SheafSystem  0.0.0.0
sec_e2.cc
Go to the documentation of this file.
1 
2 //
3 // Copyright (c) 2014 Limit Point Systems, Inc.
4 //
5 // Licensed under the Apache License, Version 2.0 (the "License");
6 // you may not use this file except in compliance with the License.
7 // You may obtain a copy of the License at
8 //
9 // http://www.apache.org/licenses/LICENSE-2.0
10 //
11 // Unless required by applicable law or agreed to in writing, software
12 // distributed under the License is distributed on an "AS IS" BASIS,
13 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
14 // See the License for the specific language governing permissions and
15 // limitations under the License.
16 //
17 
20 
21 #include "SheafSystem/sec_e2.h"
22 
23 #include "SheafSystem/assert_contract.h"
24 #include "SheafSystem/base_space_poset.h"
25 #include "SheafSystem/binary_section_space_schema_member.impl.h"
26 #include "SheafSystem/at1_space.h"
27 #include "SheafSystem/fiber_bundles_namespace.h"
28 #include "SheafSystem/index_space_iterator.h"
29 #include "SheafSystem/sec_at0.h"
30 #include "SheafSystem/sec_at0_space.h"
31 #include "SheafSystem/sec_at1_space.h"
32 #include "SheafSystem/sec_tuple.impl.h"
33 #include "SheafSystem/sec_tuple_space.impl.h"
34 #include "SheafSystem/sec_vd.impl.h"
35 
36 
37 using namespace std;
38 using namespace fiber_bundle; // Workaround for MS C++ bug.
39 
40 //==============================================================================
41 // CLASS SEC_E2
42 //==============================================================================
43 
44 // ===========================================================
45 // HOST FACTORY FACET OF CLASS SEC_E2
46 // ===========================================================
47 
48 // PUBLIC MEMBER FUNCTIONS
49 
53  const poset_path& xhost_path,
54  const poset_path& xschema_path,
55  const poset_path& xscalar_space_path,
56  bool xauto_access)
57 {
58  // cout << endl << "Entering sec_e2::new_host." << endl;
59 
60  // Preconditions:
61 
62  require(xns.state_is_auto_read_write_accessible(xauto_access));
63 
64  require(!xhost_path.empty());
65  require(!xns.contains_path(xhost_path, xauto_access));
66 
67  require(xschema_path.full());
68  require(xns.path_is_auto_read_accessible<schema_type::host_type>(xschema_path, xauto_access));
69  require(host_type::fiber_space_conforms<fiber_type::host_type>(xns, xschema_path, xauto_access));
70 
71  require(xns.path_is_auto_read_accessible<scalar_type::host_type>(xscalar_space_path, xauto_access));
72 
73  require(host_type::same_scalar_fiber_space(xns, xschema_path, xscalar_space_path, xauto_access));
74 
75  // Body:
76 
77  host_type& result = host_type::new_table(xns, xhost_path, xschema_path, xscalar_space_path, xauto_access);
78 
79  // Postconditions:
80 
81  ensure(xns.owns(result, xauto_access));
82  ensure(result.path(true) == xhost_path);
83  ensure(result.state_is_not_read_accessible());
84  ensure(result.schema(true).path(xauto_access) == xschema_path);
85 
86  ensure(result.factor_ct(true) == result.schema(true).fiber_space<fiber_type::host_type>().factor_ct(xauto_access));
87  ensure(result.d(true) == result.schema(true).fiber_space<fiber_type::host_type>().d(xauto_access));
88  ensure(result.d(true) == result.dd(true));
89  ensure(result.scalar_space_path(true) == xscalar_space_path);
90  ensure(result.p(true) == result.schema(true).fiber_space<fiber_type::host_type>().p(xauto_access));
91  ensure(result.p(true) == 1);
92  ensure(result.dd(true) == result.schema(true).fiber_space<fiber_type::host_type>().dd(xauto_access));
93  ensure(result.vector_space_path(true) == xhost_path);
94 
95  // Exit:
96 
97  // cout << "Leaving sec_e2::new_host." << endl;
98  return result;
99 }
100 
104  const poset_path& xbase_path,
105  const poset_path& xrep_path,
106  const std::string& xsection_suffix,
107  const std::string& xfiber_suffix,
108  bool xauto_access)
109 {
