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 19 <h1>global-analysis-and-the-banach-manifold-of-class-h1-curvers</h1>
 20 <p>Riemannian Geometry course project on the manifold H¹(I, M) of class 
 21 H¹ curves on a Riemannian manifold M and its applications to the 
 22 geodesics problem
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 37 <pre id="blob"><a href="#l1" class="line" id="l1">      1</a>                     GNU GENERAL PUBLIC LICENSE
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250 <a href="#l214" class="line" id="l214">    214</a>     a) The work must carry prominent notices stating that you modified
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252 <a href="#l216" class="line" id="l216">    216</a> 
253 <a href="#l217" class="line" id="l217">    217</a>     b) The work must carry prominent notices stating that it is
254 <a href="#l218" class="line" id="l218">    218</a>     released under this License and any conditions added under section
255 <a href="#l219" class="line" id="l219">    219</a>     7.  This requirement modifies the requirement in section 4 to
256 <a href="#l220" class="line" id="l220">    220</a>     "keep intact all notices".
257 <a href="#l221" class="line" id="l221">    221</a> 
258 <a href="#l222" class="line" id="l222">    222</a>     c) You must license the entire work, as a whole, under this
259 <a href="#l223" class="line" id="l223">    223</a>     License to anyone who comes into possession of a copy.  This
260 <a href="#l224" class="line" id="l224">    224</a>     License will therefore apply, along with any applicable section 7
261 <a href="#l225" class="line" id="l225">    225</a>     additional terms, to the whole of the work, and all its parts,
262 <a href="#l226" class="line" id="l226">    226</a>     regardless of how they are packaged.  This License gives no
263 <a href="#l227" class="line" id="l227">    227</a>     permission to license the work in any other way, but it does not
264 <a href="#l228" class="line" id="l228">    228</a>     invalidate such permission if you have separately received it.
265 <a href="#l229" class="line" id="l229">    229</a> 
266 <a href="#l230" class="line" id="l230">    230</a>     d) If the work has interactive user interfaces, each must display
267 <a href="#l231" class="line" id="l231">    231</a>     Appropriate Legal Notices; however, if the Program has interactive
268 <a href="#l232" class="line" id="l232">    232</a>     interfaces that do not display Appropriate Legal Notices, your
269 <a href="#l233" class="line" id="l233">    233</a>     work need not make them do so.
270 <a href="#l234" class="line" id="l234">    234</a> 
271 <a href="#l235" class="line" id="l235">    235</a>   A compilation of a covered work with other separate and independent
272 <a href="#l236" class="line" id="l236">    236</a> works, which are not by their nature extensions of the covered work,
273 <a href="#l237" class="line" id="l237">    237</a> and which are not combined with it such as to form a larger program,
274 <a href="#l238" class="line" id="l238">    238</a> in or on a volume of a storage or distribution medium, is called an
275 <a href="#l239" class="line" id="l239">    239</a> "aggregate" if the compilation and its resulting copyright are not
276 <a href="#l240" class="line" id="l240">    240</a> used to limit the access or legal rights of the compilation's users
277 <a href="#l241" class="line" id="l241">    241</a> beyond what the individual works permit.  Inclusion of a covered work
278 <a href="#l242" class="line" id="l242">    242</a> in an aggregate does not cause this License to apply to the other
279 <a href="#l243" class="line" id="l243">    243</a> parts of the aggregate.
280 <a href="#l244" class="line" id="l244">    244</a> 
281 <a href="#l245" class="line" id="l245">    245</a>   6. Conveying Non-Source Forms.
282 <a href="#l246" class="line" id="l246">    246</a> 
283 <a href="#l247" class="line" id="l247">    247</a>   You may convey a covered work in object code form under the terms
284 <a href="#l248" class="line" id="l248">    248</a> of sections 4 and 5, provided that you also convey the
285 <a href="#l249" class="line" id="l249">    249</a> machine-readable Corresponding Source under the terms of this License,
286 <a href="#l250" class="line" id="l250">    250</a> in one of these ways:
287 <a href="#l251" class="line" id="l251">    251</a> 
288 <a href="#l252" class="line" id="l252">    252</a>     a) Convey the object code in, or embodied in, a physical product
289 <a href="#l253" class="line" id="l253">    253</a>     (including a physical distribution medium), accompanied by the
290 <a href="#l254" class="line" id="l254">    254</a>     Corresponding Source fixed on a durable physical medium
291 <a href="#l255" class="line" id="l255">    255</a>     customarily used for software interchange.
292 <a href="#l256" class="line" id="l256">    256</a> 
293 <a href="#l257" class="line" id="l257">    257</a>     b) Convey the object code in, or embodied in, a physical product
294 <a href="#l258" class="line" id="l258">    258</a>     (including a physical distribution medium), accompanied by a
295 <a href="#l259" class="line" id="l259">    259</a>     written offer, valid for at least three years and valid for as
296 <a href="#l260" class="line" id="l260">    260</a>     long as you offer spare parts or customer support for that product
297 <a href="#l261" class="line" id="l261">    261</a>     model, to give anyone who possesses the object code either (1) a
298 <a href="#l262" class="line" id="l262">    262</a>     copy of the Corresponding Source for all the software in the
299 <a href="#l263" class="line" id="l263">    263</a>     product that is covered by this License, on a durable physical
300 <a href="#l264" class="line" id="l264">    264</a>     medium customarily used for software interchange, for a price no
301 <a href="#l265" class="line" id="l265">    265</a>     more than your reasonable cost of physically performing this
302 <a href="#l266" class="line" id="l266">    266</a>     conveying of source, or (2) access to copy the
303 <a href="#l267" class="line" id="l267">    267</a>     Corresponding Source from a network server at no charge.
