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<title>Yacas future plans</title>
<h1>Yacas todo list</h1>
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Current:
<ul>
<li> Test code, documentation for multivariate polys.
<li> Solve broken, and not as powerful as if can be.
<li> Clean up this file: prioritize.
<li> Document some long-standing undocumented functions.
</ul>
<H1>Future plans</h1>
This is a todo list of things I want to get out of the way before version
2.0.
<h1>emergencies</h1>
<ul>
<li> Support for scientific notation in anumber.
<li> Multi-line epoc version.
<li> revisit MathPower: MathPower(0,0.5) locks up.
<li> revisit all analytic functions implemented in anumber, including
log, sin, arctan, etc.
<li> remove the final references to stdlib in the code.
<li> integrating x ln x goes into infinite recursion.
<li> Improved complex numbers. Ln(x) for x < 0 not working yet.
<li> put Nl() in a common place.
<li> test Apart for polys. This might have to be adjusted by adding
using the same mechanism used for the integer version.
<li> loading dll only once (defload mechanism), DllUse iso DllLoad
<li> the refcount 0xffff problem? Problem is actually the intermediate
expression swell.
<li> improved TraceExp
<li> multivariate polynomials, groebner bases.
<li> Ascii graph plotter.
<li> Ascii help when no browser is around
<li> Taylor on functions containing Abs/Sign can not be trusted.
</ul>
<ul>
<li> better error reporting.
<ul>
<li> show function the error occurred in
<li> if the error was based on an argument type, show the argument
<li> If the error was on the number of arguments, specify number
expected and number received.
<li> To detect recursion problems, show the stack (ar the last few
items in the stack). Show it in a form
Function(internal)
Function(rule number)
Function
And show only the last few.
</ul>
<li> Need to improve debugging facilities and tracing facilities. Would be
good to see how yacas is stepping through rule applications.
<li> Sin(Pi/6) etc.
<li> Allow TSimplify() on TSum()..-TSum()..
<li> Sin(Pi/5) = Sqrt(5-Sqrt(5))/Sqrt(8)
<li> Fix the Debian package to not require the new gmp.
<li> External function API, and plugin interface (dynamic link libraries).
<li>
<H2>Bugs to be fixed</H2>
<UL>
<li> factorization of poly's can not do all polys yet. As a consequence:
<UL>
<li> integrals over rational polys don't always work correctly.
<li> partial fraction expansion does not always return correct result (esp. the example in MCA).
<li> roots of a polynomial doesn't work yet.
<li> eigenvalues of a matrix doesn't work fully yet
</UL>
<li> BUG: InverseTaylor not working correctly for Sin and Tan???
<li> BUG: complex^float.
<li> Mod(a,b) generates an error "Argument is not a list" if a or b or
both are undefined (I expected it to return unevaluated).
Mod(-4,-3) generates 1 but Mod(-4,-3) generates -1. I'm not sure what
the "correct" meaning of Mod is for negative moduli bases, but the
answer should in any case be non-negative. Mod(a,b) is defined as the
smallest non-negative number c such that a-c is divisible by b.
</UL>
<H2>Engine functionality</H2>
These are the items specifying functionality that can not be implemented
from within Yacas, so have a rather high priority if the functionality
is needed.
<UL>
<li> Define the Local,.. functions based on their Macro counterparts,
in the scripts.
<li> Remove the {} [] [[]] brackets support from the engine to the scripts.
<li> Faster numerical calculation, by caching the internal format,
and only converting back to ascii when needed.
<LI> Add Karatsuba multiplication.
<LI> also define a Head and Tail for arrays, and append/concat/
insert/delete/copy. This will ease swapping between lists
and arrays.
<LI> Allow for type convertors in pattern matchers. For instance: IsUniVar,
should be combined with CanBeUni and NormalForm to get the correct
one back.
<LI> A plugin interface for yacas, so it can be extended with external
libraries (fast numerical algorithms for instance).
<li> A RuleBaseDefined-like function that returns a list of defined
arities.
<li> HoldEvaluation(function-list)body that holds evaluation of
these functions.
</UL>
<H2>Math high priority</H2>
This is the real meat, the functionality that should be in Yacas 2.0.
<ul>
<li> render matrices and square roots nicely too, in PrettyForm.
<li> FindZeroes (polynoms and other functions)
<li> redivide some code ('newly')
<li> make suchthat more powerful, so it simplifies sin(x)=cos(x) to tan(x)=1 to x/Pi/4
<li> groebner bases
<li> see if using arrays for matrices speeds up things.