110  // cout << endl << "Entering sec_e2::new_host." << endl;
111 
112  // Preconditions:
113 
114  require(xns.state_is_auto_read_write_accessible(xauto_access));
115 
116  require(xbase_path.full());
117  require(xns.path_is_auto_read_accessible<base_space_poset>(xbase_path, xauto_access));
118 
119  require(xrep_path.empty() || xrep_path.full());
120  require(xrep_path.empty() || xns.path_is_auto_read_accessible<sec_rep_descriptor_poset>(xrep_path, xauto_access));
121 
122  require(xsection_suffix.empty() || poset_path::is_valid_name(xsection_suffix));
123 
124  require(xfiber_suffix.empty() || poset_path::is_valid_name(xfiber_suffix));
125 
126  require(standard_host_is_available<sec_e2>(xns, xbase_path, xrep_path, xsection_suffix, xfiber_suffix, xauto_access));
127  require(fiber_type::standard_host_is_available<fiber_type>(xns, xfiber_suffix, xauto_access));
128  require(schema_type::standard_host_is_available<sec_e2>(xns, xbase_path, xrep_path, xfiber_suffix, xauto_access));
129 
130  // Body:
131 
132  poset_path lstd_path = standard_host_path<sec_e2>(xbase_path, xrep_path, xsection_suffix, xfiber_suffix);
133 
134  host_type* lresult_ptr;
135 
136  if(xns.contains_path(lstd_path, xauto_access))
137  {
138  // Standard host already exists, just return it.
139 
140  lresult_ptr = &xns.member_poset<host_type>(lstd_path, xauto_access);
141  }
142  else
143  {
144  // Standard host doesn't exist, have to create it.
145 
146  // Apply default for rep path if needed.
147 
148  poset_path lrep_path = (!xrep_path.empty() ? xrep_path : standard_rep_path());
149 
150  // Find or create the standard schema member.
151 
152  poset_path lstd_schema_path =
153  schema_type::standard_member<sec_e2>(xns, xbase_path, lrep_path, xfiber_suffix, xauto_access);
154 
155  // Find or create the standard scalar space.
156 
157  poset_path lscalar_space_path =
158  scalar_type::standard_host(xns, xbase_path, lrep_path, xsection_suffix, xfiber_suffix, xauto_access).path(xauto_access);
159 
160  // Create the standard host.
161 
162  lresult_ptr = &new_host(xns, lstd_path, lstd_schema_path, lscalar_space_path, xauto_access);
163  }
164 
165  host_type& result = *lresult_ptr;
166 
167  // Postconditions:
168 
169  ensure(xns.owns(result, xauto_access));
170  ensure(result.path(true) == standard_host_path<sec_e2>(xbase_path, xrep_path, xsection_suffix, xfiber_suffix));
171  ensure(result.state_is_not_read_accessible());
172  ensure(result.schema(true).path(xauto_access) ==
173  schema_type::standard_member_path<sec_e2>(xbase_path, xrep_path, xfiber_suffix));
174 
175  ensure(result.factor_ct(true) == result.schema(true).fiber_space<fiber_type::host_type>().factor_ct(xauto_access));
176  ensure(result.d(true) == result.schema(true).fiber_space<fiber_type::host_type>().d(xauto_access));
177  ensure(result.d(true) == result.dd(true));
178  ensure(result.scalar_space_path(true) ==
179  scalar_type::standard_host_path<scalar_type>(xbase_path, result.rep().path(xauto_access), xsection_suffix, xfiber_suffix));
180  ensure(result.p(true) == result.schema(true).fiber_space<fiber_type::host_type>().p(xauto_access));
181  ensure(result.p(true) == 1);
182  ensure(result.dd(true) == result.schema(true).fiber_space<fiber_type::host_type>().dd(xauto_access));
183  ensure(result.vector_space_path(true) == result.path(true));
184 
185  // Exit:
186 
187  // cout << "Leaving sec_e2::new_host." << endl;
188  return result;
189 }
190 
191 // PROTECTED MEMBER FUNCTIONS
192 
193 // PRIVATE MEMBER FUNCTIONS
194 
195 
196 //==============================================================================
197 // E2 FACET OF CLASS SEC_E2
198 //==============================================================================
199 
200 // PUBLIC MEMBER FUNCTIONS
201 
204 {
205  // Preconditions:
206 
207  // Body:
208 
209  // Postconditions:
210 
211  ensure(invariant());
212 }
213 
215 sec_e2(const sec_rep_space* xhost, pod_index_type xhub_id)
216 {
217  // Preconditions:
218 
