All Overloaded Functions

The following functions from Base have been overloaded for operations with TPS:

+, -, *, /, ^, ∘, inv, atan, hypot, abs, sqrt, exp, log, sin, cos, 
tan, csc, sec, cot, sinc, sinh, cosh, tanh, csch, sech, coth, asin, 
acos, atan, acsc, asec, acot, asinh, acosh, atanh, acsch, asech, 
acoth, zero, zeros, one, ones, real, imag, conj, angle, complex, 
promote_rule, getindex, setindex!, ==, <, >, <=, >=, !=, isequal, 
isless, isinf, isnan, show, copy!, lastindex, firstindex, rand, 
unsafe_convert, eps, floatmin, floatmax

zeros and ones are overloaded from Base so that allocated TPSs are placed in each element. Because of the mutability of TPS, if we didn't explicity overload these functions every element would correspond to the exact same heap-allocated TPS.

GTPSA.jl overloads (and exports) the following functions from the corresponding packages: LinearAlgebra: norm, mul! SpecialFunctions: erf, erfc, erfcx, erfi

GTPSA.jl also provides the following math functions NOT included in Base or any of the above packages (and not already documented in TPS Methods):

unit, sincu, sinhc, sinhcu, asinc, asincu, asinhc, asinhcu, wf, polar, rect

If there is a mathematical function in Base which you'd like and is not included in the above list, feel free to submit an issue.

Mutable Mathematics Interface

For every math function, GTPSA.jl provides mutating functions to set an allocated TPS in-place. For non-arithmetic operators, this is denoted with a bang (!) symbol. E.g. for sin(a), there also exists GTPSA.sin!(b, a) where b is set equal to sin(a). Aliasing (b === a) for all operators is allowed in GTPSA.

For the arithmetic operators +, -, *, /, ^, there are the corresponding in-place functions GTPSA.add!(c, a, b), GTPSA.sub!(c, a, b), GTPSA.mul!(c, a, b), GTPSA.div!(c, a, b), and GTPSA.pow!(c, a, b). While c must be an allocated TPS, a and b could be a TPS or any Number type, so long as they can be appropriately converted to the destination TPS parametric number type. Aliasing for all arithmetic operators (a === b === c) is allowed in GTPSA.