304 <a href="#l268" class="line" id="l268">    268</a> 
305 <a href="#l269" class="line" id="l269">    269</a>     c) Convey individual copies of the object code with a copy of the
306 <a href="#l270" class="line" id="l270">    270</a>     written offer to provide the Corresponding Source.  This
307 <a href="#l271" class="line" id="l271">    271</a>     alternative is allowed only occasionally and noncommercially, and
308 <a href="#l272" class="line" id="l272">    272</a>     only if you received the object code with such an offer, in accord
309 <a href="#l273" class="line" id="l273">    273</a>     with subsection 6b.
310 <a href="#l274" class="line" id="l274">    274</a> 
311 <a href="#l275" class="line" id="l275">    275</a>     d) Convey the object code by offering access from a designated
312 <a href="#l276" class="line" id="l276">    276</a>     place (gratis or for a charge), and offer equivalent access to the
313 <a href="#l277" class="line" id="l277">    277</a>     Corresponding Source in the same way through the same place at no
314 <a href="#l278" class="line" id="l278">    278</a>     further charge.  You need not require recipients to copy the
315 <a href="#l279" class="line" id="l279">    279</a>     Corresponding Source along with the object code.  If the place to
316 <a href="#l280" class="line" id="l280">    280</a>     copy the object code is a network server, the Corresponding Source
317 <a href="#l281" class="line" id="l281">    281</a>     may be on a different server (operated by you or a third party)
318 <a href="#l282" class="line" id="l282">    282</a>     that supports equivalent copying facilities, provided you maintain
319 <a href="#l283" class="line" id="l283">    283</a>     clear directions next to the object code saying where to find the
320 <a href="#l284" class="line" id="l284">    284</a>     Corresponding Source.  Regardless of what server hosts the
321 <a href="#l285" class="line" id="l285">    285</a>     Corresponding Source, you remain obligated to ensure that it is
322 <a href="#l286" class="line" id="l286">    286</a>     available for as long as needed to satisfy these requirements.
323 <a href="#l287" class="line" id="l287">    287</a> 
324 <a href="#l288" class="line" id="l288">    288</a>     e) Convey the object code using peer-to-peer transmission, provided
325 <a href="#l289" class="line" id="l289">    289</a>     you inform other peers where the object code and Corresponding
326 <a href="#l290" class="line" id="l290">    290</a>     Source of the work are being offered to the general public at no
327 <a href="#l291" class="line" id="l291">    291</a>     charge under subsection 6d.
328 <a href="#l292" class="line" id="l292">    292</a> 
329 <a href="#l293" class="line" id="l293">    293</a>   A separable portion of the object code, whose source code is excluded
330 <a href="#l294" class="line" id="l294">    294</a> from the Corresponding Source as a System Library, need not be
331 <a href="#l295" class="line" id="l295">    295</a> included in conveying the object code work.
332 <a href="#l296" class="line" id="l296">    296</a> 
333 <a href="#l297" class="line" id="l297">    297</a>   A "User Product" is either (1) a "consumer product", which means any
334 <a href="#l298" class="line" id="l298">    298</a> tangible personal property which is normally used for personal, family,
335 <a href="#l299" class="line" id="l299">    299</a> or household purposes, or (2) anything designed or sold for incorporation
336 <a href="#l300" class="line" id="l300">    300</a> into a dwelling.  In determining whether a product is a consumer product,
337 <a href="#l301" class="line" id="l301">    301</a> doubtful cases shall be resolved in favor of coverage.  For a particular
338 <a href="#l302" class="line" id="l302">    302</a> product received by a particular user, "normally used" refers to a
339 <a href="#l303" class="line" id="l303">    303</a> typical or common use of that class of product, regardless of the status
340 <a href="#l304" class="line" id="l304">    304</a> of the particular user or of the way in which the particular user
341 <a href="#l305" class="line" id="l305">    305</a> actually uses, or expects or is expected to use, the product.  A product
342 <a href="#l306" class="line" id="l306">    306</a> is a consumer product regardless of whether the product has substantial
343 <a href="#l307" class="line" id="l307">    307</a> commercial, industrial or non-consumer uses, unless such uses represent
344 <a href="#l308" class="line" id="l308">    308</a> the only significant mode of use of the product.
345 <a href="#l309" class="line" id="l309">    309</a> 
346 <a href="#l310" class="line" id="l310">    310</a>   "Installation Information" for a User Product means any methods,
347 <a href="#l311" class="line" id="l311">    311</a> procedures, authorization keys, or other information required to install
348 <a href="#l312" class="line" id="l312">    312</a> and execute modified versions of a covered work in that User Product from
349 <a href="#l313" class="line" id="l313">    313</a> a modified version of its Corresponding Source.  The information must
350 <a href="#l314" class="line" id="l314">    314</a> suffice to ensure that the continued functioning of the modified object
351 <a href="#l315" class="line" id="l315">    315</a> code is in no case prevented or interfered with solely because
352 <a href="#l316" class="line" id="l316">    316</a> modification has been made.
353 <a href="#l317" class="line" id="l317">    317</a> 
354 <a href="#l318" class="line" id="l318">    318</a>   If you convey an object code work under this section in, or with, or
355 <a href="#l319" class="line" id="l319">    319</a> specifically for use in, a User Product, and the conveying occurs as
356 <a href="#l320" class="line" id="l320">    320</a> part of a transaction in which the right of possession and use of the
357 <a href="#l321" class="line" id="l321">    321</a> User Product is transferred to the recipient in perpetuity or for a
358 <a href="#l322" class="line" id="l322">    322</a> fixed term (regardless of how the transaction is characterized), the
359 <a href="#l323" class="line" id="l323">    323</a> Corresponding Source conveyed under this section must be accompanied
360 <a href="#l324" class="line" id="l324">    324</a> by the Installation Information.  But this requirement does not apply
361 <a href="#l325" class="line" id="l325">    325</a> if neither you nor any third party retains the ability to install
362 <a href="#l326" class="line" id="l326">    326</a> modified object code on the User Product (for example, the work has
363 <a href="#l327" class="line" id="l327">    327</a> been installed in ROM).
