From 642a83a2666d519404dc609b27081f328f823ace Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Fri, 24 Feb 2023 08:49:04 -0500 Subject: [PATCH 1/8] eja: rename operator_inner_product -> operator_trace inner_product. ...and add an operator_trace_norm() method, for elements. It would have been weird to have it called operator_norm(), wouldn't it? --- mjo/eja/eja_element.py | 174 ++++++++++++++++++++++++++--------------- 1 file changed, 112 insertions(+), 62 deletions(-) diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py index a229fa3..f4d5995 100644 --- a/mjo/eja/eja_element.py +++ b/mjo/eja/eja_element.py @@ -555,7 +555,7 @@ class EJAElement(IndexedFreeModuleElement): If computing my determinant will be fast, we do so and compare with zero (Proposition II.2.4 in Faraut and - Koranyi). Otherwise, Proposition II.3.2 in Faraut and Koranyi + Korányi). Otherwise, Proposition II.3.2 in Faraut and Korányi reduces the problem to the invertibility of my quadratic representation. @@ -1575,7 +1575,75 @@ class EJAElement(IndexedFreeModuleElement): # we want the negative of THAT for the trace. return -p(*self.to_vector()) - def operator_inner_product(self, other): + + def trace_inner_product(self, other): + """ + Return the trace inner product of myself and ``other``. + + SETUP:: + + sage: from mjo.eja.eja_algebra import random_eja + + TESTS: + + The trace inner product is commutative, bilinear, and associative:: + + sage: J = random_eja() + sage: x,y,z = J.random_elements(3) + sage: # commutative + sage: x.trace_inner_product(y) == y.trace_inner_product(x) + True + sage: # bilinear + sage: a = J.base_ring().random_element() + sage: actual = (a*(x+z)).trace_inner_product(y) + sage: expected = ( a*x.trace_inner_product(y) + + ....: a*z.trace_inner_product(y) ) + sage: actual == expected + True + sage: actual = x.trace_inner_product(a*(y+z)) + sage: expected = ( a*x.trace_inner_product(y) + + ....: a*x.trace_inner_product(z) ) + sage: actual == expected + True + sage: # associative + sage: (x*y).trace_inner_product(z) == y.trace_inner_product(x*z) + True + + """ + if not other in self.parent(): + raise TypeError("'other' must live in the same algebra") + + return (self*other).trace() + + + def trace_norm(self): + """ + The norm of this element with respect to :meth:`trace_inner_product`. + + SETUP:: + + sage: from mjo.eja.eja_algebra import (JordanSpinEJA, + ....: HadamardEJA) + + EXAMPLES:: + + sage: J = HadamardEJA(2) + sage: x = sum(J.gens()) + sage: x.trace_norm() + 1.414213562373095? + + :: + + sage: J = JordanSpinEJA(4) + sage: x = sum(J.gens()) + sage: x.trace_norm() + 2.828427124746190? + + """ + return self.trace_inner_product(self).sqrt() + + + def operator_trace_inner_product(self, other): r""" Return the operator inner product of myself and ``other``. @@ -1587,10 +1655,10 @@ class EJAElement(IndexedFreeModuleElement): Euclidean Jordan algebra, this is another associative inner product under which the cone of squares is symmetric. - This *probably* works even if the basis hasn't been - orthonormalized because the eigenvalues of the corresponding - matrix don't change when the basis does (they're preserved by - any similarity transformation). + This works even if the basis hasn't been orthonormalized + because the eigenvalues of the corresponding matrix don't + change when the basis does (they're preserved by any + similarity transformation). SETUP:: @@ -1610,7 +1678,7 @@ class EJAElement(IndexedFreeModuleElement): sage: x,y = J.random_elements(2) sage: n = J.dimension() sage: r = J.rank() - sage: actual = x.operator_inner_product(y) + sage: actual = x.operator_trace_inner_product(y) sage: expected = (n/r)*x.trace_inner_product(y) sage: actual == expected True @@ -1621,7 +1689,7 @@ class EJAElement(IndexedFreeModuleElement): sage: x,y = J.random_elements(2) sage: n = J.dimension() sage: r = J.rank() - sage: actual = x.operator_inner_product(y) + sage: actual = x.operator_trace_inner_product(y) sage: expected = (n/r)*x.trace_inner_product(y) sage: actual == expected True @@ -1632,7 +1700,7 @@ class EJAElement(IndexedFreeModuleElement): sage: x,y = J.random_elements(2) sage: n = J.dimension() sage: r = J.rank() - sage: actual = x.operator_inner_product(y) + sage: actual = x.operator_trace_inner_product(y) sage: expected = (n/r)*x.trace_inner_product(y) sage: actual == expected True @@ -1645,98 +1713,80 @@ class EJAElement(IndexedFreeModuleElement): sage: J = random_eja() sage: x,y,z = J.random_elements(3) sage: # commutative - sage: x.operator_inner_product(y) == y.operator_inner_product(x) + sage: actual = x.operator_trace_inner_product(y) + sage: expected = y.operator_trace_inner_product(x) + sage: actual == expected True sage: # bilinear sage: a = J.base_ring().random_element() - sage: actual = (a*(x+z)).operator_inner_product(y) - sage: expected = ( a*x.operator_inner_product(y) + - ....: a*z.operator_inner_product(y) ) + sage: actual = (a*(x+z)).operator_trace_inner_product(y) + sage: expected = ( a*x.operator_trace_inner_product(y) + + ....: a*z.operator_trace_inner_product(y) ) sage: actual == expected True - sage: actual = x.operator_inner_product(a*(y+z)) - sage: expected = ( a*x.operator_inner_product(y) + - ....: a*x.operator_inner_product(z) ) + sage: actual = x.operator_trace_inner_product(a*(y+z)) + sage: expected = ( a*x.operator_trace_inner_product(y) + + ....: a*x.operator_trace_inner_product(z) ) sage: actual == expected True sage: # associative - sage: actual = (x*y).operator_inner_product(z) - sage: expected = y.operator_inner_product(x*z) + sage: actual = (x*y).operator_trace_inner_product(z) + sage: expected = y.operator_trace_inner_product(x*z) sage: actual == expected True - """ - if not other in self.parent(): - raise TypeError("'other' must live in the same algebra") - - return (self*other).operator().matrix().trace() + Despite the fact that the implementation uses a matrix representation, + the answer is independent of the basis used:: - - def trace_inner_product(self, other): - """ - Return the trace inner product of myself and ``other``. - - SETUP:: - - sage: from mjo.eja.eja_algebra import random_eja - - TESTS: - - The trace inner product is commutative, bilinear, and associative:: - - sage: J = random_eja() - sage: x,y,z = J.random_elements(3) - sage: # commutative - sage: x.trace_inner_product(y) == y.trace_inner_product(x) - True - sage: # bilinear - sage: a = J.base_ring().random_element() - sage: actual = (a*(x+z)).trace_inner_product(y) - sage: expected = ( a*x.trace_inner_product(y) + - ....: a*z.trace_inner_product(y) ) - sage: actual == expected - True - sage: actual = x.trace_inner_product(a*(y+z)) - sage: expected = ( a*x.trace_inner_product(y) + - ....: a*x.trace_inner_product(z) ) + sage: J = RealSymmetricEJA(3, field=QQ, orthonormalize=False) + sage: V = RealSymmetricEJA(3) + sage: x,y = J.random_elements(2) + sage: w = V(x.to_matrix()) + sage: z = V(y.to_matrix()) + sage: expected = x.operator_trace_inner_product(y) + sage: actual = w.operator_trace_inner_product(z) sage: actual == expected True - sage: # associative - sage: (x*y).trace_inner_product(z) == y.trace_inner_product(x*z) - True """ if not other in self.parent(): raise TypeError("'other' must live in the same algebra") - return (self*other).trace() + return (self*other).operator().matrix().trace() - def trace_norm(self): + def operator_trace_norm(self): """ - The norm of this element with respect to :meth:`trace_inner_product`. + The norm of this element with respect to + :meth:`operator_trace_inner_product`. SETUP:: sage: from mjo.eja.eja_algebra import (JordanSpinEJA, ....: HadamardEJA) - EXAMPLES:: + EXAMPLES: + + On a simple algebra, this will differ from :meth:`trace_norm` + by the scalar factor ``(n/r).sqrt()``, where `n` is the + dimension of the algebra and `r` its rank. This follows from + the corresponding result (Proposition III.4.2 of Faraut and + Korányi) for the trace inner product:: sage: J = HadamardEJA(2) sage: x = sum(J.gens()) - sage: x.trace_norm() + sage: x.operator_trace_norm() 1.414213562373095? :: sage: J = JordanSpinEJA(4) sage: x = sum(J.gens()) - sage: x.trace_norm() - 2.828427124746190? + sage: x.operator_trace_norm() + 4 """ - return self.trace_inner_product(self).sqrt() + return self.operator_trace_inner_product(self).sqrt() class CartesianProductParentEJAElement(EJAElement): -- 2.43.2 From 0fb8fd5a702c660e3773a07d0141e19e78a5bbec Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Mon, 6 May 2024 14:51:18 -0400 Subject: [PATCH 2/8] COPYING,LICENSE: add (AGPL-3.0+) --- COPYING | 15 ++ LICENSE | 661 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 676 insertions(+) create mode 100644 COPYING create mode 100644 LICENSE diff --git a/COPYING b/COPYING new file mode 100644 index 0000000..10b6a06 --- /dev/null +++ b/COPYING @@ -0,0 +1,15 @@ +sage.d: my personal library of SageMath code +Copyright (C) 2024 Michael Orlitzky + +This program is free software: you can redistribute it and/or modify +it under the terms of the GNU Affero General Public License as +published by the Free Software Foundation, either version 3 of the +License, or (at your option) any later version. + +This program is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU Affero General Public License for more details. + +You should have received a copy of the GNU Affero General Public License +along with this program. If not, see . diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..be3f7b2 --- /dev/null +++ b/LICENSE @@ -0,0 +1,661 @@ + GNU AFFERO GENERAL PUBLIC LICENSE + Version 3, 19 November 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU Affero General Public License is a free, copyleft license for +software and other kinds of works, specifically designed to ensure +cooperation with the community in the case of network server software. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +our General Public Licenses are intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. + + When we speak of free software, we are referring to freedom, not +price. Our General Public Licenses are designed to make sure that you +have the freedom to distribute copies of free software (and charge for +them if you wish), that you receive source code or can get it if you +want it, that you can change the software or use pieces of it in new +free programs, and that you know you can do these things. + + Developers that use our General Public Licenses protect your rights +with two steps: (1) assert copyright on the software, and (2) offer +you this License which gives you legal permission to copy, distribute +and/or modify the software. + + A secondary benefit of defending all users' freedom is that +improvements made in alternate versions of the program, if they +receive widespread use, become available for other developers to +incorporate. Many developers of free software are heartened and +encouraged by the resulting cooperation. However, in the case of +software used on network servers, this result may fail to come about. +The GNU General Public License permits making a modified version and +letting the public access it on a server without ever releasing its +source code to the public. + + The GNU Affero General Public License is designed specifically to +ensure that, in such cases, the modified source code becomes available +to the community. It requires the operator of a network server to +provide the source code of the modified version running there to the +users of that server. Therefore, public use of a modified version, on +a publicly accessible server, gives the public access to the source +code of the modified version. + + An older license, called the Affero General Public License and +published by Affero, was designed to accomplish similar goals. This is +a different license, not a version of the Affero GPL, but Affero has +released a new version of the Affero GPL which permits relicensing under +this license. + + The precise terms and conditions for copying, distribution and +modification follow. + + TERMS AND CONDITIONS + + 0. Definitions. + + "This License" refers to version 3 of the GNU Affero General Public License. + + "Copyright" also means copyright-like laws that apply to other kinds of +works, such as semiconductor masks. + + "The Program" refers to any copyrightable work licensed under this +License. Each licensee is addressed as "you". "Licensees" and +"recipients" may be individuals or organizations. + + To "modify" a work means to copy from or adapt all or part of the work +in a fashion requiring copyright permission, other than the making of an +exact copy. The resulting work is called a "modified version" of the +earlier work or a work "based on" the earlier work. + + A "covered work" means either the unmodified Program or a work based +on the Program. + + To "propagate" a work means to do anything with it that, without +permission, would make you directly or secondarily liable for +infringement under applicable copyright law, except executing it on a +computer or modifying a private copy. Propagation includes copying, +distribution (with or without modification), making available to the +public, and in some countries other activities as well. + + To "convey" a work means any kind of propagation that enables other +parties to make or receive copies. Mere interaction with a user through +a computer network, with no transfer of a copy, is not conveying. + + An interactive user interface displays "Appropriate Legal Notices" +to the extent that it includes a convenient and prominently visible +feature that (1) displays an appropriate copyright notice, and (2) +tells the user that there is no warranty for the work (except to the +extent that warranties are provided), that licensees may convey the +work under this License, and how to view a copy of this License. If +the interface presents a list of user commands or options, such as a +menu, a prominent item in the list meets this criterion. + + 1. Source Code. + + The "source code" for a work means the preferred form of the work +for making modifications to it. "Object code" means any non-source +form of a work. + + A "Standard Interface" means an interface that either is an official +standard defined by a recognized standards body, or, in the case of +interfaces specified for a particular programming language, one that +is widely used among developers working in that language. + + The "System Libraries" of an executable work include anything, other +than the work as a whole, that (a) is included in the normal form of +packaging a Major Component, but which is not part of that Major +Component, and (b) serves only to enable use of the work with that +Major Component, or to implement a Standard Interface for which an +implementation is available to the public in source code form. A +"Major Component", in this context, means a major essential component +(kernel, window system, and so on) of the specific operating system +(if any) on which the executable work runs, or a compiler used to +produce the work, or an