ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Thu, 23 Feb 2017 08:29:32 -0600to_directed() affects original graphhttp://ask.sagemath.org/question/36705/to_directed-affects-original-graph/ I've stumbled on what I think is a bug. When you create a directed graph from some original graph and then making changes on the new, this can affect the old one. I'm not sure if it should be like this and one should always copy the graph first. Here's a minimal example that for be gives an error "KeyError: 0".
G1=graphs.RandomGNP(5,0.5)
G1.plot(save_pos=True)
G2=G1.to_directed()
G2.delete_vertex(0)
G2.add_vertex(5)
G2.plot()
G1.plot()AckslThu, 23 Feb 2017 04:27:23 -0600http://ask.sagemath.org/question/36705/Overflow when defining points on elliptic curvehttp://ask.sagemath.org/question/36709/overflow-when-defining-points-on-elliptic-curve/I have the following elliptic curve in SAGE:
p1 = 2^256-189
E10 = EllipticCurve(GF(p1),[-3,0])
I want to find points of different orders and multiply them with a number. However when I try to get SAGE to define or print a point like P=E10.points()[19] I get the following error:
Error in lines 1-1
Traceback (most recent call last):
File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 982, in execute
exec compile(block+'\n', '', 'single') in namespace, locals
File "", line 1, in <module>
File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/ell_finite_field.py", line 214, in points
v = self._points_via_group_structure()
File "/projects/sage/sage-7.5/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/ell_finite_field.py", line 156, in _points_via_group_structure
for m in range(1,ni[0]):
OverflowError: Python int too large to convert to C long
So far I have only suceeded in finding the point (0,0) of order 2 but I also need points of higher order. Is there any way to fix this overflow error or find points of different orders that SAGE can actually handle without getting overflow or is my curve just impossible to work with?
I started out trying to print the list of all points and their orders but that resulted in the error. Then I tried printing only one point and now I am simply trying to define the points without printing them (however I need to print k*P for some k later on for all the points).
I got the point (112810383992036387042877104932833846002363090508032041943368137894367452952778,85347934490306136025376423714596250175969011873639765034628869535783033211301) using `E10.gens()` but I can't define it getting the error:
ValueError: libGAP: Error, E: <n> must be a positive integer (not a integer (>= 2^60))
So I am suspecting that it is not possible to get any useful points on this curve. If so can anyone explain to me why it is so (with some references if possible)?AliceThu, 23 Feb 2017 06:27:27 -0600http://ask.sagemath.org/question/36709/Trigonometric equality (with arctan and arcsin)http://ask.sagemath.org/question/36710/trigonometric-equality-with-arctan-and-arcsin/Hi,
I found a strange issue:
ex = (arctan(1/2) + arcsin(sqrt(5)/5) == arctan(4/3))
bool(ex)
And it gives False.
A simple numeric approximation allows to see that it's true, and wolfram alpha for instance gives the correct answer.
But why is it like that and how can I fix it?
ThanksRomuald_314Thu, 23 Feb 2017 08:29:32 -0600http://ask.sagemath.org/question/36710/Linear Algebra Conditionshttp://ask.sagemath.org/question/36625/linear-algebra-conditions/ imgur.com/a/xIydC
The answers is b) ab≠1, but I have no clue how to get to that answer... Can someone help me? :D Terry D. DestefanoWed, 15 Feb 2017 05:30:02 -0600http://ask.sagemath.org/question/36625/More Complex Interact Layouthttp://ask.sagemath.org/question/36697/more-complex-interact-layout/I know i can use layout to specify top, left, right, bottom. However, I've been able to figure out how to layout more than a few rows. For instance, I would like to place 5 rows each containing 1 textbox and 1 button side by side. Also, in between each row of button/textbox I would like to have additional text. Is this possible to do inside of one cell or will I have to get creative with it?mcweihingWed, 22 Feb 2017 15:07:40 -0600http://ask.sagemath.org/question/36697/Installation problem on Machttp://ask.sagemath.org/question/36698/installation-problem-on-mac/I followed the steps in readme.txt but when I double click on sage, it did not pop up, instead it says
Last login: Wed Feb 22 13:05:21 on console
MacBook-Pro/Applications/SageMath/sage ; exit;
RecursionError: maximum recursion depth exceeded during compilation
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 7.5.1, Release Date: 2017-01-15 │
│ Type "notebook()" for the browser-based notebook interface. │
│ Type "help()" for help. │
└────────────────────────────────────────────────────────────────────┘
ERROR: The Sage installation tree has moved
from /Users/buildslave-sage/slave/binary_pkg/build/source/SageMath/jc4b6yulaujayb9sr94ia88eourzeqip0oidma
to /Applications/SageMath
This is not supported, and Sage will not work. To install Sage from a
binary package:
1. Open the .tar.bz2 archive (or .dmg on OSX)
2. Move the SageMath folder/app to where you want it to be. You can
also rename the directory now.