364 <a href="#l328" class="line" id="l328">    328</a> 
365 <a href="#l329" class="line" id="l329">    329</a>   The requirement to provide Installation Information does not include a
366 <a href="#l330" class="line" id="l330">    330</a> requirement to continue to provide support service, warranty, or updates
367 <a href="#l331" class="line" id="l331">    331</a> for a work that has been modified or installed by the recipient, or for
368 <a href="#l332" class="line" id="l332">    332</a> the User Product in which it has been modified or installed.  Access to a
369 <a href="#l333" class="line" id="l333">    333</a> network may be denied when the modification itself materially and
370 <a href="#l334" class="line" id="l334">    334</a> adversely affects the operation of the network or violates the rules and
371 <a href="#l335" class="line" id="l335">    335</a> protocols for communication across the network.
372 <a href="#l336" class="line" id="l336">    336</a> 
373 <a href="#l337" class="line" id="l337">    337</a>   Corresponding Source conveyed, and Installation Information provided,
374 <a href="#l338" class="line" id="l338">    338</a> in accord with this section must be in a format that is publicly
375 <a href="#l339" class="line" id="l339">    339</a> documented (and with an implementation available to the public in
376 <a href="#l340" class="line" id="l340">    340</a> source code form), and must require no special password or key for
377 <a href="#l341" class="line" id="l341">    341</a> unpacking, reading or copying.
378 <a href="#l342" class="line" id="l342">    342</a> 
379 <a href="#l343" class="line" id="l343">    343</a>   7. Additional Terms.
380 <a href="#l344" class="line" id="l344">    344</a> 
381 <a href="#l345" class="line" id="l345">    345</a>   "Additional permissions" are terms that supplement the terms of this
382 <a href="#l346" class="line" id="l346">    346</a> License by making exceptions from one or more of its conditions.
383 <a href="#l347" class="line" id="l347">    347</a> Additional permissions that are applicable to the entire Program shall
384 <a href="#l348" class="line" id="l348">    348</a> be treated as though they were included in this License, to the extent
385 <a href="#l349" class="line" id="l349">    349</a> that they are valid under applicable law.  If additional permissions
386 <a href="#l350" class="line" id="l350">    350</a> apply only to part of the Program, that part may be used separately
387 <a href="#l351" class="line" id="l351">    351</a> under those permissions, but the entire Program remains governed by
388 <a href="#l352" class="line" id="l352">    352</a> this License without regard to the additional permissions.
389 <a href="#l353" class="line" id="l353">    353</a> 
390 <a href="#l354" class="line" id="l354">    354</a>   When you convey a copy of a covered work, you may at your option
391 <a href="#l355" class="line" id="l355">    355</a> remove any additional permissions from that copy, or from any part of
392 <a href="#l356" class="line" id="l356">    356</a> it.  (Additional permissions may be written to require their own
393 <a href="#l357" class="line" id="l357">    357</a> removal in certain cases when you modify the work.)  You may place
394 <a href="#l358" class="line" id="l358">    358</a> additional permissions on material, added by you to a covered work,
395 <a href="#l359" class="line" id="l359">    359</a> for which you have or can give appropriate copyright permission.
396 <a href="#l360" class="line" id="l360">    360</a> 
397 <a href="#l361" class="line" id="l361">    361</a>   Notwithstanding any other provision of this License, for material you
398 <a href="#l362" class="line" id="l362">    362</a> add to a covered work, you may (if authorized by the copyright holders of
399 <a href="#l363" class="line" id="l363">    363</a> that material) supplement the terms of this License with terms:
400 <a href="#l364" class="line" id="l364">    364</a> 
401 <a href="#l365" class="line" id="l365">    365</a>     a) Disclaiming warranty or limiting liability differently from the
402 <a href="#l366" class="line" id="l366">    366</a>     terms of sections 15 and 16 of this License; or
403 <a href="#l367" class="line" id="l367">    367</a> 
404 <a href="#l368" class="line" id="l368">    368</a>     b) Requiring preservation of specified reasonable legal notices or
405 <a href="#l369" class="line" id="l369">    369</a>     author attributions in that material or in the Appropriate Legal
406 <a href="#l370" class="line" id="l370">    370</a>     Notices displayed by works containing it; or
407 <a href="#l371" class="line" id="l371">    371</a> 
408 <a href="#l372" class="line" id="l372">    372</a>     c) Prohibiting misrepresentation of the origin of that material, or
409 <a href="#l373" class="line" id="l373">    373</a>     requiring that modified versions of such material be marked in
410 <a href="#l374" class="line" id="l374">    374</a>     reasonable ways as different from the original version; or
411 <a href="#l375" class="line" id="l375">    375</a> 
412 <a href="#l376" class="line" id="l376">    376</a>     d) Limiting the use for publicity purposes of names of licensors or
413 <a href="#l377" class="line" id="l377">    377</a>     authors of the material; or
414 <a href="#l378" class="line" id="l378">    378</a> 
415 <a href="#l379" class="line" id="l379">    379</a>     e) Declining to grant rights under trademark law for use of some
416 <a href="#l380" class="line" id="l380">    380</a>     trade names, trademarks, or service marks; or
417 <a href="#l381" class="line" id="l381">    381</a> 
418 <a href="#l382" class="line" id="l382">    382</a>     f) Requiring indemnification of licensors and authors of that
419 <a href="#l383" class="line" id="l383">    383</a>     material by anyone who conveys the material (or modified versions of
420 <a href="#l384" class="line" id="l384">    384</a>     it) with contractual assumptions of liability to the recipient, for
421 <a href="#l385" class="line" id="l385">    385</a>     any liability that these contractual assumptions directly impose on
422 <a href="#l386" class="line" id="l386">    386</a>     those licensors and authors.