<li> Fix CanBeUni so that it deals correctly with 1/c
<li> Test script has been disregarded recently. Make a tests subdir,
install it also, with a lot of small files that can be loaded,
each implementing some tests.
<li> EquateCoefs equate coefficients in two polys, and return as list.
<li> /. as with mathematica, treat args as locals.
<li> allow solve to return a list usable in /.
<li> matrix^negative is inverse^positive
<li> BesselJ
<li> Get started on differential equations: first order
<li> try support for sparse objects (matrices, vectors, polynomials).
<li> try support for iterators.
<li> support for Atom("a"):=2;
</ul>
<H2>Documentation</H2>
The documentation can be improved.
<UL>
<li> Add more of a general overview:
<ul>
<li> what is Yacas? How did it come into existence? Why did I write it? Who is it for?
Why no user interface? Why no plotting?
</ul>
<li> document the algorithms used, and expand on all of the functions
currently implemented.
<li> separate manual chapter on tensors. (Serge? Is it going to change?). TSimplify and TExplicitSum, TD, X
<li> chapter on unix tools. yacas_client, Vi, GnuPlot
<li> document the source code.
<li> mention the use of lists for passing multiple arguments.
<li> document HoldArg in combination with <--
<li> ~/.yacas_history and ~/.yacasrc
<li> document the following commands:
<UL>
<li> ExpressionDepth, SylvesterMatrix, PAdicExpandInternal, GetPrimeFactors,
Rem, Roots, Apart, Together
<li> UnHoldable, GcdReduce, ApplyPure
DestructiveAppendList, PatternMatches, PatternCreate, RuleBaseDefined, RuleBaseArgList,
FindFunction, TemplateFunction, HoldArgNr, Lambda (in combination with Apply),
Primes, OpLeftPrecedence, OpRightPrecedence, MapArgs, Substitute,
<li> quit, Version(), GarbageCollect()
<li> V, GetExtraInfo, SetExtraInfo
<li> %, |, &, ^, if, else (else binds to the last if)
<li> DivPoly, RootsWithMultiples,
<li> OdeSolve
<li> Deriv, Berlekamp, ExtendedEuclidean, ExtendedEuclideanMonic
<li> IsVariable
<li> the fact that VarList can also be called with a second argument, a
filter predicate.
<li> Extended predicates in the pattern matcher (needs to be explained).
<li> CTokenizer(), DefaultTokenizer()
<li> II, ReII, ImII, IsComplexII
<li> XmlTokenizer, XmlExplodeTag
<li> BSearch, FindIsq Search for a zero in a monotonously
growing function. BSearch returns -1 if not found,
FindIsq returns the insertion point.
<li> MultiDivide, MultiGcd, Groebner
</UL>
<li> Add a 'History of Yacas' to the introduction.
<li> Explain what is destructive about the Destructive... routines,
why they are there, and when to use them.
<li> Do slightly more on pure functions, to show why they are useful. Show for example Select.
<li> Explain what Simplify currently does (internal algorithm).
<li> Vi: edit will try to edit a file, or if the argument passed is a
function, it will try to edit the file the function is defined in.
It will try to do so by invoking vi.
It finds the function by scanning the *.def files that have been
reported to the system.
To be really useful, you need to go to the directory containing
the original files, to edit the original files.
<li> Html... commands.
<li> FakeDb... functions.
<li> some blurb on the pattern matching/multivirtual functionality.
</UL>
<H2>Engine internal improvements</H2>
These are nice to haves in the engine.
<UL>
<li> An environment object. Within(environment)body should then
evaluate something within the environment. Together with
Apply this would allow for packages.
<li> engine-side apply "op" for speed.
<li> faster Pi() calculation
<li> LispCleanupStack: implement LocalLispString and LocalLispPtr.
<li> Clean up c++ code a little: Remove ALL TODO's and write javadoc-able-comments in the
source code.
<li> allow access to the rules database from within yacas, for showing
the rules to the user.
<li> optimize string concatenation.
<li> Try to find all the places that can use the CArrayGrower with the
iArrayOwnedExternally set.
<li> it seems I can still optimize InternalEval
<li> Finish arb. math stuff. (ASin, Acos, ATan)
</UL>
<H2>Math nice to have</H2>
<ul>
<li> Clean up TrigSimpCombine and Simplify in such a way as to make the
code reusable for other simplifications.
<li> QSort
<li> BinarySearch (array!)
<li> FourierTransform?
<li> LaplaceTransform?
<li> Singular Value Decomposition.
<li> FortranForm
<li> Resultants
<li> some DE algos.
<li> implement Diff(f(x),x)
<li> Try all the 131 Wester tests.
</ul>
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