3. Start sage for the first time. This will then automatically patch
paths in binaries.
After starting Sage for the first time you cannot change the
installation any more. To install Sage elsewhere, start over from the
binary package. Or recompile Sage from scratch in the new location
("make distclean && make")
logout
Saving session...
...copying shared history...
...saving history...truncating history files...
...completed.
[Process completed]
My computer info:
macOS 10.12.3 (16D32)
2 GHz Intel Core i7
The one I downloaded:
sage-7.5.1-OSX_10.11.6-x86_64.dmg
Has anyone encountered the same problem?MooreWed, 22 Feb 2017 15:18:11 -0600http://ask.sagemath.org/question/36698/How do I clear this PDFLATEX error in Sage Notebook?http://ask.sagemath.org/question/36701/how-do-i-clear-this-pdflatex-error-in-sage-notebook/I'm running OS X Sierra with Sage 7.5.1 App version. TEXlive 2016 is installed. PDFLATEX runs from a terminal command. I've followed each step to get SAGETEX to see TEX and probably a few more. I still get: “Error: PDFLaTeX does not seem to be installed. Download it from ctan.org and try again.” I'm running out of things to try. Any assistance would be appreciated.
RWBUMPWed, 22 Feb 2017 17:25:08 -0600http://ask.sagemath.org/question/36701/Taylor Series With Order (Big O)http://ask.sagemath.org/question/36665/taylor-series-with-order-big-o/ I'm trying to replicate some Mathematica code, and I know very little about Mathematica and Sage.
The Mathematica code creates a Taylor series for f(x) about (x0), with degree 5. I was able to replicate that.
x, x0, dt = var('x, x0, dt')
f = function('f')
t = f(x).taylor(x, x0, 5)
Next it does a substitution.
k1 = f(x0)*dt
s = x0 + k1/2
k2 = t.subs(x=s)
The problem is it that it then removes the higher order terms using the big O notation.
k2 = Expand[g[x] \[CapitalDelta]t /. x -> s] + O[\[CapitalDelta]t]^5
It looks like this is available for series and polynomial rings (no clue what those are) in SageMath, but I haven't figured out how to apply it to the Taylor series expansion.
Is there a way to truncate certain order terms off of an expression?
Is there a way to replicate the Taylor series expression I want with `.series()` or polynomial rings?
I tried importing `sage.rings.big_oh` and using `Order()` but neither seemed applicable to the expression I had. I also made half an attempt to recreate a Taylor series with `.series()` but didn't quite get what I was hoping for.
tq = 1/factorial(n)*f(x)*x^n
tq.series(n, 5)
Thanks for the help, both my math and SageMath skills are lacking.douggardSun, 19 Feb 2017 16:56:02 -0600http://ask.sagemath.org/question/36665/How to find inverse laplace transformhttp://ask.sagemath.org/question/36656/how-to-find-inverse-laplace-transform/Hi!
I'm trying to find the inverse laplace transform from the following equation:
(5 * s * e^(-2*s))/(s^2 + 9).inverse_laplace(s,t),
although sage responds with:
ilt((5 * s * e^(-2*s))/(s^2 + 9)).
How do I find the inverse laplace transform from the equation above?
Sincerly SimonismonSat, 18 Feb 2017 13:13:43 -0600http://ask.sagemath.org/question/36656/force 0/1 in V-representation of a set of inequalitieshttp://ask.sagemath.org/question/36691/force-01-in-v-representation-of-a-set-of-inequalities/Hi,
If I have an array of inequalities (ieqs) that I define as a polyhedron through the command p = Polyhedron(ieqs = ieqs) and then I get the list of vertices of that polyhedron using [p.Vrepresentation( )], however the vertices are fractional so is there any way to force the vertices to be 0-1?
