Caspy - A Python CAS

Caspy is a CAS that has been developed using Lark parser and Python. Some of the key feautures are:

• Factorisation of univariate polynomials
• Integration and differentiation of symbollic variables
• Expansion of trigonometric expressions, eg expand sin(2x) as 2sin(x)cos(x)
• Expansion of expressions in brackets
• Automatic simplification of fractions and roots

Dependencies

Requires Python 3.7 or later.

To just use the command line interface the only dependency is lark-parser, this can be installed with

pip install lark-parser

Command line usage

To run Caspy you can either execute the start-caspy.py file with python start-caspy.py or execute the Caspy module with python -m caspy. There are some command line arguments that can be passed to Caspy which determines how verbose the output is and the type of the output Caspy will give these are

  -h, --help  show this help message and exit
  --timer     Time execution of statements
  --verbose   Enable verbose logging
  --debug     Enable more verbose logging for debugging purposes
  --ascii     Output string using ASCII characters
  --latex     Output representation of string in LaTeX form
  --unicode   Output string using Unicode characters

Jupyter kernel

To use the Jupyter kernel interface the jupyter module must also be installed, this can be installed with

pip install jupyter

Then the jupyter kernel can be installed with

jupyter kernelspec install --user caspy

Functions implemented

Available functions in the system:

• integrate(f(x),x) : Integrate a function with respect to a variable x
• diff(f(x),x) : Differentiates a function with respect to a variable x
• factor(f(x)) : Factorises a polynomial g(x) using Kronecker's algorithm
• expand_trig(...) : Expands a trigonometric expression, for instance sin(2x) is expanded as 2sin(x)cos(x)
• expand(...) : Expands brackets in an expression
• re(...) : Returns floating point answer where possible, for instance re(sqrt(2)) gives 1.4142...

Example usage

Integration

To calculate the integral of (x+e^x )^2 with respect to x in Caspy we just need to use the integrate(...) function, as shown bellow

>> integrate((x+e^x)^2)
(1/3) · x³ + 2 · e^(x)x - 2 · e^(x) + (1/2) · e^(2 · x)

If we wish to integrate with respect to some other variable, say y, we can give a second argument to the integrate(...) function, as shown bellow

>> integrate(x*sin(y),y)
- cos(y)x

Differentiation

The differentiation function diff(...) works similarly to the integration function, in that the second, optional, argument specifies what we're differentiating with respect to. For example to differentiate xy^2 with respect to y we exectute the code shown bellow.

>> diff(x*y^2,y)
2 · yx

Factorisation

The factor(...) function computes the irreducible factorisation of a polynomial in x with rational coefficients. For instance to factor x^8-1 we can run the code shown bellow.

>> factor(x^8-1)
(-x⁴ - 1)(-x + 1)(x² + 1)(x + 1)

Conversion to floats

To maintain accuracy and readibility Caspy uses symbolic representations of expressions where possible. This means if we use Caspy to evaluate sin(pi/4), Caspy will return √(2)/2. If we wish to get a floating point representation of this value we can use the re(...) function as shown bellow.

>> re(sin(pi/4))
0.7071067811865476