MathAction changed pages
https://wiki.fricas.org
MathAction changed pagesenFri, 12 Jan 2024 14:31:02 +0000[FriCAS Library Examples]
https://wiki.fricas.org/FriCASLibraryExamples
https://wiki.fricas.org/FriCASLibraryExamples
++added:
[Root denesting]
Fri, 12 Jan 2024 14:38:07 +0000[Root denesting]
https://wiki.fricas.org/RootDenesting
https://wiki.fricas.org/RootDenesting
??changed:

FriCAS can denest many nested roots. This is implemented in an extra package so
befor use we need to expose it:
\begin{axiom}
)expose RootSimplification
\end{axiom}
Now we can try
\begin{axiom}
r := sqrt(102*sqrt(7) + 272)
rsimp(r)
r := sqrt(66000162*1000003^(1/2) + 11000159000324)
rsimp(r)
r := sqrt(((4030008370)*700001^(1/2)+12090025110)*1000003^(1/2)+((78000162)*700001^(1/2)+312335685800846295))
rsimp(r)
\end{axiom}
We can denest roots of higher degree:
\begin{axiom}
r := (((6670600520850)*7^(1/2)+73781123539185)*13^(1/2)+((77245760121201)*7^(1/2)+89932095680661))^(1/7)
rsimp(r)
\end{axiom}
Note: Current code supports root of degree 2, 3 or 4 outside. With square root outside inside can contain
roots of degree up to 12. Roots of degree 3 outside more limited concerning what can appear inside.
And we can have roots of higher degree inside:
\begin{axiom}
r := (((827820)*(17^(1/3))^2+(58105080)*17^(1/3)+(134584260))*19^(1/2)+(17045208*(17^(1/3))^2+79043889*17^(1/3)+1426984144))^(1/4)
rsimp(r)
\end{axiom}
Denesting is not limited to numbers, it works for algebraic functions and more general expressions:
\begin{axiom}
)set output tex off
)set output algebra on
r := ((x^6+3*x^5+73*x^4+429*x^3+63*x^2+213*x1287)*(x^33)^(1/2)+3*x^7+37*x^6+39*x^5+451*x^4+1545*x^3+315*x^2+351*x4860)^(1/3)
rsimp(r)
)set output algebra off
)set output tex on
r := ((2*exp(x)^212*exp(x)14)*(exp(x)+3)^(1/2)+exp(x)^312*exp(x)^2+39*exp(x)+52)^(1/2)
rsimp(r)
\end{axiom}
Fri, 12 Jan 2024 14:31:01 +0000[noncommutative Groebner bases] correct according to 96da3341640d9b207218400f485e66c453114241 (remove VarSet from NGroebnerPackage)
https://wiki.fricas.org/NoncommutativeGroebnerBases
https://wiki.fricas.org/NoncommutativeGroebnerBases
??changed:
gPak := NGroebnerPackage(Polynomial(Integer), IndexedExponents(Symbol), Symbol, Pdo)
gPak := NGroebnerPackage(Polynomial(Integer), IndexedExponents(Symbol), Pdo)
Tue, 09 Jan 2024 17:15:47 +0000[SandboxErik]
https://wiki.fricas.org/SandboxErik
https://wiki.fricas.org/SandboxErik
??changed:
How can I rewrite a expression to with respect to a variable? For example v=H*r and to make axiom rewrite this as r=H/r?
How can I rewrite a expression to with respect to a variable? For example v=H*r and to make FriCAS rewrite this as r=H/r?
++added:
lcm([2, 6, 9])
Fri, 08 Dec 2023 13:56:02 +0000[FriCAS]
https://wiki.fricas.org/FriCAS
https://wiki.fricas.org/FriCAS
??changed:
(http://www.math.uni.wroc.pl/~hebisch).
(http://fricas.org/~hebisch).
??changed:
When editing pages on this wiki you can specify which
version/fork of Axiom you wish to use to execute the
commands in the !\begin{axiom} ... \end{axiom} environment.
This page is currently set to 'Axiom: friCAS20090114':
Pages on this wiki are rendered using current version of FriCAS:
++added:
After a page was rendered its content is cached and will change only
after edit or explicit request for refresh.
Tue, 05 Dec 2023 16:46:13 +0000[HyperDoc]
https://wiki.fricas.org/HyperDoc
https://wiki.fricas.org/HyperDoc
??changed:
 1) Add page to database used by HyperDoc. For this change to
 directory contaning ht.db file (this directory also contains .ht
 and .pht files)  relative to top of you installation this is

 target/platform/share/hyperdoc/pages subdirectory

 where platform is name of your platform (something like
 x86_64unknownlinux or i386pcmingw32). Next

 rm ht.db # remove the old ht.db file.
 /path/to/your/fricas/installation/target/platform/bin/htadd *.ht

 Note: htadd program only add things to database. So, to avoid
 keeping old entries (which may be wrong if you change a page)
 we remove database first.