If not, is there a way so that I convert the vertices myself?
Thanks and sorry if my question is so basicmoatiTue, 21 Feb 2017 18:07:12 -0600http://ask.sagemath.org/question/36691/Updating from old SageNotebook fileshttp://ask.sagemath.org/question/36689/updating-from-old-sagenotebook-files/ I've recently inherited some html files that incorporated sagenb files to perform algebraic computations in the browser. Essentially, they generate calculus practice problems, but they don't work anymore. I was wondering if there's any way to update them to work again.
ThanksmcweihingTue, 21 Feb 2017 16:51:18 -0600http://ask.sagemath.org/question/36689/How to make a symbolic function of a matrix ?http://ask.sagemath.org/question/36681/how-to-make-a-symbolic-function-of-a-matrix/ Hi,
I'm beginning with Sage. I've got two matrix Qf and Xf defined by :
Qf = 1000000*matrix([[0,0],[0,1]]);
Xf = matrix([1],[1675]);
I would like to write a symbolic function "f" which would take a matrix X with 2 rows & 1 column.
X = var('X');
f(X) = ((X-Xf).transpose()*Qf*(X-Xf));
I easily wrote it with python non-symbolic function syntax, but i didn't find a way to make it symbolic. Because I'll need his gradient later (which is easy to calculate by hand, that I conceed ^^).
Maybe, it's related with SR matrix, no idea, i'm beginning with Sage and that's why I'm asking for help x)
Thank you in advance.
Babacool51Mon, 20 Feb 2017 19:33:00 -0600http://ask.sagemath.org/question/36681/help on using chain rule in Sagehttp://ask.sagemath.org/question/36673/help-on-using-chain-rule-in-sage/Does anyone have any tips for using Sage to take derivatives of functions of many variables?
For example, if I define
```w(x,y) = x^2 + y^2``` (say)
and then if I suppose that ```x``` and ```y``` depend on an independent variable ```t```, the chain rule applies for finding ```w.diff(t)```. The only way I found to do this in Sage is
```var('t')```
```x(t) = cos(t)``` (say)
```y(t) = sin(t)```
```w(x,y) = x^2 + y^2```
```w.diff(t)```
But this isn't really using the chain rule. If I instead try
```var('x,y')```
```(define w again)```
```(define x and y again)```
```w.diff(t)```
```Out: (x,y) |--> 0```
Apparently it thinks the derivative is zero because it still thinks ```x``` and ```y``` are two independent variables where they appear in ```w```, even though you get
```x```
```Out: t |--> cos(t)```
and similarly for ```y```. Any suggestions? Thanks.
lefthandstanderMon, 20 Feb 2017 01:25:01 -0600http://ask.sagemath.org/question/36673/Need only the final result of for loophttp://ask.sagemath.org/question/36669/need-only-the-final-result-of-for-loop/Suppose I want to increase each off diagonal element of a matrix by 1. Myy program gives me a sequence of matrices each time changing only one entry. I just need the final matrix of the sequence.
Please check the following program. What modification is required so that the program changes all the entries at a time?
A=random_matrix(QQ,5,5)
B=copy(A)
for i in range(A.nrows()):
for j in range(A.nrows()):
if i!=j:
B[i,j]=A[i,j]+1
print A,BDeepak SarmaMon, 20 Feb 2017 00:19:51 -0600http://ask.sagemath.org/question/36669/random element in user defined classhttp://ask.sagemath.org/question/36668/random-element-in-user-defined-class/ Can I get random element of a user defined class of objects?
For example if I define xyz(n) to generate all the $n \times n$ matrices with a particular property. How can I get a random matrix in my class xyz(5).
Deepak SarmaMon, 20 Feb 2017 00:09:04 -0600http://ask.sagemath.org/question/36668/How to scale threejs graphs?http://ask.sagemath.org/question/24228/how-to-scale-threejs-graphs/ Hi,
jmol works nicely in scaling 3d graphs in sagecell, however threejs does not. Even manual scaling using aspect_ratio does not seem to work; aspect_ratio is apparently ignored.
Example:
%var x,y
g=plot3d(x^3*y^3, (x,-2,2),(y,-2,2),aspect_ratio=[1.0,1.0,.001])
threejs(g)
Is there another way to scale graphs with threejs?
