,18) = 9

#### least common multiple

Syntax: lcm(x,y)
Example: lcm(3,15) = 15