 2) Generate the .pht file (this file contains output from examples).

 To do this use command like:
[18 more lines...]
1 Add page to database used by HyperDoc. For this change to
directory contaning ht.db file (this directory also contains .ht
and .pht files)  relative to top of you installation this is:
target/platform/share/hyperdoc/pages subdirectory
where platform is name of your platform (something like
x86_64unknownlinux or i386pcmingw32). Next:
rm ht.db # remove the old ht.db file.
/path/to/your/fricas/installation/target/platform/bin/htadd *.ht
Note: htadd program only add things to database. So, to avoid
keeping old entries (which may be wrong if you change a page)
we remove database first.
2 Generate the .pht file (this file contains output from examples).
To do this use command like:
export FRICAS=/path/to/your/fricas/installation/target/platform;
$FRICAS/bin/sman noihere paste file.ht
3 Regenerate database adding freshly produced .pht file:
rm ht.db # remove the old ht.db file.
/path/to/your/fricas/installation/target/platform/bin/htadd *.ht *.pht
Note1: in the first step it is better to add only .ht pages to database.
In the third step we add both .ht and .pht files (otherwise the examples
would be missing).
Note2: the second step also produces .input file. This file may be
safely deleted.
Tue, 05 Dec 2023 16:45:09 +0000[AldorForFriCAS]
https://wiki.fricas.org/AldorForFriCAS
https://wiki.fricas.org/AldorForFriCAS
??changed:
option is needed to avoid failures due to mismatche autotools versions.
option is needed to avoid failures due to mismatched autotools versions.
Tue, 05 Dec 2023 16:03:00 +0000[PanAxiomCommunity]
https://wiki.fricas.org/PanAxiomCommunity
https://wiki.fricas.org/PanAxiomCommunity
removed:
"axiomcommit":https://lists.sourceforge.net/lists/listinfo/axiomcommit ("archive":http://sourceforge.net/mailarchive/forum.php?forum=axiomcommit)  tracks all commits to the SourceForge SVN repository
(dubbed "silver branch")

"axiomtestresults":https://lists.sourceforge.net/lists/listinfo/axiomtestresults ("archive":http://sourceforge.net/mailarchive/forum.php?forum=axiomtestresults)  everything having to do with the results of building and testing
Axiom

"aldorl":http://www.aldor.org/mailman/listinfo/aldorl ("archive":http://www.aldor.org/pipermail/aldorl) 
 public mailing list used by aldor users


Tue, 05 Dec 2023 15:59:33 +0000[PanAxiom]
https://wiki.fricas.org/PanAxiom
https://wiki.fricas.org/PanAxiom
??changed:
OpenAxiom developement stopped in 2015.
OpenAxiom developement stopped in 2015 and Tim Daly did no release
in last several years. So FriCAS is the only "live" fork, that
is the only fork with visible active development.
Tue, 05 Dec 2023 15:56:43 +0000[Symbolic Integration]
https://wiki.fricas.org/SymbolicIntegration
https://wiki.fricas.org/SymbolicIntegration
??changed:
RischBronsteinTrager algorithm (Risch algorithm in short) is a complete algorithom
RischBronsteinTrager algorithm (Risch algorithm in short) is a complete algorithm
??changed:
"most complete" existing implementation. Unfortunatly "most complete" does
"most complete" existing implementation. Unfortunately "most complete" does
??changed:
almost surely there is on elementary integral. Almost surely, because
almost surely there is no elementary integral. Almost surely, because
??changed:
fresnelS, fresnelC, incomplete Gamma and
polylog. There is complete extended algorithm for large class of functions
(but 'polylog' causes tricky theoretical problems). Compared to
fresnelS, fresnelC, incomplete Gamma, polylogs and elliptic integrals. There is complete
extended algorithm for large class of functions. However 'polylog' and elliptic integrals cause
tricky theoretical problems. Compared to
??changed:
Additionaly to Risch integrator FriCAS contains relativly weak pattern matching
integrator which can generate a few special functions  Ei, li, dilog
and erf. However, if integral really requires
elliptic functions then the best thing which FriCAS can do is to prove that integral
is nonelementary.
FriCAS used to contain relatively weak pattern matching integrator capable of generating a few special functions  Ei, li, dilog
and erf. Currently pattern matching is only used for one case of definite integration, all indefinite
integrals are done by Risch algorithm or extentions and shortcuts.
??changed:
In this case FriCAS neither can compute elementry result nor can it prove that result is not elementary,
is it gives up with error message indicating that the handling this integral requires unimplemented
In this case FriCAS neither can compute elementary result nor can it prove that result is not elementary,
so it gives up with error message indicating that the handling this integral requires unimplemented
??changed:
 This time FriCAS can prove that result is nonelementary (it needs elliptic functions).
This time FriCAS can prove that result is nonelementary and returns answer in terms of elliptic functions.
Tue, 05 Dec 2023 15:54:10 +0000