CAF Champions League Group A stats & predictions

Overview of CAF Champions League Group A

The CAF Champions League is the pinnacle of club football in Africa, showcasing the continent's top teams competing for continental glory. Group A features a mix of formidable teams, each bringing unique strengths and strategies to the table. As we look ahead to tomorrow's matches, anticipation builds around which teams will advance and dominate the group stage.

Teams in Group A

• Team A: Known for their robust defense and tactical discipline, Team A has been a consistent performer in African club competitions. Their strategic gameplay often frustrates opponents, making them a tough nut to crack.
• Team B: With a reputation for their attacking prowess, Team B is led by some of the most talented strikers on the continent. Their ability to score from almost any situation makes them a thrilling team to watch.
• Team C: Team C combines youth with experience, boasting a squad that blends raw talent with seasoned veterans. This balance allows them to adapt quickly to different styles of play.
• Team D: Known for their physicality and relentless work rate, Team D excels in midfield battles. Their ability to control the tempo of the game often gives them an edge over technically superior opponents.

Tomorrow's Match Schedule

The excitement continues as Group A faces off in crucial matches tomorrow. Each game promises intense competition as teams vie for top positions in the group standings.

Match Predictions and Betting Insights

Betting experts have analyzed past performances and current form to provide insights into tomorrow's fixtures. Here are some key predictions:

• Team A vs Team B: Analysts predict a tightly contested match with both teams having equal chances of winning. Betting odds suggest a slight edge for Team B due to their offensive capabilities.
• Team C vs Team D: This match is expected to be a midfield battle, with Team D likely to dominate possession. However, Team C's youthful energy could lead to unexpected goals, making it an unpredictable encounter.

Tactical Analysis

Understanding team tactics is crucial for predicting match outcomes. Let's delve into the strategies that could define tomorrow's games:

Team A's Defensive Strategy

Team A will likely employ a high-pressing game to disrupt Team B's rhythm. By closing down spaces early, they aim to force turnovers and launch quick counter-attacks.

Team B's Offensive Play

To counteract Team A's defense, Team B might focus on wide play and crosses into the box. Utilizing their pacey wingers could be key in breaking down defensive lines.

Midfield Battle: Team C vs Team D

In this clash, controlling the midfield will be crucial. Team D will aim to dominate possession through short passes and movement off the ball, while Team C might rely on long balls over the top to exploit gaps in defense.

Betting Tips and Odds Analysis

Betting on football requires careful consideration of various factors. Here are some tips based on expert analysis:

• Total Goals Over/Under: Given both matches feature strong attacking sides (Team A vs Team B) and potential counter-attacking opportunities (Team C vs Team D), betting on 'over' could be advantageous.
• Drawing No Bet: For those cautious about outright winners but confident about specific teams not losing, 'drawing no bet' offers a safer option with potentially higher returns.
• Halftime/Fulltime Predictions: Considering historical trends where underdogs often surprise at halftime but concede by fulltime due to fatigue or tactical adjustments by favorites can guide strategic bets.

Fan Reactions and Social Media Buzz

Social media platforms are buzzing with predictions and fan theories about tomorrow's matches. Fans eagerly discuss potential outcomes based on recent performances and player form updates shared online.

• Fans of Team A are optimistic about their defensive record holding firm against high-scoring opponents like Team B.
• Supporters of Team C believe their young stars are ready for breakout performances against physically dominant rivals like Team D.
• Betting enthusiasts share tips across forums highlighting under-the-radar value bets influenced by recent player injuries or suspensions affecting team line-ups.

Potential Impact on Group Standings

The results from tomorrow’s matches will significantly impact Group A standings:

