[fricas-devel] Re: [Axiom-mail] Programming with BTREEs.
but [e,[5,1],[[a,[1,1],b],[1,1],[c,[1,2],d...@bt cannot work, I think, because the argument types don't match. You will need to allow also binary trees. Ooops. You are completely right. The last part in the input file can be replaced by S==Symbol L==List Integer U==Union(BT,S) construct(x: U, l: L, y: U): U == u: BT := if x case S then binaryTree(x::N) else x::BT v: BT := if y case S then binaryTree(y::N) else y::BT binaryTree(u, l, v)::U l: List U := [a,b,c,d,e] (a,b,c,d,e):=(l 1, l 2, l 3, l 4, l 5) u: U := [e,[5,1],[[a,[1,1],b...@u,[1,1],[c,[1,2],d...@u]@U] bt2: BT := u :: BT where the @U part is necessary (though ugly) since otherwise Axiom (oh, FriCAS in my case) falsely creates (25) - [a,[1,2],b] (25) [a,[1,2],b] Type: List(Any) which is a very unspecific (and bad) choice in the pressence of my new function from above and a and b being both variables of type U. Yet another instance of why I hate Any. Ralf --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
[fricas-devel] input bug?
What's going on here? (1) - 2r (1) 2R0 Type: Variable(2R0) (2) - 3r (2) 3R0 Type: Variable(3R0) (3) - 3s Cannot find a definition or applicable library operation named 3 with argument type(s) Variable(s) Perhaps you should use @ to indicate the required return type, or $ to specify which version of the function you need. Martin --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
[fricas-devel] Re: [Axiom-mail] Programming with BTREEs.
Yet another instance of why I hate Any. ... The interpreter seems to like List(Any) more than my specific types. See bolow... :-( Let's do a little programming ... this is the more complicated form. Simon, my example is not completely finished since the MyBinaryTree you find below, doesn't have much functionality (except equality), but it is preferable to BinaryTree, because if you construct a tree in MyBinaryTree(I, L) then you have no chance to construct a tree that has inner nodes that are not of type I and leaves of any other type than L. So the code below is an example of how to translate your tree structure into SPAD code. The input then is B := MyBinaryTree(List Integer, Symbol) t: B := [e,[5,1],[[a,[1,1],b...@b,[1,1],[c,[1,2],d...@b]] The @B is still needed since otherwise the Axiom/FriCAS interpreter tries to construct again something of type List(Any)... Extremely bad behaviour of the interpreter in my eyes... The @B is even needed if you add l: List Symbol := [a,b,c,d,e] (a,b,c,d,e):=(l 1, l 2, l 3, l 4, l 5) before the assignment to t. You have to live with that for the moment, at least you have the chance that adding @B gives a hint to the interpreter of what you actually intended with your input. Try for example t: B := [a,b,c] You get (5) - t:B := [a,b,c] Cannot convert right-hand side of assignment [a,b,c] to an object of the type MyBinaryTree(List(Integer),Symbol) of the left-hand side. Seeing such error message in Axiom is quite common, but wait. Think of it for a moment. You just asked to system to create a tree for you (namely an element t of type B) which would have the inner node b. However, b is of type Symbol and inner nodes should not be of type Symbol, but rather of type List(Integer). So the system is completely right throwing that error message at you. Imagine you are inside a big program and you've put there an assignment like (5). The SPAD compiler will detect that you are doing things where the types do not match and will tell you at compile time (not at runtime). So here is your code... put it into aaa.spad and in Axiom say )co aaa.spad followed by the assignments at the beginning of this mail. Ralf ---rhxBEGIN aaa.spad -- Note that I and L must always be different types. -- MyBinaryTree(Integer, Integer) is forbidden. COUT==CoercibleTo(OutputForm) )abbrev domain MBTREE MyBinaryTree MyBinaryTree(I: COUT, L: COUT): COUT with construct: L - % construct: (L, I, L) - % construct: (%, I, L) - % construct: (L, I, %) - % construct: (%, I, %) - % == add N := Union(I, L) Rep := BinaryTree N construct(l: L): % == binaryTree(l::N)$Rep V == construct construct(l: L, i: I, r: L): % == binaryTree(V l, i, V r) construct(l: %, i: I, r: L): % == binaryTree( l, i, V r) construct(l: L, i: I, r: %): % == binaryTree(V l, i, r) construct(l: %, i: I, r: %): % == binaryTree( l, i, r) coerce(x: %): OutputForm == coerce(x)$Rep ((x: %) = (y: %)): Boolean == (x::Rep) =$Rep (y::Rep) ---rhxEND aaa.spad --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
[fricas-devel] Re: input bug?