object code interpreter used to run it. + + The "Corresponding Source" for a work in object code form means all +the source code needed to generate, install, and (for an executable +work) run the object code and to modify the work, including scripts to +control those activities. However, it does not include the work's +System Libraries, or general-purpose tools or generally available free +programs which are used unmodified in performing those activities but +which are not part of the work. For example, Corresponding Source +includes interface definition files associated with source files for +the work, and the source code for shared libraries and dynamically +linked subprograms that the work is specifically designed to require, +such as by intimate data communication or control flow between those +subprograms and other parts of the work. + + The Corresponding Source need not include anything that users +can regenerate automatically from other parts of the Corresponding +Source. + + The Corresponding Source for a work in source code form is that +same work. + + 2. Basic Permissions. + + All rights granted under this License are granted for the term of +copyright on the Program, and are irrevocable provided the stated +conditions are met. This License explicitly affirms your unlimited +permission to run the unmodified Program. The output from running a +covered work is covered by this License only if the output, given its +content, constitutes a covered work. This License acknowledges your +rights of fair use or other equivalent, as provided by copyright law. + + You may make, run and propagate covered works that you do not +convey, without conditions so long as your license otherwise remains +in force. You may convey covered works to others for the sole purpose +of having them make modifications exclusively for you, or provide you +with facilities for running those works, provided that you comply with +the terms of this License in conveying all material for which you do +not control copyright. Those thus making or running the covered works +for you must do so exclusively on your behalf, under your direction +and control, on terms that prohibit them from making any copies of +your copyrighted material outside their relationship with you. + + Conveying under any other circumstances is permitted solely under +the conditions stated below. Sublicensing is not allowed; section 10 +makes it unnecessary. + + 3. Protecting Users' Legal Rights From Anti-Circumvention Law. + + No covered work shall be deemed part of an effective technological +measure under any applicable law fulfilling obligations under article +11 of the WIPO copyright treaty adopted on 20 December 1996, or +similar laws prohibiting or restricting circumvention of such +measures. + + When you convey a covered work, you waive any legal power to forbid +circumvention of technological measures to the extent such circumvention +is effected by exercising rights under this License with respect to +the covered work, and you disclaim any intention to limit operation or +modification of the work as a means of enforcing, against the work's +users, your or third parties' legal rights to forbid circumvention of +technological measures. + + 4. Conveying Verbatim Copies. + + You may convey verbatim copies of the Program's source code as you +receive it, in any medium, provided that you conspicuously and +appropriately publish on each copy an appropriate copyright notice; +keep intact all notices stating that this License and any +non-permissive terms added in accord with section 7 apply to the code; +keep intact all notices of the absence of any warranty; and give all +recipients a copy of this License along with the Program. + + You may charge any price or no price for each copy that you convey, +and you may offer support or warranty protection for a fee. + + 5. Conveying Modified Source Versions. + + You may convey a work based on the Program, or the modifications to +produce it from the Program, in the form of source code under the +terms of section 4, provided that you also meet all of these conditions: + + a) The work must carry prominent notices stating that you modified + it, and giving a relevant date. + + b) The work must carry prominent notices stating that it is + released under this License and any conditions added under section + 7. This requirement modifies the requirement in section 4 to + "keep intact all notices". + + c) You must license the entire work, as a whole, under this + License to anyone who comes into possession of a copy. This + License will therefore apply, along with any applicable section 7 + additional terms, to the whole of the work, and all its parts, + regardless of how they are packaged. This License gives no + permission to license the work in any other way, but it does not + invalidate such permission if you have separately received it. + + d) If the work has interactive user interfaces, each must display + Appropriate Legal Notices; however, if the Program has interactive + interfaces that do not display Appropriate Legal Notices, your + work need not make them do so. + + A compilation of a covered work with other separate and independent +works, which are not by their nature extensions of the covered work, +and which are not combined with it such as to form a larger program, +in or on a volume of a storage or distribution medium, is called an +"aggregate" if the compilation and its resulting copyright are not +used to limit the access or legal rights of the compilation's users +beyond what the individual works permit. Inclusion of a covered work +in an aggregate does not cause this License to apply to the other +parts of the aggregate. + + 6. Conveying Non-Source Forms. + + You may convey a covered work in object code form under the terms +of sections 4 and 5, provided that you also convey the +machine-readable Corresponding Source under the terms of this License, +in one of these ways: + + a) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by the + Corresponding Source fixed on a durable physical medium + customarily used for software interchange. + + b) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by a + written offer, valid for at least three years and valid for as + long as you offer spare parts or customer support for that product + model, to give anyone who possesses the object code either (1) a + copy of the Corresponding Source for all the software in the + product that is covered by this License, on a durable physical + medium customarily used for software interchange, for a price no + more than your reasonable cost of physically performing this + conveying of source, or (2) access to copy the + Corresponding Source from a network server at no charge. + + c) Convey individual copies of the object code with a copy of the + written offer to provide the Corresponding Source. This + alternative is allowed only occasionally and noncommercially, and + only if you received the object code with such an offer, in accord + with subsection 6b. + + d) Convey the object code by offering access from a designated + place (gratis or for a charge), and offer equivalent access to the + Corresponding Source in the same way through the same place at no + further charge. You need not require recipients to copy the + Corresponding Source along with the object code. If the place to + copy the object code is a network server, the Corresponding Source + may be on a different server (operated by you or a third party) + that