423 <a href="#l387" class="line" id="l387">    387</a> 
424 <a href="#l388" class="line" id="l388">    388</a>   All other non-permissive additional terms are considered "further
425 <a href="#l389" class="line" id="l389">    389</a> restrictions" within the meaning of section 10.  If the Program as you
426 <a href="#l390" class="line" id="l390">    390</a> received it, or any part of it, contains a notice stating that it is
427 <a href="#l391" class="line" id="l391">    391</a> governed by this License along with a term that is a further
428 <a href="#l392" class="line" id="l392">    392</a> restriction, you may remove that term.  If a license document contains
429 <a href="#l393" class="line" id="l393">    393</a> a further restriction but permits relicensing or conveying under this
430 <a href="#l394" class="line" id="l394">    394</a> License, you may add to a covered work material governed by the terms
431 <a href="#l395" class="line" id="l395">    395</a> of that license document, provided that the further restriction does
432 <a href="#l396" class="line" id="l396">    396</a> not survive such relicensing or conveying.
433 <a href="#l397" class="line" id="l397">    397</a> 
434 <a href="#l398" class="line" id="l398">    398</a>   If you add terms to a covered work in accord with this section, you
435 <a href="#l399" class="line" id="l399">    399</a> must place, in the relevant source files, a statement of the
436 <a href="#l400" class="line" id="l400">    400</a> additional terms that apply to those files, or a notice indicating
437 <a href="#l401" class="line" id="l401">    401</a> where to find the applicable terms.
438 <a href="#l402" class="line" id="l402">    402</a> 
439 <a href="#l403" class="line" id="l403">    403</a>   Additional terms, permissive or non-permissive, may be stated in the
440 <a href="#l404" class="line" id="l404">    404</a> form of a separately written license, or stated as exceptions;
441 <a href="#l405" class="line" id="l405">    405</a> the above requirements apply either way.
442 <a href="#l406" class="line" id="l406">    406</a> 
443 <a href="#l407" class="line" id="l407">    407</a>   8. Termination.
444 <a href="#l408" class="line" id="l408">    408</a> 
445 <a href="#l409" class="line" id="l409">    409</a>   You may not propagate or modify a covered work except as expressly
446 <a href="#l410" class="line" id="l410">    410</a> provided under this License.  Any attempt otherwise to propagate or
447 <a href="#l411" class="line" id="l411">    411</a> modify it is void, and will automatically terminate your rights under
448 <a href="#l412" class="line" id="l412">    412</a> this License (including any patent licenses granted under the third
449 <a href="#l413" class="line" id="l413">    413</a> paragraph of section 11).
450 <a href="#l414" class="line" id="l414">    414</a> 
451 <a href="#l415" class="line" id="l415">    415</a>   However, if you cease all violation of this License, then your
452 <a href="#l416" class="line" id="l416">    416</a> license from a particular copyright holder is reinstated (a)
453 <a href="#l417" class="line" id="l417">    417</a> provisionally, unless and until the copyright holder explicitly and
454 <a href="#l418" class="line" id="l418">    418</a> finally terminates your license, and (b) permanently, if the copyright
455 <a href="#l419" class="line" id="l419">    419</a> holder fails to notify you of the violation by some reasonable means
456 <a href="#l420" class="line" id="l420">    420</a> prior to 60 days after the cessation.
457 <a href="#l421" class="line" id="l421">    421</a> 
458 <a href="#l422" class="line" id="l422">    422</a>   Moreover, your license from a particular copyright holder is
459 <a href="#l423" class="line" id="l423">    423</a> reinstated permanently if the copyright holder notifies you of the
460 <a href="#l424" class="line" id="l424">    424</a> violation by some reasonable means, this is the first time you have
461 <a href="#l425" class="line" id="l425">    425</a> received notice of violation of this License (for any work) from that
462 <a href="#l426" class="line" id="l426">    426</a> copyright holder, and you cure the violation prior to 30 days after
463 <a href="#l427" class="line" id="l427">    427</a> your receipt of the notice.
464 <a href="#l428" class="line" id="l428">    428</a> 
465 <a href="#l429" class="line" id="l429">    429</a>   Termination of your rights under this section does not terminate the
466 <a href="#l430" class="line" id="l430">    430</a> licenses of parties who have received copies or rights from you under
467 <a href="#l431" class="line" id="l431">    431</a> this License.  If your rights have been terminated and not permanently
468 <a href="#l432" class="line" id="l432">    432</a> reinstated, you do not qualify to receive new licenses for the same
469 <a href="#l433" class="line" id="l433">    433</a> material under section 10.
470 <a href="#l434" class="line" id="l434">    434</a> 
471 <a href="#l435" class="line" id="l435">    435</a>   9. Acceptance Not Required for Having Copies.
472 <a href="#l436" class="line" id="l436">    436</a> 
473 <a href="#l437" class="line" id="l437">    437</a>   You are not required to accept this License in order to receive or
474 <a href="#l438" class="line" id="l438">    438</a> run a copy of the Program.  Ancillary propagation of a covered work
475 <a href="#l439" class="line" id="l439">    439</a> occurring solely as a consequence of using peer-to-peer transmission
476 <a href="#l440" class="line" id="l440">    440</a> to receive a copy likewise does not require acceptance.  However,
477 <a href="#l441" class="line" id="l441">    441</a> nothing other than this License grants you permission to propagate or
478 <a href="#l442" class="line" id="l442">    442</a> modify any covered work.  These actions infringe copyright if you do
479 <a href="#l443" class="line" id="l443">    443</a> not accept this License.  Therefore, by modifying or propagating a
480 <a href="#l444" class="line" id="l444">    444</a> covered work, you indicate your acceptance of this License to do so.
