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.Tue, 17 Mar 2020 15:51:29 -0500SageMath is not solving this inequalityhttp://ask.sagemath.org/question/50287/sagemath-is-not-solving-this-inequality/I have the following inequality:
ineqal=T1Sol[0].rhs().numerator() > 0
ineqal
$$-\kappa m^{4} + 8 \pi m^{3} r - 4 \pi r^{2} > 0$$
So it's a quadratic, but I would imagine it's solveable. Find the zeros, check the sign on either side of them, and tell me where it's positive. If you need more info, yell at me about assumptions. But instead:
solve(ineqal,r)
$$\left[\left[-\kappa m^{4} + 8 \pi m^{3} r - 4 \pi r^{2} > 0\right]\right]$$
Sometimes I can trick it into behaving with some expand() or simplify_full(), but that seems not to be working here. Any ideas?thethinkerTue, 17 Mar 2020 15:51:29 -0500http://ask.sagemath.org/question/50287/Incomplete answer to inequalityhttp://ask.sagemath.org/question/50119/incomplete-answer-to-inequality/Consider the following inequality:
Q - `1 < (2*x + 3) < 9`
Ans - `x` lies between `(-1, 3)`
But sagemath is only returning `x > -1` as the answer, which is incomplete. Why is that?
sage:
sage: solve([ 1 < 2*x + 3 < 9 ], x)
[[x > -1]]
sage:ggSat, 29 Feb 2020 08:30:57 -0600http://ask.sagemath.org/question/50119/Obtain a particular solution for a system of inequalities whose variables can only take certain valueshttp://ask.sagemath.org/question/47447/obtain-a-particular-solution-for-a-system-of-inequalities-whose-variables-can-only-take-certain-values/I want to get a particular solution (assuming it exists) of a system of inequalities, with 4 variables, having that those variables can take only certain values. What I have so far is:
SRC = 64
a, b, c, d = var('a', 'b', 'c', 'd')
assume(a >= 1 and a <= 8)
assume(b >=4 and b <= 512)
assume(c >= 2 and c <= 128)
assume(d, 'integer')
eq1 = (SRC / a) * b <= 418
eq2 = (((SRC / a) * b) / c) / d <= 200
eq3 = ((SRC / a) * b) / c <= 480
res = solve([eq1, eq2, eq3], a, b, c, d=1)
for i in res:
print(i)
The first result I obtain is:
[a < 0, 0 < c, -d > 0, 25*a*c*d - 8*b > 0, -15*a*c + 2*b > 0]
As you can see, `a < 0`, but I have stated that `a` must be greater than `1`. Why this happens?
How can I obtain a particular solution (if it exists)?DanDanFri, 09 Aug 2019 05:07:47 -0500http://ask.sagemath.org/question/47447/How to use sagemath to generate inequalitieshttp://ask.sagemath.org/question/47238/how-to-use-sagemath-to-generate-inequalities/ In cryptography, sbox is used to substitute a number with another for hiding the original one. For a 4 bit sbox, there will be 16 inputs and 16 outputs. I need to get the inequalities for the sboxjithendrakbMon, 22 Jul 2019 01:26:12 -0500http://ask.sagemath.org/question/47238/How to use sagemath to generate inequalitieshttp://ask.sagemath.org/question/47237/how-to-use-sagemath-to-generate-inequalities/ In cryptography sbox is used to substitute a number with another number(which doesn't have a linear relation to the previous one). So for a 4 bit sbox 16 different inputs give 16 different outputs. I need to get the inequalities of the sbox while giving all the inputs and outputs jithendrakbMon, 22 Jul 2019 01:21:48 -0500http://ask.sagemath.org/question/47237/Verifying inequalitieshttp://ask.sagemath.org/question/44645/verifying-inequalities/ I would like to give SageMath some inequalities, and then ask it if other inequalities follow from them.
For example, I would like to tell SageMath "a > 2*b > 0" and then ask it whether "a - b > b/2" and the answer should be "True", but if I ask whether "a - b > 3*b/2" the answer should be "False" (since it is not implied by the given inequalities).
How can I do this?
Erel Segal-HaleviTue, 11 Dec 2018 22:41:14 -0600http://ask.sagemath.org/question/44645/testing if system of inequalities has solutionhttp://ask.sagemath.org/question/40741/testing-if-system-of-inequalities-has-solution/Hi there,
I have a big system of inequalities (~1500 inequalities, 45 variables) and want to check, if there exists a real solution to it.