219  require(xhost != 0);
220  require(xhost->state_is_read_accessible());
221  require(xhost->contains_member(xhub_id));
222 
223  // Body:
224 
225  attach_to_state(xhost, xhub_id);
226 
227  // Postconditions:
228 
229  ensure(invariant());
230  //ensure(host() == xhost);
231  ensure(index() == xhub_id);
232  ensure(is_attached());
233  ensure(!is_restricted());
234 }
235 
237 sec_e2(const sec_rep_space* xhost, const scoped_index& xid)
238 {
239  // Preconditions:
240 
241  require(xhost != 0);
242  require(xhost->state_is_read_accessible());
243  require(xhost->contains_member(xid));
244 
245  // Body:
246 
247  attach_to_state(xhost, xid.hub_pod());
248 
249  // Postconditions:
250 
251  ensure(invariant());
252  //ensure(host() == xhost);
253  ensure(index() ==~ xid);
254  ensure(is_attached());
255  ensure(!is_restricted());
256 }
257 
259 sec_e2(const sec_rep_space* xhost, const std::string& xname)
260 {
261  // Preconditions:
262 
263  require(xhost != 0);
264  require(xhost->state_is_read_accessible());
265  require(!xname.empty());
266  require(xhost->contains_member(xname));
267 
268  // Body:
269 
270  attach_to_state(xhost, xname);
271 
272  // Postconditions:
273 
274  ensure(invariant());
275  //ensure(host() == xhost);
276  ensure(name() == xname);
277  ensure(is_attached());
278  ensure(!is_restricted());
279 
280 }
281 
283 sec_e2(const namespace_poset* xnamespace,
284  const poset_path& xpath,
285  bool xauto_access)
286 {
287  // Preconditions:
288 
289  require(precondition_of(attach_to_state(same args)));
290 
291  // Body:
292 
293  attach_to_state(xnamespace, xpath, xauto_access);
294 
295  // Postconditions:
296 
297  ensure(postcondition_of(attach_to_state(same args)));
298 
299  // Exit:
300 
301  return;
302 }
303 
306 {
307  // Preconditions:
308 
309  require(xother != 0);
310 
311  // Body:
312 
313  attach_to_state(xother);
314 
315  // Postconditions:
316 
317  ensure(invariant());
318  ensure(is_attached());
319  ensure(is_same_state(xother));
320  ensure(is_same_restriction(xother));
321 
322 }
323 
325 sec_e2(sec_rep_space* xhost, section_dof_map* xdof_map, bool xauto_access)
326 {
327  // Preconditions:
328 
329  require(precondition_of(new_jim_state(xhost, xdof_map, false, xauto_access)));
330 
331  // Body:
332 
333  new_jim_state(xhost, xdof_map, false, xauto_access);
334 
335  // Postconditions:
336 
337  ensure(postcondition_of(new_jim_state(xhost, xdof_map, false, xauto_access)));
338 
339  // Exit:
340 
341  return;
342 }
343 
346  abstract_poset_member& xbase_mbr,
347  int xbase_version, bool xauto_access)
348 {
349 
350  // Preconditions:
351 
352  require(precondition_of(new_jim_state(xhost, xbase_mbr, xbase_version, xauto_access)));
353 
354  // Body:
355 
356  new_jim_state(xhost, xbase_mbr, xbase_version, xauto_access);
357 
358  // Postconditions:
359 
360  ensure(postcondition_of(new_jim_state(xhost, xbase_mbr, xbase_version, xauto_access)));
361 
362  // Exit:
363 
364  return;
365 }
366 
368 sec_e2(sec_rep_space* xhost, const subposet& xbase_parts, bool xauto_access)
369 {
370  // Preconditions:
371 
372  require(precondition_of(new_jim_state(xhost, xbase_parts, xauto_access)));
373 
374  // Body:
375 
376  new_jrm_state(xhost, xbase_parts, xauto_access);
377 
378  // Postconditions:
379 
380  require(postcondition_of(new_jim_state(xhost, xbase_parts, xauto_access)));
381 
382  // Exit:
383 
384  return;
385 }
386 
390 {
391  // Preconditions:
392 
393  require(is_ancestor_of(&xother));
394  require(precondition_of(attach_to_state(&xother)));
395 
396  // Body:
397 
398  attach_to_state(&xother);
399 
400  // Postconditions:
401 
402  ensure(postcondition_of(attach_to_state(&xother)));
403 
404  // Exit:
405 
406  return *this;
407 }
408 
411 operator=(const sec_e2& xother)
412 {
413  // Preconditions:
414 
415  require(precondition_of(attach_to_state(&xother)));
416 
417  // Body:
418 
419  attach_to_state(&xother);
420 
421  // Postconditions:
