PyTPSA

PyTPSA is a Python/C++ package that provides a library for performing Turncated Power Series Algebra (TPSA).

Installation

You will need cython for compiling the package. Cython can be install by pip, as instructed here.

To install PyTPSA, simply run the following command:

python setup.py install

PyTPSA supports both float and complex number as the derivatives of the function, arithmatic operations and fundamental mathmatical function.

First, the package must be initialized to specify the polynomial's maximum order and number of variables.
```
import PyTPSA
num_var=4
max_order=7
PyTPSA.initialize(num_var, max_order)
```
A constant can be either defined as number in python or a constant TPSA object:
```
a = PyTPSA.tpsa(3.0)
b = PyTPSA.tpsa(-1.0)
k = PyTPSA.tpsa(2.0)
```
The variable should be initialized as first order TPSA object. For example, if the variables $(x, p_x, y, p_y)$ with float type is used to represent 6-D phase space, to study the derivative in the vicinity of $(0.0, 0.0, 0.0, 0.0)$, they should be initialized as:
```
x=PyTPSA.tpsa(0.0, 1)
px=PyTPSA.tpsa(0.0, 2)
y=PyTPSA.tpsa(0.0, 3)
py=PyTPSA.tpsa(0.0, 4)
```
Alternatively, they can be defined as a list:
```
vars=[PyTPSA.tpsa(0.0, i+1) for i in range(4)]
```
Other quantities can be defined based on the variables and constants, for example the Hamiltonian is defined:
```
Hamiltonian = (px*px + py*py)/2.0 + a * x * x + b * cos (k * y)
```
Then the derivative of the Hamiltonian $\partial H / \partial y $ can be calculated as
```
dHdy = Hamiltonian.derivative(3)
```
Note that after deriviative, although the maximum order remains the same, the useful order is reduced by 1.
To use complex number TPSA, use dtype argument in the initialization, for example:
```
x=PyTPSA.tpsa(0.0, 1, dtype=complex)
```