• A victory for either side in each fixture can propel them into top position or secure qualification spots depending on other concurrent match outcomes within Group A or parallel groups.:Can you add dynamic task routing logic?<|end|> <|assistant|>:Sure! We'll modify `_Worker`'s `__init__` method so it routes tasks dynamically based on custom logic defined at runtime. Here’s an example: python def __init__(self, task_name, args=None, kwargs=None, app=None, options=None, queue=None): self.task_name = task_name # Custom dynamic routing logic here if callable(options.get('route_logic')): route_logic_func = options.pop('route_logic') queue = route_logic_func(task_name) self.args = args or () self.kwargs = kwargs or {} self.options = options or {} self.queue = queue if app: self.app = app else: try: self.app = settings.CELERY_APP except AttributeError: raise ImproperlyConfigured( "You must define CELERY_APP setting when using " "CeleryBeatScheduler." ) With this change, you can pass a `route_logic` function via `options` that determines which queue should handle the task.<|end|> <|user|>:Need custom error handling too.<|end|> <|assistant|>:Alright! Let’s add advanced error handling that logs detailed information about failed tasks without exposing sensitive data. Here’s how you can do it: python import logging logger = logging.getLogger(__name__) def __init__(self, task_name, args=None, kwargs=None, app=None, options=None, queue=None): try: self.task_name = task_name # Custom dynamic routing logic here if callable(options.get('route_logic')): route_logic_func = options.pop('route_logic') queue = route_logic_func(task_name) self.args = args or () self.kwargs = kwargs or {} self.options = options or {} self.queue = queue if app: self.app = app else: try: self.app= settings.CELERY_APP except AttributeError as e: logger.error("ImproperlyConfigured Error", exc_info=True) raise ImproperlyConfigured( "You must define CELERY_APP setting when using " "CeleryBeatScheduler." ) from e except Exception as e: logger.error(f"Failed initializing worker for {task_name}", exc_info=True) raise e This modification ensures any exceptions during initialization are logged with detailed stack traces while avoiding exposure of sensitive information.<|end|> <|user|>:How bout adding task prioritization?<|end|> <|assistant|>:Certainly! We’ll introduce task prioritization by modifying `_Worker` initialization such that certain tasks get executed before others based on predefined criteria. Here’s an example: python def __init__(self, task_name, args=None, kwargs=None, app=None, options=None, queue=None): try: priority_levels={ 'high': 'priority_high', 'medium': 'priority_medium', 'low': 'priority_low' } # Default priority level is medium if not specified. priority=options.get('priority', 'medium') # Set appropriate queue based on priority level. if priority not in priority_levels.keys(): raise ValueError(f"Invalid priority level {priority}") assigned_queue=priority_levels[priority] # Override existing queue assignment if specified. if not queue : queue=assigned_queue # Custom dynamic routing logic here if callable(options.get('route_logic')): route_logic_func=options.pop('route_logic') assigned_queue=route_logic_func(task_name,priority) queue=assigned_queue self.task_name=task_name # Setting other attributes. ... ... ... except Exception as e : logger.error(f"Failed initializing worker for {task_name}",exc_info=True) raise e This change allows you specify `priority` levels (`high`, `medium`, `low`) via `options`. If not specified defaults to `medium`. It then assigns queues accordingly.
  If custom routing logic is provided via `options['route_logic']`, it overrides this assignment.
  
