Built-in functions

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


All Functions

For Input of Complex and Real Numbers

Current angle unit is indicated by last letter on button for each function. E.g.: sinr, cosr, tanr for radians.
{inverse} sine, cosine, tangentsin(x), cos(x), tan(x), { asin(x), acos(x), atan(x) }
hyperbolic {inverse} sine, cosine, tangentsinh(x), cosh(x), tanh(x), { asinh(x), acosh(x), atanh(x) }
square rootsqrt(x) or √(x)
logarithms: natural, base 10ln(x), log(x)
absolute value, magnitudeabs(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 angleangle(x)
complex conjugateconj(x)
imaginary partimag(x)
real partreal(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)


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(.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


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