ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 05 Dec 2016 04:08:09 -0600What is the meaning of the ouptput:Polynomial Sequence with 634 Polynomials in 35 Variableshttps://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/ I am doing calculations of finding Groebner basis of a toric ideal associated with one matrix. At the end I am getting output as **Polynomial Sequence with 634 Polynomials in 35 Variables** . I want a complete output which involves all these polynomials. Is there any command to do this?Sat, 03 Dec 2016 04:50:01 -0600https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/Answer by slelievre for <p>I am doing calculations of finding Groebner basis of a toric ideal associated with one matrix. At the end I am getting output as <strong>Polynomial Sequence with 634 Polynomials in 35 Variables</strong> . I want a complete output which involves all these polynomials. Is there any command to do this?</p>
https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/?answer=35890#post-id-35890The documentation for polynomial sequences is here:
[http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html](http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html)
It says
> We call a finite list of polynomials a `Polynomial Sequence`.
To see all the polynomials in the sequence, you can use the `list` command.
Example.
sage: sr = mq.SR(2,1,2,4,gf2=True,polybori=True)
sage: F,s = sr.polynomial_system()
sage: F
Polynomial Sequence with 112 Polynomials in 64 Variables
sage: list(F)
This outputs the list of all polynomials in the polynomial sequence.
Note that the representation of `F` is a string of the list itself if the sequence `F` has less than 20 elements, while if `F` has 20 elements or more, a summary is printed.
Example: compare
sage: P = PolynomialRing(GF(127), 2, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
4
sage: F
[a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0, a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0]
and
sage: P = PolynomialRing(GF(127), 10, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
20
sage: F
Polynomial Sequence with 20 Polynomials in 10 Variables
Note that this information is in the documentation for the `_repr_` method of `F`,
which you can access by typing
sage: F._repr_?
See also the source code by typing
sage: F._repr_??
Sat, 03 Dec 2016 05:30:18 -0600https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/?answer=35890#post-id-35890Comment by Nilesh for <p>The documentation for polynomial sequences is here:</p>
<p><a href="http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html">http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html</a></p>
<p>It says</p>
<blockquote>
<p>We call a finite list of polynomials a <code>Polynomial Sequence</code>.</p>
</blockquote>
<p>To see all the polynomials in the sequence, you can use the <code>list</code> command.</p>
<p>Example.</p>
<pre><code>sage: sr = mq.SR(2,1,2,4,gf2=True,polybori=True)
sage: F,s = sr.polynomial_system()
sage: F
Polynomial Sequence with 112 Polynomials in 64 Variables
sage: list(F)
</code></pre>
<p>This outputs the list of all polynomials in the polynomial sequence.</p>
<p>Note that the representation of <code>F</code> is a string of the list itself if the sequence <code>F</code> has less than 20 elements, while if <code>F</code> has 20 elements or more, a summary is printed.</p>
<p>Example: compare</p>
<pre><code>sage: P = PolynomialRing(GF(127), 2, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
4
sage: F
[a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0, a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0]
</code></pre>
<p>and</p>
<pre><code>sage: P = PolynomialRing(GF(127), 10, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
20
sage: F
Polynomial Sequence with 20 Polynomials in 10 Variables
</code></pre>
<p>Note that this information is in the documentation for the <code>_repr_</code> method of <code>F</code>,
which you can access by typing</p>
<pre><code>sage: F._repr_?
</code></pre>
<p>See also the source code by typing</p>
<pre><code>sage: F._repr_??