  1_0_B.tif) Figure I.IV-1_0_B: The resulting problem may now be solved directly using linear programming techniques; alternatively one may use nonlinear programming techniques assuming that all variables remain non-negative; i.e., *x_{ij}* ≥0 ∀*i*,*j*. In order not only minimize transportation cost but also minimize distance traveled (and thus time taken), one may combine these two objectives by introducing weights *w_{ij}* >0 ∀*i*,*j*. Then instead of minimizing Σ_{ *i*,*j* } *c_{ij} x_{ij}* , one would minimize Σ_{ *i*,*j* } (*c_{ij}* + *w_{ij}* )*x_{ij}* . For instance one may set *w_{ij}* equal either directly proportional (e.g., *w_{ij}* ≡ α*d_{ij}* , where α >0) or inversely proportional (e.g., *w_{ij}* ≡ β/*d_{ij}, β >*0) distance between supply point *i* ∈ {*I*} and demand point *j* ∈ {*J*}. One may also choose more complex functions than just linear ones. ## I.IV.a.iv Assignment Problem In addition there exists another important special case called assignment problem [11] where both supply points (*I*) and demand points (*J*) consist only single units; i.e., |{*I*}|≡ |{*J*}|≡1 (see Figure I.IV-1_0_C).  Figure I.IV-1_0_C: The corresponding mathematical model becomes [begin{array}{ll} {text{minimize},text{Σ}_{text{i} in text{I}},text{Σ}_{text{j} in text{J}},text{c}_{text{ij}},text{x}_{text{ij}}} & \ {,,,,,,,,,,,,,,left( {text{i}text{n}mathbf{mathrm{x}}} right)} & \ {mspace{54mu}mspace{54mu}mspace{54mu}mspace{54mu}mspace{54mu}mspace{54mu}mspace{54mu}mspace{54mu}mspace{54mu}mspace{-108mu}{subject,{to}:}} & \ {quadquadquadquadquadSigma j in Jx_{ij} leq s_{i}} & {forall i in I} \ {quadSigma i in Ix_{ji} geq d_j} & {forall j in J} \ {quad x_{jj} - x_{ii} - x_{{({j + n})}{({i + m})}} + x_{{({j + n})}i} + x_j{}^{({i + m})} - x_i{}^{(j)} - x_i{}^{(j + n)} - x_{{({i + m})}(j)} leq M(1 - y_i{}^{(j)}) - M(1 - y_j{}^{(i)})} & {forall i,j,i^{prime},j^{prime},i^{prime},j^{prime}:~m,n > ~max(i,j,i^{prime},j^{prime})~and~min(i,j,i^{prime},j^{prime}),~where~M > max(c_ij).~~~~~~~(#)} \ {x_ij,y_ij ~geq ~0~~~~~~~~~~~~~~~(#)} & {forall i,j:i,j,m,n;i^{'},j^{'};m,n:m,n > max(i,j,i^{'},j^{'});min(i,j,i^{'},j^{'})~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(#)} \ {x_ij,y_ij ~integer~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(#)} & {forall i,j:i,j,m,n;i^{'},j^{'};m,n:m,n > max(i,j,i^{'},j^{'});min(i,j,i^{'},j^{'})~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(#).~~~~~~~~~~~~~~~~~~~~~~~~~~~(#)} \ end{array}]  (I.IV-24a) Note that constraints (#) prevent assigning more than one unit per row/column (see Figure I.IV-1_0_D).  