Trying out the 'solve' and 'solve_ineq' takes a huge amount of time or it breaks during calculation and after checking
some of the questions here I even assume the solve-function is broken and sometimes gives wrong results. Does anybody know about a function/system which returns in a responsible time and reliable if there exists a solution or not (existence is enough) (I want to use this in an actual proof, so it would be useless, if I can't trust the result).
In my use case I have the variables $a1, ..., a15, b1,...,b15,c1,...,c15 \in \mathbb R^+$ and my inequalities are all of the form
$$ \frac{f(a1,...,a15)}{g(c1,\dots, c15)} \geq \frac{f'(a1,\dots,a15)}{g'(c1,\dots, c15)}$$
(and same for combinations of (a,b) and (b,c)) for given linear functions $f,f',g,g'$ (i.e. multivariate polynomials with degree at most 1), so restricting to the variables $ai$ we get a system of linear inequalities (but even trying to solve these takes long/doesn't work with the solve function).
Actually more accuratly I have indexed sets $$F_{a,b} =\{{(f_i,g_i) | i \in I \}, F_{c,b} =\{(p_i,q_i) | i \in I \} ,F_{a,c} =\{(r_i,s_i) | i \in I \} $$
and want to show, that if there exists a solution $(a,b)$ of
$$\frac{f_k(a)}{g_k(b)} = max_i \frac{f_i(a)}{g_i(b)}$$
then there exists a solution $(c)$ to
$$\frac{r_k(a)}{s_k(c)} = max_i \frac{r_i(a)}{s_i(c)}$$
$$\frac{p_k(c)}{q_k(b)} = max_i \frac{p_i(c)}{q_i(b)}$$
So far I have a the follwing snippet:
#fractionAB are the saved fractions from above, a,b,c are arrays with e.g. a=[a1,a2,...,a15]
stopIt=False
for maxStretch in cands: #cands is the index set I
ineq=[fractionAB.get(maxStretch) >= fractionAB.get(cand) for cand in cands]
if solve(ineq,a+b):
#try here if there exists a middle point on the geodesic, i.e. geodesic exists
ineq.extend([fractionAC.get(maxStretch) >= fractionAC.get(cand) for cand in cands])
ineq.extend([fractionCB.get(maxStretch) >= fractionCB.get(cand) for cand in cands])
if not solve(ineq, a+b+c):
stopIt=True
print 'Tested for candidate ' , maxStretch
if stopIt:
break
I know, there is room for improvement e.g. at reusing to first solution from (a+b), the problem is, that even that first system pretty much kills the calculation. Also multiplying the denominators on each side doesn't seem to help.
PS: The mathjax seems to be broken on this site, since the code for leftbraces seems to vanish (hence the ugly "fix" above).ctstMon, 22 Jan 2018 13:05:31 -0600http://ask.sagemath.org/question/40741/find one interior point of a polyhedronhttp://ask.sagemath.org/question/10829/find-one-interior-point-of-a-polyhedron/Hi,
I have a bunch of inequations and I would like to know if there is a solution. What is the simplest way to achieve this in Sage ? I tried using MILP with success... but the point returned is not very fancy (often on the boundary). In an ideal world, I would like to optimize some quadratic function in order for the solution to be the nicest possible.
Here is a sample and simple example with only one inequality (other constraints are equalities) where I reproduced the output of MILP:
Constraints:
2.0 <= x_0 + x_7 + x_8 <= 2.0
2.0 <= x_1 + x_2 <= 2.0
2.0 <= x_3 + x_5 + x_9 <= 2.0
2.0 <= x_4 + x_6 <= 2.0
1.0 <= x_0 + x_2 + x_9 <= 1.0
1.0 <= x_5 + x_6 + x_8 <= 1.0
0.0 <= x_2 + x_6 <= 1.0
Variables:
x_0 is a continuous variable (min=0.0, max=2.0)
x_1 is a continuous variable (min=0.0, max=2.0)
x_2 is a continuous variable (min=0.0, max=2.0)
x_3 is a continuous variable (min=0.0, max=2.0)
x_4 is a continuous variable (min=0.0, max=2.0)
x_5 is a continuous variable (min=0.0, max=2.0)
x_6 is a continuous variable (min=0.0, max=2.0)
x_7 is a continuous variable (min=0.0, max=2.0)
x_8 is a continuous variable (min=0.0, max=2.0)
x_9 is a continuous variable (min=0.0, max=2.0)
There are plenty of *nice* solutions, one is
x0 = x2 = x5 = x6 = x8 = 1/3
x1 = x4 = 5/3
x3 = x7 = 4/3
But with the solver I got:
sage: p.solve()
sage: p.get_values(p[1],p[2],p[3],p[4],p[5],p[6],p[7],p[8],p[9])
[1, 2, 0, 2, 2, 0, 0, 0, 1]
ThanksvdelecroixFri, 13 Dec 2013 01:39:30 -0600http://ask.sagemath.org/question/10829/Solving system of polynomial inequalities in SageMath 8.1http://ask.sagemath.org/question/41056/solving-system-of-polynomial-inequalities-in-sagemath-81/ Hi everyone!