481 <a href="#l445" class="line" id="l445">    445</a> 
482 <a href="#l446" class="line" id="l446">    446</a>   10. Automatic Licensing of Downstream Recipients.
483 <a href="#l447" class="line" id="l447">    447</a> 
484 <a href="#l448" class="line" id="l448">    448</a>   Each time you convey a covered work, the recipient automatically
485 <a href="#l449" class="line" id="l449">    449</a> receives a license from the original licensors, to run, modify and
486 <a href="#l450" class="line" id="l450">    450</a> propagate that work, subject to this License.  You are not responsible
487 <a href="#l451" class="line" id="l451">    451</a> for enforcing compliance by third parties with this License.
488 <a href="#l452" class="line" id="l452">    452</a> 
489 <a href="#l453" class="line" id="l453">    453</a>   An "entity transaction" is a transaction transferring control of an
490 <a href="#l454" class="line" id="l454">    454</a> organization, or substantially all assets of one, or subdividing an
491 <a href="#l455" class="line" id="l455">    455</a> organization, or merging organizations.  If propagation of a covered
492 <a href="#l456" class="line" id="l456">    456</a> work results from an entity transaction, each party to that
493 <a href="#l457" class="line" id="l457">    457</a> transaction who receives a copy of the work also receives whatever
494 <a href="#l458" class="line" id="l458">    458</a> licenses to the work the party's predecessor in interest had or could
495 <a href="#l459" class="line" id="l459">    459</a> give under the previous paragraph, plus a right to possession of the
496 <a href="#l460" class="line" id="l460">    460</a> Corresponding Source of the work from the predecessor in interest, if
497 <a href="#l461" class="line" id="l461">    461</a> the predecessor has it or can get it with reasonable efforts.
498 <a href="#l462" class="line" id="l462">    462</a> 
499 <a href="#l463" class="line" id="l463">    463</a>   You may not impose any further restrictions on the exercise of the
500 <a href="#l464" class="line" id="l464">    464</a> rights granted or affirmed under this License.  For example, you may
501 <a href="#l465" class="line" id="l465">    465</a> not impose a license fee, royalty, or other charge for exercise of
502 <a href="#l466" class="line" id="l466">    466</a> rights granted under this License, and you may not initiate litigation
503 <a href="#l467" class="line" id="l467">    467</a> (including a cross-claim or counterclaim in a lawsuit) alleging that
504 <a href="#l468" class="line" id="l468">    468</a> any patent claim is infringed by making, using, selling, offering for
505 <a href="#l469" class="line" id="l469">    469</a> sale, or importing the Program or any portion of it.
506 <a href="#l470" class="line" id="l470">    470</a> 
507 <a href="#l471" class="line" id="l471">    471</a>   11. Patents.
508 <a href="#l472" class="line" id="l472">    472</a> 
509 <a href="#l473" class="line" id="l473">    473</a>   A "contributor" is a copyright holder who authorizes use under this
510 <a href="#l474" class="line" id="l474">    474</a> License of the Program or a work on which the Program is based.  The
511 <a href="#l475" class="line" id="l475">    475</a> work thus licensed is called the contributor's "contributor version".
512 <a href="#l476" class="line" id="l476">    476</a> 
513 <a href="#l477" class="line" id="l477">    477</a>   A contributor's "essential patent claims" are all patent claims
514 <a href="#l478" class="line" id="l478">    478</a> owned or controlled by the contributor, whether already acquired or
515 <a href="#l479" class="line" id="l479">    479</a> hereafter acquired, that would be infringed by some manner, permitted
516 <a href="#l480" class="line" id="l480">    480</a> by this License, of making, using, or selling its contributor version,
517 <a href="#l481" class="line" id="l481">    481</a> but do not include claims that would be infringed only as a
518 <a href="#l482" class="line" id="l482">    482</a> consequence of further modification of the contributor version.  For
519 <a href="#l483" class="line" id="l483">    483</a> purposes of this definition, "control" includes the right to grant
520 <a href="#l484" class="line" id="l484">    484</a> patent sublicenses in a manner consistent with the requirements of
521 <a href="#l485" class="line" id="l485">    485</a> this License.
522 <a href="#l486" class="line" id="l486">    486</a> 
523 <a href="#l487" class="line" id="l487">    487</a>   Each contributor grants you a non-exclusive, worldwide, royalty-free
524 <a href="#l488" class="line" id="l488">    488</a> patent license under the contributor's essential patent claims, to
525 <a href="#l489" class="line" id="l489">    489</a> make, use, sell, offer for sale, import and otherwise run, modify and
526 <a href="#l490" class="line" id="l490">    490</a> propagate the contents of its contributor version.
527 <a href="#l491" class="line" id="l491">    491</a> 
528 <a href="#l492" class="line" id="l492">    492</a>   In the following three paragraphs, a "patent license" is any express
529 <a href="#l493" class="line" id="l493">    493</a> agreement or commitment, however denominated, not to enforce a patent
530 <a href="#l494" class="line" id="l494">    494</a> (such as an express permission to practice a patent or covenant not to
531 <a href="#l495" class="line" id="l495">    495</a> sue for patent infringement).  To "grant" such a patent license to a
532 <a href="#l496" class="line" id="l496">    496</a> party means to make such an agreement or commitment not to enforce a
533 <a href="#l497" class="line" id="l497">    497</a> patent against the party.