Best
IngoIngo DahnSun, 21 Sep 2014 06:23:12 -0500http://ask.sagemath.org/question/24228/inverse laplace transforms of shiftshttp://ask.sagemath.org/question/9013/inverse-laplace-transforms-of-shifts/I've been trying to get Sage to solve an ODE using Laplace transforms. Unfortunately, shifted functions appear to cause a problem for the `inverse_laplace` command. David Joyner's ODE book (dated 2008) says that Sage does not have the functionality to do this. Has this situation changed? Do I need to do something differently here to get this to work?
Here is a snippet of something I tried.
u=piecewise([[(0,3),0],[(3,infinity),exp(-2*(t-3))]],t)
u.laplace(t,s)
inverse_laplace(_,s,t)
The first two lines work properly, but the last line returns a formal result:
ilt(e^(-3*s)/(s + 2), s, t)
calc314Tue, 29 May 2012 10:39:07 -0500http://ask.sagemath.org/question/9013/HTML with SageCellServer - Interactive Webpageshttp://ask.sagemath.org/question/31388/html-with-sagecellserver-interactive-webpages/Hi,
I have put together an interact using HTML-characters to display chess pieces, which display perfectly fine in the notebook. When I use the interact in a html-file (to make it available on an interactive website) via the SageCellServer, however HTML is not displayed as expected.
Moreover the buttons on the selector list look differently (different size, shape and color) as in the notebook. Is there a way to display the interact on a website just as it would appear in the notebook?
Another probably related question: Can I influence how buttons and lists appear in an interact by pre-formatting them? For example in my interact the 32 buttons for question 2 are wrapped around due to the page-width limit and then are displayed as two rows of different length. I would like to display those 32 buttons in two (or four shorter) rows of equal length. Is there a way to fine tune this? (I looked at the interact and found something about "canvas", but not sure how to properly use this in an interact.)
Is there any other way to formatting the input part of an interact?
Here is a <a href="http://www.dim.uchile.cl/~mschraudner/files/Screenshot.png">link</a> to a screenshot of how things look in the notebook.
Here is the <a href="http://www.dim.uchile.cl/~mschraudner/files/Zeros.html">.html-file</a> I am using website and here is a <a href="http://www.dim.uchile.cl/~mschraudner/files/Screenshot2.png">link</a> to a screenshot of the badly-formatted output I get.
Thanks in advance for any hints or ideas.
Best
Michael
Here is my (shortened) code for the interact:
<pre><code>
L1=["<font size=5>♕</font>","<font size=5>♖</font>","<font size=5>♗</font>","<font size=5>♘</font>","<font size=5>♙</font>","<font size=5>♛</font>","<font size=5>♜</font>","<font size=5>♝</font>","<font size=5>♞</font>","<font size=5>♟</font>"]
L2=["a1","a3","a5","a7","b2","b4","b6","b8","c1","c3","c5","c7","d2","d4","d6","d8","e1","e3","e5","e7", "f2","f4","f6","f8","g1","g3","g5","g7","h2","h4","h6","h8"]
L3=["Yes <font color=#647345>(Sí)</font>","No <font color=#647345>(No)</font>"]
@interact
def ChessCoords(Q1=selector(L1,buttons=True,label="Question 1: <b>g4</b> "), Q2=selector(L2,width=4,buttons=True,label="Question 2: <font size=5>♗</font>"), Q3=selector(L3,width=15,buttons=True,label="Question 3: ")):
if L1.index(Q1)==0 and L2.index(Q2)==0 and L3.index(Q3)==0:
pretty_print(html(""))
pretty_print(html("<font size=4 color=#000000><b>To compute final coordinates, select your answers.</b></font>"))
else:
pass
</code>
</pre>NoviceMSMon, 07 Dec 2015 15:11:25 -0600http://ask.sagemath.org/question/31388/How to make a function of 'fname' that produce a file named 'fname'http://ask.sagemath.org/question/36655/how-to-make-a-function-of-fname-that-produce-a-file-named-fname/ Hi all,
Typing a correction on some recurrent sequences $u_{n+1}=f(u_n)$ I use sage to build a nice plot illustrating the behavior of the sequence depending on the initial data.
