These reports and the web pages themselves were written in LaTeX using TeXLive distribution and compiled to HTML using TeX4ht.
These reports show the result of using full CAS test suite on different CAS’s at same time. This compares how one CAS perform against another.
Summer 2021 build Completed. Started May 15, 2021, finished July 28, 2021.
Number of integrals [71,994], with grading for all CAS systems except for Mupad.
Eight CAS systems were tested:
Rubi 4.16.1.
Mathematica 12.3 on windows 10.
Maple 2021.1 on windows 10.
Maxima 5.44/sagemath 9.3 on Linux/Manjaro.
Fricas 1.3.7/sagemath 9.3 on Linux/Manjaro.
Giac 1.7.0/sagemath 9.3 on Linux/Manjaro.
Sympy 1.8 Using Python 3.7.9 on Linux/Ubuntu 18.
Mupad/Matlab 2021a on windows 10.
Started March 9, 2020, Completed April 6, 2020.
Uses Rubi 4.16.1 input data. Number of integrals [71,994]. With grading for all CAS systems.
CAS systems used are : Rubi 4.16.1, Mathematica 12.1, Maple 2020, Maxima 5.43, Fricas 1.3.6, Sympy 1.5, Giac/XCAS 1.5 and Sagemath.
Number of tests completed [28,425]. Completed December 16, 2018.
CAS systems used are : Rubi 4.15.2, Mathematica 11.3, Maple 2018, Maxima 5.41, Fricas 1.3.3, Sympy 1.1.1, Giac/XCAS 1.4.9, SageMath version 8.3 and Rubi in Sympy implemetation (port of Rubi to Sympy)
Sympy 1.3 was used in this test for both Sympy itself and for Rubi in Sympy.
This report uses the integrals provided thanks to Waldek Hebisch taken from this sci.math.symbolic post
The Number of integrals is [10,335]. With grading for all CAS systems except for Mupad.
These CAS systems were tested : Rubi 4.16.1, Mathematica 12.3.1, Maple 2021.1, Maxima 5.45, Fricas 1.3.7, Sympy 1.8 under Python 3.7.9, Giac/XCAS 1.7 and Mupad/Matlab 2021a and Sagemath 9.4.
Maxima, Fricas and Giac were used from within Sagemath 9.4 interface.
Number of integrals [22,622]. With grading for all CAS systems except for Mupad.
Nine CAS systems were tested : Rubi 4.16.1, Mathematica 12.3.1, Maple 2021.1, Maxima 5.44, Fricas 1.3.7, Sympy 1.8 under Python 3.7.9, Giac/XCAS 1.7 and Mupad/Matlab 2021a and Sagemath 9.3 and IntegrateAlgebraic under Mathematica 12.3.1 on windows 10.
Maxima, Fricas and Giac were used from within Sagemath 9.3 interface.
IntegrateAlgebraic test problems
Finished August 26, 2021.
This test Uses IntegrateAlgebraic test suite provided thanks to Sam Blake.
Number of integrals [3,154]. With grading for all CAS systems except for Mupad.
Nine CAS systems were tested : Rubi 4.16.1, Mathematica 12.3.1, Maple 2021.1, Maxima 5.44, Fricas 1.3.7, Sympy 1.8 under Python 3.7.9, Giac/XCAS 1.7 and Mupad/Matlab 2021a and Sagemath 9.3 and IntegrateAlgebraic under Mathematica 12.3.1 on windows 10.
Maxima, Fricas and Giac were used from within Sagemath 9.3 interface.
These reports show the result of using same test suite on different versions of same CAS. Only Maple, Mathematica and Rubi are used. This is for regression testing to find how different version of the same CAS improved over the years. The test suite used is the lite version of the full CAS intergation tests. It contains smaller number of integrals compared to the full test suite used above.
This zip file contains the raw input tests used which was obtained from Rubi web site.
Uses same zip file as above for input.
This zip file contains the raw input tests used which was obtained from Rubi web site.
The following diagram gives a high level view of the current test build system.
I really need a faster PC with much more RAM !
This below shows example of CAS suddenly consuming all RAM in PC, and I had to terminate the process, since it did not time out as instructed, and just hanged.