</code></pre>
https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/?comment=35919#post-id-35919Dear Sir, as per your suggestion I asked this as a separate question.Please go through it. Thanks.Mon, 05 Dec 2016 04:08:09 -0600https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/?comment=35919#post-id-35919Comment by slelievre for <p>The documentation for polynomial sequences is here:</p>
<p><a href="http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html">http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html</a></p>
<p>It says</p>
<blockquote>
<p>We call a finite list of polynomials a <code>Polynomial Sequence</code>.</p>
</blockquote>
<p>To see all the polynomials in the sequence, you can use the <code>list</code> command.</p>
<p>Example.</p>
<pre><code>sage: sr = mq.SR(2,1,2,4,gf2=True,polybori=True)
sage: F,s = sr.polynomial_system()
sage: F
Polynomial Sequence with 112 Polynomials in 64 Variables
sage: list(F)
</code></pre>
<p>This outputs the list of all polynomials in the polynomial sequence.</p>
<p>Note that the representation of <code>F</code> is a string of the list itself if the sequence <code>F</code> has less than 20 elements, while if <code>F</code> has 20 elements or more, a summary is printed.</p>
<p>Example: compare</p>
<pre><code>sage: P = PolynomialRing(GF(127), 2, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
4
sage: F
[a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0, a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0]
</code></pre>
<p>and</p>
<pre><code>sage: P = PolynomialRing(GF(127), 10, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
20
sage: F
Polynomial Sequence with 20 Polynomials in 10 Variables
</code></pre>
<p>Note that this information is in the documentation for the <code>_repr_</code> method of <code>F</code>,
which you can access by typing</p>
<pre><code>sage: F._repr_?
</code></pre>
<p>See also the source code by typing</p>
<pre><code>sage: F._repr_??
</code></pre>
https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/?comment=35916#post-id-35916It could be that the computation is taking a long time. Please ask this as a separate question. Be sure to provide code to define the ideal in question.Mon, 05 Dec 2016 00:25:49 -0600https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/?comment=35916#post-id-35916Comment by Nilesh for <p>The documentation for polynomial sequences is here:</p>
<p><a href="http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html">http://doc.sagemath.org/html/en/reference//polynomial_rings/sage/rings/polynomial/multi_polynomial_sequence.html</a></p>
<p>It says</p>
<blockquote>
<p>We call a finite list of polynomials a <code>Polynomial Sequence</code>.</p>
</blockquote>
<p>To see all the polynomials in the sequence, you can use the <code>list</code> command.</p>
<p>Example.</p>
<pre><code>sage: sr = mq.SR(2,1,2,4,gf2=True,polybori=True)
sage: F,s = sr.polynomial_system()
sage: F
Polynomial Sequence with 112 Polynomials in 64 Variables
sage: list(F)
</code></pre>
<p>This outputs the list of all polynomials in the polynomial sequence.</p>
<p>Note that the representation of <code>F</code> is a string of the list itself if the sequence <code>F</code> has less than 20 elements, while if <code>F</code> has 20 elements or more, a summary is printed.</p>
<p>Example: compare</p>
<pre><code>sage: P = PolynomialRing(GF(127), 2, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
4
sage: F
[a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0, a0 + 2*a1 - 1, a0^2 + 2*a1^2 - a0]
</code></pre>
<p>and</p>
<pre><code>sage: P = PolynomialRing(GF(127), 10, names='a')
sage: I = sage.rings.ideal.Katsura(P)
sage: F = Sequence([I.gens(),I.gens()], I.ring())
sage: len(F)
20
sage: F
Polynomial Sequence with 20 Polynomials in 10 Variables
</code></pre>
<p>Note that this information is in the documentation for the <code>_repr_</code> method of <code>F</code>,
which you can access by typing</p>
<pre><code>sage: F._repr_?
</code></pre>
<p>See also the source code by typing</p>
<pre><code>sage: F._repr_??
</code></pre>
https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/?comment=35911#post-id-35911Dear Sir, I had again done sage computations for finding a Groebner basis of an ideal in polynomial ring in 35 variables with coefficients from finite field with 2 elements. This time as soon as I enter a command I.groebner_basis()
No output is coming. Why this is so? What to do , to get an output?Sun, 04 Dec 2016 06:51:41 -0600https://ask.sagemath.org/question/35887/what-is-the-meaning-of-the-ouptputpolynomial-sequence-with-634-polynomials-in-35-variables/?comment=35911#post-id-35911