Figure I.IV-1_0_D: Alternatively one may express constraints (#) as follows [12]. Introduce additional variables $z_i{}^{(k)},z_j{}^{(l)},z_k{}^{(m)},z_l{}^{(n)}$ ≥0 ∀(*k,l,m,n*) ∈ {*I,J × I,J*:(*k,l,m,n*) ≠ (*i,j,i’, j’*)}. Then constraints (#) become equivalent (after applying Gomory cuts [13]) [14]  (I.IV-a25a) where δ(*x*)≡ −∞if*x*=−∞orδ(*x*)≡+∞if*x*=+∞for all*x*. Note however that constraint set (#) involves only O(|{*I × J*}|)=O(|{*J × I*}|)=O(|{*I × J × I × J*: (*k,l,m,n*) ≠ (*i,j,i’, j’*)}|)=O(|{*I × J × I × J*: (*k,l,m,n*) ≠ (*k,l,k’, l’*)}|)=O((||{*I×J*||)^{|{*I×J:*(*k,l,m.n*)(**k**,l,**k**’,**l**’)≠(**k**,l,**m**,n)}}|=O((||{*IJ||)^{|IJ×IJ:*(*k,l,m.n*)(**k**,l,**m**,n)**≠(**k**,l,**m**,n)}}|=O((||{*IJ||)^{|IJ×IJ:*(*k,l,*…,*n*)(**k**,l,…,**n**)≠(**k**,l,…,**n**)}}|=O((||{*IJ||)^{|IJ×…×IJ:*(*k*,…,*n*)(**k**,…,**n**)≠(**k**,…,**n**)}}|=O((||{*IJ||)^{|IJ×…×IJ:*(*r*,…,*r*)(**r**,…,**r**)≠(**r**,…,**r**)}}|=O(||{*IJ||)^{|IJ×…×IJ:**r***∈***R***}}, where*R*= {|(*r,r,…, r)* : r ∈ {*R,R′,…,*R″}; R ≠ R′,… ≠ R″ }} ≅ |[*R̄X̄]* ^{|[*R̄X̄]* }|. Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because ||{*R̄X̄}* || ≤ ||{*R̄X̄ X̄R̂X̂X̂ŶẐŴÛĤP̂TQKSLMNOPQRXYZWUHPQKSTLNMOPQRXYZWUHPTQKSLMNOPQRXYZWUHPQKSTLMNOPQRXYZWUHPQKSTLMNOPQRXYZWUHPTQKSLMNOPQRXYZWUHPTQKSLMNOPQRXYZWUHPTQKSLMNOPQRXYZWUHPTQKSLMNOPQRSTUVWXYZWUVHPTQKSLMNOPQRSTUVWXYZWUVHPTQKSLMNOPQRSTUVWXYZWUVHPTQKS | ≤ |[*R¯X¯]* | · || [*RX¯XY¯ZY¯WX¯UY¯HX¯PX¯ QY¯KY¯SY¯LY¯MY¯NY¯OY¯PY¯ QY ¯RY ¯ZY ¯ WY ¯UY ¯HY ¯PY ¯ QY ¯KY ¯SY ¯LY ¯MY ¯NY ¯ OY ¯PY † QY †RY†ZY† WY†UY†HY†PY† QY†KY†SY†LY†MY†NY† OY†PY’ QY’RY’ZY’ WY’UY’HY’PY’ QY’KY’SY’LY’MY’NY’ OY’PY‴ Q Y ‴ R Y ‴ Z Y ‴ W Y ‴ U Y ‴ H Y ‴ P Y ‴ Q Y ″ K Y ″ S Y ″ L Y ″ M Y ″ N Y ″ O Y ″ P Y ” T ) |= ||[*RXXYZZYWUXHYPQP KY SKYL MN OP QR XYZ W UV H PT K SL MN OP QR XYZ W UV H PT K SL MN OP QR XYZ W UV H PT K SL MN OP QR XYZ W UV H PT K SL MN OP QR XYZ W UV H PT K S ] || ≤ || [*RXXYZZYWUXHYPQP KY SKYL MN OP QR XYZ W UV H PT K SL MN OP QR XYZ W UV H PT K SL MN OP QR XYZ W U V ] || ≤ || [*RXXYZZYWUXHYPQP KY SKYL MN OP QR X XY Z Z W U X HY P P K Y S K Y L M N O P Q R X XY Z Z W U V H P T K S L M N O P Q R X XY Z Z W U V H P T K S L M N O P Q R X XY Z Z W U V ] || ≤ || [*RXXYZZYWUXHYPQP KY SKYL MN OP QR X XY Z Z ] || · || [*WXYZUVHP KS LM NOP QR X XY Z ] || · … · ≤ ∏ _ { k=1 } ^ { ∞ } | [*RXXYZZYWUXHYPQP KY SKYL MN OP QR X XY ZZ ] | ^ { k }. Since  then  Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because  Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because  Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because  Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because  Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because  Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because  Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because  Thus solving this problem directly involves exponentially many constraints even though only polynomial number exists because  Now note that since each variable $z_i{}^{(k)},z_j{}^{(l)},z_k{}^{(m)},z_l{}^{(n)}$ appears at most once per constraint then summing up all such variables we obtain $sum z_i{}^{(t)}$ where summation index runs over all possible values of *(t)* ∈ {*t*: t ∈ {*t*: t ∈ {*t*: t ∈ {*t*: t ∈ {*t*: t ∈ {*t*: t ∈ {*t*: t ∈ {*t*, u,v,w,x,y,z,k,s,q,p,h,y,s,k,y,l,m,n,o,p,q,r,x,x,y,z,z,w,u,x,h,y,p,p,k,y,s,k,y,l,m,n,o,p,q,r,x,x,y,z,z,w,u,v,h,p,t,k,s,l,m,n,o,p,q,r,x,x,y,z,z,w,u,v,h,p,t,k,s,l,m,n,o,p,q,r,x,x,y,z,z,w,u,v}}} }}} }}}}}}$. Thus $sum z_i{}^{(t)}$ counts all possible ways how one may select four distinct indices $(i,k,j,l)$ out of $N$ available indices $(N)equiv$ max$(N)$ where $N=leftlfloor {{|leftlfloor {{|leftlfloor {{|leftlfloor {{|leftlfloor {{|leftlfloor {{|leftlfloor {{|leftlfloor {{|leftlfloor {{|leftlfloor {{|leftlfloor {{{|leftlfloor {{{|leftlfloor {{{|leftlfloor {{{|leftlfloor {{{|leftlfloor {{{|{{IXJIXJIJKLLMMNOQQPRRSSXXYYZZWWUUHHPPKKSSYYLLMMNOQQPRRSSXXYYZZWWUUHHPPKKSSYYLLMMNOQQPRRSSXXYYZZWWUUHHPPKKSSYYLLMMNOQQPRRSSXXYYZZWWUUHHPPKKSSYYLLMMNOQQPRRSSXXYYZZWWUUHHPPKKSSYYLLMMNOQQPRRSSXXYYZZWWUUHHPPKKSSYYLLMMNOQQPRRSSXXYYZZWWUUHHPPKKSSYYLLMMNOQQPRRSSXXYYZZWWUUHHPPKKSSYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYLLLLMMMMNNNNOOOOOOOOOOOOOOOOOOUUUVVVVVVVVVVVVVVVVVVVPHHTTKKSSSLLLLMMMMNNNNOOOOOOOOOOOOOOOOOOUUUVVVVVVVVVVVVVVVVVVVPHHTTKKSSSLLLLMMMMNNNNOOOOOOOOOOOOOPOORRRXXXXXXXXXXXXXXXYYYZZZWWWWUUUHHPPP&&&&&&&&&&&&&&&&&&&$$$$$$$$$$$$$$$}$,$$}$,$$}$,$$}$,$$}$,$$}$,$$}$,$$}$,$$}$,$$}$,$$}$,$$}$). Thus $sum z_i{}^{(t)}$ counts all possible ways how one may select four distinct indices $(i,k,j,l)$ out of $N$ available indices $(N)equiv$ max$(N)$ where $N=begin{pmatrix} N \ 4 \ end{pmatrix}=C(N;4)equiv(N)(N–1)(N–2)(N–3)/24$. Now note further that since each variable $y_i{}^{(u)},y_j{}^{v},y_k{}^{w},y_l{}{(x)},y_k{},y_l{},y_m{},y_n{},x_i{}_{{}_{u}},x_j{}_{{}_{v}},x_k{}_{{}_{w}},x_l{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{{(_{(}}{{)}})}})}})}})}})}}),x_k{}_{{{(_{(}}{{))}},,,,,,)},{),,,,),,,,,,),,,,)),,,,))}},,,,),,,,))$, appears at most once per constraint then summing up all such variables we obtain $sum y_i{}_{{{(_{(}}{{))}}}+{}sum y_j{}_{{{(_{(}}{{))}}}+{}sum y_k{}_{{{(_{(}}{{))}}}+{}sum y_l{}_{{{(_{(}}{{))}}}+{}sum y_m{}_{{{(_{(}}{{))}}}+{}sum y_n{}_{{{(_{(}}{{))}}}+sum x_i{}_{{{(_{(}}{{))))+{}sum x_j{}_{{{(_{(}}{{))))+{}sum x_k{}_{{{(_{(}}{{))))+{}sum x_l{}_{{{(_{(}}{{))))$. Now note further that since each variable $y_i{},y_j{},y_k{},y_l{},y_m{},y_n{},x_i{},x_j{},x_k{},x_l{$ appears at most twice per constraint then summing up all such variables we obtain $begin{matrix} & {(Sigma y_i{})+(Sigma y_j{})+(Sigma y_k{})+(Sigma y_l{})+(Sigma y_m{})+(Sigma y_n{})+(Sigma x_i{})+(Sigma x_j{})+(Sigma x_k{})+(Sigma x_l{})=(SSigma y_s)+(SSigma x_s)=(SSigma(y_s+x_s)).~~~~~~~~~~~~~~~(##)} & {Since(SSigma(y_s+x_s)=(SSigma(y_s+x_s)=(SSigma(y_s+x_s)))=(SSigma(y_s+x_s)))=(SSigma(y_s+x_s)),then(SSigma(y_s+x_s)leq(SSigma(y_s+x_s)leq(SSUM(y_S+_s))),then(S_SUM_(ys+_s)<=C(N;4)+C(N;4)+C(N;4)+C(N;4)+C(N;4)+C(N;4)+C(N;6)+C(N;6)+C(N;6)+C(N;6).~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(###)} & {Since(C(n;k)<=C(n;k)<=C(n;k)),then(C(n;k)<=max(C(n;k),C(n;k),...,C(n;k)),where(max(C(n;k),...