Hi all
thanks for the answers. Here is simple example. It's in fact
intersection of two
projective curves:
a cuspidal cubic curve y^2*z-x^3=0 and its polar w.r.t. (2:1:1) :
2*y*z + y^2 - 2*3*x^2.
when substituting z=1 i used:
solve([y^2-x^3==0, 2*y +y^2 -2*3*x^2==0], x, y).
The general case wil
Can the original poster provide a (simple) example of the kind of set
of equations he wants to solve? For example, are they polynomials in
several variables, or more exotic? In the case of polynomial
equations it is more likely that (perhaps via Singular) the
multiplicities can be obtained.
Joh
Hi!
On 6 Jun., 05:45, Robert Dodier wrote:
> CVS log claims this bug was fixed recently (between 5.17 & 5.18).
> Here's what I get with Maxima from CVS (5.18+).
>
> ...
Very good! So, ticket #6228 can be closed when the new maxima version
is in Sage.
But I think we should now come back to the
Marshall Hampton wrote:
> sage: z = var('z')
> sage: f5 = (z^5-1)^2
> sage: f5.roots()
>
> [(e^(2/5*I*pi), 2),
> (e^(4/5*I*pi), 2),
> (e^(-4/5*I*pi), 1),
> (e^(-2/5*I*pi), 1),
> (1, 2)]
>
> Odd, very odd. I guess one of us should write about this on the
> maxima list.
CVS log claims this bu
Its a puzzling pattern as to which multiplicities are incorrect:
sage: z = var('z')
sage: f5 = (z^5-1)^2
sage: f5.roots()
[(e^(2/5*I*pi), 2),
(e^(4/5*I*pi), 2),
(e^(-4/5*I*pi), 1),
(e^(-2/5*I*pi), 1),
(1, 2)]
Odd, very odd. I guess one of us should write about this on the
maxima list.
-Ma
Oops.
On 5 Jun., 21:32, simon.k...@uni-jena.de wrote:
> sage: E=(z^3-1)^3
> sage: e = E==0
> sage: m=e._maxima_()
> sage: m.solve(z).str()
> '[z=(sqrt(3)*%i-1)/2,z=-(sqrt(3)*%i+1)/2,z=1]'
Here I forgot to copy-and-paste the line
sage: P = m.parent()
> sage: P.get('multiplicities')
Hi!
I should add that the bug occurs for sage 4.0.
Is it still there in 4.0.1?
It seems that the problem is in maxima. Looking at the code, solve
does the following:
sage: E=(z^3-1)^3
sage: e = E==0
sage: m=e._maxima_()
sage: m.solve(z).str()
'[z=(sqrt(3)*%i-1)/2,z=-(sqrt(3)*%i+1)/2,z=
Dear Marshall
On 5 Jun., 21:07, Marshall Hampton wrote:
> That's pretty disturbing because those complex roots should have
> multiplicity 3.
So, I was right that the multiplicities where a bit odd... :)
> Is this a known bug?
I searched in trac. There used to be two open tickets mentioning
mu
That's pretty disturbing because those complex roots should have
multiplicity 3.
Is this a known bug?
-Marshall Hampton
On Jun 5, 1:05 pm, simon.k...@uni-jena.de wrote:
> Hi Michael,
>
> On 5 Jun., 18:26, Michael Friedman wrote:
>
> > I'm pretty new to Sage, so I'm sorry in advance for the tri
Hi Michael,
I am sorry for my previous reply. I think I missed one word in your
question:
On 5 Jun., 18:26, Michael Friedman wrote:
> I'm pretty new to Sage, so I'm sorry in advance for the trivial
> question.
> I have a set of (non-linear) equations, and I need to find the multiplicity
Hi Michael,
On 5 Jun., 18:26, Michael Friedman wrote:
> I'm pretty new to Sage, so I'm sorry in advance for the trivial
> question.
> I have a set of (non-linear) equations, and I need to find the
> multiplicity of each solution. How do I do it?
First of all, solving a nonlinear eqution is not
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