Calcupy

Calculus powered graphical calculator with Python. Enter a function, equality, inequality, or matrix, and Calcupy will try to detect your input and give relevant visuals. Because Calcupy is powered by the SymPy computer algebra system, it is possible to manipulate expressions in the input field (see SymPy syntax).

Quickly jump to a section in this document:

1. Calcupy
   1. Released app
   2. Roadmap
2. Usage
3. Examples
4. SymPy syntax
5. Contributions
6. Thanks

Released app

The app has been deployed to https://calcupy.herokuapp.com/. It may take some time initially, because the server has to wake up if it has not been used for 30 minutes.

Check out the release notes to see what functionality has been developed and released recently.

Roadmap

The roadmap covers a list of functionality that we like to have Calcupy be able to understand. The following areas of mathematics will be added:

• Algebra, calculus, linear algebra
• Graph theory
• Statistics / Probability theory
• Linear programming solvers
• Constraint satisfaction problem (CSP) solvers

Currently the app is in a proof-of-concept mode, which means that we will develop rapidly. In later stages the design patterns that have emerged will be extrapolated, and the entire app will be rebuild around those patterns.

Usage

Enter an expression to get started. The calculator will evaluate the expression and determine if it is an expression, equality or inequality. If it is an expression with one variable, a line plot, and single variable calculus is available. If the expression has two variables, a surface, contour and gradient plot are available, as well as multivariable calculus functions. Otherwise there are basic algebra methods available, such as solving for one variable, expanding, factoring, finding factors, and trigonometric expansions.

Based on what type of expression and how many variables there are, the following functionality is available:

Variables	Type	Action
0	Expression	Evaluate
1+	Expression, equality, inequality	Simplify
1+	Expression, equality, inequality	Expand
1+	Expression, equality, inequality	Expand trig
1+	Expression, equality, inequality	Factor
1+	Expression	Factors
1	Expression	Line plot
1	Expression	Derivative
1	Expression	Second derivative
1	Expression	Indefinite integral
1	Expression	Integrate from 0 to T
1	Expression	Integrate from -inf to inf
2	Expression	Surface plot
2	Expression	Contour plot
2	Expression	Gradient plot
2+	Expression	Partial derivatives
2+	Expression	Second partial derivatives
2+	Expression	Gradient
2	Expression	Hessian matrix
1+	Equality, inequality	Solve for variable
0+	Matrix	Transpose
0+	Square matrix	Inverse
0+	Square matrix	Determinant
0+	Square matrix	Eigenvectors and values
1	Column vector	Line plot of vectors
1	Matrix 2x1	Parametric plot 2D
1	Matrix 3x1	Parametric plot 3D
1	Matrix NxM where M,N >= 2	Matrix plot
0	Symmetric square matrix	Undirected graph
0	Square matrix	Directed graph
0	Simple graph	Graph complement
0	Graph	Degree matrix
0	Undirected graph	Minimum spanning tree (MST)
1	Expression	Polar plot
1	Matrix	Polar plot

Not what you want? Submit what you are missing, as an issue, on Github.

Examples

The following are examples of expressions that are understood:

• Constants (evaluate):
  • exp((sqrt(-1)*pi))
  • 32!
• One variable:
  • 1 / (1 + x^2)
• Two variables:
  • x*y
  • sin(1/2*x*y)
  • 1 / (1 + x^2 + y^2)
  • sqrt(x^2 + y^2)
  • (-3*x) / (x^2 + y^2 + 1)
  • exp(y) * cos(x) + exp(x) * sin(y)
  • sqrt(4*x^2 + y^2) + cos(4*x) * y
• Equalities:
  • z^3 + z^2 + z^1 + z = 0
  • a*x^2 + b*x + c = 0
  • x^2 + p*x + q = 0
• Inequalities:
  • x^2 < 5
  • sqrt(x) < x
• Matrices:
  • [1,2,3]
  • [[1,2],[3,4]]
• Parametric:
  • [sin(2*t), cos(3*t)]
  • [cos(3*t), sin(3*t), t]
  • [cos(13*t), 0, sin(7*t)]
  • [cos(5*t), 0, t]
• Polar:
  • cos(phi)
  • cos(6*phi)+2
  • 0.5*phi + sin(3*phi)
• Graphs:
  • 8x8 weighted graph

There is no UI component yet to change the plot limits. However, it can be done manually by opening the console and entering app.plot_xlim = app.plot_ylim = [-10,10]; app.plot().

SymPy syntax

Algebra simplify, factor, expand, cancel, apart, trigsimp, expand_trig, ln, expand_log, logcombine, expr.rewrite(sin), expr.rewrite(gamma), expr.rewrite(exp).

Calculus diff(expr, x), diff(expr, x, 2), expr.diff((x, n)), integrate(expr, x), integrate(expr, (x, 0, oo)), integrate(expr, (x, -oo, oo), (y, -oo, oo)), limit(expr x, 0), limit(expr, x, oo), limit(1/x, x, 0, '+'), expr.series(x, 0, 4), expr.series(x, 0, 4).removeO().

Matrices: M.T, eye(n), zeros(n), ones(n), diag(1, 2, 3), M.det(), M.charpoly(t), randMatrix(n).

Contributions

Feel free to contribute! Also, if you have an idea, please let me know (or submit it as an issue on Github)!

Contributors

Special thanks to all of our contributors!

• @johannesheesterman

Thanks

Made possible by:

• SymPy for computer algebra capabilities.
• Matplotlib for plotting.
• Graphviz for drawing graphs.
• Flask as back-end.
• Vue.js as front-end.
• Mathjax for equation typesetting.

Hosted on Heroku with gUnicorn.