slelievre's profile - activity

The Python identifier can't have brackets so this fails:

sage: var('x[0]')
Traceback (most recent call last)
...
ValueError: The name "x[0]" is not a valid Python identifier.

but the LaTeX name can, so you can do:

sage: X = [SR.var('x_{}'.format(i), latex_name='x[{}]'.format(i)) for i in (0 .. 7)]

and then you would have in the Sage REPL:

sage: X
[x_0, x_1, x_2, x_3, x_4, x_5, x_6, x_7]
sage: show(X)
\newcommand{\Bold}[1]{\mathbf{#1}}\left[{x[0]}, {x[1]}, {x[2]}, {x[3]}, {x[4]}, {x[5]}, {x[6]}, {x[7]}\right]

but in a Jupyter notebook, show(X) would give a LaTeX-rendered $$[x[0],x[1],x[2],x[3],x[4],x[5],x[6],x[7]]$$

The SageMath installer works by installing a "Linux-like" layer for Windows called Cygwin. This operates at a rather low level, and various anti virus scanners tend to consider this low-level activity as "virus-like", and as a consequence they tend to get in the way of the SageMath installer, or of the Cygwin it installs. Depending on the antivirus software and how one configures it, it might just raise an alert, or block the software it thinks is virus-like, or try to destroy it.

Recommendations:

• download the SageMath installer for Windows
• tell all antivirus software to ignore the SageMath installer for Windows
• run the installer; this installs SageMath
• tell the antivirus software to ignore SageMath
• run SageMath

If one runs the installer, or SageMath, before having told antivirus software to ignore it, and if antivirus software considers some of the low-level activity by the installer or by SageMath as virus-like, then such antivirus software might decide not only to block the installer or SageMath, but to remove it, or parts of it, making it non-working later on, even if one later tells the antivirus software to ignore it.

This applies not only to "trend micro" but also to "windows defender", "kaspersky", etc.

Trend Micro is a cyber security company, and Trend Micro office scan is likely an anti-virus scanner by that company.

• Trend Micro on Wikipedia

Yes, checking that a number is not prime can be very easy, without factoring it: you just check that it does not satisfy some condition that all primes satisfy.

For example, if $n$ is a prime, then for any integer $a$, we have $a^n$ is congruent to $a$ modulo $n$.

Another way to say that is that if $n$ is an integer, and if there is any integer $a$ such that $a^n$ is not congruent to $a$ modulo $n$, then $n$ is not prime. Finding such an $a$ can be very cheap but it would not give a way to factor $n$.

See the notion of probable prime and pseudo-prime.

To display blocks of code or error messages, skip a line above and below, and do one of the following (all give the same result):

• indent all code lines with 4 spaces
• select all code lines and click the "code" button (the icon with '101 010')
• select all code lines and hit ctrl-K

For instance, typing

If we define `f` by

    def f(x, y, z):
        return x * y * z

then `f(2, 3, 5)` returns `30` but `f(2*3*5)` gives:

    TypeError: f() takes exactly 3 arguments (1 given)

produces:

If we define f by

def f(x, y, z):
    return x * y * z

then f(2, 3, 5) returns 30 but f(2*3*5) gives:

TypeError: f() takes exactly 3 arguments (1 given)

Please edit your question to do that.

To display blocks of code or error messages, skip a line above and below, and do one of the following (all give the same result):

• indent all code lines with 4 spaces
• select all code lines and click the "code" button (the icon with '101 010')
• select all code lines and hit ctrl-K

For instance, typing

If we define `f` by

    def f(x, y, z):
        return x * y * z

then `f(2, 3, 5)` returns `30` but `f(2*3*5)` gives:

    TypeError: f() takes exactly 3 arguments (1 given)

produces:

If we define f by

def f(x, y, z):
    return x * y * z

then f(2, 3, 5) returns 30 but f(2*3*5) gives:

TypeError: f() takes exactly 3 arguments (1 given)

Please edit your question to do that.

Could you post code that can be copy-pasted into a fresh Sage session to illustrate your problem?

Please edit the question to do that.

Welcome to Ask Sage. Thank you for your question.

Thanks for your appreciation of SageMath! I find a lot of happiness in it too!

There used to be a donation button for donating to "The Sage Foundation", a foundation supporting SageMath which was operated by the University of Washington; however this foundation has been discontinued.

SageMath applying to become a sponsored project of NumFOCUS (or of its European equivalent, which is in the process of being created) is regularly discussed; this has not happened yet but I am sure it will become a reality in the not so distant future.