Martin, As you may or may not know the 'r' in your input below is supposed to stand for radix. So '2r...' indicates an integer written in base 2 notation. 8r would be octal notation etc. This works in OpenAxiom: wsp...@debian:~$ open-axiom -nox GCL (GNU Common Lisp) 2.6.7 CLtL1Sep 1 2008 14:01:57 Source License: LGPL(gcl,gmp), GPL(unexec,bfd,xgcl) Binary License: GPL due to GPL'ed components: (XGCL READLINE BFD UNEXEC) Modifications of this banner must retain notice of a compatible license Dedicated to the memory of W. Schelter Use (help) to get some basic information on how to use GCL. Temporary directory for compiler files set to /tmp/ OpenAxiom: The Open Scientific Computation Platform Version: OpenAxiom 1.3.0-2009-03-08 Built on Tuesday March 17, 2009 at 08:13:56 - Issue )copyright to view copyright notices. Issue )summary for a summary of useful system commands. Issue )quit to leave OpenAxiom and return to shell. - (1) - 2r101 (1) 5 Type: PositiveInteger (2) - 8r777 (2) 511 Type: PositiveInteger --- But this is apparently currently broken in FriCAS. I vaguely recall a patch Gaby made to OpenAxiom some months ago which may have been the correction to this problem. Regards, Bill Page. On Tue, Apr 7, 2009 at 9:52 AM, Martin Rubey wrote: What's going on here? (1) - 2r (1) 2R0 Type: Variable(2R0) (2) - 3r (2) 3R0 Type: Variable(3R0) (3) - 3s Cannot find a definition or applicable library operation named 3 with argument type(s) Variable(s) Perhaps you should use @ to indicate the required return type, or $ to specify which version of the function you need. Martin --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
[fricas-devel] Re: input bug?
Bill Page bill.p...@newsynthesis.org writes: Martin, As you may or may not know the 'r' in your input below is supposed to stand for radix. No, I didn't. So '2r...' indicates an integer written in base 2 notation. 8r would be octal notation etc. This works in OpenAxiom: wsp...@debian:~$ open-axiom -nox [...] (1) - 2r101 (1) 5 Oh dear, this looks terribly dangerous. My 2r was a typo, I wanted to type 2*r. I just checked OpenAxiom, it gives 0 for 2r*x I'd vote for turning this feature off in FriCAS altogether (and replace it by something less error prone)! Martin --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
[fricas-devel] Re: input bug?
On Tue, Apr 7, 2009 at 12:44 PM, Martin Rubey martin.ru...@math.uni-hannover.de wrote: Oh dear, this looks terribly dangerous. My 2r was a typo, I wanted to type 2*r. I just checked OpenAxiom, it gives 0 for 2r*x What result were you expecting? Just curious. --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
[fricas-devel] Re: input bug?
http://www.aldor.org/docs/HTML/chap5.html#2 '2r' should give a syntax error if neither 0 or 1 is following. Ralf On 04/07/2009 06:55 PM, Martin Rubey wrote: Alfredo Portes doyenatc...@gmail.com writes: On Tue, Apr 7, 2009 at 12:44 PM, Martin Rubey martin.ru...@math.uni-hannover.de wrote: Oh dear, this looks terribly dangerous. My 2r was a typo, I wanted to type 2*r. I just checked OpenAxiom, it gives 0 for 2r*x What result were you expecting? Just curious. I'd hope for an error. r is a variable name I use often, and at times I miss the multiplication sign. Martin --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
[fricas-devel] Re: input bug?
