Weighted Projective Tools

WeightedProjectiveTools is a Python project designed to provide tools and functionalities related to weighted projective geometry. Specifically, given a weighted projective space $\mathbf{P}(a_0,\dots,a_n)$ it calculates its well-formed version following section $\S 3.\text{C}$ of [BelRo]. It also calculates the dimension of $\mathbf{C}_{(a_0,\dots,a_n)}[x_0,\dots,x_n]_d$ the weighted homogeneous polynomials of degree $d$. The later is done using a formula I found and prooved as part of my master's thesis entitled "The Dimension of Linear Systems on Weighted Projective Varieties".

Features

• Graphical Interface: The GraphicalInterface.py module offers a user-friendly interface for interacting with the tools.
• Core Functionalities: The WeightedProjTools.py module contains the primary functions and classes for weight reduction and dimension calculation.

Installation

Clone the project and move to the project directory

  git clone https://github.com/van512/WeightedProjectiveTools
  cd WeightedProjectiveTools

Create a new conda environment named wpsenv and activate it

  conda create -n wpsenv
  conda activate wpsenv

Setup the environment by installing the necessary libraries

  conda install numpy, sympy

Or directly create the environment from the requirements.txt file

  conda create --name wpsenv --file requirements.txt

If you want to try the examples in the notebook also install jupyter

  conda install jupyter

Usage/Examples

1. After installation, you can start the graphical interface by running:

python GraphicalInterface.py

The following window appears.

Fill in the weights and degree and click calculate. For example for weights (16 30 10) and degree 60 the window now shows the calculation results :

2. For direct usage of the functions and classes in WeightedProjTools.py open and run the examples.ipynb file in jupyter notebooks.

License