## TODO list for the pynac interface

#### "fully get rid of maxima-based symbolic variables"

### remaining items

- hash is random
- pyobject deallocations, memory leaks
- noncommutative symbols
- symbol domains (ginac supports real, complex, integer)
- gcd (William's list)

Maybe change SAGE's Ginac to make a call to a cython gcd function, then use singular, since singular's gcd over QQ is much better than ginac's, I think, and ginac *only* does GCD over QQ. Actually, just make everything in normal.cpp be implemented via Singular, probably...

- unevaluated expressions?
- piecewise expressions, substitution and pattern matching
- Series expansions

### long term

- find a better scheme for handling compare()

### in progress

### done

- pickling (William's list)

Support pickle via the "archive" print mode.

- precision for numeric evaluation (evalf, _mpfr_, William's list)

genuine coercions to real field, etc.

- Arithmetic with infinity
- 1/gamma(-1) = 0
- better latex output for symbol names, use sage.misc.latex.latex_variable_name
- configurable printing for symbolic functions
- ability to change how partial derivatives are printed

- symbolic matrices, vectors

#### Sage 3.3 - pynac-0.1.2

- symbolic binomial and factorial
- iterator for sage.symbolic.expression.Expression
- operator method
- (similar to current _operator(), but returns the function if the expression is a function application)

sage: var('x,y,z,n,i,j',ns=1) (x, y, z, n, i, j) sage: sin(x).operator() sin sage: type(sin(x).operator()) <class 'sage.calculus.calculus.Function_sin'> sage: factorial(n).operator() factorial sage: type(factorial(n).operator()) <class 'sage.calculus.calculus.Function_factorial'>

- evaluation
- Substitution for more than variable done, call semantics/syntax needs more thought

- print order (William's list)

This text was a part of William's original todo notes, perhaps now it's confusing to include it here. Now, sage: x^2 + x^4 + x^3 x^2 + x^3 + x^4 sage: a^3*x^10 + x^12 - a^15 x^12 + a^3*x^10 - a^15 So it is printing from lowest to highest degree, like mathematica (or power series), but unlike the standard sage convention (or maple, singular, MATH, etc.): sage: R.<a,x> = QQ[] sage: a^3*x^10 + x^12 - a^15 -a^15 + a^3*x^10 + x^12 sage: singular(a^3*x^10 + x^12 - a^15) -a^15+a^3*x^10+x^12

- collect_common_factors (William's list)

need to be able to do this (from ginsh): > collect_common_factors(x/(x^2 + x)); (1+x)^(-1)

- pretty printing (latex() method, a/b instead of a*b^{-1}, etc.)
- callable symbolic expressions