supports equivalent copying facilities, provided you maintain + clear directions next to the object code saying where to find the + Corresponding Source. Regardless of what server hosts the + Corresponding Source, you remain obligated to ensure that it is + available for as long as needed to satisfy these requirements. + + e) Convey the object code using peer-to-peer transmission, provided + you inform other peers where the object code and Corresponding + Source of the work are being offered to the general public at no + charge under subsection 6d. + + A separable portion of the object code, whose source code is excluded +from the Corresponding Source as a System Library, need not be +included in conveying the object code work. + + A "User Product" is either (1) a "consumer product", which means any +tangible personal property which is normally used for personal, family, +or household purposes, or (2) anything designed or sold for incorporation +into a dwelling. In determining whether a product is a consumer product, +doubtful cases shall be resolved in favor of coverage. For a particular +product received by a particular user, "normally used" refers to a +typical or common use of that class of product, regardless of the status +of the particular user or of the way in which the particular user +actually uses, or expects or is expected to use, the product. A product +is a consumer product regardless of whether the product has substantial +commercial, industrial or non-consumer uses, unless such uses represent +the only significant mode of use of the product. + + "Installation Information" for a User Product means any methods, +procedures, authorization keys, or other information required to install +and execute modified versions of a covered work in that User Product from +a modified version of its Corresponding Source. The information must +suffice to ensure that the continued functioning of the modified object +code is in no case prevented or interfered with solely because +modification has been made. + + If you convey an object code work under this section in, or with, or +specifically for use in, a User Product, and the conveying occurs as +part of a transaction in which the right of possession and use of the +User Product is transferred to the recipient in perpetuity or for a +fixed term (regardless of how the transaction is characterized), the +Corresponding Source conveyed under this section must be accompanied +by the Installation Information. But this requirement does not apply +if neither you nor any third party retains the ability to install +modified object code on the User Product (for example, the work has +been installed in ROM). + + The requirement to provide Installation Information does not include a +requirement to continue to provide support service, warranty, or updates +for a work that has been modified or installed by the recipient, or for +the User Product in which it has been modified or installed. Access to a +network may be denied when the modification itself materially and +adversely affects the operation of the network or violates the rules and +protocols for communication across the network. + + Corresponding Source conveyed, and Installation Information provided, +in accord with this section must be in a format that is publicly +documented (and with an implementation available to the public in +source code form), and must require no special password or key for +unpacking, reading or copying. + + 7. Additional Terms. + + "Additional permissions" are terms that supplement the terms of this +License by making exceptions from one or more of its conditions. +Additional permissions that are applicable to the entire Program shall +be treated as though they were included in this License, to the extent +that they are valid under applicable law. If additional permissions +apply only to part of the Program, that part may be used separately +under those permissions, but the entire Program remains governed by +this License without regard to the additional permissions. + + When you convey a copy of a covered work, you may at your option +remove any additional permissions from that copy, or from any part of +it. (Additional permissions may be written to require their own +removal in certain cases when you modify the work.) You may place +additional permissions on material, added by you to a covered work, +for which you have or can give appropriate copyright permission. + + Notwithstanding any other provision of this License, for material you +add to a covered work, you may (if authorized by the copyright holders of +that material) supplement the terms of this License with terms: + + a) Disclaiming warranty or limiting liability differently from the + terms of sections 15 and 16 of this License; or + + b) Requiring preservation of specified reasonable legal notices or + author attributions in that material or in the Appropriate Legal + Notices displayed by works containing it; or + + c) Prohibiting misrepresentation of the origin of that material, or + requiring that modified versions of such material be marked in + reasonable ways as different from the original version; or + + d) Limiting the use for publicity purposes of names of licensors or + authors of the material; or + + e) Declining to grant rights under trademark law for use of some + trade names, trademarks, or service marks; or + + f) Requiring indemnification of licensors and authors of that + material by anyone who conveys the material (or modified versions of + it) with contractual assumptions of liability to the recipient, for + any liability that these contractual assumptions directly impose on + those licensors and authors. + + All other non-permissive additional terms are considered "further +restrictions" within the meaning of section 10. If the Program as you +received it, or any part of it, contains a notice stating that it is +governed by this License along with a term that is a further +restriction, you may remove that term. If a license document contains +a further restriction but permits relicensing or conveying under this +License, you may add to a covered work material governed by the terms +of that license document, provided that the further restriction does +not survive such relicensing or conveying. + + If you add terms to a covered work in accord with this section, you +must place, in the relevant source files, a statement of the +additional terms that apply to those files, or a notice indicating +where to find the applicable terms. + + Additional terms, permissive or non-permissive, may be stated in the +form of a separately written license, or stated as exceptions; +the above requirements apply either way. + + 8. Termination. + + You may not propagate or modify a covered work except as expressly +provided under this License. Any attempt otherwise to propagate or +modify it is void, and will automatically terminate your rights under +this License (including any patent licenses granted under the third +paragraph of section 11). + + However, if you cease all violation of this License, then your +license from a particular copyright holder is reinstated (a) +provisionally, unless and until the copyright holder explicitly and +finally terminates your license, and (b) permanently, if the copyright +holder fails to notify you of the violation by some reasonable means +prior to 60 days after the cessation. + + Moreover, your license from a particular copyright holder is +reinstated permanently if the