jacamar 0.1.0

A tiny computer algebra system for Python.

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Jacamar.

A lightweight framework for computer algebra using FLINT and Python-FLINT.

What it is.

• Jacamar is designed to provide a minimal layer of abstraction, giving a SAGE-like feel to Python-FLINT. The goal is for parity to Python-FLINT in terms of speed.
• Its audience is mathematicians and computer scientists who need to use algebraic objects (commutative rings, polynomials, chain complexes, and categories) to easily build new algebraic objects.
• A Python package, which plays well with the ecosystem of packages. Eventually, this will include wheel builds and pip install capabilities.
• Built for parallelizability?
• Mathematical.
• Fundamental principle: no automatic coercions.

Coercion model.

We more or less inherit some basic coercions from Python-FLINT. Where it makes sense, binary operations like __add__(self,other) or __mul__(self,other) return elements of type other.__class__. Thus, the constructor for this class must be able to take the output of the underlying data self._data + other._data and construct a new element with it. In practice, this corresponds to pretending like all such operations correspond to a left action of the ring of self on the ring or module of other.

We try for this to fail whenever something non-obvious is happening. In particular, all arithmetic operations should fail when mixing Jacamar classes with bare Python classes.

Python integers are not automatically coerced. Thus, if n is an int and x is an element in some ring, x**n will raise a TypeError.

In general, __truediv__ is not defined for non-fields. Similarly, powering by non-integer (Integer or IntegerPy) elements in polynomial rings raises a TypeError. Powering by rational numbers or real numbers might eventually be well-defined in certain Puiseux or power series rings.

What it is not.

• Jacamar is not meant to be a replacement for SAGE or SymPy. It has a tiny fraction of the capabilities of SAGE, a tiny fraction of the lifetime of tests that SAGE has passed, and none of the printing and display options.

Remarks.

• We do not provide a universal element-parent approach as in SAGE. Rather, instances of rings point to element classes via self.element_class and instances of ring elements have self.ring. We use this as well for objects like polynomial rings or matrices.
• We prefer to access immutable characteristics of elements, like self.ring for an element, or self.codomain for some kind of morphism, as attributes (or @properties) rather than as functions.
• We do not automatically coerce numbers into Integers. A number such as 7 in the Python prompt will always still produce an int, so it can be used as an index in lists, etc.

Tools.

• pygount
• ruff
• black
• pylint
• coverage
• python environments

Style.

from art import *
tprint("JACAMAR", font="tarty2")