Re: [sage-support] Re: Group action
thnx, this looks nice. I'll have a deeper look at it in the next days. bg, Johannes On 19.04.2013 17:53, Simon King wrote: Hi Johannes, On 2013-04-18, Johannes dajo.m...@web.de wrote: Hi guys, I have the following setting: Given a finite subgroup G of GL_\C(n) of order k, acting on C[x_1,...,x_n] by multiplication with (potenz of a ) k-th root of unity. What is the best way, to translate this setting to sage? In the end I'm interested into the ring of invariants under G and it's representation as quotient. Towards an answer: Since you want to compute an invariant ring, and since CC is not exactly a field (rounding errors), it might make sense to work over a number field that contains a k-th root of unity. For example: # Create the number field sage: F.zeta = NumberField(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) sage: zeta^7 == 1 True # Create a 3x3 matrix that acts by multiplication with zeta sage: MS = MatrixSpace(F, 3) sage: g = MS(zeta) # Create the corresponding matrix group. It has the correct order # Note that the method multiplicative_order or the matrix fails! sage: G = MatrixGroup([g]) sage: G.order() 7 # Compute a minimal generating set of the invariant ring, as a sub-ring sage: G.invariant_generators() [x3^7, x2*x3^6, x1*x3^6, x2^2*x3^5, x1*x2*x3^5, x1^2*x3^5, x2^3*x3^4, x1*x2^2*x3^4, x1^2*x2*x3^4, x1^3*x3^4, x2^4*x3^3, x1*x2^3*x3^3, x1^2*x2^2*x3^3, x1^3*x2*x3^3, x1^4*x3^3, x2^5*x3^2, x1*x2^4*x3^2, x1^2*x2^3*x3^2, x1^3*x2^2*x3^2, x1^4*x2*x3^2, x1^5*x3^2, x2^6*x3, x1*x2^5*x3, x1^2*x2^4*x3, x1^3*x2^3*x3, x1^4*x2^2*x3, x1^5*x2*x3, x1^6*x3, x2^7, x1*x2^6, x1^2*x2^5, x1^3*x2^4, x1^4*x2^3, x1^5*x2^2, x1^6*x2, x1^7] So, the invariant ring could be represented as a ring with not less than 36 generators, modulo algebraic relations. Now, I am afraid I don't know an easy way to find algebraic relations of the above sub-algebra generators---I am afraid I can't answer how to represent it as a quotient ring. Best regards, Simon -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: plot3d using real-valued real-parameter functions but involving complex numbers as intermediates
On 04/18/2013 03:13 AM, Gary McConnell wrote: I am very keen to help - my problem is utter incompetence at following the high-level instructions in the manual for developers. Also I am on the VM and I cannot access the sage directories directly. Is there a way you could send me a manual file that I could modify and send back to you? Sorry :( I promise I will learn this one day ... the page I was referring to is http://www.sagemath.org/doc/reference/numerical/sage/numerical/optimize.html#sage.numerical.optimize.minimize Also there are presumably many functions to which this syntax difference applies ... how can I find them? Thanks! I failed to notice this reply earlier. I think it is better if you can submit a patch to trac. The patch is generated by mercurial and it can automatically populate the author attribution and other information. These information is used by a patchbot that automatically tests the patches for validity and performs other tests. To generate the patch, you can either install the sage library code. If you don't want to install the sage from source, you can download the sage spkg and work with that. This is OK since you intend to do only documentation changes. In this case, follow the steps below: 1. download the sage spkg from http://www.sagemath.org/packages/standard/sage-5.8.spkg This contains the source code. 2. Create a file in $HOME/.hgrc containing your name as mentioned here: http://www.sagemath.org/doc/developer/producing_patches.html 3. Open a ticket in trac so that you can get the ticket number. Let's say the number is 12345. 4. Use the inbuilt mercurial inside Sage to create the patch. i) First change directory to the unpacked sage/sage directory ii) Next, run the command (where /path/to/sage is where the sage script is present and 12345 is the ticket number) /path/to/sage -hg qnew 12345_documentation.patch iii) Hack hack hack and make your changes :) You will need to follow the developer documentation for syntax and formatting. iv) Now that you are satisfied with your changes, run /path/to/sage -hg qref -m a one line description of your changes v) Make hg generate the patch: /path/to/sage -hg export qtip ~/$(/path/to/sage -hg qtop) 5. Go back to the ticket and upload the patch that is present at ~/12345_documentation.patch Hopefully, this procedure will become much simpler after the move to git, since trivial changes can be made directly in github (if the project remains hosted in github). -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Conjunctive Normal Form
Dear all, I want to convert the polynomial f into Conjunctive Normal Form (CNF) in Sage. How can I do this? B.a,b,c = BooleanPolynomialRing() f=a+b*c -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
[sage-support] Re: Conjunctive Normal Form
sage: import sage.logic.propcalc as propcalc sage: f = propcalc.formula(a^(bc)) sage: f.convert_cnf() sage: f (a|b|c)(a|b|~c)(a|~b|c)(~a|~b|~c) Le samedi 20 avril 2013 20:39:47 UTC+2, Santanu a écrit : Dear all, I want to convert the polynomial f into Conjunctive Normal Form (CNF) in Sage. How can I do this? B.a,b,c = BooleanPolynomialRing() f=a+b*c -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
Re: [sage-support] Conjunctive Normal Form
sage: B.a,b,c = BooleanPolynomialRing() sage: f=a+b*c sage: from sage.sat.converters.polybori import CNFEncoder sage: from sage.sat.solvers.dimacs import DIMACS sage: solver = DIMACS() sage: ce = CNFEncoder(solver, B) sage: ce([f]) [None, a, b, c] sage: solver.clauses() [((-2, -3, 1), False, None), ((3, -1), False, None), ((2, -1), False, None)] On Saturday 20 Apr 2013, Santanu Sarkar wrote: Dear all, I want to convert the polynomial f into Conjunctive Normal Form (CNF) in Sage. How can I do this? B.a,b,c = BooleanPolynomialRing() f=a+b*c Cheers, Martin -- name: Martin Albrecht _pgp: http://pgp.mit.edu:11371/pks/lookup?op=getsearch=0x8EF0DC99 _otr: 47F43D1A 5D68C36F 468BAEBA 640E8856 D7951CCF _www: http://martinralbrecht.wordpress.com/ _jab: martinralbre...@jabber.ccc.de -- You received this message because you are subscribed to the Google Groups sage-support group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at http://groups.google.com/group/sage-support?hl=en. For more options, visit https://groups.google.com/groups/opt_out.