534 <a href="#l498" class="line" id="l498">    498</a> 
535 <a href="#l499" class="line" id="l499">    499</a>   If you convey a covered work, knowingly relying on a patent license,
536 <a href="#l500" class="line" id="l500">    500</a> and the Corresponding Source of the work is not available for anyone
537 <a href="#l501" class="line" id="l501">    501</a> to copy, free of charge and under the terms of this License, through a
538 <a href="#l502" class="line" id="l502">    502</a> publicly available network server or other readily accessible means,
539 <a href="#l503" class="line" id="l503">    503</a> then you must either (1) cause the Corresponding Source to be so
540 <a href="#l504" class="line" id="l504">    504</a> available, or (2) arrange to deprive yourself of the benefit of the
541 <a href="#l505" class="line" id="l505">    505</a> patent license for this particular work, or (3) arrange, in a manner
542 <a href="#l506" class="line" id="l506">    506</a> consistent with the requirements of this License, to extend the patent
543 <a href="#l507" class="line" id="l507">    507</a> license to downstream recipients.  "Knowingly relying" means you have
544 <a href="#l508" class="line" id="l508">    508</a> actual knowledge that, but for the patent license, your conveying the
545 <a href="#l509" class="line" id="l509">    509</a> covered work in a country, or your recipient's use of the covered work
546 <a href="#l510" class="line" id="l510">    510</a> in a country, would infringe one or more identifiable patents in that
547 <a href="#l511" class="line" id="l511">    511</a> country that you have reason to believe are valid.
548 <a href="#l512" class="line" id="l512">    512</a> 
549 <a href="#l513" class="line" id="l513">    513</a>   If, pursuant to or in connection with a single transaction or
550 <a href="#l514" class="line" id="l514">    514</a> arrangement, you convey, or propagate by procuring conveyance of, a
551 <a href="#l515" class="line" id="l515">    515</a> covered work, and grant a patent license to some of the parties
552 <a href="#l516" class="line" id="l516">    516</a> receiving the covered work authorizing them to use, propagate, modify
553 <a href="#l517" class="line" id="l517">    517</a> or convey a specific copy of the covered work, then the patent license
554 <a href="#l518" class="line" id="l518">    518</a> you grant is automatically extended to all recipients of the covered
555 <a href="#l519" class="line" id="l519">    519</a> work and works based on it.
556 <a href="#l520" class="line" id="l520">    520</a> 
557 <a href="#l521" class="line" id="l521">    521</a>   A patent license is "discriminatory" if it does not include within
558 <a href="#l522" class="line" id="l522">    522</a> the scope of its coverage, prohibits the exercise of, or is
559 <a href="#l523" class="line" id="l523">    523</a> conditioned on the non-exercise of one or more of the rights that are
560 <a href="#l524" class="line" id="l524">    524</a> specifically granted under this License.  You may not convey a covered
561 <a href="#l525" class="line" id="l525">    525</a> work if you are a party to an arrangement with a third party that is
562 <a href="#l526" class="line" id="l526">    526</a> in the business of distributing software, under which you make payment
563 <a href="#l527" class="line" id="l527">    527</a> to the third party based on the extent of your activity of conveying
564 <a href="#l528" class="line" id="l528">    528</a> the work, and under which the third party grants, to any of the
565 <a href="#l529" class="line" id="l529">    529</a> parties who would receive the covered work from you, a discriminatory
566 <a href="#l530" class="line" id="l530">    530</a> patent license (a) in connection with copies of the covered work
567 <a href="#l531" class="line" id="l531">    531</a> conveyed by you (or copies made from those copies), or (b) primarily
568 <a href="#l532" class="line" id="l532">    532</a> for and in connection with specific products or compilations that
569 <a href="#l533" class="line" id="l533">    533</a> contain the covered work, unless you entered into that arrangement,
570 <a href="#l534" class="line" id="l534">    534</a> or that patent license was granted, prior to 28 March 2007.
571 <a href="#l535" class="line" id="l535">    535</a> 
572 <a href="#l536" class="line" id="l536">    536</a>   Nothing in this License shall be construed as excluding or limiting
573 <a href="#l537" class="line" id="l537">    537</a> any implied license or other defenses to infringement that may
574 <a href="#l538" class="line" id="l538">    538</a> otherwise be available to you under applicable patent law.
575 <a href="#l539" class="line" id="l539">    539</a> 
576 <a href="#l540" class="line" id="l540">    540</a>   12. No Surrender of Others' Freedom.
577 <a href="#l541" class="line" id="l541">    541</a> 
578 <a href="#l542" class="line" id="l542">    542</a>   If conditions are imposed on you (whether by court order, agreement or
579 <a href="#l543" class="line" id="l543">    543</a> otherwise) that contradict the conditions of this License, they do not
580 <a href="#l544" class="line" id="l544">    544</a> excuse you from the conditions of this License.  If you cannot convey a
581 <a href="#l545" class="line" id="l545">    545</a> covered work so as to satisfy simultaneously your obligations under this
582 <a href="#l546" class="line" id="l546">    546</a> License and any other pertinent obligations, then as a consequence you may
583 <a href="#l547" class="line" id="l547">    547</a> not convey it at all.  For example, if you agree to terms that obligate you
584 <a href="#l548" class="line" id="l548">    548</a> to collect a royalty for further conveying from those to whom you convey
585 <a href="#l549" class="line" id="l549">    549</a> the Program, the only way you could satisfy both those terms and this
586 <a href="#l550" class="line" id="l550">    550</a> License would be to refrain entirely from conveying the Program.
587 <a href="#l551" class="line" id="l551">    551</a> 
588 <a href="#l552" class="line" id="l552">    552</a>   13. Use with the GNU Affero General Public License.