Home page https://fricas.github.io/index.html
To install fricas on Linux Manjaro sudo pacman -S sagemath.
in case of error while installing the package, try sudo pacman -Rs sagemath and then repeat the previous command
If copy paste does not work between windows and Linux VBox, try VBoxClient --clipboard
To use Fricas online, go to http://fricas-wiki.math.uni.wroc.pl/SandBox
Go to bottom of page, type
\begin{axiom} setSimplifyDenomsFlag(true) integrate(sin(x),x) \end{axiom}
Then click the preview button
to send email to supprt group use fricas-devel@googlegroups.com
To download go to https://sourceforge.net/projects/fricas
To installl on Linux Manjaro, type yay -S fricas . Do not use the Manjaro GUI package manager, it always gives build error for some reason. Make sure to install yay first using GUI manager.
Make sure when installing Linux on VBox, to add second CPU to configuration of VBox. i.e. do not use ONE CPU (which is default). There is a bug in fricas installation which makes it fail due to use of multi-threading if only one CPU exist. This should be fixed in future, but just in case.
To install directly, see http://fricas.sourceforge.net/doc/INSTALL.txt
To build directly (but I use yay now and not this any more)
#install sbcl #sudo apt-get install sbcl #do not use this. bug sudo apt-get install clisp #This lisp works sudo apt-get install dvipng sudo apt-get install auctex bzip2 -dk fricas-1.3.2-full.tar.bz2 tar -xf fricas-1.3.2-full.tar
Now build it
make clean fricas-1.3.2>./configure --with-lisp=/usr/bin/clisp checking build system type... x86_64-linux-gnu checking host system type... x86_64-linux-gnu checking target system type... x86_64-linux-gnu checking for make... make checking for gcc... gcc checking whether the C compiler works... yes checking for C compiler default output file name... a.out checking for suffix of executables... checking whether we are cross compiling... no checking for suffix of object files... o checking whether we are using the GNU C compiler... yes checking whether gcc accepts -g... yes checking for gcc option to accept ISO C89... none needed checking for a BSD-compatible install... /usr/bin/install -c checking for touch... touch checking for mktemp... mktemp checking for gawk... gawk checking for gtar... no checking for tar... tar checking for ranlib... ranlib checking for ar... ar checking for latex... /usr/local/texlive/2017/bin/x86_64-linux/latex checking for makeindex... makeindex checking PREGENERATED... "/home/me/data/fricas/fricas-1.3.2/pre-generated" checking for sbcl... /usr/bin/sbcl checking Lisp implementation... This is SBCL 1.3.1.debian, an implementation of ANSI Common Lisp. More information about SBCL is available at <http://www.sbcl.org/>. SBCL is free software, provided as is, with absolutely no warranty. It is mostly in the public domain; some portions are provided under BSD-style licenses. See the CREDITS and COPYING files in the distribution for more information. * sbcl checking how to run the C preprocessor... gcc -E checking for grep that handles long lines and -e... /bin/grep checking for egrep... /bin/grep -E checking for ANSI C header files... yes checking for sys/types.h... yes checking for sys/stat.h... yes checking for stdlib.h... yes checking for string.h... yes checking for memory.h... yes checking for strings.h... yes checking for inttypes.h... yes checking for stdint.h... yes checking for unistd.h... yes fasl checking dirent.h usability... yes checking dirent.h presence... yes checking for dirent.h... yes checking whether closedir is declared... yes checking whether opendir is declared... yes checking whether readdir is declared... yes checking whether dirfd is declared... yes checking whether fchdir is declared... yes checking signal.h usability... yes checking signal.h presence... yes checking for signal.h... yes checking whether sigaction is declared... yes checking for sys/stat.h... (cached) yes checking for unistd.h... (cached) yes checking whether getuid is declared... yes checking whether geteuid is declared... yes checking whether getgid is declared... yes checking whether getegid is declared... yes checking whether kill is declared... yes checking sys/socket.h usability... yes checking sys/socket.h presence... yes checking for sys/socket.h... yes