konn / computational-algebra Goto Github PK
View Code? Open in Web Editor NEWGeneral-Purpose Computer Algebra System as an EDSL in Haskell
Home Page: http://konn.github.io/computational-algebra/
License: BSD 3-Clause "New" or "Revised" License
computational-algebra's Issues
doesn't build on 8.2
Hello!
this lib sadly doesn't seem to build on ghc 8.2
in some cases this may be because of dependencies. If theres any way I or other hackage trustees can help make it happen do let me or other know via the tools / issue tracker over at https://github.com/haskell-infra/hackage-trustees/
many thanks!
-Carter
the docs links aren't working :)
Improve representation of monomials
Currently, monomials are represented as unboxed vectors of Ints. This seems rather inefficient: an unboxed vector stores an offset, a length, and the data is stored byte-per-byte instead of word-per-word.
Two ideas come to mind instead:
newtype Monomial ( n :: Nat ) = Monomial ( Array# Word )or, avoiding all indirections entirely:
data family Monomial ( n :: Nat ) :: TYPE ( 'TupleRep ( Replicate n WordRep ) )
newtype instance Monomial 0 = M0 (# #)
newtype instance Monomial 1 = M1 (# Word# #)
newtype instance Monomial 2 = M2 (# Word#, Word# #)
newtype instance Monomial 3 = M3 (# Word#, Word#, Word# #)
newtype instance Monomial 4 = M4 (# Word#, Word#, Word#, Word# #)
...I'm also wondering if a Map is the best data-structure to use to represent polynomials, but I suppose that's best left to a separate ticket.
Haddock failure
cabal haddock yields this error:
dist/build/tmp-21791/Algebra/Algorithms/ZeroDim.hs:319:46:
parse error on input `-- ^ lex-Groebner basis of the kernel of the given linear map.'
because although Haddock lets you attach documentation to individual function parameters, it does not let you attach it to individual members of a tuple.
Solving quantified formulas (quantifier elimination)
It might be useful to extend the computational-algebra library to solve quantified formulas instead of quantifier-free formulas.
I found a Haskell library that eliminates quantifiers formulas using cylindrical algebraic decomposition: could this library be used to solve quantified formulas in computational-algebra?
Floating-point algorithms?
Apologies if I've missed something, but I couldn't figure out how to use solveM or solve' with floating point coefficients (e.g. Double). Is this possible?
In my situation, the algorithms using Fraction Integer seem much too slow. Something that takes less than a second in Mathematica or Macaulay2 doesn't even terminate after 15 minutes with solveM/solve'.
Here's an example of a system that I've been working with (I cleared the denominators manually, for simplicity)
p = -495 - 5625 * t + 27891 * t^2 - 33372 * t^3 + 13824 * t^4 - 2367 * t^5 + 6345 * u + 25110 * t * u - 170721 * t^2 * u + 230166 * t^3 * u - 110682 * t^4 * u + 15354 * t^5 * u - 18765 * u^2 + 22140 * t * u^2 + 148581 * t^2 * u^2 - 256878 * t^3 * u^2 + 148446 * t^4 * u^2 - 24300 * t^5 * u^2 + 25110 * u^3 - 100440 * t * u^3 + 56970 * t^2 * u^3 + 4860 * t^3 * u^3 - 29160 * t^4 * u^3 + 16740 * t^5 * u^3 - 12960 * u^4 + 51840 * t * u^4 - 27540 * t^2 * u^4 + 33750 * t^3 * u^4 - 21600 * t^4 * u^4 - 8370 * t^5 * u^4 - 3240 * t^2 * u^5 - 25920 * t^3 * u^5 + 25920 * t^4 * u^5