copyright holder notifies you of the +violation by some reasonable means, this is the first time you have +received notice of violation of this License (for any work) from that +copyright holder, and you cure the violation prior to 30 days after +your receipt of the notice. + + Termination of your rights under this section does not terminate the +licenses of parties who have received copies or rights from you under +this License. If your rights have been terminated and not permanently +reinstated, you do not qualify to receive new licenses for the same +material under section 10. + + 9. Acceptance Not Required for Having Copies. + + You are not required to accept this License in order to receive or +run a copy of the Program. Ancillary propagation of a covered work +occurring solely as a consequence of using peer-to-peer transmission +to receive a copy likewise does not require acceptance. However, +nothing other than this License grants you permission to propagate or +modify any covered work. These actions infringe copyright if you do +not accept this License. Therefore, by modifying or propagating a +covered work, you indicate your acceptance of this License to do so. + + 10. Automatic Licensing of Downstream Recipients. + + Each time you convey a covered work, the recipient automatically +receives a license from the original licensors, to run, modify and +propagate that work, subject to this License. You are not responsible +for enforcing compliance by third parties with this License. + + An "entity transaction" is a transaction transferring control of an +organization, or substantially all assets of one, or subdividing an +organization, or merging organizations. If propagation of a covered +work results from an entity transaction, each party to that +transaction who receives a copy of the work also receives whatever +licenses to the work the party's predecessor in interest had or could +give under the previous paragraph, plus a right to possession of the +Corresponding Source of the work from the predecessor in interest, if +the predecessor has it or can get it with reasonable efforts. + + You may not impose any further restrictions on the exercise of the +rights granted or affirmed under this License. For example, you may +not impose a license fee, royalty, or other charge for exercise of +rights granted under this License, and you may not initiate litigation +(including a cross-claim or counterclaim in a lawsuit) alleging that +any patent claim is infringed by making, using, selling, offering for +sale, or importing the Program or any portion of it. + + 11. Patents. + + A "contributor" is a copyright holder who authorizes use under this +License of the Program or a work on which the Program is based. The +work thus licensed is called the contributor's "contributor version". + + A contributor's "essential patent claims" are all patent claims +owned or controlled by the contributor, whether already acquired or +hereafter acquired, that would be infringed by some manner, permitted +by this License, of making, using, or selling its contributor version, +but do not include claims that would be infringed only as a +consequence of further modification of the contributor version. For +purposes of this definition, "control" includes the right to grant +patent sublicenses in a manner consistent with the requirements of +this License. + + Each contributor grants you a non-exclusive, worldwide, royalty-free +patent license under the contributor's essential patent claims, to +make, use, sell, offer for sale, import and otherwise run, modify and +propagate the contents of its contributor version. + + In the following three paragraphs, a "patent license" is any express +agreement or commitment, however denominated, not to enforce a patent +(such as an express permission to practice a patent or covenant not to +sue for patent infringement). To "grant" such a patent license to a +party means to make such an agreement or commitment not to enforce a +patent against the party. + + If you convey a covered work, knowingly relying on a patent license, +and the Corresponding Source of the work is not available for anyone +to copy, free of charge and under the terms of this License, through a +publicly available network server or other readily accessible means, +then you must either (1) cause the Corresponding Source to be so +available, or (2) arrange to deprive yourself of the benefit of the +patent license for this particular work, or (3) arrange, in a manner +consistent with the requirements of this License, to extend the patent +license to downstream recipients. "Knowingly relying" means you have +actual knowledge that, but for the patent license, your conveying the +covered work in a country, or your recipient's use of the covered work +in a country, would infringe one or more identifiable patents in that +country that you have reason to believe are valid. + + If, pursuant to or in connection with a single transaction or +arrangement, you convey, or propagate by procuring conveyance of, a +covered work, and grant a patent license to some of the parties +receiving the covered work authorizing them to use, propagate, modify +or convey a specific copy of the covered work, then the patent license +you grant is automatically extended to all recipients of the covered +work and works based on it. + + A patent license is "discriminatory" if it does not include within +the scope of its coverage, prohibits the exercise of, or is +conditioned on the non-exercise of one or more of the rights that are +specifically granted under this License. You may not convey a covered +work if you are a party to an arrangement with a third party that is +in the business of distributing software, under which you make payment +to the third party based on the extent of your activity of conveying +the work, and under which the third party grants, to any of the +parties who would receive the covered work from you, a discriminatory +patent license (a) in connection with copies of the covered work +conveyed by you (or copies made from those copies), or (b) primarily +for and in connection with specific products or compilations that +contain the covered work, unless you entered into that arrangement, +or that patent license was granted, prior to 28 March 2007. + + Nothing in this License shall be construed as excluding or limiting +any implied license or other defenses to infringement that may +otherwise be available to you under applicable patent law. + + 12. No Surrender of Others' Freedom. + + If conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot convey a +covered work so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you may +not convey it at all. For example, if you agree to terms that obligate you +to collect a royalty for further conveying from those to whom you convey +the Program, the only way you could satisfy both those terms and this +License would be to refrain entirely from conveying the Program. + + 13. Remote Network Interaction; Use with the GNU General Public License. + + Notwithstanding any other provision of this License, if you modify the +Program, your modified version must prominently offer all users +interacting with it remotely through a computer network (if your version +supports such interaction) an opportunity to receive the Corresponding +Source of your version by providing access to the Corresponding Source +from a network server at no charge, through some standard or customary +means of facilitating