I am currently trying to use SageMath for the solution of a system of polynomial inequalities. In the first place based on the documentation and because solutions were returned I used the "solve" command and the "solve_ineq" command. However, when I tried to verify the answers with the one computed by Mathematica I realised the solutions were not the same. Is this a bug in the current version?
Also, I am trying to do it the normal way by computing the CAD using QEPCAD but when I tried to replicate the example on the website I get the following error:
> RuntimeError: unable to start QEPCAD
I am using SageMath 8.1 in Windows 7 64bit and jupyter notebook for interface that I call using the SageMath shell, if that is of any help.
The system I am referring to is the following:
> sys=[0.800000000000000*theta1*x1 + 0.100000000000000*theta2*x2 - 24000,
0.100000000000000*theta2*x2 + 0.0500000000000000*x1 - 2000,
0.100000000000000*x1 + 0.360000000000000*x2 - 6000,
-x1, -x2, -theta1 - 5, theta1 - 5, -theta2 - 5, theta2 - 5, -lamda1, -lamda2, -lamda3, -lamda4, -lamda5]
and using the following substitution:
> sol=[x1 == 440000/(16*theta1 - 1),
x2 == 80000*(4*theta1 - 3)/(16*theta1*theta2 - theta2),
lamda1 == 54*(3*theta2 - 2)/(16*theta1*theta2 - theta2),
lamda2 == 54*(32*theta1 - 3*theta2)/(16*theta1*theta2 - theta2),
lamda3 == 0, lamda4 == 0, lamda5 == 0]
The output of
> solve([sys[i].subs(sol)<=0 for i in range(0,len(sys))], theta1, theta2)
is
> []
Sorry for the long post but I would really appreciate and help with regards on how to solve such as system of inequalities and whether solve command has a bug?
Best,
Jason JasonKSat, 10 Feb 2018 07:58:03 -0600http://ask.sagemath.org/question/41056/Graphing ineqalitieshttp://ask.sagemath.org/question/39216/graphing-ineqalities/ So I'm trying to graph the inequality x+y+3u>=0
I want to keep the u fixed, but I'm having issues finding out how to do that.
Also, I was wondering if it would be possible to have some type of dynamic slider for u, so that this way I can change the value of u.kaylavb23Thu, 19 Oct 2017 09:37:54 -0500http://ask.sagemath.org/question/39216/exponential inequalityhttp://ask.sagemath.org/question/37692/exponential-inequality/Hi all, I am trying to solve, using sage, the inequality `exp(x) >= 5`, but this is what I get
sage: solve(exp(x)>=5,x)
#0: solve_rat_ineq(ineq=%e^_SAGE_VAR_x >= 5)
[[e^x - 5 == 0], [e^x - 5 > 0]]
Can anyone tell me what's wrong and how to solve this kind of inequalities?
