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import numpy
import sympy

from mpl_toolkits.mplot3d import Axes3D
import matplotlib
from matplotlib import cm, colors
from matplotlib import pyplot as plt

branching_number = 2

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Performance profile on the following Python script:

  from sage.all_cmdline import *   # import sage library
  _sage_const_3 = Integer(3); _sage_const_2 = Integer(2); _sage_const_7 = Integer(7)

  from abelfunctions import *
  R = QQ['x, y']; (x, y,) = R._first_ngens(2)
  X = RiemannSurface(y**_sage_const_3  + _sage_const_2 *x**_sage_const_3 *y - x**_sage_const_7 )

  X.riemann_matrix()   

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/*
  Cached Factory
  
  Sometimes you want to make objects with a lifetime managed
  by their target owner but you also want to hold reference
  to them in a custom cache. The target owner, naturally, will
  be given a shared_ptr to the output object. However, we don't
  want the lifetime of the output object to be tied to the
  internal cache. I.e. if the owner dies then the object should
  die even if referenced in the cache.

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/// A forest contains a collection of trees and a shared storage for
/// points in the tree. However, each of the trees need to mutably access
/// the point store. For convenience, the trees are initialized using a 
/// pointer to the shared point store.
/// 
/// This code shows one way to perform this two-way mutable share where the
/// forest owns all of the constituent data structures. 
/// 
/// * Rc: allows multiple (reference counted) pointers to a type
/// * RefCell: wraps the type in a mechanism that allows mutation through

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My Problems (There Are Many)

The C++ standard library containers are nice. Like, really nice. As the kind of person who worries about performance to the point that they were shy of anything other than a raw data array I've come to appreciate the usability (and speed!) of ye olde std::vector. Does that many me sound like a wannabe oldie?

Recently I came across a situation where I had, say, a vector [a, b, c, d] and wanted to create the vectors [a, b, c], [a, b, d], [a, c, d], and [b, c, d]. I didn't want to actually allocate O(N(N-1)) additional memory but learned that std::vector didn't support holding references. That's when I came across std::reference_wrapper.

Reference Wrappers

From the Cppreference page:

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import pandas as pd
import matplotlib.pyplot as plt

# obtain example dataset
iris = pd.read_csv('https://raw.githubusercontent.com/mwaskom/seaborn-data/master/iris.csv')

# get the matplotlib default color cycle
cycle = iter(plt.rcParams['axes.prop_cycle'].by_key()['color'])

# use pandas to plot by label

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# A custom prompt that looks like this:
#
#     <NEWLINE>
#     (conda-environment) (current-datetime) [current-full-directory]
#     username@host $
#
# First clear the PS1 variable. This allows conda setup to populate the PS1 with
# the current anaconda environment before we create a custom prompt. Necessary
# because I want a newline before each prompt. (Maybe better way?)
#

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(Work in progress. Please suggest improvements.)

Creating External Sage Packages

• Pure Python Package
• Using Cython
• Running Tests
• Current Examples

Sometimes you want to write code that uses Sage and make it available to the

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# coding: utf-8

# In[1]:

R = QQbar['x,y']
x,y = R.gens()

g1 = x^4 + x^2*y^2 + (-2)*x^2*y - x*y^2 + y^2
g2 = -x^7 + 2*x^3*y + y^3

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Table of Contents

1. Introduction
2. Registering and Operator
   1. Operator Registration Attributes
3. Inferring Shapes
4. Inferring Types

Introduction