422 
423  ensure(postcondition_of(attach_to_state(&xother)));
424 
425  // Exit:
426 
427  return *this;
428 }
429 
432 operator=(const e2& xfiber)
433 {
434  // Preconditions:
435 
436  require(precondition_of(sec_vd::operator=(xfiber)));
437 
438  // Body:
439 
440  sec_vd::operator=(xfiber);
441 
442  // Postconditions:
443 
444  ensure(postcondition_of(sec_vd::operator=(xfiber)));
445 
446  // Exit:
447 
448  return *this;
449 }
450 
453 operator=(const e2_lite& xfiber)
454 {
455  // Preconditions:
456 
457  require(precondition_of(sec_vd::operator=(xfiber)));
458 
459  // Body:
460 
461  sec_vd::operator=(xfiber);
462 
463  // Postconditions:
464 
465  ensure(postcondition_of(sec_vd::operator=(xfiber)));
466 
467  // Exit:
468 
469  return *this;
470 }
471 
474 {
475  // Preconditions:
476 
477  // Body:
478 
479  // Postconditions:
480 
481 }
482 
486 {
487  // Preconditions:
488 
489  // Body:
490 
491  static const fiber_type result;
492 
493  // Postconditions:
494 
495  // Exit:
496 
497  return result;
498 }
499 
500 // PROTECTED MEMBER FUNCTIONS
501 
502 // PRIVATE MEMBER FUNCTIONS
503 
504 
505 //==============================================================================
506 // ED FACET OF CLASS SEC_E2
507 //==============================================================================
508 
509 // PUBLIC MEMBER FUNCTIONS
510 
511 // PROTECTED MEMBER FUNCTIONS
512 
513 // PRIVATE MEMBER FUNCTIONS
514 
515 
516 //==============================================================================
517 // AT1 FACET OF CLASS SEC_E2
518 //==============================================================================
519 
520 // PUBLIC MEMBER FUNCTIONS
521 
522 // PROTECTED MEMBER FUNCTIONS
523 
524 // PRIVATE MEMBER FUNCTIONS
525 
526 
527 //==============================================================================
528 // ATP FACET OF CLASS SEC_E2
529 //==============================================================================
530 
531 // PUBLIC MEMBER FUNCTIONS
532 
533 // PROTECTED MEMBER FUNCTIONS
534 
535 // PRIVATE MEMBER FUNCTIONS
536 
537 
538 //==============================================================================
539 // TP FACET OF CLASS SEC_E2
540 //==============================================================================
541 
542 // PUBLIC MEMBER FUNCTIONS
543 
544 // PROTECTED MEMBER FUNCTIONS
545 
546 // PRIVATE MEMBER FUNCTIONS
547 
548 
549 //==============================================================================
550 // VD FACET OF CLASS SEC_E2
551 //==============================================================================
552 
553 // PUBLIC MEMBER FUNCTIONS
554 
555 // PROTECTED MEMBER FUNCTIONS
556 
557 // PRIVATE MEMBER FUNCTIONS
558 
559 
560 //==============================================================================
561 // TUPLE FACET OF CLASS SEC_E2
562 //==============================================================================
563 
564 // PUBLIC MEMBER FUNCTIONS
565 
566 // PROTECTED MEMBER FUNCTIONS
567 
568 // PRIVATE MEMBER FUNCTIONS
569 
570 
571 //==============================================================================
572 // ABSTRACT POSET MEMBER FACET OF CLASS SEC_E2
573 //==============================================================================
574 
575 // PUBLIC MEMBER FUNCTIONS
576 
577 const std::string&
579 class_name() const
580 {
581  // Preconditions:
582 
583  // Body:
584 
585  const string& result = static_class_name();
586 
587  // Postconditions:
588 
589  ensure(!result.empty());
590 
591  // Exit:
592 
593  return result;
594 }
595 
596 const std::string&
599 {
600  // Preconditions:
601 
602  // Body:
603 
604  static const string result("sec_e2");
605 
606  // Postconditions:
607 
608  ensure(!result.empty());
609 
610  // Exit:
611 
612  return result;
613 }
614 
617 clone() const
618 {
619  // Preconditions:
620 
621  // Body:
622 
623  // Create new handle of the current class.
