Abs(n)
Description
Calculates the absolute value of n.
Returns
Returns a positive number of the same magnitude as the value of n.
Argument
n
Any number.
Ceiling(n)
Description
If n is not an integer, rounds n to the next highest integer.
Returns
Returns the smallest integer greater than or equal to n.
Argument
n
Any number.
Derivative(expr, {name, ...}, ...)
Description
Calculates the derivative of the expr expression with respect to name.
Returns
Returns the derivative.
Arguments
expr
Any expression. Indirect arguments (for example, Name Expr, Expr, Eval) are supported.
name
Can be a single variable or a list of variables.
Note
Adding an additional variable (Derivative(expr, name, name2)) takes the second derivative.
Floor(n)
Description
If n is not an integer, rounds n to the next lowest integer.
Returns
Returns the largest integer less than or equal to n.
Argument
n
Any number.
Examples
Floor( 2.7 );
2
Floor( –.5 );
–1
Integrate(expr, varname, lowLimit, upLimit, <<Tolerance(1e-10), <<StoreInfo({list }), <<StartingValue(val))
Description
Integrates an expression with respect to a scalar value, using the adaptive quadrature method from Gander and Gautschi (2000).
Arguments
expr an expression that defines the integrand.
varname the name of the variable of integration. If this variable contains a value, that value specifies a starting value that is used as a typical value to improve the accuracy of the integral.
lowLimit specifies the lower limit of integration. To specify negative infinity as the lower limit of integration, set this to missing.
upLimit specifies the upper limit of integration. To specify positive infinity as the upper limit of integration, set this to missing.
StoreInfo saves diagnostics of the numerical integration routine to the argument of StoreInfo().
StartingValue specifies a starting value that is used as a typical value to improve the accuracy of the integral.
Invert Expr(expr, name)
Description
Attempts to unfold expr around name.
Mod()
Modulo(number, divisor)
Mod(number, divisor)
Description
Returns the remainder when number is divided by divisor.
Examples
Modulo( 6, 5 );
1
Normal Integrate(muVector, sigmaMatrix, expr, x, nStrata, nSim)
Description
Returns the result of radial-spherical integration for smooth functions of multivariate, normally distributed variables.
Arguments
muVector
A vector.
sigmaMatrix
A matrix.
expr
An expression in terms of the variable x.
x
The variable used in the expression expr.
nStrata
Number of strata.
nSim
Number of simulations.
Num Deriv(f(x,...), <parnum=1>)
Description
Returns the numerical derivative of the f( x,... ) function with respect to one of its arguments. You can specify that argument as the second argument in the Num Deriv function. If no second argument is specified, the derivative is taken with respect to the function's first argument. The derivative is evaluated using numeric values specified in the f( x,... ) function expression.
Notes
The Num Deriv() function might appear not to produce the correct results as seen here:
x = 3;
n = Num Deriv( 3 * x ^ 2 );
// 9.00000000001455
The preceding usage is not correct. The function was designed to be used in the Nonlinear platform to differentiate functions for which it does not know the analytic derivatives. The proper usage takes the following form:
x = 3;
f = Function( {x}, 3 * x ^ 2 );
n = Num Deriv( f( x ), 1 );
// 18.000029999854
Num Deriv2(f(x,...))
Description
Returns the numerical second derivative of the f( x,... ) function with respect to x. The derivative is evaluated using numeric values specified in the f( x,... ) function expression.
Round(n, places)
Description
Rounds n to number of decimal places given.
Simplify Expr(expr(expression))
Simplify Expr(nameExpr(global))
Description
Algebraically simplifies an expression