This is my unfinished experiment in writing a computer algebra system.
This has been tested under Python 3:
>>> sys.version
'3.3.0 (default, Dec 4 2012, 05:53:31) \n[GCC 4.6.3]'
demo_calculator.py is an interpreter mostly for debug purposes but also to demonstrate current capabilities.
python3 demo_calculator.py
The language is mathematical and built on top of Python's int, float, and complex types.
>> 3^4
81
>> sqrt(-1)
1j
>> 8 % 3
2
>> e
2.718281828459045
>> pi
3.141592653589793
>> 5!
120
There's a single global symbol table for function definitions. To define functions, use brackets, [], and :=. To call functions, use parentheses. Function calls do not always require parentheses, and whitespace has no effect on the result.
>> f[x] := 3*x + 4
(f[x] := ((3 * x) + 4))
>> g[x,y,z] := x + y + z
(g[x,y,z] := ((x + y) + z))
>> f(3)
13
>> g(1,2,3)
6
>> f 3
13
>> g1,2,3
6
>> g(f(1), f(2), f(3))
30
An @ is inserted for every implicit multiplication. Additionally, each variable or function identifier can be only one letter long.
>> 3x + 4
((3 @ x) + 4)
>> wxyz
(((w @ x) @ y) @ z)
You can expand expressions with expand.
>> expand((a+b)*(c+d))
(((a * c) + (b * c)) + ((a * d) + (b * d)))
>> expand((x+1)^3)
((((x ^ 3) + ((3 * (x ^ 2)) * 1)) + ((3 * x) * (1 ^ 2))) + (1 ^ 3))
Use simplify to group like terms together. Currently, this works for polynomial addition, subtraction, and multiplication (but not division).
>> simplify(expand((x+1)^3))
(((1 + (3 * x)) + (3 * (x ^ 2))) + (x ^ 3))
Run demo_calculator.py with the --types flag to show type recognition:
>> 1/x
Expression has type: RationalExpr[ConstantExpr[1], PolynomialExpr[Var[x], degree=1]]
Reduced expression has type: RationalExpr[ConstantExpr[1], PolynomialExpr[Var[x], degree=1]]
...
>> (x^2 + 3x + 4) * (x^5 + 4x^3 + 1)
Expression has type: PolynomialExpr[Var[x], degree=7]
Reduced expression has type: PolynomialExpr[Var[x], degree=7]
...