ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Wed, 23 Dec 2020 01:22:04 +0100A Simple Exponential Equationhttps://ask.sagemath.org/question/54862/a-simple-exponential-equation/Sage can solve the equation $8^t =37$ for $t$:
solve( (8)^t ==37, t )
But strangely, cannot solve $\left(\frac 89\right)^t =37$
solve( (8/9)^t ==37, t )
Any ideas?KapcakWed, 23 Dec 2020 01:22:04 +0100https://ask.sagemath.org/question/54862/Finding solution of expression with fractional powerhttps://ask.sagemath.org/question/53299/finding-solution-of-expression-with-fractional-power/I'm trying to solve this equation
$ 3(2.2+(\frac{64}{r})^{(1/3)})= 4(2.2+(\frac{128}{r-1})^{(1/4)})$ using solve function
I want to obtain the numerical solution
**but when i use `sol[0].n(30)`**
**TypeError:** cannot evaluate symbolic expression numerically
**when i try to `find_root(0,1,r)`**
**ValueError:** negative number to a fractional power not real
How to find the solution of this expression ?
deeppaul589Fri, 04 Sep 2020 11:18:45 +0200https://ask.sagemath.org/question/53299/Solving equation with algebraic numbershttps://ask.sagemath.org/question/52927/solving-equation-with-algebraic-numbers/ Hello, SAGE gives me error when I load this:
solve(x^2-AA(sqrt(3))==0,x)
but it gives no problem when I load
solve(x^2-sqrt(3)==0,x)
This is a small example of a bigger problem I have in which I must solve a system of equations involving algebraic numbers through AA(.) and QQbar(.). How can I make SAGE solve equations with this type of numbers? or there is no way? Thanks!creyesm1992Mon, 10 Aug 2020 15:23:58 +0200https://ask.sagemath.org/question/52927/Solving a polynomial system in a quotient ringhttps://ask.sagemath.org/question/52254/solving-a-polynomial-system-in-a-quotient-ring/I want to compute all solutions in $\mathbb{Z}_9[\sqrt2,x]$, where $x$ is such that $(x+\sqrt2)^2=2(x+\sqrt2)$, of the equation
$$X^2=1.$$
I'm first defining the polynomial ring over $\mathbb{Z}_9$ in variables $x,y$, then factoring by the ideal generated by
$$y^2-2, (x+y)^2-2(x+y),$$
to get the ring $S$, but then I don't know which command to use in order to get the solutions of $X^2-1$. I have tried "solve" and "variety" (defining $S[X]$ first and then the ideal of $X^2-1$), but they do not seem to work. The code up to this point is just
R.<x,y> = PolynomialRing(IntegerModRing(9),order='lex')
J= R.ideal(x^2-2,(x+y)^2-2*(x+y))
S=R.quotient(J)
Which function should I use?Jose BroxMon, 29 Jun 2020 16:55:09 +0200https://ask.sagemath.org/question/52254/problem: sage is not able to find solution to an equation.https://ask.sagemath.org/question/46841/problem-sage-is-not-able-to-find-solution-to-an-equation/ Hi everybody, I want to solve this non linear equation: omega_nf_eq = 0.