q1 = 52785 + 56943 * t - 4037688 * t^2 + 15883803 * t^3 - 26239221 * t^4 + 20703357 * t^5 - 7724700 * t^6 + 989361 * t^7 - 66015 * u + 487134 * t * u + 27385938 * t^2 * u - 113650722 * t^3 * u + 181819755 * t^4 * u - 135044982 * t^5 * u + 48046662 * t^6 * u - 6530274 * t^7 * u - 2478195 * u^2 + 6294834 * t * u^2 - 111627882 * t^2 * u^2 + 417376962 * t^3 * u^2 - 654613569 * t^4 * u^2 + 478520946 * t^5 * u^2 - 162633582 * t^6 * u^2 + 21861414 * t^7 * u^2 + 13768380 * u^3 - 50360616 * t * u^3 + 247545072 * t^2 * u^3 - 696128256 * t^3 * u^3 + 1052548344 * t^4 * u^3 - 789620400 * t^5 * u^3 + 272718252 * t^6 * u^3 - 36077400 * t^7 * u^3 - 28987470 * u^4 + 118189368 * t * u^4 - 321295572 * t^2 * u^4 + 526662486 * t^3 * u^4 - 679607010 * t^4 * u^4 + 541760724 * t^5 * u^4 - 204607620 * t^6 * u^4 + 26871750 * t^7 * u^4 + 27060480 * u^5 - 113821200 * t * u^5 + 244827360 * t^2 * u^5 - 186998220 * t^3 * u^5 + 124853400 * t^4 * u^5 - 150553080 * t^5 * u^5 + 83446200 * t^6 * u^5 - 9491580 * t^7 * u^5 - 9331200 * u^6 + 39074400 * t * u^6 - 91154160 * t^2 * u^6 + 40979520 * t^3 * u^6 - 5093280 * t^4 * u^6 + 57678480 * t^5 * u^6 - 44634240 * t^6 * u^6 + 3013200 * t^7 * u^6 + 233280 * t * u^7 + 3265920 * t^2 * u^7 + 14929920 * t^3 * u^7 - 22161600 * t^4 * u^7 - 3732480 * t^5 * u^7 + 9331200 * t^6 * u^7
q2 = 919350 - 1206090 * t - 18350955 * t^2 + 58802085 * t^3 - 67806099 * t^4 + 35782614 * t^5 - 8371728 * t^6 + 651591 * t^7 - 5576850 * u + 32915970 * t * u - 20491785 * t^2 * u - 89979930 * t^3 * u + 154823643 * t^4 * u - 98196624 * t^5 * u + 26236818 * t^6 * u - 2518830 * t^7 * u + 9173250 * u^2 - 91559970 * t * u^2 + 183517245 * t^2 * u^2 - 118728180 * t^3 * u^2 - 7137315 * t^4 * u^2 + 55358640 * t^5 * u^2 - 33001290 * t^6 * u^2 + 5753700 * t^7 * u^2 + 1069200 * u^3 + 54276480 * t * u^3 - 129054870 * t^2 * u^3 + 117919800 * t^3 * u^3 - 53146530 * t^4 * u^3 - 19948680 * t^5 * u^3 + 38889720 * t^6 * u^3 - 9797760 * t^7 * u^3 - 11372400 * u^4 + 12733200 * t * u^4 - 9379800 * t^2 * u^4 - 12830400 * t^3 * u^4 + 49223700 * t^4 * u^4 - 15870330 * t^5 * u^4 - 16692480 * t^6 * u^4 + 7690950 * t^7 * u^4 + 4665600 * u^5 - 4665600 * t * u^5 + 21724200 * t^2 * u^5 - 38296800 * t^3 * u^5 + 5297400 * t^4 * u^5 + 1628100 * t^5 * u^5 - 356400 * t^6 * u^5 - 2762100 * t^7 * u^5 - 583200 * t * u^6 - 11664000 * t^2 * u^6 + 23328000 * t^3 * u^6 - 4422600 * t^4 * u^6 + 6536700 * t^5 * u^6 - 2721600 * t^6 * u^6 + 753300 * t^7 * u^6 - 874800 * t^4 * u^7 - 4665600 * t^5 * u^7 + 2332800 * t^6 * u^7
These are polynomials in two variables t, u. Both Mathematica and Macaulay2 can solve the system {p, q1, q2} in less than a second, whereas neither solveM nor solve' can finish under 15 minutes.
In this case, I'm looking for the real solutions with t,u in the unit interval, which are:
- t = 0.376357, u = 0.106547
- t = 0.886678, u = 0.626615
I also tried to use Fraction Int, but a lack of instances prevented that from working.
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