checking util.h usability... no checking util.h presence... no checking for util.h... no checking pty.h usability... yes checking pty.h presence... yes checking for pty.h... yes checking whether openpty is declared... yes checking for openpty in -lc... no checking for openpty in -lutil... yes checking sys/wait.h usability... yes checking sys/wait.h presence... yes checking for sys/wait.h... yes checking whether wait is declared... yes checking whether fork is declared... yes checking for X... no configure: The Graphics and HyperDoc components are disabled. configure: WARNING: Aldor interface will not be built. configure: creating ./config.status config.status: creating src/clef/Makefile config.status: creating src/sman/Makefile config.status: creating src/hyper/Makefile config.status: creating src/doc/Makefile config.status: creating Makefile config.status: creating src/Makefile config.status: creating src/lib/Makefile config.status: creating src/lisp/Makefile config.status: creating src/boot/Makefile config.status: creating src/interp/Makefile config.status: creating src/algebra/Makefile config.status: creating src/input/Makefile config.status: creating src/etc/Makefile config.status: creating src/aldor/Makefile config.status: creating src/aldor/Makefile2 config.status: creating src/aldor/Makefile3 config.status: creating contrib/emacs/Makefile config.status: creating config/fricas_c_macros.h extracting list of SPAD type definitions Type 'make' (without quotes) to build FriCAS
And
make
Add these to .bashrc
export PATH=/home/me/data/fricas/fricas-1.3.2/target/x86_64-linux-gnu/bin:$PATH export AXIOM=/home/me/data/fricas/fricas-1.3.2/target/x86_64-linux-gnu export DAASE=/home/me/data/fricas/fricas-1.3.2/target/x86_64-linux-gnu
Example of integral which fails in Fricas
ii:=integrate(log(1+x)/x/(1+(1+x)^(1/2))^(1/2),x) >> Error detected within library code: integrate: implementation incomplete (constant residues)
For Fricas, use these commands to get 1D plain text output
setSimplifyDenomsFlag(true) )set output algebra on ii:=integrate(1/(x*(3*x^2 - 6*x + 4)^(1/3)),x); unparse(ii::InputForm) \end{lstlisting} Otherwise the output will go to console in 2D. To get Latex output do \begin{lstlisting} setSimplifyDenomsFlag(true) )set message prompt plain )set output algebra off )set output tex on s:=asin(sqrt(1-x^2))/sqrt(1-x^2); ii:=integrate(s,x)
To record console session to file, use (from https://github.com/daly/axiom/blob/master/faq)
)spool filename starts sending output to the file called filename )spool )off stops sending output to the file
Like this
)spool /home/me/data/output.txt )set message prompt plain )set output algebra off )set output tex on ii:=integrate(sin(x), x) )set output tex off )set output algebra on unparse(ii::InputForm) )spool )off
To send Latex output to file do
)set output tex on )set output tex filename
To turn off, just do )set output tex off. Make sure to tex on first. To send back to console, do )set output tex console
To read an input file into Axiom, use the )read system command. read For example, you can read a file in a particular directory by issuing
)read /spad/src/input/matrix.input
To make record
)clear prop r r: Record(a: String,b:Integer) r:=["hello",10]
Some hints below thanks to Waldek Hebisch http://mathforum.org/kb/message.jspa?messageID=9791385
copied here so easy for me to get to:
1. How to measure CPU time used from the int call? (3) -> )set messages time on (3) -> integrate(x^(3/2)/sqrt(1 + x^5), x) Type: Union(Expression(Integer),...) Time: 0.06 (EV) + 0.00 (OT) = 0.06 sec That is command ')set messages time on' tell FriCAS to print time needed to execute following command. The (EV) part means actual computation (OT) printing and at the end there is total 2. How to measure leaf count/size of result? (Maple and Mathematica have build in function to do this) That is a bit tricky. FriCAS (like Axiom) has quite different representation of expressions tham Maple or Mathematica. In FriCAS expression is a quotient of two polnomials, with variables beeing kernels: (13) -> f := exp(x^3 + 1/x) + 1 (14) -> numer(f) 4 x + 1 ------ x (15) -> denom(f) (16) -> variables(numer(f)) 4 x + 1 ------ x (16) [%e ] Type: List(Kernel(Expression(Integer))) Time: 0.00 (OT) = 0.00 sec From FriCAS point of view natural measure of size is number of monomials in numerator and denominator: (17) -> numberOfMonomials(numer(f)) (17) 2 (18) -> numberOfMonomials(denom(f)) (18) 1 but this may underestimate size because kernels may be big. Also internally given kernel is stored only once, but in printed output it may appear several times. It is possible to traverse expression is somewhat tree like manner, so it is possible to give better approximation to say Maple result, but that would require investigating what Maple is doing. I personally never used Maple node count so I do not know it this is simple or if there are some traps. 