Alfredo Portes doyenatc...@gmail.com writes: | On Tue, Apr 7, 2009 at 12:44 PM, Martin Rubey | martin.ru...@math.uni-hannover.de wrote: | | Oh dear, this looks terribly dangerous. My 2r was a typo, I wanted | to type 2*r. I just checked OpenAxiom, it gives 0 for | | 2r*x | | What result were you expecting? Just curious. I think the scanner should have signaled a syntax error. I'll fix that tonight. Except that, I don't think integer literals expressed in radix other than 10 are dangerous at all. -- Gaby --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
[fricas-devel] Issue 443 and order on expressions.
AFAICS issue 443 is a latent bug which surfaced due to changes in FriCAS-1.0.4. Namely, keep kernels unique: when created kerenel is inserted into a cache and later comparison just use position in the cache. Currently kernels in the cache are sorted. Earlier versions used linear search, starting from 1.0.4 we use binary search. The core problem is that up to now order on kernels is _not_ a mathematical order. Namely, it is possible to have kernels k1, k2, k3 such that k1 k2, k3 k3, but k1 = k3. This can happen due to %specialEqual property -- using this property we can cause some kernels to be treated us equal, but for unequal kernels we use old comparison function. In particular, product(f(j), j = 1..n) and product(f(k), k = 1..n) are considered equal. OTOH product(f(k), k = 1..i) may be bigger or smaller than the other depending on order in which they are created. Using binary search for k3, after inserting k1 and k2 may search for k3 in wrong part of the cache (the one which does not contain k1), so that k3 is suddenly treated as different than k1. AFAICS the same problem may happen using linear search, but with much lower probability (the search for k3 is considered unsuccessful if we find k2 k3, so k3 will be inserted twice, however all subseqent searches will find k3 which limits potential for damage). Now, how to solve the problem? One way is to avoid using order for searching (more on this later). Another is to make sure that we have mathematical order. Note: by mathematical order I mean that '=' and '' satisfy axioms of ordered sets -- relations of '=' and '' to any natural notions of equality and order is a separate topic. Unfortunatly, the problem is deeper. One thing is a technical difficulty: to compare product(f(j), j = 1..n) and product(f(k), k = 1..n) we substitute into f the same dummy variable. However, the result of ordered comparison may depend on choice of variable, so we would need to come with some canonical choice. Another problem is that in the process we need to compare fractions. However '' on fractions is a mathematical order only if base ring is ordered ring or represetation is canonical. Neither of them is satisfied for expressions: algebraic numbers do not form ordered ring and we keep algebraic quantities both in numerator and denominator, which means that the mathematically equal expressions may have quite different forms as fractions. ATM it is not clear for me fixing this issue is feasible: eliminating algebraic quantities from denominators should may help but it is not clear what would be performance impact and how much code would we need to get proper order. Concerning avoiding order: we need order for printing so we can not avoid it completely. For search we could use linear search (without early exit) and only later ordered insertion (if we know that the kernel is different that the old ones). However linear search may be a too costly. Alternatively we could spead up search using hashing. For that we need a mathematical hash function, that is a functions h, such that if k1 = k2 than h(k1) = h(k2). Defining such function has similar problems to defining mathematical order. ATM I am not sure if problems of hash function are easier to solve than problems of order. -- Waldek Hebisch hebi...@math.uni.wroc.pl --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups FriCAS - computer algebra system group. To post to this group, send email to fricas-devel@googlegroups.com To unsubscribe from this group, send email to fricas-devel+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en -~--~~~~--~~--~--~---