m,J_d,J_p,y,Y,omega,Omega,phi,Phi,z,Z,theta,Theta,k_yy,k_zz,k_phiphi,k_yphi,k_ztheta,k_thetatheta,plane_xy1,plane_xy2,plane_xz1,plane_xz2 = var('m J_d J_p y Y omega Omega phi Phi z Z theta Theta k_yy k_zz k_phiphi k_yphi k_ztheta k_thetatheta plane_xy1 plane_xy2 plane_xz1 plane_xz2')
t = var('t')
omega_nf_eq = -J_d^2*k_yy*k_zz*omega^4 + 0.382*J_d^2*k_yy*omega^6 + 0.382*J_d^2*k_zz*omega^6 - 0.145924*J_d^2*omega^8 + J_d*k_phiphi*k_yy*k_zz*omega^2 - 0.382*J_d*k_phiphi*k_yy*omega^4 - 0.382*J_d*k_phiphi*k_zz*omega^4 + 0.145924*J_d*k_phiphi*omega^6 + J_d*k_thetatheta*k_yy*k_zz*omega^2 - 0.382*J_d*k_thetatheta*k_yy*omega^4 - 0.382*J_d*k_thetatheta*k_zz*omega^4 + 0.145924*J_d*k_thetatheta*omega^6 - J_d*k_yphi^2*k_zz*omega^2 + 0.382*J_d*k_yphi^2*omega^4 - J_d*k_yy*k_ztheta^2*omega^2 + 0.382*J_d*k_ztheta^2*omega^4 + J_p^2*Omega^2*k_yy*k_zz*omega^2 - 0.382*J_p^2*Omega^2*k_yy*omega^4 - 0.382*J_p^2*Omega^2*k_zz*omega^4 + 0.145924*J_p^2*Omega^2*omega^6 - k_phiphi*k_thetatheta*k_yy*k_zz + 0.382*k_phiphi*k_thetatheta*k_yy*omega^2 + 0.382*k_phiphi*k_thetatheta*k_zz*omega^2 - 0.145924*k_phiphi*k_thetatheta*omega^4 + k_phiphi*k_yy*k_ztheta^2 - 0.382*k_phiphi*k_ztheta^2*omega^2 + k_thetatheta*k_yphi^2*k_zz - 0.382*k_thetatheta*k_yphi^2*omega^2 - k_yphi^2*k_ztheta^2 == 0
solve(omega_nf_eq, omega)
But the Sage is unable to find the solution, damn it.
I get this error message:
TypeError: ECL says: Memory limit reached. Please jump to an outer pointer, quit program and enlarge the memory limits before executing the program again.
I know the equation is big but i didn't expected such many problems.
I've already tried sympy but nothing.
Is there another way?
pull_over93Fri, 07 Jun 2019 00:35:14 +0200https://ask.sagemath.org/question/46841/AttributeError: 'dict' object has no attribute 'solve'https://ask.sagemath.org/question/46729/attributeerror-dict-object-has-no-attribute-solve/How I can fix this error '''AttributeError: 'dict' object has no attribute 'solve'
It appears after I tried to `solve(P)`:
G = I.groebner_basis()
P = {}
ind = 0
for i in range (n):
if (G[i].degree() < num):
ind = ind+1
P[ind] = G[i]
solve(P)MaoriThu, 30 May 2019 23:56:09 +0200https://ask.sagemath.org/question/46729/exponential equation solve problemhttps://ask.sagemath.org/question/45450/exponential-equation-solve-problem/ b=4*3^(2*x-1)==5*4^(x+2)
show(b)
solve(b,x)
The Solution is:
[4^(x + 2) == 4/5*3^(2*x - 1)]
Should the solve alg. solve for x?thethaWed, 13 Feb 2019 15:20:11 +0100https://ask.sagemath.org/question/45450/Solving linear congruencehttps://ask.sagemath.org/question/44618/solving-linear-congruence/ Is there a simple way to solve a linear congruence modulo an integer with large prime factors in Sage? `solve_mod` function cannot handle such large moduli apparently.kdr01Sun, 09 Dec 2018 20:28:31 +0100https://ask.sagemath.org/question/44618/How to get all (numerical) solutions of an equation?https://ask.sagemath.org/question/7634/how-to-get-all-numerical-solutions-of-an-equation/Mathematica's NSolve can produce all roots of a polynomial equation, like this:
sage: mathematica('NSolve[9*x^6 + 4*x^4 + 3*x^3 + x - 17 == 0, x]')
{{x -> -1.1030150726298147},
{x -> -0.49110203599909275 - 0.9883314953720708*I},
{x -> -0.49110203599909275 + 0.9883314953720708*I},
{x -> 0.5426095723140001 - 1.0543115206871092*I},
{x -> 0.5426095723140001 + 1.0543115206871092*I}, {x -> 1.}}
OTOH, Sage's solve gives just one real solution:
sage: solve(9*x^6 + 4*x^4 + 3*x^3 + x - 17 == 0, x)
[x == 1, 0 == 9*x^5 + 9*x^4 + 13*x^3 + 16*x^2 + 16*x + 17]
Is there a simple way to get all solutions?kkumerWed, 25 Aug 2010 11:42:23 +0200https://ask.sagemath.org/question/7634/Sage says equation isn't true while Mathematica says it ishttps://ask.sagemath.org/question/38795/sage-says-equation-isnt-true-while-mathematica-says-it-is/I have the following equation, of which I know that it is true when ```sigma > 0``` and ```mu > 0```.