624 
625  sec_e2* result = new sec_e2();
626 
627  // Postconditions:
628 
629  ensure(result != 0);
630  ensure(result->invariant());
631 
632  // Exit:
633 
634  return result;
635 
636 }
637 
638 // PROTECTED MEMBER FUNCTIONS
639 
640 // PRIVATE MEMBER FUNCTIONS
641 
642 
643 //==============================================================================
644 // ANY FACET OF CLASS SEC_E2
645 //==============================================================================
646 
647 // PUBLIC MEMBER FUNCTIONS
648 
649 bool
651 fiber_is_ancestor_of(const any* xother) const
652 {
653  // Preconditions:
654 
655  require(xother != 0);
656 
657  // Body:
658 
659  // If xother may be dynamically cast to the type of this fiber then this
660  // fiber is an ancestor of xother.
661 
662  bool result = dynamic_cast<const e2*>(xother) != 0;
663 
664  // Postconditions:
665 
666  ensure(invariant());
667  ensure(xother->invariant());
668 
669  // Exit:
670 
671  return result;
672 }
673 
674 bool
676 is_ancestor_of(const any* xother) const
677 {
678  // Preconditions:
679 
680  require(xother != 0);
681 
682  // Body:
683 
684  // If other may be dynamically cast to the type of this then this is an
685  // ancestor of other.
686 
687  bool result = dynamic_cast<const sec_e2*>(xother) != 0;
688 
689  // Postconditions:
690 
691  //ensure(invariant());
692 
693  // Exit:
694 
695  return result;
696 
697 }
698 
699 bool
701 invariant() const
702 {
703  bool result = true;
704 
705  // Preconditions:
706 
707  // Body:
708 
709  // Must satisfy base class invariant.
710 
711  invariance(sec_ed::invariant());
712 
713  if (invariant_check())
714  {
715  // Prevent recursive calls to invariant.
716 
717  disable_invariant_check();
718 
719  invariance(is_attached() ? df() == 2 : true);
720 
721  // Finished, turn invariant checking back on.
722 
723  enable_invariant_check();
724  }
725 
726  // Postconditions:
727 
728  ensure(is_derived_query);
729 
730  // Exit:
731 
732  return result;
733 }
734 
735 // PROTECTED MEMBER FUNCTIONS
736 
737 // PRIVATE MEMBER FUNCTIONS
738 
virtual bool invariant() const
Class invariant, intended to be redefined in each descendant. See below for template for invariant in...
Definition: any.cc:153
static int factor_ct(int xd)
Factor_ct() as a function of dimension xd.
virtual poset_path path(bool xauto_access=true) const
The path of this poset.
bool state_is_auto_read_write_accessible(bool xauto_access) const
True if state is auto accessible for read and write, that is, if the state is already accessible for ...
A client handle for a subposet.
Definition: subposet.h:86
bool full() const
True if both poset name and member name are not empty.
Definition: poset_path.cc:311
A Cartesian product section space.
The abstract map from section dof ids to section dof values of heterogeneous type.
~sec_e2()
Destructor.
Definition: sec_e2.cc:473
Euclidean vector space of dimension 2 (persistent version).
Definition: e2.h:405
virtual const fiber_type & fiber_prototype() const
Virtual constructor for the associated fiber type.
Definition: sec_e2.cc:485
A space of scalars viewed as an antisymmetric tensor section space of degree 1.
Definition: sec_at1_space.h:48
virtual const std::string & class_name() const
The name of this class.
Definition: sec_e2.cc:579
poset_path path(bool xauto_access=true) const
A path to this component.
The default name space; a poset which contains other posets as members.
bool state_is_read_accessible() const
True if this is attached and if the state is accessible for read or access control is disabled...
bool path_is_auto_read_accessible(const poset_path &xpath, bool xauto_access) const
True if the state referred to xpath exists and is auto read accessible.