3. How to check if int passed or failed? Aborted? nil result? etc.. integrate may produce an error (in particular it will do so if it can not decide if integral is elementary). Or may produce unevaluated integral. Or normal result. At programistic level it is possible to catch errors, but a bit tricky, If you look at printed output, than errors are reasonably easy to match via a regex: (22) -> integrate(1/sqrt(exp(x) - x + 1), x) integrate: implementation incomplete (constant residues) the '>> Error' part indicates error. Unevaluated integrals always have integral sign at top level. FriCAS never returns partial results, so text match is relatively easy. Or you may use code like: test_int(f) == res : Union(Expression Integer, LE) res := integrate(f, 'x) res0 : List Expression Integer := res case Expression Integer => [res::(Expression Integer)]@(List Expression Integer) res case List Expression Integer => res::(List Expression Integer) error "test_int: impossible 1" for ri in res0 repeat #(kernels ri) > 0 and is?(operator first kernels ri, 'integral) => print("Unevaluated integral"::OutputForm) Note1: this is part extracted from bigger test script, I did not test it alone. Note2: FriCAS may either return list of results or a single result. Middle part converts this to have always a list (typically of length 1). The last part is a loop so that all solutions can be examined. It you only want to know if result is evaluated, than loop is not needed: more than one result means that integral is evaluated. Note3: In FriCAS testsuite I use a bit different test for evaluated integrals. Namely, FriCAS can do useful computations on unevaluated integrals and in particular unevaluated integrals may appear in the argument to integrate. Such unevaluated integrals of course may propagate form input to the output. The test above may misclasify such integral as unevaluated, while better test checks that unevaluated integral came from the input. 4. And most importantly, how to export the result (if it passed) to a plain text file in _Latex_ format? (24) -> )set output tex on (24) -> integrate(exp(x)*exp(1/(exp(x)+1)-x), x) Here one have to decide what to do with errors. Without error trapping error will abort currently executing function and propagate to top level (up to command line). After doing: )set break resume after error FriCAS will continue executing file from next command (but still abort current command). If you need real loop then I can provide error catcher, but it is a bit more complicated than snippets above. Waldek Hebisch
To get type of value in fricas do typeOf(r)
To clear everything do
)clear all )clear completely
First install anaconda using Linux Manjaro package manager.
To install latest sympy in anaconda try conda install -c anaconda sympy see https://anaconda.org/anaconda/sympy
To update to latest conda do
sudo -i #conda update conda
To update to latest sympy do
sudo -i #conda update sympy ... now check version #python >>> import sympy >>> sympy.__version__ '1.8'
Next must install matchpy, without it Rubi will not worK:
>sudo conda install -c conda-forge matchpy [sudo] password for me: Collecting package metadata: done Solving environment: done ## Package Plan ## environment location: /opt/anaconda added / updated specs: - matchpy The following packages will be downloaded: package | build ---------------------------|----------------- ca-certificates-2019.3.9 | hecc5488_0 146 KB conda-forge certifi-2019.3.9 | py37_0 149 KB conda-forge conda-4.6.14 | py37_0 2.1 MB conda-forge hopcroftkarp-1.2.4 | py_0 20 KB conda-forge matchpy-0.5.1 | py_0 52 KB conda-forge multiset-2.1.1 | py_0 11 KB conda-forge openssl-1.1.1b | h14c3975_1 4.0 MB conda-forge ------------------------------------------------------------ Total: 6.4 MB The following NEW packages will be INSTALLED: hopcroftkarp conda-forge/noarch::hopcroftkarp-1.2.4-py_0 matchpy conda-forge/noarch::matchpy-0.5.1-py_0 multiset conda-forge/noarch::multiset-2.1.1-py_0 The following packages will be UPDATED: ca-certificates pkgs/main::ca-certificates-2019.1.23-0 --> conda-forge::ca-certificates-2019.3.9-hecc5488_0 The following packages will be SUPERSEDED by a higher-priority channel: certifi pkgs/main --> conda-forge conda pkgs/main --> conda-forge openssl pkgs/main::openssl-1.1.1b-h7b6447c_1 --> conda-forge::openssl-1.1.1b-h14c3975_1 Proceed ([y]/n)? y Downloading and Extracting Packages multiset-2.1.1 | 11 KB | ####################################################################### | 100% openssl-1.1.1b | 4.0 MB | ####################################################################### | 100% matchpy-0.5.1 | 52 KB | ####################################################################### | 100% conda-4.6.14 | 2.1 MB | ####################################################################### | 100% hopcroftkarp-1.2.4 | 20 KB | ####################################################################### | 100% ca-certificates-2019 | 146 KB | ####################################################################### | 100% certifi-2019.3.9 | 149 KB | ####################################################################### | 100% Preparing transaction: done Verifying transaction: done Executing transaction: done >
In general, To install python package do conda install package-name to update do conda update package for example conda update spyder
To use Rubi in sympy, do
>python Python 3.7.3 (default, Mar 27 2019, 22:11:17) [GCC 7.3.0] :: Anaconda, Inc. on linux Type "help", "copyright", "credits" or "license" for more information. >>> from sympy import * >>> from sympy.integrals.rubi.rubimain import rubi_integrate
For testing do
from sympy import * or import sympy #but now have to add sympy. to each call import os os.getcwd() os.chdir('X:\\data\\public_html\\my_notes\\CAS_integration_tests\\reports\\rubi_4_11\\code') os.getcwd() import math init_printing() init_printing(use_unicode=False, wrap_line=False, no_global=True) x = symbols('x', real=True) r=integrate(x,x) r0=latex(r) text_file = open("python.txt", "w") text_file.write("\"%s\"" % r0) text_file.close()
To check if integral failed
r=integrate(f*g, (x, L/2, L)) type(r) is integrals.Integral Out[41]: True or isinstance(r, integrals.Integral) Out[48]: True r=integrate(x,x) type(r) is integrals.Integral Out[43]: False if isinstance(r, integrals.Integral): result = 0 else: result=1
To get cwd
os.getcwd() To get list of folder in cwd do os.listdir(os.getcwd()) or ls Out[85]: ['1_Algebraic_functions', '2_Exponentials', '3_Logarithms', '4_Trig_functions', '5_Inverse_trig_functions', '6_Hyperbolic_functions', '7_Inverse_hyperbolic_functions', '8_Special_functions', 'Independent_test_suites'] f = open('Hebisch_Problems.txt','r') f.readline() f.close()
how to do timeout? simple timeouts using signal.alarm module check http://stackoverflow.com/questions/492519/timeout-on-a-function-call for some code. There is also talk about it here https://groups.google.com/forum/#!topic/sympy/qsPImy6WqcI code from above is
def _timeout(self, function, timeout): def callback(x, y): signal.alarm(0) raise Skipped("Timeout") signal.signal(signal.SIGALRM, callback) signal.alarm(timeout) # Set an alarm with a given timeout function() signal.alarm(0) # Disable the alarm
elementry functions http://docs.sympy.org/latest/modules/functions/elementary.html and http://docs.sympy.org/dev/modules/functions/special.html
and http://docs.sympy.org/latest/modules/functions/index.html
Need to change
AppellF1 --> #hypergeometric function of two variables Ellipticpi--> arctanh -->atanh arctan --> atan arccosh->acosh Pi --> pi. arcsin -> asin arccos -> acos hypergeom -> hyper, arccoth -> acoth GAMMA -> uppergamma() arccsc -> acsc arcsec -> asec arccot -> acot, EllipticF -> elliptic_f EllipticE -> elliptic_e Li -> Li Si -> Si Ci -> Ci Ei -> Ei FresnelS -> fresnels FresnelC -> fresnelc
I also removed 4th field that contains integrate(...) in it as it hangs the reading of the input file.