eq = mu + 0.5*log(2*pi*sigma^2*e) == log(sqrt(2)*sqrt(pi)*sigma*e^(mu + 0.5))
So I set the constraints ```assume(sigma > 0)``` and ```assume(mu > 0)```. When evaluating it with ```bool(eq)```, Sage says ```False``` while Mathematica says that the equation holds. What am I doing wrong?muxamilianTue, 12 Sep 2017 15:22:24 +0200https://ask.sagemath.org/question/38795/solving systems of equations returns [] Reduxhttps://ask.sagemath.org/question/34608/solving-systems-of-equations-returns-redux/I searched the wiki and found the "solve always returns []" question. But it doesn't help me. I will admit that I am a complete neophyte with Sagemath and have been playing with version 7.2 on my windows machine.
I was trying to do something very simple: solve a basic Lagrange Multiplier problem, so I defined the following:
- var('x' ,'y' ,'z', 'lam')
- var('F')
- F = x*y*z - lam * (x*y*z-9)
- var('dFx', 'dFy', 'dFz', 'dFlam')
- dFx=diff(F,x)
- dFy=diff(F,y)
- dFz=diff(F,z)
- dFlam=diff(F,lam)
- solve([dFx==0,dFy==0,dFz==0,dFlam==0],x,y,z,lam)
but the **solve** returns []. It should return something like x==3, y==3, z==3, shouldn't it? Is there an alternative way to approach this?
Thanks.
BobM
BobMSat, 27 Aug 2016 10:28:29 +0200https://ask.sagemath.org/question/34608/Not understandable error when solving polynomial equationhttps://ask.sagemath.org/question/33050/not-understandable-error-when-solving-polynomial-equation/Hi all,
when I enter command
solve(symbolic_expression(x^12 - x^11 - 12*x^10 + 11*x^9 + 54*x^8 - 43*x^7 - 113*x^6 + 71*x^5 + 110*x^4 - 46*x^3 - 40*x^2 + 8*x + 1)==0, var(x), to_poly_solve=True)
I get the expected result, but when I enter command
solve(symbolic_expression(x^10 - 10*x^8 + 35*x^6 + x^5 - 50*x^4 - 5*x^3 + 25*x^2 + 5*x - 1), var(x), to_poly_solve=True)
I get the error message
---------------------------------------------------------------------------
TypeError Traceback (most recent call last)
<ipython-input-203-6108bea90b72> in <module>()
----> 1 solve(symbolic_expression(x**Integer(10) - Integer(10)*x**Integer(8) + Integer(35)*x**Integer(6) + x**Integer(5) - Integer(50)*x**Integer(4) - Integer(5)*x**Integer(3) + Integer(25)*x**Integer(2) + Integer(5)*x - Integer(1)),var(x),to_poly_solve=True)
/usr/local/sage-6.4.1-x86_64-Linux/local/lib/python2.7/site-packages/sage/symbolic/relation.py in solve(f, *args, **kwds)
732 from sage.symbolic.expression import is_Expression
733 if is_Expression(f): # f is a single expression
--> 734 ans = f.solve(*args,**kwds)
735 return ans
736
/usr/local/sage-6.4.1-x86_64-Linux/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.solve (build/cythonized/sage/symbolic/expression.cpp:47061)()
/usr/local/sage-6.4.1-x86_64-Linux/local/lib/python2.7/site-packages/sage/symbolic/expression.so in sage.symbolic.expression.Expression.solve (build/cythonized/sage/symbolic/expression.cpp:46887)()
TypeError: 'sage.symbolic.expression.Expression' object does not support indexing
What happened here? The error message is totally misleading (no index in the command!) and it is not to understand why the second command fails while the first works fine.
By the way, the polynomial in question has ten simple real roots, so there should be no problem to compute the roots if symbolic evaluation is not possible.
Thanks in advance
Wolfgang
wjansenSun, 10 Apr 2016 18:29:46 +0200https://ask.sagemath.org/question/33050/Solving a quartic equationhttps://ask.sagemath.org/question/26993/solving-a-quartic-equation/ I'm attempting to rearrange an equation from an [answer on the Mathematics StackExchange](http://math.stackexchange.com/questions/1298722/find-parametric-line-between-two-2d-line-segments-that-is-an-exact-distance-from).