In the meantime, you could make a donation to one or several of the NumFOCUS-sponsored projects that underly SageMath, for example NumPy, Matplotlib, Jupyter, IPython, SymPy, Conda-Forge, MathJax... Or to other NumFOCUS-affiliated projects, for example Cython... Or to the Python Software Foundation.

The "14 USD/month" you refer to is probably a CoCalc plan; note that you can subscribe to it once in a while for just a month or two, if that is the kind of amount you want to spend.

Another way to help is to get Google Cloud starting credits and to set up some GitLab runners to help with the continuous development / continuous integration of SageMath. See the GitLab-CI page on the SageMath wiki.

Note: instead of

for i in range(len(equations)):
    for j in equations[i]:
        if j == 1:
            print 'true'

you could use

for eq in equations:
    for j in eq:
        if j == P.one():
            print('true')

As @Emmanuel_Charpentier hints at in his comment, this requires using Sage's Python.

If you built from source, you can call Sage's Python with sage --python.

Or you could change your path so that Sage's Python is found first. Use with caution, as other apps / scripts / uses may rely on python calling the system Python.

Note that you can install SageMath using Conda; it will install for Python 3. With the corresponding Conda environment activated, python will be the Python 3 which has SageMath installed on top of it. In that Python, from sage.all import * will work.

What is SRC?

Suppose one has installed SageMath using the conda package.

How does one then install optional packages? It seems sage -i is not active there.

For example, what would be the replacement for

$ sage -i gap_jupyter         # install Jupyter kernel for GAP 4.8
$ sage -i pari_jupyter        # install Jupyter kernel for PARI/GP
$ sage -i r_jupyter           # install Jupyter kernel for R
$ sage -i singular_jupyter    # install Jupyter kernel for Singular

if one is using a conda-installed Jupyter and SageMath?

The documentation can be accessed with ?:

sage: graphs?

and it says this generator produces one representative for each isomorphism class.

To get "all graphs", run through all subsets of the set of unordered pairs of integers among the first n integers and construct the corresponding graphs.

There are several ways to write 74 as a product: $74 = 1 \times 74 = 2 \times 37 = 37 \times 2 = 74 \times 1$.

OpenCV-Python provides Python bindings for OpenCV (free software for computer vision).

To install it you need OpenCV itself, as well as Python, to be installed.

Maybe try the following, in a Sage shell (which, if you installed Sage using the Sage-Windows installer, runs in Cygwin):

apt-cyg install libopencv-devel

Then install opencv-python with the command:

pip install opencv-python

Use point2d instead of list_plot in this case.

How to generate elliptic curve from the following code as B is in hexadecimal form. The elliptic curve generated from the following code is ... which is not showing B in irreducible polynomial form.

Elliptic Curve defined by $y^2 = x^3 + x^2 + 1$ over Finite Field in $a$ of size $3^{151}$

F1.<x> = GF(3)[]
F.<a> = GF(3^151, 'a', modulus=x^151 + 2*x^2 + 1)
F.modulus()
F
A = 1
A
B = (0x1fc4865afe00a9216b0b5fd32c6300c4bed0707ae4072a03e55299f157b)
B
E = EllipticCurve(F, (0, A, 0, 0, B))
E

Please edit your question to specify how Sage was installed:

• using Debian's "aptitude" package manager: apt-get install sagemath-jupyter
• using Conda: conda install sage
• from binaries downloaded from https://www.sagemath.org/download-linux.html
• built from source
• other

Try using show to display the graph:

H.show()

The documentation is at

• http://doc.sagemath.org/html/en/reference/graphs/

and especially

• http://doc.sagemath.org/html/en/reference/graphs/sage/graphs/graph_generators.html

In particular the following generators exist:

sage: graphs(5)
<generator object GraphGenerators.__call__ at 0x...>
sage: graphs.nauty_geng("5")
<generator object GraphGenerators.nauty_geng at 0x...>
sage: graphs.nauty_geng("5 -c")
<generator object GraphGenerators.nauty_geng at 0x...>

and there are many more options to nauty's geng.

Congratulations on building SageMath on this legacy macOS!

@werner1717 if that answers your question please mark the answer as accepted by clicking the "accept" button (the one with a tick mark) at the top left of the answer. This marks the question as answered in the list of questions on the home page of Ask Sage.