I took a nice function from this awesome [book.](http://sagebook.gforge.inria.fr/)
def escargot(f,x,u0,n,xmin,xmax,file):
u = u0
P = plot(x, x, xmin, xmax, color='gray')
for i in range(n):
P+= line([[u,u],[u,f(u)],[f(u),f(u)]], color ='red')
u = f(u)
P += f.plot(x, xmin, xmax, color='blue')
P.save('/home/myfolder/f1a.png')
So everyhting work perfectly but, since there is a lot of examples to produce, I would like to make the function to have an extra argument say filename so that now the file so that now the plot is saved in /home/myfolder/filename.png,
but I have no idea how sage manipulate string.
Help would be welcome !
Laurent BSat, 18 Feb 2017 12:38:48 -0600http://ask.sagemath.org/question/36655/where is the SageMath "Demonstrations Project"?http://ask.sagemath.org/question/35347/where-is-the-sagemath-demonstrations-project/I am sure most of you are aware of the [Wolfram Demonstrations Project](http://demonstrations.wolfram.com/topics.html). If not, it’s a library of interactive models demonstrating different mathematical concepts. If you *buy* Mathematica you can edit and experiment with the code yourself. I find it really helpful to be able to investigate something in a interactive graph to understand the relationships in say an economic model, e.g. this example of a [basic supply and demand model](http://demonstrations.wolfram.com/BasicSupplyAndDemand/), this more intricate [Keynesian IS-LM Model](http://demonstrations.wolfram.com/TheKeynesianISLMModel/), or this model that allows you to [investigate income and substitution effects with different utility functions](http://demonstrations.wolfram.com/IncomeAndSubstitutionEffectsWithDifferentUtilityFunctions/).
Friendly people here at ask.sagemath have a couple of times answered my questions by posting code to http://sagecell.sagemath.org, which I really appreciate, e.g. this [visualization of logistic population growth](http://sagecell.sagemath.org/?q=uwecsj), but **is there a way to search for SageMath code examples or some library of interactive SageMath models demonstrating different mathematical concepts like the Wolfram Demonstrations Project?** I'm also interested to share projects myself.
I think something like a SageMath "Demonstrations Project" could be a great way to demonstrate the power of SageMath in an very accessible way, and possibly contribute to spreading the awareness of SageMath.etbWed, 02 Nov 2016 06:33:58 -0500http://ask.sagemath.org/question/35347/Restricted usability of Singular after upgradehttp://ask.sagemath.org/question/36480/restricted-usability-of-singular-after-upgrade/Today I upgraded SageMath from 7.3 to 7.5.1, then I tried to continue yesterday's work: generating a sparse univariate polynomial using Singular, the polynomial has degree beyond that of toy polynomials. Yesterday, this worked fine,
today I get the error message
exponent overflow (117649)
How can this happen? And what can I do to get the previous facilities of Singular (possibly, this means the previous facilities of SageMath)?
Thanks in advance
wjansenTue, 07 Feb 2017 12:28:01 -0600http://ask.sagemath.org/question/36480/How to save my work locallyhttp://ask.sagemath.org/question/36648/how-to-save-my-work-locally/ Hey!
I'm new with SageMath, but after some days reading and working I'm quite familiar with the main concepts, so working in the terminal an the notebook isn't a problem for me now.
The problem I have is: How can I save the code I wrote locally, in a .sage-file on my drive or something like that? How can I organize my work well?
I haven't fount anything in tutorials, maybe someone could give me an explanation or a useful link! (:
Thanks a lot,
python_15python_15Fri, 17 Feb 2017 04:00:26 -0600http://ask.sagemath.org/question/36648/how can i contribute to sage documentation v7.5?I have found a few glitches in documentationhttp://ask.sagemath.org/question/36649/how-can-i-contribute-to-sage-documentation-v75i-have-found-a-few-glitches-in-documentation/ I want to fix a few typos in the sage documentation v7.5. I would love to know where to make the changes.asutosh7hotaFri, 17 Feb 2017 06:35:43 -0600http://ask.sagemath.org/question/36649/How can I stop sagemath program without quitting sage session?http://ask.sagemath.org/question/36640/how-can-i-stop-sagemath-program-without-quitting-sage-session/Hello. First of all, I think it is good to describe how I use SageMath before asking the question.
I installed SageMath in my laptop using Ubuntu 16.04.
It is installed in directory "~/sage".
I usually run SageMath in terminal. That is, I follow the following steps to run SageMath.