The answer given is this equation:
$$L^2 = (-ab(t)+p)^2-\left(\frac{(-ab(t)+p).(cd(t)-ab(t))}{(cd(t)-ab(t))^2}(cd(t)-ab(t))\right)^2$$
Where $a$, $b$, $c$, $d$, and $p$ are known 2D points, $L$ is a known length, and $t$ is an unknown scalar. $ab(t)$ indicates interpolation between $a$ and $b$.
I am interested in rearranging this to solve for $t$. Here's what I've tried in Sage:
<pre><code>def sqr(var): return var.dot_product(var)
var('ax bx cx dx px ay by cy dy py t L')
a = vector([ax, ay])
b = vector([bx, by])
c = vector([cx, cy])
d = vector([dx, dy])
p = vector([px, py])
g = a - a*t + b*t
h = c - c*t + d*t
u = p - g
v = h - g
eq = L^2 == sqr(u) - sqr((u.dot_product(v)/sqr(v)) * v)
eq.solve(t)
</pre></code>
At the `solve` step I have observed it to sit for quite a while without producing a result. Two questions:
1. Am I inputting the problem correctly?
2. Is there any way to know if this is likely to terminate in a reasonable time? I have no idea what the solver looks like under the hood, and wouldn't want to wait for some `O(n!)` calculation to terminate :)
nicholasbishopMon, 01 Jun 2015 04:51:26 +0200https://ask.sagemath.org/question/26993/solve equation with double sumhttps://ask.sagemath.org/question/26465/solve-equation-with-double-sum/Hi!
Please help me with my porblem. I have two no-linear equations:
1) f(x)==h(x)
2) g(x)+S_{i,j,k}(x) == 0
I know I can solve (numerically) eq.(1) doing:
x=var('x')
find_root(f(x)==h(x),x,x_min,x_max)
In eq.(2) S_{i,j,k}(x) is a triple sum function of 'x' and i,j and k are the index of the sum.
How can I solve (numerically) eq.(2)?
Waiting for your answers. Thanks a lot!
Best regards
----------------------------------------------------------
Update:
If I run the next code:
import sympy.mpmath
N=20
A=0.7
G_0 = 37.7
B = 0.36
x = sympy.symbols('x')
def S(x_):
return sympy.mpmath.nsum(lambda i, j, k: (12*A**4*x_**6*i**4-30*A**2*x_**3*i**2*(j**2+k**2)+3*(j**2+k**2)**2)/(2*(A**2*x_**3*i**2+j**2+k**2)**(7/2)),[1,N],[1,N],[1,N])
def F(x_):
return G_0 * (x_ - 1/(x_**2))
print(sympy.mpmath.findroot(F(x) + B*A*sqrt(x)*S(x), [0.85,1]) )
I get the next error:
TypeError: unsupported operand parent(s) for '*': 'Symbolic Ring' and '<class 'sympy.mpmath.ctx_mp_python.mpf'>'
What am I doing wrong?
Best regards!
mresimulatorWed, 08 Apr 2015 14:59:34 +0200https://ask.sagemath.org/question/26465/Equations solvinghttps://ask.sagemath.org/question/25479/equations-solving/ Hi everybody, i've got this two equations:
eqq0: V_f*cos(delta(t))=v(t)
eqq1: V_f*sin(delta(t))=l*diff(psi(t))
I need to isolate V_f from the first equation, obtaining V_f=v(t)/cos(delta(t)) and substitute it in the second equation. Then i have to isolate diff(psi(t))=[v(t)*tan(delta(t))]/l.
I did :
a=solve (eqq0,V_f)
V_ff=a.right()
but it says *"AttributeError: 'Sequence_generic' object has no attribute 'right'"*
How can i solve this two equations?
Thank you.
SilviaSun, 11 Jan 2015 20:16:36 +0100https://ask.sagemath.org/question/25479/why can't sage solve the equation x^n == 2*x ?https://ask.sagemath.org/question/10374/why-cant-sage-solve-the-equation-xn-2x/ sage: var('x n')
(x, n)
sage: solve(x^n==2*x,x)
[x == 1/2*x^n]
This is not what I expect.
Who can help?
Thanks.
amaleaMon, 22 Jul 2013 13:50:43 +0200https://ask.sagemath.org/question/10374/Extended Euclid with polynomialshttps://ask.sagemath.org/question/10884/extended-euclid-with-polynomials/Suppose given polynomials $e,q,h,r$ in $R[x]$, $p \in R$ (R a ring), how can I use Sage to find $f$ in $R[x]$ so $f e = q h + r (\text{mod } p)$?