A general antisymmetric tensor of degree 1 over an abstract vector space (persistent version)...
Definition: at1.h:211
The standard fiber bundles name space; extends the standard sheaves namespace by defining base space...
A path defined by a poset name and a member name separated by a forward slash (&#39;/&#39;). For example: "cell_definitions/triangle".
Definition: poset_path.h:48
A member of a sec_rep_space; a section.
poset_path vector_space_path() const
The path of the underlying vector space.
STL namespace.
A schema poset for a section space. A binary Cartesian product subspace of the binary tensor product ...
poset_state_handle & member_poset(pod_index_type xhub_id, bool xauto_access=true) const
The poset_state_handle object referred to by hub id xhub_id.
virtual sec_e2 & operator=(const abstract_poset_member &xother)
Assignment operator; synonym for attach_to_state(&xother).
Definition: sec_e2.cc:389
The poset for sec_rep_descriptors.
Abstract base class with useful features for all objects.
Definition: any.h:39
int p() const
The tensor degree of this space.
The lattice of closed cells of a cellular space; a lattice representation of a computational mesh...
sec_rep_descriptor & rep()
A representation descriptor for this sec rep space (mutable version).
virtual section_space_schema_member & schema()
The schema for this poset (mutable version)
Euclidean vector space of dimension 2 (volatile version).
Definition: e2.h:112
bool owns(const poset_state_handle &xposet, bool xauto_access) const
True if and only if this contains the poset xposet. synonym for contains_poset(xposet.poset_path(true), xauto_access)
An index within the external ("client") scope of a given id space.
Definition: scoped_index.h:116
bool contains_path(const poset_path &xpath, bool xauto_access=true) const
True if this contains the poset or poset member specified by xpath.
virtual bool contains_member(pod_index_type xmbr_hub_id, bool xauto_access=true) const
True if some version of this poset contains poset member with hub id xmbr_hub_id. ...
int dd() const
The dimension of the underlying ("domain") vector space.
bool empty() const
True if both poset name and member name are empty.
Definition: poset_path.cc:291
static host_type & standard_host(namespace_type &xns, const poset_path &xbase_path, const poset_path &xrep_path, const std::string &xsection_suffix, const std::string &xfiber_suffix, bool xauto_access)
The standard host for sections of this type with base space xbase_path, representation xrep_path...
Definition: sec_e2.cc:103
An abstract vector space viewed as an antisymmetric tensor space of degree 1.
Definition: at1_space.h:42
static host_type & new_host(namespace_type &xns, const poset_path &xhost_path, const poset_path &xschema_path, const poset_path &xscalar_space_path, bool xauto_access)
Creates a new host table for members of this type. The poset is created in namespace xns with path xh...
Definition: sec_e2.cc:52
bool is_ancestor_of(const any *xother) const
True if xother conforms to current.
Definition: sec_e2.cc:676
bool invariant() const
Class invariant.
Definition: sec_e2.cc:701
int_type pod_index_type
The plain old data index type.
Definition: pod_types.h:49
poset_path scalar_space_path() const
The path of the underlying space of scalars.
poset & fiber_space()
The fiber space for section spaces on this schema (mutable version).
bool fiber_is_ancestor_of(const any *xother) const
True if xother conforms to an instance of the fiber of current.
Definition: sec_e2.cc:651
sec_e2()
Default constructor.
Definition: sec_e2.cc:203
static const std::string & static_class_name()
The name of this class.
Definition: sec_e2.cc:598
An abstract client handle for a member of a poset.
std::string path() const
The full path as a string.
Definition: poset_path.cc:450
virtual sec_e2 * clone() const
Make a new handle, no state instance of current.
Definition: sec_e2.cc:617
Namespace for the fiber_bundles component of the sheaf system.
virtual int d(int xp, int xdd) const
Dimension d() as a function of degree xp and domain dimension xdd.
bool state_is_not_read_accessible() const
True if this is attached and if the state is accessible for read or if access control is disabled...
pod_type hub_pod() const
The pod value of this mapped to the unglued hub id space.
Definition: scoped_index.h:710
A section of a fiber bundle with a 2-dimensional Euclidean vector space fiber.
Definition: sec_e2.h:48
A handle for a poset whose members are numerical representations of sections of a fiber bundle...
Definition: sec_rep_space.h:61