Thanks
sorry for the presentation of the code, I am new on this plateform.sokingThu, 25 May 2017 02:56:44 -0500http://ask.sagemath.org/question/37692/Unable to create a contour_plot of a system of inequalitieshttp://ask.sagemath.org/question/34111/unable-to-create-a-contour_plot-of-a-system-of-inequalities/I am trying to plot a system of inequalities, dependent on a matrix H. Here is my function I am planning to contour_plot: <br>
def reg(x, y):
f1 = H[0,0] * H[0,0] * x + H[1,0] * H[1,0] * y
f2 = H[0,0] * H[0,1] * x + H[1,0] * H[1,1] * y
f3 = H[0,1] * H[0,1] * x + H[1,1] * H[1,1] * y
if f1 < 0 or f2 < 0 or f3 < 0:
return 0
else:
return 1
I then have H be
> H
> [2.220446049250313e-16 -0.9999999999999998]
> [ -0.9999999999999998 2.220446049250313e-16]
However
contour_plot(reg, (x,-Integer(5),Integer(5)), (y,-Integer(5),Integer(5)))
yields an error. It says
zero-size array to reduction operation minimum which has no identity
The strange part is that when
> H
> [-1 0]
> [ 0 1]
the same contour_plot yields exactly what I want without any errors <br>
Help would be much appreciated, I have just picked up SAGE this week and have much to learn
petkusSat, 16 Jul 2016 14:30:45 -0500http://ask.sagemath.org/question/34111/get range of values for inequalitieshttp://ask.sagemath.org/question/33653/get-range-of-values-for-inequalities/If I have a bunch of inequalities like $ x>y, y>z, z \\neq 5,x<z+y $
how do I get a range of values of each variable for which all these inequalities are satisfied? Thanks.
Edit: I found that this can be achieved with mathematica as mentioned in the below link:
mathematica.stackexchange.com/questions/38507/solve-the-system-of-equalities-and-inequalities
But, I want an open source solution. Is it possible with sage at all?abs_kumarFri, 03 Jun 2016 01:02:02 -0500http://ask.sagemath.org/question/33653/Plotting an inequality in 3D regionhttp://ask.sagemath.org/question/33277/plotting-an-inequality-in-3d-region/
Ideally I would like to plot a region in 3D space which is defined by a bunch of inequalities. For example let us consider the region $R$ defined by $$ \{ (x,y, z): x \le 0 \text{ and } y \le 0 \text{ and } x+y \le z \} $$.
I am wondering what would be an easier way to do it.
With my limited knowledge I came up with these two approaches.
*Approach 1 :* Generate points in this region and plot them in 3D. Is there a way to extend the function in <code> region_plot () </code> that generates plot points for my needs?
*Approach 2 :* Concatenate implicit -3D plots of functions of the form $ x + y - (z+t) $, where $t$ is a small positive parameter, for different values of $t$. Then plot all these simultaneously.
I would appreciate any alternate way to do this or any improvements on these approaches.
Thank you for your time in advance.
DBSSun, 01 May 2016 11:36:45 -0500http://ask.sagemath.org/question/33277/Simplifying an inequalityhttp://ask.sagemath.org/question/32786/simplifying-an-inequality/I ask:
var('x,y')
ineq = (x+2<y+2)
simplify(ineq)
and get:
x + 2 < y + 2
How can I get Sage to simplify this inequality to:
x < y
?
Erel Segal-HaleviSun, 13 Mar 2016 03:27:08 -0500http://ask.sagemath.org/question/32786/Checking if two inequalities are equivalenthttp://ask.sagemath.org/question/32798/checking-if-two-inequalities-are-equivalent/I ask:
var("x y")
assume(x,'integer')
assume(y,'integer')
print (x>y)==(y<x)
print (x>y)==(x-y>0)
and get:
True
False
So Sage recognizes the equivalence in the first pair but not in the second pair. Is there a way to handle this?
Erel Segal-HaleviSun, 13 Mar 2016 08:06:41 -0500http://ask.sagemath.org/question/32798/solve_ineq returns strange outputhttp://ask.sagemath.org/question/32789/solve_ineq-returns-strange-output/I ask:
var("x y")
ineq = [x==y, y<=0]
s = solve_ineq(ineq,[x])
s
and get:
[[x == y, y], [x == y, -y > 0]]
I understand the second set, but not the first. What does it mean when the inequality is just "**y**"?
A related question: how do I differentiate between inequalities with "==" or ">" and inequalities without?
Currently, when I ask:
print type(s[0][0])
print type(s[0][1])
I get the same result:
<type 'sage.symbolic.expression.Expression'>
<type 'sage.symbolic.expression.Expression'>
Erel Segal-HaleviSun, 13 Mar 2016 04:40:27 -0500http://ask.sagemath.org/question/32789/Solving a simple system of inequalitieshttp://ask.sagemath.org/question/32784/solving-a-simple-system-of-inequalities/I asked:
var('x','y','z')
solve_ineq([x<y,y<z])
and got:
[[y < z, x < y]]
What should I do to get the expected inequality:
x < z
?