Similarly, given $f,g$ in $R[x]$ with $\text{gcd}(f,g)=1$, what function can I use to compute $s,t$ in $R[x]$ so $s f + g h = 1 (\text{mod } p)$ ?
erinbFri, 03 Jan 2014 19:31:55 +0100https://ask.sagemath.org/question/10884/A bug with solve xy=x ?https://ask.sagemath.org/question/10868/a-bug-with-solve-xyx/For solving the equation "xy=x", we can do:
sage: x,y=var('x,y')
sage: solve([x*y==x],[x,y])
[x == 0]
But this is not the complete solution.
We need to add the trivial equation "0==0" for having the complete solution:
sage: solve([x*y==x,0==0],[x,y])
[[x == 0, y == r1], [x == r2, y == 1]]
> Is it a bug ?
Sébastien PalcouxMon, 30 Dec 2013 11:58:08 +0100https://ask.sagemath.org/question/10868/Real Solution of x^3+8 == 0?https://ask.sagemath.org/question/8393/real-solution-of-x38-0/I do not understand the following:
sage: assume(x,'real')
sage: solve(x^3+8==0,x)
[]
Why does this equation have no solution?
But -2 is a solution!
Thanks for help!
amaleaTue, 18 Oct 2011 15:07:48 +0200https://ask.sagemath.org/question/8393/How to make solve to use certain variables on the right sidehttps://ask.sagemath.org/question/8247/how-to-make-solve-to-use-certain-variables-on-the-right-side/if I have
I1, IR1, IR2, U1, R1, R2 = var('I1 IR1 IR2 U1 R1 R2')
equations = [
I1 == IR1 + IR2,
IR1 == U1/R1,
IR2 == U1/R2
]
how can I make solve to return
I == (R1 + R2)*U1/(R1*R2)
?
solve(equations, I)
now returns just an empty list
or similait problem is with
I1, IC1, IC2, U1d, U2d, C1, C2 = var('I1, IC1, IC2, U1d, U2d, C1, C2')
equations = [
I1 == IC1 + IC2,
IC1 == C1*U1d,
IC2 == C2*U1d
]
and desired result is
I1 == (C1 + C2)*IC2/C2
OndraFri, 29 Jul 2011 19:56:54 +0200https://ask.sagemath.org/question/8247/Difficulty solving some second order differential equationshttps://ask.sagemath.org/question/10177/difficulty-solving-some-second-order-differential-equations/I have trouble finding 10% and 90% of the rise time in a second order differential equation.
I have tried to search but i have not solved my issue, so now i ask here.
I have added the code to aleph.sagemath.org however the link is crazy long so i put it in a short link: [http://bit.utoft.org/138hfAz](http://bit.utoft.org/138hfAz)
The code is also on pastebin
[http://pastebin.com/4hwdLJuT](http://pastebin.com/4hwdLJuT)
Please help :)
Cheers
J. UtoftjesperFri, 31 May 2013 13:51:05 +0200https://ask.sagemath.org/question/10177/Trigonometric Equation Solving: Not Terminatinghttps://ask.sagemath.org/question/9898/trigonometric-equation-solving-not-terminating/## The Background
I want to write a script which is able to do the following:
- **INPUT:** **`x`** - A list of triangle items. These items are considered as given.
- **INPUT:** **`y`** - A list of triangle items. We want to know the abstract formulas of these items.
- **OUTPUT:** **`z`** - A list of formulas to calculate the items from `y`
For example:
- **INPUT:** **`x`** - `[alpha, beta]` (considered as given)
- **INPUT:** **`y`** - `[gamma]` (we want to know the formula of `gamma`)
- **OUTPUT:** **`z`** - `[gamma == pi - alpha - beta]`
I want to do that using `sage`'s `solve()`.