I tried to solve a differential system numerically as follows:

R = 5
g = 9.8
t = var('t')
x = function('x')(t)
y = function('y')(t)
de1 = diff(x,t) - y == 0
de2 = diff(y,t) + (g/R)*sin(x) == 0
desolve_system_rk4([de1,de2],[x,y],ics = [0,(20/180)*pi,0],ivar=t)

and got a type error:

Traceback (most recent call last)
...
TypeError: Error executing code in Maxima
CODE:
    sage4 : rk(['diff('x(_SAGE_VAR_t),_SAGE_VAR_t,1)-'y(_SAGE_VAR_t)=0,'diff('y(_SAGE_VAR_t),_SAGE_VAR_t,1)+1.96*sin('x(_SAGE_VAR_t))=0],['x(_SAGE_VAR_t),'y(_SAGE_VAR_t)],[%pi/9,0],[_SAGE_VAR_t,0,10,0.1])        $
Maxima ERROR:

rk: variable name expected; found: 'x(_SAGE_VAR_t)
 -- an error. To debug this try: debugmode(true);

My code.

def POLYNOMIAL_OBTAINED_BY_RECURSION(p,n):
    R=Zmod(p)
    Z.<x>=PolynomialRing(R)
    All=[]
    if n==1:
        h=[]
        for i in range(0,p):
            pol=x+i
            h.append(pol)
            return(pol)
        All.append(Set(h))
    else :
        h=[]
        for i in range(0,p):
            Pol=POLYNOMIAL_OBTAINED_BY_RECURSION(p,n-1)+i*(x^(n-1))+x^n
            h.append(Pol)
            return(Pol)
        All.append(Set(h))
    return(All)

def MYSIEVE(n,All)
    for d in range(1,floor(n/2)+1):
        for j in range(d+1,n+1):
            for polinomio1 in All[j]:
                for polinomio2 in All[d]:
                    if polinomio1%polinomio2==0:
                        k={polinomio1}
                        All[j].difference(k)
    return(All)

def project(p,n):
    if not(is_prime(p)):
        print('p is not prime',p)
    R=Zmod(p)
    Z.<x>=PolynomialRing(R)
    All=[]
    All=POLYNOMIAL_OBTAINED_BY_RECURSION(p,n)
    All=MYSIEVE(n,All)
    return(All)

Duplicate of Ask Sage question 47184.

This is because the default color scheme in Sage is adapted to a light background, while Sage-Windows starts on dark background.

There is an "ipython magic" that allows to choose the color scheme for syntax highlighting.

At the Sage prompt, type:

sage: %colors Linux

To make that permanent, add that line to your init.sage file, which is read each time Sage starts.

Having defined:

sage: a = sqrt(-7)

This works:

sage: number_field_elements_from_algebraics([a])
(Number Field in a with defining polynomial y^2 - y + 2,
 [-2*a + 1],
 Ring morphism:
   From: Number Field in a with defining polynomial y^2 - y + 2
   To:   Algebraic Field
   Defn: a |--> 0.50000000000000000? - 1.322875655532296?*I)

This fails:

sage: number_field_elements_from_algebraics([a], embedded=True)
Traceback (most recent call last)
...
NotImplementedError:

The reason for why only embeddings of real numbers are supported is that nobody has done it yet. If you can do it, your contribution will be appreciated.

Regarding your worry that there was a good reason: if so, the correct thing to do would have been to add as a comment about the reason, and to raise a ValueError rather than a NotImplementedError.

The package you have in mind is probably Dirac3 by Ted Woollett, right?

Duplicate of Ask Sage question 47129.

Please give an example of what you would like to input and what output you would hope to get.

Instead of "I have some function f(x, y, z)", please paste the actual code you wrote, for example f(x, y, z) = x*y*z + x*x*y + 5*y*z^2 + 3*x*y^2.

Also, instead of "I want to use some commands like [...] on it, but it is no more possible if it's a function", you could give an example of input and output that works, and an example of input that does not work, and say what you were expecting to get, and what error message you got.

@Sha -- since this answers your question, please accept the answer (by clicking on the button with a tick mark); this will mark the question as answered in the main list of question on the Ask Sage homepage.

Polynomial with fractional exponents are also called Puiseux polynomials.

Implementing Puiseux polynomials and Puiseux series in Sage is tracked at:

• Sage Trac ticket 9289: Puiseux polynomials
• Sage Trac ticket 4618: Puiseux series

See also this other Ask Sage question

• Ask Sage question 32861: Puiseux series expansion