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Exponential Expressions
An exponential expression is an expression made up (mainly) of exponential functions. UltimaCalc Algebra provides some functions for working with such expressions. The automatic simplifier may modify such expressions when it looks at them.
Examples:
exp(0) is automatically simplified to 1
exp(a + b)^2 is automatically simplified to exp(2*a + 2*b).
expexpand
This function converts exponential functions that have arguments that are sums, or are integer products, into exponential expressions using functions which have arguments that are neither sums nor integer products.
Examples:
expexpand(exp(a + b)) returns exp(a)*exp(b)
expexpand(exp(3*x)) returns exp(x)^3
expexpand(exp(3*x) / exp(2*y)) returns exp(x)^3 / exp(y)^2
expcontract
This function converts a product of exponential functions into a sum of exponential functions with different arguments.
Examples:
expcontract(exp(3*x)/exp(2*y)) returns exp(3*x - 2*y)
expcontract(exp(x + y)^3) returns exp(3*x + 3*y)
expsimp
This function uses expcontract to simplify an exponential expression.
Examples:
expsimp(exp(3*x + y)^3*exp(-2*x + y)) returns exp(7*x + 4*y)
expsimp(exp(x + y)*exp(-x - y)) returns 1