## My Problem:
This is a simplified script. It is just able to output formulas for `alpha`, `beta` and `gamma` when `a`, `b` and `c` are considered as given:
rings = RR[('a', 'b', 'c')].gens()[:3] # considered as given
x = dict([(str(rings_), rings_) for rings_ in rings])
varbs = SR.var(['alpha', 'beta', 'gamma']) # looking for `alpha`, `beta` and `gamma`
x.update([(str(varbs_), varbs_) for varbs_ in varbs])
print solve([
#x['a']**2 == x['b']**2 + x['c']**2 - 2*x['b']*x['c']*cos(x['alpha']),
#x['b']**2 == x['a']**2 + x['c']**2 - 2*x['a']*x['c']*cos(x['beta']),
#x['c']**2 == x['a']**2 + x['b']**2 - 2*x['a']*x['b']*cos(x['gamma']),
x['alpha'] == arccos((x['a']**2 - x['b']**2 - x['c']**2) / 2*x['b']*x['c']),
x['beta'] == arccos((x['b']**2 - x['a']**2 - x['c']**2) / 2*x['a']*x['c']),
x['gamma'] == arccos((x['c']**2 - x['a']**2 - x['b']**2) / 2*x['a']*x['b']),
#pi == x['alpha'] + x['beta'] + x['gamma'],
], [
x['alpha'],
x['beta'],
x['gamma'],
])
This script is working correctly and outputs:
[
[alpha == pi - arccos(-0.5*a^2*b*c + 0.5*b^3*c + 0.5*b*c^3), beta == pi - arccos(0.5*a^3*c - 0.5*a*b^2*c + 0.5*a*c^3), gamma == arccos(-0.5*a^3*b - 0.5*a*b^3 + 0.5*a*b*c^2)]
]
I wanted to extend `solve()`'s knowledge base in order to be able to solve more complicated problems later on. But when I tried to uncomment the `#` lines and ran the script again, `solve()` didn't terminate any more.
## My Question:
* Why doesn't `solve()` terminate when I uncomment the `#` lines?
* How can I get `sage` to terminate? Or: How can I work around this problem?
Thanks - if anything's unclear, please leave a comment concerning that.fdj815Sun, 10 Mar 2013 09:56:09 +0100https://ask.sagemath.org/question/9898/solve an equation in terms of an expression?https://ask.sagemath.org/question/9749/solve-an-equation-in-terms-of-an-expression/Hi,
Not entirely sure if I worded the subject line of this question right,
Essentially what I am trying to do is rearrange an equation based on what I want on the left hand side of it, for example:
I have defined my variables:
var('v_o, v_i, delta, T, v_d, v_c')
Entered my equation:
eqn1= v_i * delta * T == v_o + v_d + v_c - v_i * (1-delta) * T
Made a substitution:
eqn2 = eqn1.substitute(v_c=v_i)
and now, with minimum possible effort I would like sage to put it in the form of:
delta/(1-delta)=...
Many thanks to anyone who's even read this far down,
Any help would be much appreciated
penfoldMon, 28 Jan 2013 14:12:07 +0100https://ask.sagemath.org/question/9749/Solve log equations problemhttps://ask.sagemath.org/question/8783/solve-log-equations-problem/Input
var('x')
solve((log((x**2 - x), 6) - log((6*x - 10), 6) == 0), x)
Output
[log(x^2 - x) == log(6*x - 10)]
But real roots are 5 and 2. What I doing wrong?TicksyFri, 09 Mar 2012 12:36:53 +0100https://ask.sagemath.org/question/8783/determine consistency of nonlinear system of equationshttps://ask.sagemath.org/question/8540/determine-consistency-of-nonlinear-system-of-equations/Hello,
I need to be able to determine the consistency of very large systems of polynomial equations, with 30-40 variables and as many equations. When I put such systems into ``solve``, I get the same system back again. Here are some equations typical of those in the systems I am dealing with:
``2*a0*b0 == 0,``
``2*a0*b5 + 2*a1*b4 + 2*a4*b1 + 2*a5*b0 - 4*a8*b8 == 0,``
``2*a0*b10 + 2*a1*b9 + 2*a10*b0 + 2*a2*b8 + 2*a8*b2 + 2*a9*b1 == 0,``
``3*b0^2*c6 + 6*b0*b1*c5 + 6*b0*b2*c4 + 6*b0*b4*c2 + 6*b0*b5*c1 + 6*b0*b6*c0 - 12*b0*b8*c9 - 12*b0*b9*c8 + 3*b1^2*c4 + 6*b1*b4*c1 + 6*b1*b5*c0 - 12*b1*b8*c8 + 6*b2*b4*c0 - 6*b8^2*c1 - 12*b8*b9*c0 + 2*a0*a6 + 2*a1*a5 + 2*a2*a4 - 4*a8*a9 == 0``
This is not a complete system - just a few equations to show the lengths of equations that tend to come up. Again, I don't care what any solutions are; I just need to know if any exist. Is there a way to do this in sage?
