# Difference between revisions of "Timescalecalculus python library documentation"

(→Defining a time scale) |
(→Defining a time scale) |
||

Line 6: | Line 6: | ||

After extracting the files, open a Python instance in its folder and type | After extracting the files, open a Python instance in its folder and type | ||

<pre> >>> from timescalecalculus import *</pre> | <pre> >>> from timescalecalculus import *</pre> | ||

− | == | + | ==Time scale basics== |

Right now, a [[time scale]] in this library can consist of only a finite list of numbers. Fraction types are available. | Right now, a [[time scale]] in this library can consist of only a finite list of numbers. Fraction types are available. | ||

− | <pre>>>> ts=[1,2,3,4,5,6,7]</pre> | + | Let $\mathbb{T}=\left\{0,\dfrac{1}{3},\dfrac{1}{2},\dfrac{7}{9},1,2,3,4,5,6,7 \right\}$.<br /> |

− | The [[forward jump]] $\sigma$ can be used: | + | <pre>>>> ts=[0,Fraction(1,3),Fraction(1,2),Fraction(7,9),1,2,3,4,5,6,7]</pre> |

− | <pre>>>> sigma(3,ts) | + | The [[forward jump]] $\sigma$ can be used:<br /> |

− | + | $\sigma(0)=\dfrac{1}{3}$ | |

− | The [[backward jump]] $\rho$ can be used: | + | <pre>>>> sigma(0,ts) |

+ | Fraction(1, 3)</pre> | ||

+ | $\sigma(4)=5$ | ||

+ | <pre>>>> sigma(4,ts) | ||

+ | 5</pre> | ||

+ | $\sigma(7)=7$ | ||

+ | <pre>>>> sigma(7,ts) | ||

+ | 7</pre> | ||

+ | |||

+ | The [[backward jump]] $\rho$ can be used:<br /> | ||

+ | $\rho(1)=\dfrac{7}{9}$ | ||

+ | <pre>>>> rho(1,ts) | ||

+ | Fraction(7, 9)</pre> | ||

+ | $\rho(3)=2$ | ||

<pre>>>> rho(3,ts) | <pre>>>> rho(3,ts) | ||

2</pre> | 2</pre> | ||

+ | $\rho(0)=0$ | ||

+ | <pre>>>> rho(0,ts) | ||

+ | 0</pre> | ||

The [[delta derivative]] works as expected. The delta derivative of a constant is zero: | The [[delta derivative]] works as expected. The delta derivative of a constant is zero: | ||

<pre>>>> dderivative(lambda x: 1,5,ts) | <pre>>>> dderivative(lambda x: 1,5,ts) |

## Revision as of 06:22, 23 December 2016

This is the documentation for the Python repository timescalecalculus.

# The basics

After extracting the files, open a Python instance in its folder and type

>>> from timescalecalculus import *

## Time scale basics

Right now, a time scale in this library can consist of only a finite list of numbers. Fraction types are available.
Let $\mathbb{T}=\left\{0,\dfrac{1}{3},\dfrac{1}{2},\dfrac{7}{9},1,2,3,4,5,6,7 \right\}$.

>>> ts=[0,Fraction(1,3),Fraction(1,2),Fraction(7,9),1,2,3,4,5,6,7]

The forward jump $\sigma$ can be used:

$\sigma(0)=\dfrac{1}{3}$

>>> sigma(0,ts) Fraction(1, 3)

$\sigma(4)=5$

>>> sigma(4,ts) 5

$\sigma(7)=7$

>>> sigma(7,ts) 7

The backward jump $\rho$ can be used:

$\rho(1)=\dfrac{7}{9}$

>>> rho(1,ts) Fraction(7, 9)

$\rho(3)=2$

>>> rho(3,ts) 2

$\rho(0)=0$

>>> rho(0,ts) 0

The delta derivative works as expected. The delta derivative of a constant is zero:

>>> dderivative(lambda x: 1,5,ts) 0

and obeying the delta derivative of squaring function, we see

>>> dderivative(lambda x: x*x,5,ts) 11

The delta exponential is supported. For example if $\mathbb{T}=\{1,2,3,4,5,6,7\}$ then $e_1(3,1)=(1+\mu(1))(1+\mu(2))=(2)(2)=4$ which is correctly computed:

>>> dexpf(lambda x: 1, 3, 1, ts) 4