Erel Segal-HaleviSat, 12 Mar 2016 23:57:36 -0600http://ask.sagemath.org/question/32784/Finding an assignment that satisfies a set of inequalitieshttp://ask.sagemath.org/question/32788/finding-an-assignment-that-satisfies-a-set-of-inequalities/ I have the following simple set of inequalities:
var('x,y')
assume(x,'integer')
assume(y,'integer')
assume(x>0)
assume(y>0)
ineq = [x<y, y<3]
I would like to find an assignment that satisfies this set of inequalities. In this case there is one such assignment:
x=1, y=2
In general there may be many assignments; I only need to find one. Is there a way to do this in SageMath?Erel Segal-HaleviSun, 13 Mar 2016 03:59:52 -0500http://ask.sagemath.org/question/32788/Extract equalities from a list of assumptionshttp://ask.sagemath.org/question/32008/extract-equalities-from-a-list-of-assumptions/Hi,
how can I recognize an equality from an inequality, in a list of assumptions?
thanks, danieleSun, 03 Jan 2016 07:49:04 -0600http://ask.sagemath.org/question/32008/Graph or plot a system of inequalitieshttp://ask.sagemath.org/question/29560/graph-or-plot-a-system-of-inequalities/Disclaimer: I'm somewhat new to Sage.
Is it possible to graph a system of inequalities in Sage? I'd like to reproduce the following system (top of image) and its graph (bottom of image). Based on (http://www.sagemath.org/tour-graphics.html), it seems like I need a region plot, but I'm not sure.
![image description](https://dl.dropboxusercontent.com/u/22824199/forums/sagemath/Systems%20of%20inequalities.png)mellow_yellowThu, 24 Sep 2015 07:34:10 -0500http://ask.sagemath.org/question/29560/(Unexpanded) symbolic inequalities yield erroneous resultshttp://ask.sagemath.org/question/29228/unexpanded-symbolic-inequalities-yield-erroneous-results/ I'm a SAGE novice, but have at least looked around this forum a bit on this matter. Apologies if this is a FAQ that I missed.
I am working with pretty simple symbolic expressions (type 'sage.symbolic.expression.Expression') involving rational numbers and some square roots. I have encountered several instances in which SAGE returns incorrect booleans when asking about inequalities between these things. For what it's worth, SAGE seems to get the answer right when I expand the expressions (simply by appending a .expand() to the end of them).
In particular, SAGE sometimes returns True when given "A < B" where A and B are symbolic expressions that are (not-obviously) equal. Here's an example that actually came up.
bool((1/8\*sqrt(2)\*(sqrt(2)\*(sqrt(2) - 2) + 4\*sqrt(2)) + 1/4\*sqrt(2)\*(sqrt(2) - 2) + 3/4\*sqrt(2) - 1/2) < (1/8\*sqrt(2)\*(sqrt(2) + 2) + 1/4\*sqrt(2) + 1/4))
SAGE returns True to this strict inequality. It also returns True when < is replaced by ==, as it should since these are equal. As mentioned, appending an .expand() to each side causes SAGE to return False to the strict inequality, which it should.
Any idea what's going wrong here?DrNickThu, 20 Aug 2015 11:39:48 -0500http://ask.sagemath.org/question/29228/Solving a symbolic inequalityhttp://ask.sagemath.org/question/26765/solving-a-symbolic-inequality/I'm trying to solve the inequality $18bcd - 4b^3d + b^2c^2 - 4c^3 - 27d^2 > 0$ with ${b,c,d} \in \mathbb{R}$ and $c < 0$. The goal is to obtain an expression for $d$.
My guess would be to use `solve_ineq()` and perhaps `assume()` for the additional condition, but I can't figure out how. In case of a symbolic equation I'd use
b,c,d = var('b,c,d')
Delta = (18*b*c*d - 4*b^3*d + b^2*c^2 - 4*c^3 - 27*d^2 == 0)
solve(Delta,d)AilurusFri, 08 May 2015 12:39:14 -0500http://ask.sagemath.org/question/26765/Solving system of inequalities in one variablehttp://ask.sagemath.org/question/26941/solving-system-of-inequalities-in-one-variable/ I am probably missing something about how to use sage:
If I run this:
x = var('x')
a = var('a')
solve([a*x>0,a>0],[x])
I get this results:
[[0 < x, a > 0], [x < 0, -a > 0, a > 0]]
However, I would expect something like:
[0 < x, a > 0]
What am I missing?