Thanks!shacsmugglerThu, 08 Dec 2011 14:32:48 +0100https://ask.sagemath.org/question/8540/strange behaviour when solving equations symbolicallyhttps://ask.sagemath.org/question/8452/strange-behaviour-when-solving-equations-symbolically/I'm new to sage and wanted to get startet. However, i tried solving equations symbolically and found a strang behaviour i do not understand. Can anybody explain to me this behaviour?
$ sage
----------------------------------------------------------------------
| Sage Version 4.7.1, Release Date: 2011-08-11 |
| Type notebook() for the GUI, and license() for information. |
----------------------------------------------------------------------
sage: r, u, m, M = var('r, u, m, M')
sage: qe = (u == sqrt(r^2 + m^2) + sqrt(r^2 + M^2))
sage: qe
u == sqrt(m^2 + r^2) + sqrt(M^2 + r^2)
sage: print solve(qe, r)
[
sqrt(M^2 + r^2) == u - sqrt(m^2 + r^2)
]
sage:
Any suggestions?carstenTue, 08 Nov 2011 09:14:51 +0100https://ask.sagemath.org/question/8452/unsolved equationhttps://ask.sagemath.org/question/8265/unsolved-equation/Dear sage user,
Could you help me to find z = z(t)?, if:
((2.867e28) / (sqrt (r^3 - (2.1e13)^3 )) ) == (( (2.121e8)*(sqrt(2*(z^2) -1))) / ( z - sqrt (z^2 - 1)))
with,
r == ((1.97774e13)*(sqrt(sqrt(t)))) + ((3.55214e12)*(sqrt(t)))
1 < t < 6000
z(t= 1) = 100
r (t= 1) = 2.332954e13
thanks!!
I couldn't solve it!!!
milofisMon, 08 Aug 2011 12:48:57 +0200https://ask.sagemath.org/question/8265/Solving symbolically equation systemhttps://ask.sagemath.org/question/8242/solving-symbolically-equation-system/I have an equation system:
*U(t) = R * I(t) + L * I'(t) + uC(t)*
*I(t) = C * uC'(t)*
I want to know value of *I'(t)* and *uC'(t)*, which is *(-I(t) * R + U - uC(t))/L* and *I(t)/C* respectively.
In sage I represent it this way:
R = 6; C = 10^(-4); L = 0.1
t = var('t')
U = function('U', t).function(t); I = function('I', t).function(t); uC = function('uC', t).function(t)
equations = [
U == R * I + L * I.diff(t) + uC,
I == C * uC.diff(t)
]
but
solve(equations, I.diff(t), uC.diff(t))
does't seem to be working. (*TypeError: 'sage.symbolic.expression.Expression' object is not iterable*)
why? how can I do this?
OndraSat, 23 Jul 2011 21:24:08 +0200https://ask.sagemath.org/question/8242/System of nonlinear equationshttps://ask.sagemath.org/question/8224/system-of-nonlinear-equations/Hello,
Is it possible to solve the following using Sage?
http://www.wolframalpha.com/input/?i=solve%28%5Bx1%2Bx2%2Bx3-6%3D%3D0%2Cx1*x2*x3-6%3D%3D0%2Cx1%5E2%2Bx2%5E2%2Bx3%5E2-14%3D%3D0%5D%2Cx1%29
Thanks in advance.Eviatar BachWed, 13 Jul 2011 23:40:44 +0200https://ask.sagemath.org/question/8224/Solve system of equations with additional conditions in sagehttps://ask.sagemath.org/question/8120/solve-system-of-equations-with-additional-conditions-in-sage/Hi Sage users,
I've got a system of equations like the following example:
- **eq1 = a + b == n * (c + d)**
- **eq2 = b == k * d**
with n and k must be integers.
for the other variables, there are additional conditions like
- **a >= 80**
- **b >= 1000**
- **c >= 20**
- **d >= 40**
- **a + b <= 2000**
- **c + d <= 90**
I want to get all solutions of this system where n and k are integers.
Is there a way to find these with sage?
Would be great to get any possible hint to do this!
Thanks for your suggestions,
TobitwkWed, 18 May 2011 17:54:35 +0200https://ask.sagemath.org/question/8120/