589 <a href="#l553" class="line" id="l553">    553</a> 
590 <a href="#l554" class="line" id="l554">    554</a>   Notwithstanding any other provision of this License, you have
591 <a href="#l555" class="line" id="l555">    555</a> permission to link or combine any covered work with a work licensed
592 <a href="#l556" class="line" id="l556">    556</a> under version 3 of the GNU Affero General Public License into a single
593 <a href="#l557" class="line" id="l557">    557</a> combined work, and to convey the resulting work.  The terms of this
594 <a href="#l558" class="line" id="l558">    558</a> License will continue to apply to the part which is the covered work,
595 <a href="#l559" class="line" id="l559">    559</a> but the special requirements of the GNU Affero General Public License,
596 <a href="#l560" class="line" id="l560">    560</a> section 13, concerning interaction through a network will apply to the
597 <a href="#l561" class="line" id="l561">    561</a> combination as such.
598 <a href="#l562" class="line" id="l562">    562</a> 
599 <a href="#l563" class="line" id="l563">    563</a>   14. Revised Versions of this License.
600 <a href="#l564" class="line" id="l564">    564</a> 
601 <a href="#l565" class="line" id="l565">    565</a>   The Free Software Foundation may publish revised and/or new versions of
602 <a href="#l566" class="line" id="l566">    566</a> the GNU General Public License from time to time.  Such new versions will
603 <a href="#l567" class="line" id="l567">    567</a> be similar in spirit to the present version, but may differ in detail to
604 <a href="#l568" class="line" id="l568">    568</a> address new problems or concerns.
605 <a href="#l569" class="line" id="l569">    569</a> 
606 <a href="#l570" class="line" id="l570">    570</a>   Each version is given a distinguishing version number.  If the
607 <a href="#l571" class="line" id="l571">    571</a> Program specifies that a certain numbered version of the GNU General
608 <a href="#l572" class="line" id="l572">    572</a> Public License "or any later version" applies to it, you have the
609 <a href="#l573" class="line" id="l573">    573</a> option of following the terms and conditions either of that numbered
610 <a href="#l574" class="line" id="l574">    574</a> version or of any later version published by the Free Software
611 <a href="#l575" class="line" id="l575">    575</a> Foundation.  If the Program does not specify a version number of the
612 <a href="#l576" class="line" id="l576">    576</a> GNU General Public License, you may choose any version ever published
613 <a href="#l577" class="line" id="l577">    577</a> by the Free Software Foundation.
614 <a href="#l578" class="line" id="l578">    578</a> 
615 <a href="#l579" class="line" id="l579">    579</a>   If the Program specifies that a proxy can decide which future
616 <a href="#l580" class="line" id="l580">    580</a> versions of the GNU General Public License can be used, that proxy's
617 <a href="#l581" class="line" id="l581">    581</a> public statement of acceptance of a version permanently authorizes you
618 <a href="#l582" class="line" id="l582">    582</a> to choose that version for the Program.
619 <a href="#l583" class="line" id="l583">    583</a> 
620 <a href="#l584" class="line" id="l584">    584</a>   Later license versions may give you additional or different
621 <a href="#l585" class="line" id="l585">    585</a> permissions.  However, no additional obligations are imposed on any
622 <a href="#l586" class="line" id="l586">    586</a> author or copyright holder as a result of your choosing to follow a
623 <a href="#l587" class="line" id="l587">    587</a> later version.
624 <a href="#l588" class="line" id="l588">    588</a> 
625 <a href="#l589" class="line" id="l589">    589</a>   15. Disclaimer of Warranty.
626 <a href="#l590" class="line" id="l590">    590</a> 
627 <a href="#l591" class="line" id="l591">    591</a>   THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY
628 <a href="#l592" class="line" id="l592">    592</a> APPLICABLE LAW.  EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT
629 <a href="#l593" class="line" id="l593">    593</a> HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY
630 <a href="#l594" class="line" id="l594">    594</a> OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO,
631 <a href="#l595" class="line" id="l595">    595</a> THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR
632 <a href="#l596" class="line" id="l596">    596</a> PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
633 <a href="#l597" class="line" id="l597">    597</a> IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
634 <a href="#l598" class="line" id="l598">    598</a> ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
635 <a href="#l599" class="line" id="l599">    599</a> 
636 <a href="#l600" class="line" id="l600">    600</a>   16. Limitation of Liability.
637 <a href="#l601" class="line" id="l601">    601</a> 
638 <a href="#l602" class="line" id="l602">    602</a>   IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
639 <a href="#l603" class="line" id="l603">    603</a> WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
640 <a href="#l604" class="line" id="l604">    604</a> THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
641 <a href="#l605" class="line" id="l605">    605</a> GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
642 <a href="#l606" class="line" id="l606">    606</a> USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
643 <a href="#l607" class="line" id="l607">    607</a> DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
644 <a href="#l608" class="line" id="l608">    608</a> PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
645 <a href="#l609" class="line" id="l609">    609</a> EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
646 <a href="#l610" class="line" id="l610">    610</a> SUCH DAMAGES.
647 <a href="#l611" class="line" id="l611">    611</a> 
648 <a href="#l612" class="line" id="l612">    612</a>   17. Interpretation of Sections 15 and 16.
649 <a href="#l613" class="line" id="l613">    613</a> 
650 <a href="#l614" class="line" id="l614">    614</a>   If the disclaimer of warranty and limitation of liability provided
651 <a href="#l615" class="line" id="l615">    615</a> above cannot be given local legal effect according to their terms,
652 <a href="#l616" class="line" id="l616">    616</a> reviewing courts shall apply local law that most closely approximates
653 <a href="#l617" class="line" id="l617">    617</a> an absolute waiver of all civil liability in connection with the
654 <a href="#l618" class="line" id="l618">    618</a> Program, unless a warranty or assumption of liability accompanies a
655 <a href="#l619" class="line" id="l619">    619</a> copy of the Program in return for a fee.
