Many thanks for your responses, and for your com=
ments.=C2=A0

Is there a list somewhere of integrals which can=
be solved in closed form by Axiom/FriCAS, but cannot be solved by the most=
recent versions of Maple/Mathematica?=C2=A0 I would be very interested in =
seeing such a list - but I don't myself have access at the moment to ei=
ther Maple or Mathematica.Many thanks,

Ala=
sdair

On Fri, Oct 2, 2015 at 4:06 PM, Waldek Hebisch <hebisch@math.un=
i.wroc.pl> wrote:

Tim Daly= wrote:

> Alasdair McAndrew wrote:

> >Finally, I believe that Axiom is the only open-source software whi= ch

> >includes a complete implementation of the Risch decision algorithm= for

> >symbolic integration; done by the late Manuel Bronstein initially = in the

> >1970's and 1980's.=C2=A0 Is this correct?=C2=A0 I suppose = that the major commercial

> >systems support as complete integration routines as possible, but = Axiom has

> >the edge on other (free) systems as far as I know.

>

> As far as I know Axiom has the "most complete" implementatio= n.

> There are still cases which are not implemented but Manuel did more

> that anyone else.

Actually, while "most complete" when written Bronstain'= ;s implementation

contained substantial gaps.=C2=A0 FriCAS contains significant enhancementof Bronstain's code.=C2=A0 AFAICS FriCAS is the only system which canresonably claim completeness in purely transcendental case.

For the old code is is relatively to build examples that either

signal internal errors or return unevaluated.

Completing this case required about 1500 lines, while in Bronstain's

version about 2500 lines handles transcendental case.=C2=A0 So about 30%

of code was missing.

In fact in FriCAS more than 25% of integration code is new.=C2=A0 IIUC

only tiny part of this (a few bug fixes) is included in Axiom.

So FriCAS can claim to have "most complete" implementation, butAxiom no longer can.

Concerning commercial systems, Maple claim to implement

Trager algoritm and transcendental part of Risch algorithm,

which is about what Bronstain's claimed to implement.

However, at least with default Maple settings old Bronstain's

examples still return unevaluated.=C2=A0 IIRC when testing

FriCAS implementation of transcendental case I found

some other cases which Maple returns unevaluated.

Mathematica makes far reaching but imprecise claim

("almost any function"), but experimental results are

similar to Maple.

AFAICS commercial systems take mostly ad hoc approach to

integration, they probably contain a lot of special case

code (pattern, tables or routines handling some narrow

class of functions).=C2=A0 In simple cases this produces

impressive result.=C2=A0 However, it is also fairly incomplete.

FriCAS not contains extension of Risch algorithm to

special functions (integrals needing Ei, erf, Gamma, ...).

When comparing FriCAS with Ma-s I noticed that once

examples got complicated enough, then Ma-s could no

longer do them.

--

=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2= =A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 Waldek Hebisch

--

to show the output. There is
still a great deal of work to be done to port the pages from the
hyperdoc browser. The pages are created during the build in
mnt/ubuntu/doc/hypertex/*.xhtml. The last thing done on that effort
was to try to implement web-sockets so the interface was reactive.
All of the machinery has been demonstrated but it is still only
demo-ware at this stage.
One of the project goals is to re-implement (and improve) the
hyperdoc machinery. Also in-plan is to re-implement the graphics
using the browser

On=
Fri, Oct 9, 2015 at 6:36 AM, <daly@axiom-developer.org> wrote:

I built a new Ubuntu 10.04 ma= chine from scratch.

I installed the packages listed on the downloads web page on

axiom-developer

I did the git clone and subsequent instructions above.

My compile worked.

Perhaps your GCC is downlevel?

Tim

>Sorry - just tried that on my work computer (Ubuntu 14.04), and same er= rors.

>

>-Alasdair

>

>On Fri, Oct 9, 2015 at 10:18 AM, Alasdair McAndrew <amca01@gmail.com> wrote:

>

>> Thanks!=C2=A0 Will give it my best shot when I get home.

>>

>> cheers,

>> Alasdair

>>

>> On Fri, Oct 9, 2015 at 10:12 AM, <daly@axiom-developer.org> wrote:

>>

>>> git clone git://github.com/daly/axiom

>>> cd axiom

>>> export AXIOM=3D`pwd`/mnt/ubuntu

>>> export PATH=3D$AXIOM/bin:$PATH

>>> make

_______________________________________________

Axiom-developer mailing list

Axiom-developer@nongnu.org

https://lists.nongnu.org/mailman/listinfo= /axiom-developer

Thank you!=C2=A0 In fact

normalize(=
sol.particular)On=
Sun, Oct 18, 2015 at 2:04 AM, Waldek Hebisch <hebisch@math.uni.wro=
c.pl> wrote:

try> >In putting Axiom through its paces just = recently (yes: Axiom, not a fork!),

> >I experimented with the ODE

> >

> >y''+6y'+5y =3D 10x^2+4x+4exp(-x)

> >

> >Now standard techniques (such as I teach my students), produce a s= olution

> >of the form

> >

> >y =3D A*exp(-5x)+B*exp(-x)+2*x^2-4*x+4+x*exp(-x).

> >

> >This is Axiom:

> >

> >--(View this section in a fixed width font if it isn't shown a= s such)

> >

> >(1) -> y:=3Doperator 'y

> >(2) -> deq:=3DD(y(x),x,2)+6*D(y(x),x)+5*y(x)=3D10*x^2+4*x+4*exp= (-x)

> >(3) -> sol:=3Dsolve(deq,y,x)

> >=C2=A0 =C2=A0(3)

> >=C2=A0 =C2=A0[

> >=C2=A0 =C2=A0 =C2=A0 =C2=A0particular =3D

> >=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0- x 6=C2=A0 =C2=A0= =C2=A0 =C2=A02=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0- x 5= =C2=A0 =C2=A0 =C2=A0- 5x=C2=A0 - x=C2=A0 =C2=A0 =C2=A02=C2=A0 - 5x

> >=C2=A0 =C2=A0 =C2=A0 =C2=A04x (%e=C2=A0 =C2=A0)=C2=A0 + (10x=C2=A0= - 16x + 16)(%e=C2=A0 =C2=A0)=C2=A0 - %e=C2=A0 =C2=A0 %e=C2=A0 =C2=A0 - 2x = %e

> >=C2=A0 =C2=A0 =C2=A0 =C2=A0---------------------------------------= --------------------------

> >=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2= =A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0- = x 5

> >=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2= =A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A04(%e=C2=A0 =C2= =A0)

> >=C2=A0 =C2=A0 =C2=A0,

> >=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 - x=C2=A0 =C2=A0-= 5x

> >=C2=A0 =C2=A0 basis=3D [%e=C2=A0 =C2=A0,%e=C2=A0 =C2=A0 ]]

> >Type: Union(Record(particular: Expression(Integer),basis:

> >List(Expression(Integer)))

> >

> >--

> >of which the particular solution is a bit of a jumble.=C2=A0 =C2= =A0It doesn't seem to

> >be particularly simplifiable

eval(sol.particular, exp(-5*x)=3D exp(-x)^5)

--

=C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 =C2= =A0 =C2=A0 =C2=A0 =C2=A0 =C2=A0 Waldek Hebisch

--