Thanksabc321Tue, 26 May 2015 04:38:05 -0500http://ask.sagemath.org/question/26941/Test if an inequality is feasible under assumptionshttp://ask.sagemath.org/question/26410/test-if-an-inequality-is-feasible-under-assumptions/I want to test if an inequality system is feasible under non-negativity assumptions. I run into the problem that the assumptions seem not be used by the inequality solver. Here is a minimal example
sage: (l1,l2) = var("l1 l2")
sage: assume (l1>=0)
sage: assume (l2>=0)
sage: solve (l1*l2<0, [l1,l2])
[[l1 < 0, 0 < l2], [0 < l1, l2 < 0]]
Is it possible to have the solver use the assumptions and determine infeasibility of the system? ThomasWed, 01 Apr 2015 05:03:33 -0500http://ask.sagemath.org/question/26410/Can sage help determine if $|f(x) - L| < \epsilon$ is true?http://ask.sagemath.org/question/25218/can-sage-help-determine-if-fx-l-epsilon-is-true/Here's what I want to check:
Given $f(x)$, $\epsilon>0$, $L\in \mathbb{R}$ and $N(\epsilon)$, is
$$n>N(\epsilon) \Rightarrow |f(n)-L | < \epsilon$$
true?
I thought I could accomplish this using symbolic expressions and `assume()`. This is what I've tried:
forget()
var('ep, n')
f(x)=1/(n+7)
N = (1/ep)-7
assume(ep>0)
assume(n>N)
show(abs(f(n)-0)<ep)
bool(abs(f(n)-0)<ep)
But the result of is `False`. What is the proper way to do this in Sage?
ensabaThu, 11 Dec 2014 07:48:54 -0600http://ask.sagemath.org/question/25218/How to do operations that change a relation?http://ask.sagemath.org/question/25217/how-to-do-operations-that-change-a-relation/ For example, given a < b, we know that if we multiply both sides with -1, we will get -a > -b.
But in sage, if I try this:
var('a b')
exp=a>b
exp*-1
I get:
−a>−b
The `>` did not get flip (the same also happens if we take the reciprocal).
Are the functions in Sage that can perform the multiplication with properly handle the inequality as well? Otherwise, what is the recommended way to do this manually? ensabaThu, 11 Dec 2014 07:34:45 -0600http://ask.sagemath.org/question/25217/LMI (Linear Matrix Inequalities)http://ask.sagemath.org/question/7753/lmi-linear-matrix-inequalities/Hello.
I installed SAGE and I was very happy with the results it gave in the very beginning.
However, the reason I installed it was because I need an open-source alternative for solving Linear matrix inequalities (LMIs). I did not find an LMI solver in SAGE, though.
I will be very delighted if you help me with this issue.
Please let me know if you want more information on the problems I want to solve.
Yours faithfully,
Slavi Slavchev,
PA (Professor Assistant)
Sofia University 'St Kliment Ohridski', Bulgaria
SUavchoTue, 09 Nov 2010 10:50:13 -0600http://ask.sagemath.org/question/7753/semialgebraic systems in Sagehttp://ask.sagemath.org/question/10552/semialgebraic-systems-in-sage/I would like to solve systems such as
solve([x^3-y^2 == 0, x<0, x^2+y^2<1], x, y)
I get
[[x < 0, -x^2 - y^2 + 1 > 0, -x^3 + y^2 == 0]]
i.e., the same thing.
W|A, for instance, says that "no solutions exist". Also Maple can easily deal with the system. Is there any package I'm missing? Are these systems manageable with Sage (or an embedded software)?
Thank you.
fbtnFri, 20 Sep 2013 01:06:43 -0500http://ask.sagemath.org/question/10552/solving a set of equations involving both inequalities and equalitieshttp://ask.sagemath.org/question/10086/solving-a-set-of-equations-involving-both-inequalities-and-equalities/How to write a code in sage to find solutions of a set of equalities and inequalities in more than one variables.for example i want to find solutions for the equations $\sum_{1 \leq i \leq 3}x_i =10$ , x_1 < x_2 < x_3 . REKHA BISWALThu, 02 May 2013 21:59:25 -0500http://ask.sagemath.org/question/10086/