To run python tests do
cd /media/data/public_html/my_notes/CAS_integration_tests/reports/rubi_4_11 python sympy_main.py
To add new test, or run more tests, edit sympy_main.py and change the line
for n in range(0,1): #change the last number to the number of tests to do
To update conda and python do
conda update conda conda update python
To update sympy do
pip list | grep sympy pip install --upgrade sympy
To find version, from inside python, type
import sympy sympy.__version__
from github https://github.com/sympy/sympy/wiki/SymPy-vs.-Sage
To obtain a Rational in SymPy, one of these methods must be used: >>> from sympy import Rational >>> Rational(2, 7) 2/7
In python/sympy, to loop using index 1, can use this:
>>> for num,val in enumerate(sol,start=1): ... print("root number {} is {}".format(num,val))
For timeout in recent python, on windows, this seems to work
from subprocess import STDOUT, check_output output = check_output('dir', shell=True, stderr=STDOUT, timeout=5) print(output)
To download development sympy
sudo git clone git://github.com/sympy/sympy.git sudo git clone https://github.com/HPAC/matchpy.git
To install using conda sudo conda install multiset
packages are here /home/me/anaconda3/lib/python3.6/site-packages
To install pymatch
>sudo conda install -c conda-forge matchpy [sudo] password for me: Solving environment: done ## Package Plan ## environment location: /opt/anaconda added / updated specs: - matchpy The following packages will be downloaded: package | build ---------------------------|----------------- hopcroftkarp-1.2.4 | py_0 20 KB conda-forge certifi-2018.4.16 | py36_0 142 KB conda-forge conda-4.5.5 | py36_0 624 KB conda-forge matchpy-0.4.4 | py_0 49 KB conda-forge multiset-2.1.1 | py_0 11 KB conda-forge ------------------------------------------------------------ Total: 845 KB The following NEW packages will be INSTALLED: hopcroftkarp: 1.2.4-py_0 conda-forge matchpy: 0.4.4-py_0 conda-forge multiset: 2.1.1-py_0 conda-forge The following packages will be UPDATED: certifi: 2018.4.16-py36_0 --> 2018.4.16-py36_0 conda-forge conda: 4.5.4-py36_0 --> 4.5.5-py36_0 conda-forge Proceed ([y]/n)? y Downloading and Extracting Packages hopcroftkarp-1.2.4 | 20 KB | ########################################################################################### | 100% certifi-2018.4.16 | 142 KB | ########################################################################################### | 100% conda-4.5.5 | 624 KB | ########################################################################################### | 100% matchpy-0.4.4 | 49 KB | ########################################################################################### | 100% multiset-2.1.1 | 11 KB | ########################################################################################### | 100% Preparing transaction: done Verifying transaction: done Executing transaction: done >
To update sympy in conda do sudo conda update sympy I do not know now if I should always use sudo for this, but it works. To check conda version do
>conda list anaconda$ # packages in environment at /opt/anaconda: # # Name Version Build Channel anaconda 5.2.0 py36_3 >sudo conda update conda [sudo] password for me: Solving environment: done # All requested packages already installed. >conda update anaconda Solving environment: done # All requested packages already installed.
Can also do conda update --all to update other conda stuff.
To get all info about conda do
>conda info active environment : None user config file : /home/me/.condarc populated config files : conda version : 4.5.5 conda-build version : 3.10.5 python version : 3.6.5.final.0 base environment : /opt/anaconda (read only) channel URLs : https://repo.anaconda.com/pkgs/main/linux-64 https://repo.anaconda.com/pkgs/main/noarch https://repo.anaconda.com/pkgs/free/linux-64 https://repo.anaconda.com/pkgs/free/noarch https://repo.anaconda.com/pkgs/r/linux-64 https://repo.anaconda.com/pkgs/r/noarch https://repo.anaconda.com/pkgs/pro/linux-64 https://repo.anaconda.com/pkgs/pro/noarch package cache : /opt/anaconda/pkgs /home/me/.conda/pkgs envs directories : /home/me/.conda/envs /opt/anaconda/envs platform : linux-64 user-agent : conda/4.5.5 requests/2.18.4 CPython/3.6.5 Linux/4.14.53-1-MANJARO manjaro/17.1.11 glibc/2.27 UID:GID : 1000:1000 netrc file : None offline mode : False
see also https://conda.io/docs/_downloads/conda-cheatsheet.pdf
This will list all versions of specific package conda search sympy
To use sagemath to solve ODE
x = var('x') y = function('y') sage: desolve(diff(y(x),x,2) + y(x) ==0, y(x),algorithm='fricas') _C0*cos(x) + _C1*sin(x) sage: desolve(diff(y(x),x,2) + y(x) ==0, y(x),algorithm='maxima') _K2*cos(x) + _K1*sin(x)
see http://doc.sagemath.org/html/en/tutorial/programming.html
To check if integral evaluated or not, do
var('x') sage: anti=integrate(sqrt(1+x^3),x) sage: anti integrate(sqrt(x^3 + 1), x) sage: isinstance(anti.operator(), sage.symbolic.integration.integral.IndefiniteIntegral) True
To simplify, use expr.full_simplify()
to find what methods are there for some expressions to appy to, type expr.<TAB> i.e. hit TAB key after the dot.
