[sage-support] grobner bases
whats the best way to code the following I want a print out of a grobner basis for an ideal I generated by the polynomials this is respect to the reverse lexicographic and lexicographic order -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] grobner bases
On Saturday 09 October 2010, andrew ewart wrote: > whats the best way to code the following > I want a print out of a grobner basis for an ideal I generated by the > polynomials > > this is respect to the reverse lexicographic and lexicographic order sage: P. = PolynomialRing(QQ,order='neglex') sage: I = Ideal(x^5 + y^4 +z^3, x^3 + y^2 + z^2 -1) sage: I.groebner_basis() [1] See http://sagemath.org/doc/reference/sage/rings/polynomial/multi_polynomial_ideal.html Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF _www: http://martinralbrecht.wordpress.com/ _jab: martinralbre...@jabber.ccc.de -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: modulo operator for reals
On Oct 4, 7:03 pm, jpc wrote:
> Why does the plot
> plot(k%1,k,0,5)
> is not produced but the following works:
> k=var('k')
> plot( k/1, k,0,5).show()
> print 1.9%1
>
> What can be used instead ?
I can't explain the behavior. but wouldn't plot(x-floor(x),0,5)
produce the same output?
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[sage-support] Re: total differentiation
On Oct 8, 7:54 pm, Nils Bruin wrote:
> If you define x,y,z to be functions of m, it does what you want:
>
> sage: var("m")
> sage: x=function("x",m)
> sage: y=function("y",m)
> sage: z=function("z",m)
> sage: diff(f,m)
> cos(z(m))*D[0](z)(m) + 2*x(m)*D[0](x)(m) + D[0](y)(m)
Yes, but the point of total differentiation is that the parameter m
should be arbitrary. We should be able to handdle the differentials
without the need to specify with respect to what we are
differentiating, for instance:
In[1]:= Dt[x y]
Out[1]= y Dt[x] + x Dt[y]
Before reading your reply I had though it would be easy to implement
total differentiation in sage with the stuff we've already got, but on
a second thought i don't think sage can express diffrentials by
themselves right now...
Oscar
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[sage-support] What's easiest way to get Sage running on Windows for non-techie students?
What's easiest way to get Sage running on Windows for non-techie students? They'll be lost if the instructions are complicated. Possible to wrap a VMWare + Ubuntu + Sage blob into one big Windows exe file that requires no set up? -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: Plotting a function f(x) when x is not in the domain
When you know where the jump is you can use exclude: f(x) = abs(x+1) g = f.differentiate() show(plot(g(x),(-2,2),exclude=[-1]), xmin = -2,xmax = 1, ymin=-2,ymax=2) -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: total differentiation
Hi Oscar,
In Sage 4.6 (currently 4.6alpha2) you will be able to do this using
differential forms:
sage: x, y, z = var('x, y, z')
sage: U = CoordinatePatch((x, y, z))
sage: F = DifferentialForms(U)
sage: f = F(x^2 + y + sin(z)); f
(x^2 + y + sin(z))
sage: g = f.diff(); g
cos(z)*dz + 2*x*dx + dy
sage: g.parent()
Algebra of differential forms in the variables x, y, z
It's only a small step from having d f to obtaining D f.
All the best,
J.
On 9 okt, 07:26, Oscar Lazo wrote:
> On Oct 8, 7:54 pm, Nils Bruin wrote:
>
> > If you define x,y,z to be functions of m, it does what you want:
>
> > sage: var("m")
> > sage: x=function("x",m)
> > sage: y=function("y",m)
> > sage: z=function("z",m)
> > sage: diff(f,m)
> > cos(z(m))*D[0](z)(m) + 2*x(m)*D[0](x)(m) + D[0](y)(m)
>
> Yes, but the point of total differentiation is that the parameter m
> should be arbitrary. We should be able to handdle the differentials
> without the need to specify with respect to what we are
> differentiating, for instance:
>
> In[1]:= Dt[x y]
>
> Out[1]= y Dt[x] + x Dt[y]
>
> Before reading your reply I had though it would be easy to implement
> total differentiation in sage with the stuff we've already got, but on
> a second thought i don't think sage can express diffrentials by
> themselves right now...
>
> Oscar
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[sage-support] Re: grobner bases
indeed, thankyou martin -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: modulo operator for reals
This command
plot(k%1,k,0,5)
produce an error.
That % python operator does differently from "simple" modulo:
>>1.9%1
-0.1
>> 1.5%1
-0.5
>> 2.5 %1
0.5
It was strange that with "k/1" plot works fine but not with "k%1".
Pedro
On 9 Out, 15:19, Don Krug wrote:
> On Oct 4, 7:03 pm, jpc wrote:
>
> > Why does the plot
> > plot(k%1,k,0,5)
> > is not produced but the following works:
> > k=var('k')
> > plot( k/1, k,0,5).show()
> > print 1.9%1
>
> > What can be used instead ?
>
> I can't explain the behavior. but wouldn't plot(x-floor(x),0,5)
> produce the same output?
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[sage-support] Re: What's easiest way to get Sage running on Windows for non-techie students?