1. Open the terminal (It is the basic terminal from Ubuntu 16.04).
2. Go to the directory where SageMath is installed by typing "cd sage".
3. Type "./sage".
Then, sage session begins.
In sage session, I usually load a sage file which I already wrote and run it to check the result.
But sometimes, a program does not seem to finish, since computation takes a lot of time.
Then, I would like to finish the program which I am running now, but *without going out of sage session*,
since otherwise, I should follow 3 steps above again.
However, I could not find how to do it, yet.
Can anybody teach me how to do it?prosolverThu, 16 Feb 2017 02:59:25 -0600http://ask.sagemath.org/question/36640/Permutation similar matriceshttp://ask.sagemath.org/question/36631/permutation-similar-matrices/ How to generate the class of all permutation similar matrices of a given square matrix? Deepak SarmaWed, 15 Feb 2017 12:18:48 -0600http://ask.sagemath.org/question/36631/change of variable from hyperellictic curve to Weierstrass formhttp://ask.sagemath.org/question/36637/change-of-variable-from-hyperellictic-curve-to-weierstrass-form/ I have the hyperelliptic curve `v^2 = p^4-2*p^3+5*p^2+8*p+4` which I wish to change it to an elliptic curve in Weierstrass form where it returns the change of variable v=[u,r,s,t]. I got the following from Maple. Was wondering if I could get a similar thing using Sage.
-(y^2) = x^3-(121/3)*x-(1690/27)
x = -(1/3)*(5*p^2+24*p-12*v+24)/p^2
y = (-4*p^3 + 20*p^2 + (-8*v + 48)*p + (-16*v + 32))/p^3
p = (-72*x-264+36*y)/(9*x^2+30*x-119)
v = (-162*x^4+540*x^3-648*x^2*y+13176*x^2-4752*x*y+62340*x-16488*y+153994)/(81*x^4+540*x^3-1242*x^2-7140*x+14161)ShaWed, 15 Feb 2017 21:31:48 -0600http://ask.sagemath.org/question/36637/Koblitz curvehttp://ask.sagemath.org/question/36628/koblitz-curve/ how to write sage code to find point on koblitz curve.
how to write equation on koblitz curve.santoshiWed, 15 Feb 2017 10:30:19 -0600http://ask.sagemath.org/question/36628/Export to C codehttp://ask.sagemath.org/question/7922/export-to-c-code/Is it possible to export the result of a calculation to C source code? To be more specific, I have a very long equation emerging from a Sage calculation which I need to feed into a C simulation program, but C doesn't understand the x^2, x^3, ... syntax. I ended up using the re module to manually replace the terms with the proper pow function calls, but I thought maybe there is a more elegant solution to this.
hennesMon, 07 Feb 2011 01:26:21 -0600http://ask.sagemath.org/question/7922/Not evaluating the coordinateshttp://ask.sagemath.org/question/36621/not-evaluating-the-coordinates/ I have the following code
D(f,m)=16*f^4*m^4 + (-144*f^10 + 432*f^9 - 472*f^8 - 1040*f^7 + 1672*f^6 + 784*f^5 - 3256*f^4 - 2896*f^3 - 392*f^2 + 128*f - 64)*m^2 + (36*f^14 - 468*f^13 + 3321*f^12 + 1224*f^11 - 8982*f^10 + 10332*f^9 + 29583*f^8 + 144*f^7 - 21024*f^6 - 4572*f^5 + 7047*f^4 + 3816*f^3 + 306*f^2 - 108*f + 81)
[(f,m) for m in [-10..10] for f in [-10..10] if D==0]
where I want to find all values of `(f,m)` that gives `D=0`. I have checked using Pari that one of the point is `(-1,0)`, and also, `(1,2)`. But when i run the coding it gives empty set. ShaWed, 15 Feb 2017 03:04:35 -0600http://ask.sagemath.org/question/36621/Memory error mixing exact numbers and decimal oneshttp://ask.sagemath.org/question/36618/memory-error-mixing-exact-numbers-and-decimal-ones/ Hi,
I wonder why this code gives an error in Sage 7.5.1:
f(x)=3*sin(2*pi*(1.75-2*x))
if abs(f(0.7)) < 1e-12:
print 1
MemoryError: Not enough memory to calculate cyclotomic polynomial of 428914250225777franpenaTue, 14 Feb 2017 11:42:39 -0600http://ask.sagemath.org/question/36618/