copying of software. This Corresponding Source +shall include the Corresponding Source for any work covered by version 3 +of the GNU General Public License that is incorporated pursuant to the +following paragraph. + + Notwithstanding any other provision of this License, you have +permission to link or combine any covered work with a work licensed +under version 3 of the GNU General Public License into a single +combined work, and to convey the resulting work. The terms of this +License will continue to apply to the part which is the covered work, +but the work with which it is combined will remain governed by version +3 of the GNU General Public License. + + 14. Revised Versions of this License. + + The Free Software Foundation may publish revised and/or new versions of +the GNU Affero General Public License from time to time. Such new versions +will be similar in spirit to the present version, but may differ in detail to +address new problems or concerns. + + Each version is given a distinguishing version number. If the +Program specifies that a certain numbered version of the GNU Affero General +Public License "or any later version" applies to it, you have the +option of following the terms and conditions either of that numbered +version or of any later version published by the Free Software +Foundation. If the Program does not specify a version number of the +GNU Affero General Public License, you may choose any version ever published +by the Free Software Foundation. + + If the Program specifies that a proxy can decide which future +versions of the GNU Affero General Public License can be used, that proxy's +public statement of acceptance of a version permanently authorizes you +to choose that version for the Program. + + Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + + 15. Disclaimer of Warranty. + + THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY +OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, +THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM +IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF +ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. Limitation of Liability. + + IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS +THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY +GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE +USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF +DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD +PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), +EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF +SUCH DAMAGES. + + 17. Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU Affero General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU Affero General Public License for more details. + + You should have received a copy of the GNU Affero General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If your software can interact with users remotely through a computer +network, you should also make sure that it provides a way for users to +get its source. For example, if your program is a web application, its +interface could display a "Source" link that leads users to an archive +of the code. There are many ways you could offer source, and different +solutions will be better for different programs; see section 13 for the +specific requirements. + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU AGPL, see +. -- 2.43.2 From 5f6a355210842c3ca93dabb3f85bad468854f495 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sat, 18 May 2024 16:55:25 -0400 Subject: [PATCH 3/8] mjo/cone/schur.py: bye, use sage's cones.schur() instead --- mjo/cone/all.py | 1 - mjo/cone/schur.py | 131 ---------------------------------------------- 2 files changed, 132 deletions(-) delete mode 100644 mjo/cone/schur.py diff --git a/mjo/cone/all.py b/mjo/cone/all.py index 7ce56c0..18fb052 100644 --- a/mjo/cone/all.py +++ b/mjo/cone/all.py @@ -9,7 +9,6 @@ from mjo.cone.faces import * from mjo.cone.nonnegative_orthant import * from mjo.cone.permutation_invariant import * from mjo.cone.rearrangement import * -from mjo.cone.schur import * from mjo.cone.symmetric_pd import * from mjo.cone.symmetric_psd import * from mjo.cone.trivial_cone import * diff --git a/mjo/cone/schur.py b/mjo/cone/schur.py deleted file mode 100644 index 1fa1e52..0000000 --- a/mjo/cone/schur.py +++ /dev/null @@ -1,131 +0,0 @@ -""" -The Schur cone, as described in the "Critical angles..." papers by -Iusem, Seeger, and Sossa. It defines the Schur ordering on `R^{n}`. -""" - -from sage.all import * - -def schur_cone(n, lattice=None): - r""" - Return the Schur cone in ``n`` dimensions that induces the - majorization ordering. - - INPUT: - - - ``n`` -- the dimension the ambient space. - - - ``lattice`` -- (default: ``None``) an ambient lattice of rank ``n`` - to be passed to the :func:`Cone` constructor. - - OUTPUT: - - A rational closed convex Schur cone of dimension ``n``. Each - generating ray will have the integer ring as its base ring. - - If a ``lattice`` was specified, then the resulting cone will live in - that lattice unless its rank is incompatible with the dimension - ``n`` (in which case a ``ValueError`` is raised). - - REFERENCES: - - .. [GourionSeeger] Daniel Gourion and Alberto Seeger. - Critical angles in polyhedral convex cones: numerical and - statistical considerations. Mathematical Programming, 123:173-198, - 2010, doi:10.1007/s10107-009-0317-2. - - .. [IusemSeegerOnPairs] Alfredo Iusem and Alberto Seeger. - On pairs of vectors achieving the maximal angle of a convex cone. - Mathematical Programming, 104(2-3):501-523, 2005, - doi:10.1007/s10107-005-0626-z. - - .. [SeegerSossaI] Alberto Seeger and David Sossa. - Critical angles between two convex cones I. General theory. - TOP, 24(1):44-65, 2016, doi:10.1007/s11750-015-0375-y. - - SETUP:: - - sage: from mjo.cone.nonnegative_orthant import nonnegative_orthant - sage: from mjo.cone.schur import schur_cone - - EXAMPLES: - - Verify the claim that the maximal angle between any two generators - of the Schur cone and the nonnegative quintant is ``3*pi/4``:: - - sage: P = schur_cone(5) - sage: Q = nonnegative_orthant(5) - sage: G = ( g.change_ring(QQbar).normalized() for g in P ) - sage: H = ( h.change_ring(QQbar).normalized() for h in Q ) - sage: actual = max(arccos(u.inner_product(v)) for u in G for v in H) - sage: expected = 3*pi/4 - sage: abs(actual - expected).n() < 1e-12 - True - - The dual of the Schur cone is the "downward monotonic cone" - [GourionSeeger]_, whose elements' entries are in non-increasing - order:: - - sage: n = ZZ.random_element(10) - sage: K = schur_cone(n).dual() - sage: x = K.random_element() - sage: all( x[i] >= x[i+1] for i in range(n-1) ) - True - - TESTS: - - We get the trivial cone when ``n`` is zero:: - - sage: schur_cone(0).is_trivial() - True - - The Schur cone induces the majorization ordering:: - - sage: def majorized_by(x,y): - ....: return (all(sum(x[0:i]) <= sum(y[0:i]) - ....: for i in range(x.degree()-1)) - ....: and sum(x) == sum(y)) - sage: n = ZZ.random_element(10) - sage: V = VectorSpace(QQ, n) - sage: S = schur_cone(n) - sage: majorized_by(V.zero(), S.random_element()) - True - sage: x = V.random_element() - sage: y = V.random_element() - sage: majorized_by(x,y) == ( (y-x) in S ) - True - - If a ``lattice`` was given, it is actually used:: - - sage: L = ToricLattice(3, 'M') - sage: schur_cone(3, lattice=L) - 2-d cone in 3-d lattice M - - Unless the rank of the lattice disagrees with ``n``:: - - sage: L = ToricLattice(1, 'M') - sage: schur_cone(3, lattice=L) - Traceback (most recent call last): - ... - ValueError: lattice rank=1 and dimension n=3 are incompatible - - """ - if lattice is None: - lattice = ToricLattice(n) - - if lattice.rank() != n: - raise ValueError('lattice rank=%d and dimension n=%d are incompatible' - % - (lattice.rank(), n)) - - def _f(i,j): - if i == j: - return 1 - elif j - i == 1: - return -1 - else: - return 0 - - # The "max" below catches the trivial case where n == 0. - S = matrix(ZZ, max(0,n-1), n, _f) - - return Cone(S.rows(), lattice) -- 2.43.2 From 6c47f6d2dc281f8058d7b04b0f109ddc783c5121 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sat, 18 May 2024 16:56:55 -0400 Subject: [PATCH 4/8] mjo/cone/nonnegative_orthant.py: bye, use cones.nonnegative_orthant() instead --- mjo/cone/all.py | 1 - mjo/cone/nonnegative_orthant.py | 80 --------------------------------- 2 files changed, 81 deletions(-) delete mode 100644 mjo/cone/nonnegative_orthant.py diff --git a/mjo/cone/all.py b/mjo/cone/all.py index 18fb052..a8d0eb3 100644 --- a/mjo/cone/all.py +++ b/mjo/cone/all.py @@ -6,7 +6,6 @@ from mjo.cone.cone import * from mjo.cone.completely_positive import * from mjo.cone.doubly_nonnegative import * from mjo.cone.faces import * -from mjo.cone.nonnegative_orthant import * from mjo.cone.permutation_invariant import * from mjo.cone.rearrangement import * from mjo.cone.symmetric_pd import * diff --git a/mjo/cone/nonnegative_orthant.py b/mjo/cone/nonnegative_orthant.py deleted file mode 100644 index 2bd1b3c..0000000 --- a/mjo/cone/nonnegative_orthant.py +++ /dev/null @@ -1,80 +0,0 @@ -r""" -The nonnegative orthant in `\mathbb{Z}^{n}`. I'm sick and tired of -typing it. -""" - -from sage.all import * - -def nonnegative_orthant(n, lattice=None): - r""" - The nonnegative orthant in ``n`` dimensions. - - INPUT: - - - ``n`` -- the dimension of the ambient space. - - - ``lattice`` -- (default: ``None``) an ambient lattice of rank ``n`` - to be passed to the :func:`Cone` constructor. - - OUTPUT: - - The convex cone having ``n`` standard basis vectors as its - generators. Each generating ray will have the integer ring as its - base ring. - - If a ``lattice`` was specified, then the resulting cone will live in - that lattice unless its rank is incompatible with the dimension - ``n`` (in which case a ``ValueError`` is raised). - - SETUP:: - - sage: from mjo.cone.nonnegative_orthant import nonnegative_orthant - - EXAMPLES:: - - sage: nonnegative_orthant(3).rays() - N(1, 0, 0), - N(0, 1, 0), - N(0, 0, 1) - in 3-d lattice N - - TESTS: - - We can construct the trivial cone as the nonnegative orthant in a - trivial vector space:: - - sage: nonnegative_orthant(0) - 0-d cone in 0-d lattice N - - The nonnegative orthant is a proper cone:: - - sage: n = ZZ.random_element(10) - sage: K = nonnegative_orthant(n) - sage: K.is_proper() - True - - If a ``lattice`` was given, it is actually used:: - - sage: L = ToricLattice(3, 'M') - sage: nonnegative_orthant(3, lattice=L) - 3-d cone in 3-d lattice M - - Unless the rank of the lattice disagrees with ``n``:: - - sage: L = ToricLattice(1, 'M') - sage: nonnegative_orthant(3, lattice=L) - Traceback (most recent call last): - ... - ValueError: lattice rank=1 and dimension n=3 are incompatible - - """ - if lattice is None: - lattice = ToricLattice(n) - - if lattice.rank() != n: - raise ValueError('lattice rank=%d and dimension n=%d are incompatible' - % - (lattice.rank(), n)) - - I = identity_matrix(ZZ,n) - return Cone(I.rows(), lattice) -- 2.43.2 From 5a2300f7d7e72b159295ab64de2b93d15747f2fd Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sat, 18 May 2024 16:57:39 -0400 Subject: [PATCH 5/8] mjo/cone/trivial_cone.py: bye, use sage's cones.trivial() instead --- mjo/cone/all.py | 1 - mjo/cone/trivial_cone.py | 64 ---------------------------------------- 2 files changed, 65 deletions(-) delete mode 100644 mjo/cone/trivial_cone.py diff --git a/mjo/cone/all.py b/mjo/cone/all.py index a8d0eb3..7dd3c94 100644 --- a/mjo/cone/all.py +++ b/mjo/cone/all.py @@ -10,4 +10,3 @@ from mjo.cone.permutation_invariant import * from mjo.cone.rearrangement import * from mjo.cone.symmetric_pd import * from mjo.cone.symmetric_psd import * -from mjo.cone.trivial_cone import * diff --git a/mjo/cone/trivial_cone.py b/mjo/cone/trivial_cone.py deleted file mode 100644 index 17c6835..0000000 --- a/mjo/cone/trivial_cone.py +++ /dev/null @@ -1,64 +0,0 @@ -from sage.all import * - -def trivial_cone(n, lattice=None): - r""" - The trivial cone with no generators in ``n`` dimensions. - - INPUT: - - - ``n`` -- the dimension of the ambient space. - - - ``lattice`` -- (default: ``None``) an ambient lattice of rank ``n`` - to be passed to the :func:`Cone` constructor. - - OUTPUT: - - The trivial cone with no generators. - - If a ``lattice`` was specified, then the resulting cone will live in - that lattice unless its rank is incompatible with the dimension - ``n`` (in which case a ``ValueError`` is raised). - - SETUP:: - - sage: from mjo.cone.trivial_cone import trivial_cone - - EXAMPLES:: - - We can construct the trivial cone as the nonnegative orthant in a - trivial ambient space:: - - sage: trivial_cone(0) - 0-d cone in 0-d lattice N - - Or in a nontrivial ambient space:: - - sage: trivial_cone(3) - 0-d cone in 3-d lattice N - - If a ``lattice`` is given, the trivial cone will live in that lattice:: - - sage: L = ToricLattice(3, 'M') - sage: trivial_cone(3, lattice=L) - 0-d cone in 3-d lattice M - - TESTS: - - An error is raised if the rank of the lattice disagrees with ``n``:: - - sage: L = ToricLattice(1, 'M') - sage: trivial_cone(3, lattice=L) - Traceback (most recent call last): - ... - ValueError: lattice rank=1 and dimension n=3 are incompatible - - """ - if lattice is None: - lattice = ToricLattice(n) - - if lattice.rank() != n: - raise ValueError('lattice rank=%d and dimension n=%d are incompatible' - % - (lattice.rank(), n)) - - return Cone([], lattice) -- 2.43.2 From 31f49a9d987fe26c15e780fbcca74831bff56a9f Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sat, 18 May 2024 16:59:24 -0400 Subject: [PATCH 6/8] mjo/cone/rearrangement.py: bye, use sage's cones.rearrangement() instead --- mjo/cone/all.py | 1 - mjo/cone/rearrangement.py | 194 -------------------------------------- 2 files changed, 195 deletions(-) delete mode 100644 mjo/cone/rearrangement.py diff --git a/mjo/cone/all.py b/mjo/cone/all.py index 7dd3c94..2ef437f 100644 --- a/mjo/cone/all.py +++ b/mjo/cone/all.py @@ -7,6 +7,5 @@ from mjo.cone.completely_positive import * from mjo.cone.doubly_nonnegative import * from mjo.cone.faces import * from mjo.cone.permutation_invariant import * -from mjo.cone.rearrangement import * from mjo.cone.symmetric_pd import * from mjo.cone.symmetric_psd import * diff --git a/mjo/cone/rearrangement.py b/mjo/cone/rearrangement.py deleted file mode 100644 index 0bbf95b..0000000 --- a/mjo/cone/rearrangement.py +++ /dev/null @@ -1,194 +0,0 @@ -from sage.all import * - -def rearrangement_cone(p,n,lattice=None): - r""" - Return the rearrangement cone of order ``p`` in ``n`` dimensions. - - The rearrangement cone in ``n`` dimensions has as its elements - vectors of length ``n``. For inclusion in the cone, the smallest - ``p`` components of a vector must sum to a nonnegative number. - - For example, the rearrangement cone of order ``p == 1`` has its - single smallest component nonnegative. This implies that all - components are nonnegative, and that therefore the rearrangement - cone of order one is the nonnegative orthant. - - When ``p == n``, the sum of all components of a vector must be - nonnegative for inclusion in the cone. That is, the cone is a - half-space in ``n`` dimensions. - - INPUT: - - - ``p`` -- The number of components to "rearrange." - - - ``n`` -- The dimension of the ambient space for the resulting cone. - - - ``lattice`` -- (default: ``None``) an ambient lattice of rank ``n`` - to be passed to the :func:`Cone` constructor. - - OUTPUT: - - A polyhedral closed convex cone object representing a rearrangement - cone of order ``p`` in ``n`` dimensions. Each generating ray will - have the integer ring as its base ring. - - If a ``lattice`` was specified, then the resulting cone will live in - that lattice unless its rank is incompatible with the dimension - ``n`` (in which case a ``ValueError`` is raised). - - ALGORITHM: - - The generators for the rearrangement cone are given by [Jeong]_ - Theorem 5.2.3. - - REFERENCES: - - .. [GowdaJeong] Muddappa Seetharama Gowda and Juyoung Jeong. - Spectral cones in Euclidean Jordan algebras. - Linear Algebra and its Applications, 509, 286-305. - doi:10.1016/j.laa.2016.08.004 - - .. [HenrionSeeger] Rene Henrion and Alberto Seeger. - Inradius and Circumradius of Various Convex Cones Arising in - Applications. Set-Valued and Variational Analysis, 18(3-4), - 483-511, 2010. doi:10.1007/s11228-010-0150-z - - .. [Jeong] Juyoung Jeong. - Spectral sets and functions on Euclidean Jordan algebras. - University of Maryland, Baltimore County, Ph.D. thesis, 2017. - - SETUP:: - - sage: from mjo.cone.rearrangement import rearrangement_cone - - EXAMPLES: - - The rearrangement cones of order one are nonnegative orthants:: - - sage: rearrangement_cone(1,1) == Cone([(1,)]) - True - sage: rearrangement_cone(1,2) == Cone([(0,1),(1,0)]) - True - sage: rearrangement_cone(1,3) == Cone([(0,0,1),(0,1,0),(1,0,0)]) - True - - When ``p == n``, the resulting cone will be a half-space, so we - expect its lineality to be one less than ``n`` because it will - contain a hyperplane but is not the entire space:: - - sage: rearrangement_cone(5,5).lineality() - 4 - - All rearrangement cones are proper when ``p`` is less than ``n`` by - [Jeong]_ Proposition 5.2.1:: - - sage: all( rearrangement_cone(p,n).is_proper() - ....: for n in range(10) - ....: for p in range(1, n) ) - True - - The Lyapunov rank of the rearrangement cone of order ``p`` in ``n`` - dimensions is ``n`` for ``p == 1`` or ``p == n`` and one otherwise, - by [Jeong]_ Corollary 5.2.4:: - - sage: all( rearrangement_cone(p,n).lyapunov_rank() == n - ....: for n in range(2, 10) - ....: for p in [1, n-1] ) - True - sage: all( rearrangement_cone(p,n).lyapunov_rank() == 1 - ....: for n in range(3, 10) - ....: for p in range(2, n-1) ) - True - - TESTS: - - All rearrangement cones are permutation-invariant by [Jeong]_ - Proposition 5.2.1:: - - sage: n = ZZ.random_element(2,10).abs() - sage: p = ZZ.random_element(1,n) - sage: K = rearrangement_cone(p,n) - sage: P = SymmetricGroup(n).random_element().matrix() - sage: all( K.contains(P*r) for r in K ) - True - - The smallest ``p`` components of every element of the rearrangement - cone should sum to a nonnegative number (this tests that the - generators really are what we think they are):: - - sage: def _has_rearrangement_property(v,p): - ....: return sum( sorted(v)[0:p] ) >= 0 - sage: all( _has_rearrangement_property( - ....: rearrangement_cone(p,n).random_element(), - ....: p - ....: ) - ....: for n in range(2, 10) - ....: for p in range(1, n-1) - ....: ) - True - - The rearrangenent cone of order ``p`` is contained in the rearrangement - cone of order ``p + 1`` by [Jeong]_ Proposition 5.2.1:: - - sage: n = ZZ.random_element(2,10) - sage: p = ZZ.random_element(1,n) - sage: K1 = rearrangement_cone(p,n) - sage: K2 = rearrangement_cone(p+1,n) - sage: all( x in K2 for x in K1 ) - True - - The rearrangement cone of order ``p`` is linearly isomorphic to the - rearrangement cone of order ``n - p`` when ``p`` is less than ``n``, - by [Jeong]_ Proposition 5.2.1:: - - sage: n = ZZ.random_element(2,10) - sage: p = ZZ.random_element(1,n) - sage: K1 = rearrangement_cone(p,n) - sage: K2 = rearrangement_cone(n-p, n) - sage: Mp = (1/p)*matrix.ones(QQ,n) - identity_matrix(QQ,n) - sage: Cone( (Mp*K2.rays()).columns() ).is_equivalent(K1) - True - - The order ``p`` should be between ``1`` and ``n``, inclusive:: - - sage: rearrangement_cone(0,3) - Traceback (most recent call last): - ... - ValueError: order p=0 should be between 1 and n=3, inclusive - sage: rearrangement_cone(5,3) - Traceback (most recent call last): - ... - ValueError: order p=5 should be between 1 and n=3, inclusive - - If a ``lattice`` was given, it is actually used:: - - sage: L = ToricLattice(3, 'M') - sage: rearrangement_cone(2, 3, lattice=L) - 3-d cone in 3-d lattice M - - Unless the rank of the lattice disagrees with ``n``:: - - sage: L = ToricLattice(1, 'M') - sage: rearrangement_cone(2, 3, lattice=L) - Traceback (most recent call last): - ... - ValueError: lattice rank=1 and dimension n=3 are incompatible - - """ - if p < 1 or p > n: - raise ValueError('order p=%d should be between 1 and n=%d, inclusive' - % - (p,n)) - - if lattice is None: - lattice = ToricLattice(n) - - if lattice.rank() != n: - raise ValueError('lattice rank=%d and dimension n=%d are incompatible' - % - (lattice.rank(), n)) - - I = identity_matrix(ZZ,n) - M = matrix.ones(ZZ,n) - p*I - G = identity_matrix(ZZ,n).rows() + M.rows() - return Cone(G, lattice=lattice) -- 2.43.2 From 88dfaad8341867d1df155feaf2591a9acc1157a1 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sat, 18 May 2024 17:11:05 -0400 Subject: [PATCH 7/8] makefile: timeout overrides should no longer be necessary --- makefile | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/makefile b/makefile index 63b577a..79cf89a 100644 --- a/makefile +++ b/makefile @@ -1,7 +1,7 @@ SAGE = $(shell which sage) check: - PYTHONPATH="." $(SAGE) -t --timeout=0 --long --exitfirst mjo/ + PYTHONPATH="." $(SAGE) -t --long --exitfirst mjo/ clean: find ./ -type f -name '*.pyc' -delete find ./ -type d -name '__pycache__' -delete -- 2.43.2 From 976c7c7c9f69b7685c8cbfc9e845e8b3f4def326 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Sat, 18 May 2024 17:11:21 -0400 Subject: [PATCH 8/8] README: rewrite it, it was rather out-of-date --- README | 17 ++++++++--------- 1 file changed, 8 insertions(+), 9 deletions(-) diff --git a/README b/README index eb9fd9f..e7c660d 100644 --- a/README +++ b/README @@ -1,12 +1,11 @@ -My own personal library of Sage[1] code. +My personal library of SageMath code -It is intended to be loaded into every Sage session, or Python script -which imports the Sage library. Sage loads ~/.sage/init.sage upon -startup, so I've supplied a sample init.sage file which will load this -code from ~/src/sage/. +If you symlink it to ~/.sage/init.sage, the sample init.sage file will +load this stuff into your session when Sage starts. It assumes that +this repository lives at either ~/src/sage.d or ~/src/sage.d.git, but +that's easy to change. More likely though you will want to copy/paste +the relevant parts into your own personal (preexisting) init.sage. Newer versions of Sage don't load ~/.sage/init.sage during test mode, -and "packages" need to be imported explicitly. Therefore the test -suite is a little tricky to run; but "make check" should work. - -[1] http://www.sagemath.org/ +and all modules need to be imported explicitly. The test suite is +therefore a little tricky to run; but "make check" should work. -- 2.43.2