see help on http://doc.sagemath.org/html/en/genindex.html
To find versions of installed package do ver = installed_packages()
First install 1.2 sympy then install this
>sudo conda install -c conda-forge matchpy Solving environment: done ## Package Plan ## environment location: /opt/anaconda added / updated specs: - matchpy The following packages will be downloaded: package | build ---------------------------|----------------- ca-certificates-2018.8.24 | ha4d7672_0 136 KB conda-forge certifi-2018.8.24 | py36_1 139 KB conda-forge openssl-1.0.2o | h470a237_1 3.5 MB conda-forge conda-4.5.11 | py36_0 625 KB conda-forge hopcroftkarp-1.2.4 | py_0 20 KB conda-forge multiset-2.1.1 | py_0 11 KB conda-forge matchpy-0.4.4 | py_0 49 KB conda-forge ------------------------------------------------------------ Total: 4.5 MB The following NEW packages will be INSTALLED: hopcroftkarp: 1.2.4-py_0 conda-forge matchpy: 0.4.4-py_0 conda-forge multiset: 2.1.1-py_0 conda-forge The following packages will be UPDATED: ca-certificates: 2018.03.07-0 --> 2018.8.24-ha4d7672_0 conda-forge certifi: 2018.8.13-py36_0 --> 2018.8.24-py36_1 conda-forge conda: 4.5.10-py36_0 --> 4.5.11-py36_0 conda-forge The following packages will be DOWNGRADED: openssl: 1.0.2p-h14c3975_0 --> 1.0.2o-h470a237_1 conda-forge Proceed ([y]/n)? y Downloading and Extracting Packages ca-certificates-2018 | 136 KB | ####################################################### | 100% certifi-2018.8.24 | 139 KB | ####################################################### | 100% openssl-1.0.2o | 3.5 MB | ####################################################### | 100% conda-4.5.11 | 625 KB | ####################################################### | 100% hopcroftkarp-1.2.4 | 20 KB | ####################################################### | 100% multiset-2.1.1 | 11 KB | ####################################################### | 100% matchpy-0.4.4 | 49 KB | ####################################################### | 100% Preparing transaction: done Verifying transaction: done Executing transaction: done
Now try it for few commands
>python Python 3.6.5 |Anaconda, Inc.| (default, Apr 29 2018, 16:14:56) [GCC 7.2.0] on linux Type "help", "copyright", "credits" or "license" for more information. >>> from sympy import * >>> from sympy.integrals.rubi.rubimain import rubi_integrate >>> x = symbols('x') >>> rubi_integrate(exp(1-exp(x**2)*x+2*x**2)*(2*x**3+x)/(1-exp(x**2)*x)**2, x) Integral((2*x**3 + x)*exp(2*x**2 - x*exp(x**2) + 1)/(-x*exp(x**2) + 1)**2, x) >>> x,a,b = symbols('x a b') >>> rubi_integrate(1/(a**2-b**2*x), x) -log(a**2 - b**2*x)/b**2 >>> rubi_integrate(1/(a**2-b**2*x**2), x) x*hyper((1, 1/2), (3/2,), b**2*x**2/a**2)/a**2 %the above seems to be wrong >>> rubi_integrate(sec(2*a*x), x) Integral(sec(2*a*x), x) >>> rubi_integrate(1/(1+cos(x)), x) Integral(1/(cos(x) + 1), x) %why it can't do the above? >>> integrate(1/(1+cos(x)), x) tan(x/2) %it looks like not all rules are there
anaconda.txt This is build log for anaconda 5.2 on Linux on June 2018
sagemath.txt This is build log for sage math 8.2 on Linux on June 2018
fricas.txt This is build log for Fricas 1.3.3-1 on Linux on June 2018
giac.txt This is build log for giac 1.4.9.59-4 on Linux on June 2018