656 <a href="#l620" class="line" id="l620">    620</a> 
657 <a href="#l621" class="line" id="l621">    621</a>                      END OF TERMS AND CONDITIONS
658 <a href="#l622" class="line" id="l622">    622</a> 
659 <a href="#l623" class="line" id="l623">    623</a>             How to Apply These Terms to Your New Programs
660 <a href="#l624" class="line" id="l624">    624</a> 
661 <a href="#l625" class="line" id="l625">    625</a>   If you develop a new program, and you want it to be of the greatest
662 <a href="#l626" class="line" id="l626">    626</a> possible use to the public, the best way to achieve this is to make it
663 <a href="#l627" class="line" id="l627">    627</a> free software which everyone can redistribute and change under these terms.
664 <a href="#l628" class="line" id="l628">    628</a> 
665 <a href="#l629" class="line" id="l629">    629</a>   To do so, attach the following notices to the program.  It is safest
666 <a href="#l630" class="line" id="l630">    630</a> to attach them to the start of each source file to most effectively
667 <a href="#l631" class="line" id="l631">    631</a> state the exclusion of warranty; and each file should have at least
668 <a href="#l632" class="line" id="l632">    632</a> the "copyright" line and a pointer to where the full notice is found.
669 <a href="#l633" class="line" id="l633">    633</a> 
670 <a href="#l634" class="line" id="l634">    634</a>     &lt;one line to give the program's name and a brief idea of what it does.&gt;
671 <a href="#l635" class="line" id="l635">    635</a>     Copyright (C) &lt;year&gt;  &lt;name of author&gt;
672 <a href="#l636" class="line" id="l636">    636</a> 
673 <a href="#l637" class="line" id="l637">    637</a>     This program is free software: you can redistribute it and/or modify
674 <a href="#l638" class="line" id="l638">    638</a>     it under the terms of the GNU General Public License as published by
675 <a href="#l639" class="line" id="l639">    639</a>     the Free Software Foundation, either version 3 of the License, or
676 <a href="#l640" class="line" id="l640">    640</a>     (at your option) any later version.
677 <a href="#l641" class="line" id="l641">    641</a> 
678 <a href="#l642" class="line" id="l642">    642</a>     This program is distributed in the hope that it will be useful,
679 <a href="#l643" class="line" id="l643">    643</a>     but WITHOUT ANY WARRANTY; without even the implied warranty of
680 <a href="#l644" class="line" id="l644">    644</a>     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
681 <a href="#l645" class="line" id="l645">    645</a>     GNU General Public License for more details.
682 <a href="#l646" class="line" id="l646">    646</a> 
683 <a href="#l647" class="line" id="l647">    647</a>     You should have received a copy of the GNU General Public License
684 <a href="#l648" class="line" id="l648">    648</a>     along with this program.  If not, see &lt;https://www.gnu.org/licenses/&gt;.
685 <a href="#l649" class="line" id="l649">    649</a> 
686 <a href="#l650" class="line" id="l650">    650</a> Also add information on how to contact you by electronic and paper mail.
687 <a href="#l651" class="line" id="l651">    651</a> 
688 <a href="#l652" class="line" id="l652">    652</a>   If the program does terminal interaction, make it output a short
689 <a href="#l653" class="line" id="l653">    653</a> notice like this when it starts in an interactive mode:
690 <a href="#l654" class="line" id="l654">    654</a> 
691 <a href="#l655" class="line" id="l655">    655</a>     &lt;program&gt;  Copyright (C) &lt;year&gt;  &lt;name of author&gt;
692 <a href="#l656" class="line" id="l656">    656</a>     This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
693 <a href="#l657" class="line" id="l657">    657</a>     This is free software, and you are welcome to redistribute it
694 <a href="#l658" class="line" id="l658">    658</a>     under certain conditions; type `show c' for details.
695 <a href="#l659" class="line" id="l659">    659</a> 
696 <a href="#l660" class="line" id="l660">    660</a> The hypothetical commands `show w' and `show c' should show the appropriate
697 <a href="#l661" class="line" id="l661">    661</a> parts of the General Public License.  Of course, your program's commands
698 <a href="#l662" class="line" id="l662">    662</a> might be different; for a GUI interface, you would use an "about box".
699 <a href="#l663" class="line" id="l663">    663</a> 
700 <a href="#l664" class="line" id="l664">    664</a>   You should also get your employer (if you work as a programmer) or school,
701 <a href="#l665" class="line" id="l665">    665</a> if any, to sign a "copyright disclaimer" for the program, if necessary.
702 <a href="#l666" class="line" id="l666">    666</a> For more information on this, and how to apply and follow the GNU GPL, see
703 <a href="#l667" class="line" id="l667">    667</a> &lt;https://www.gnu.org/licenses/&gt;.
704 <a href="#l668" class="line" id="l668">    668</a> 
705 <a href="#l669" class="line" id="l669">    669</a>   The GNU General Public License does not permit incorporating your program
706 <a href="#l670" class="line" id="l670">    670</a> into proprietary programs.  If your program is a subroutine library, you
707 <a href="#l671" class="line" id="l671">    671</a> may consider it more useful to permit linking proprietary applications with
708 <a href="#l672" class="line" id="l672">    672</a> the library.  If this is what you want to do, use the GNU Lesser General
709 <a href="#l673" class="line" id="l673">    673</a> Public License instead of this License.  But first, please read
710 <a href="#l674" class="line" id="l674">    674</a> &lt;https://www.gnu.org/licenses/why-not-lgpl.html&gt;.
711 </pre>
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