On 10/9/10 9:53 AM, Chris Seberino wrote: What's easiest way to get Sage running on Windows for non-techie students? They'll be lost if the instructions are complicated. Possible to wrap a VMWare + Ubuntu + Sage blob into one big Windows exe file that requires no set up? Since we can't redistribute VMWare, they'll have to download and install VMWare themselves. However, once that is done, it should be simply a matter of downloading the Sage VMWare image [1] and double-clicking on it. Jason [1] http://sagemath.org/download-windows.html -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
Re: [sage-support] modulo operator for reals
On Mon, Oct 4, 2010 at 4:03 PM, jpc wrote: > Why does the plot > plot(k%1,k,0,5) For a symbolic variable 'k', k%1 returns an error since the notion of a symbolic mod operation hasn't been implemented. > What can be used instead ? You can just delay the application of the mod operation: plot(lambda z: z%1.0, 0, 5) --Mike -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: total differentiation
On Oct 9, 2:58 pm, jvkersch wrote:
> Hi Oscar,
>
> In Sage 4.6 (currently 4.6alpha2) you will be able to do this using
> differential forms:
>
> sage: x, y, z = var('x, y, z')
> sage: U = CoordinatePatch((x, y, z))
> sage: F = DifferentialForms(U)
>
> sage: f = F(x^2 + y + sin(z)); f
> (x^2 + y + sin(z))
> sage: g = f.diff(); g
> cos(z)*dz + 2*x*dx + dy
>
> sage: g.parent()
> Algebra of differential forms in the variables x, y, z
>
> It's only a small step from having d f to obtaining D f.
>
> All the best,
> J.
That's great, from your example it seems like it shouldn't be too
difficult to make an analog to mathematicas Dt. I'm not familiarized
with differential forms. I what way is your f=f = F(x^2 + y + sin(z))
different to f(x,y,z) = x^2 + y + sin(z) ?
Oscar
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[sage-support] Re: modulo operator for reals
On Oct 9, 10:53 pm, Mike Hansen wrote: > On Mon, Oct 4, 2010 at 4:03 PM, jpc wrote: > > Why does the plot > > plot(k%1,k,0,5) > > For a symbolic variable 'k', k%1 returns an error since the notion of > a symbolic mod operation hasn't been implemented. > > > What can be used instead ? > > You can just delay the application of the mod operation: > > plot(lambda z: z%1.0, 0, 5) Just to make sure it's clear, Mike is doing sage: plot( lambda k: k%1., (k,0,5)) while the original poster would have had sage: plot( lambda k: k%1, (k,0,5)) verbose 0 (3766: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 198 points. verbose 0 (3766: plot.py, generate_plot_points) Last error message: 'Cannot convert non-integral float to integer' That is to say, just changing 1 to 1. 'fixes' it because now Sage knows that the modulus isn't an integer, so it can accept non-integer inputs on the other side as well. I guess this isn't technically a bug (or not different from not having the symbolic %), but maybe should the coercion do something with this? - kcrisman -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: What's easiest way to get Sage running on Windows for non-techie students?
On Oct 9, 8:24 pm, Jason Grout wrote: > On 10/9/10 9:53 AM, Chris Seberino wrote: > > > What's easiest way to get Sage running on Windows for non-techie > > students? > > > They'll be lost if the instructions are complicated. > > > Possible to wrap a VMWare + Ubuntu + Sage blob into one big Windows > > exe file that requires no set up? > > Since we can't redistribute VMWare, they'll have to download and install > VMWare themselves. However, once that is done, it should be simply a > matter of downloading the Sage VMWare image [1] and double-clicking on it. Yeah, it's still really annoying to get the VMWare itself, though, and requires giving out semi-personal information, which is perhaps not what one would want to get students interested in mathematical software... Anyone know what the latest status of the Cygwin port is? That is to say, there exists something that works (see http://groups.google.com/group/sage-windows/browse_thread/thread/ca02b59099bda7dc) but apparently it's not yet ready/possible to distribute... - kcrisman -- To post to this group, send email to sage-support@googlegroups.com To unsubscribe from this group, send email to sage-support+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
[sage-support] Re: total differentiation
Hi Oscar,
In this context, it is sufficient to think of a differential of a
function f as being given by the formula
d f = Df dt,
where Df is the total derivative. See also
http://en.wikipedia.org/wiki/Total_derivative
The line f = F(x^2 + y + sin(z)) turns the function x^2 + y + sin(z)
into a "differential form of degree 0". Technically, f is still the
same function, but now interpreted in the realm of differential forms
so that you can take the exterior derivative by writing f.diff().
Note that diff() doesn't take any arguments, but as you can see from
inspecting the result (the differential d f), the various partial
derivatives are computed and put together in the right order.
All the best,
Joris.
On 9 okt, 19:53, Oscar Lazo wrote:
> On Oct 9, 2:58 pm, jvkersch wrote:
>
>
>
> > Hi Oscar,
>
> > In Sage 4.6 (currently 4.6alpha2) you will be able to do this using
> > differential forms:
>
> > sage: x, y, z = var('x, y, z')
> > sage: U = CoordinatePatch((x, y, z))
> > sage: F = DifferentialForms(U)
>
> > sage: f = F(x^2 + y + sin(z)); f
> > (x^2 + y + sin(z))
> > sage: g = f.diff(); g
> > cos(z)*dz + 2*x*dx + dy
>
> > sage: g.parent()
> > Algebra of differential forms in the variables x, y, z
>
> > It's only a small step from having d f to obtaining D f.
>
> > All the best,
> > J.
>
> That's great, from your example it seems like it shouldn't be too
> difficult to make an analog to mathematicas Dt. I'm not familiarized
> with differential forms. I what way is your f=f = F(x^2 + y + sin(z))
> different to f(x,y,z) = x^2 + y + sin(z) ?
>
> Oscar
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