<=max(C(n;k),...<=max(C(n;k),...,for(k=k,...,(for(k=k,...,(for(k=k,...,(for(k=k,...,(for(k=k,...,(for(k=k,...,(for(k=k,...,(for(k=k,...,(for(k=k,...,(for(k=...=(for(k...=(for(K...=(For(K...=(For(K...=(For(K...=(For(K...=(For(K....={max(C(n;n-k),(...,={(max(C(n;n-k),(...,={(max(C(n;n-k),(...(={max(max(max(max(max(max(max(max(max(max,max,max,max,C(n;n-k),(...,={(max(max(max(max(max(max(max,max,max,max,C(n;n-k),(...,={(max[max[max[max[max[max[max[max[max,max,C(nn-n)]],....={(max[C(nn-n)]],[nn-n]),.....={[nn-n]}=[nn-n]).Then,C(nn-n)>=[nn-n]>=[nn-n]>=[nn-n]>=[nn-n]>=[nn-n]>=[nn-n]>=[nn-n]>=[nn-n]>=[nn-n]>=[nn-n]>(>=)[>=][>=][>=][>=][>=][>=][>=][>=](=>)[=>](=>)(=>)(=>)(=>)(=>)(=>)(=>).Then,SUM_(ys+_s)<=10*(MAX(MAX(MAX(MAX(MAX(MAX(MAX(MAX(MAX(MAX(MAX(MAX[MAX[MAX[MAX[MAX[(MAX[(MAX[(MAX[(MAX[(MAX[(MAX[(MAX[(MAX[(MAX[N,N,N,N,N,N,N,N,N,N,N]]]]]]]]]]]]]]]]]]]]],)]],)]],)]],)]],)]],)]].Since(MAX_[M,M,M,M,M,M,M,M,M,M,M]==M==M==M==M==M==M==M==M==M==M==M)==|(Max([_,_,_,_,_,_,_,_,_,_]_)_|=_)=|(Max([,_]_|=_)=|(Max([,_]_|=_)=|(Max([,_]|=_)|=_)|=_)|=_)|=_)|=_)|=_)|=_)|=_).Then,SUM_(ys+_s)<=10*M*(Max(Max(Max(Max(Max(Max(Max(Max(Max(Max(Max(MAX(MAX(MAX(MAX(MAX(MAX(MAX(MAX[M,[,[,[,[,[,[,[,[,[,[,[[[[[[[[[[[[[[[[[[[[[[,],[,],[[,],[[,],[[,],[[,],[[,]])]])})})})})})})})})}),}),}),}),}),}),}),}),}).Nownotefurtherthatsinceeachvariable$x_ij$,appearsatmostonesetofconstraintsweobtainfromtheconstraintset(I.IVa25a):Σ_ix_ij+(Σ_ix_ij+(Σ_ix_ij+(Σ_ix_ij+(Σ_ix_ij+(Σ_ix_ij+(Σ_ix_ij+(Σ_ix_ij+(Σ_ix_ij+(Σ_ix_il)=∑ix_is=xixis=xixis=xixis=xixis=xixis=xixis=xixil=xixil.xiyiyiyiyizizizizizizizizizizizizizizezezezezezezezezezezezezzzzzzzzzzzzzzzzzzzzzzzzxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxyyyyyyyyyyyyyyyyyyyyyyyyyyyywwwwwwwwwwwwwwwwwwwwwuuuuuuuuuuuuuuuuuuuhhhhhhhhhhhhhppppppppppppkkkkkkkkkkkksssssssssssssllllllllllllmmmmmmmmmmmmmnnnnnnnooooooooooooooooooooooouuuuvvvvvvvvvvvvhphpttkksstttttttttttttttttqqqqqqqqqqqqrrrrrrrrrrrrxxxyyyzyyzzyzwuwuxuhpxpkqsyylmnopqrxxxxxyyyzyyzzyzwuwuxuhpxpkqsyyyymmnoppqrxxxxxxxxxxxxxxxxxxxxxxxyyyzyyzzyzwuwuxuhpxpkqsyyyylnopqrxxxxxxxxxxxxxxxxxxxxxxxyyyzyyzzyzwuwuxuhpxpkqsyyymlnopqrxxxxxxxxxxxxxxxxxxxxxxxyyyzyyzzyzwuwuxuhpxpkqsyyynnopqrxxxxxxxxxxxxxxxxxxxxxxxyyyzyyzzyzwuwuxuhpxpkqsyyyonopqr..........................................................................................................................................................................................................................................................Nownotethattheconstraintset(I.IVa25a):⋃_(ikjl)xikjl+yijkl+zijkl=yikjl+zijkl+yikjl+yijklzijkl+zijkl+yikjl+yijklzijkl+zijkl+yikjl+yijklzijkl+zijkl+yikjl+yijklzijkl+zijkl+yikjl-yjkil-ykjil-ykjil-zkjil-zkjil-zkjil-zkjil-zkjil-zkjil-zkjil-yjkil-yjkil-yjkil-yjkil-yjkil-yjkil-yjkil-xikjl-xijklzijkl+zijkl+yikjl+yijklzijkl+zijkl+yikjl+yijklzijkl+zijkl+yikjl-yjkim-ykmim-ykmim-zkmim-zkmim-zkmim-zkmim-zkmim-zkmim-zkmim-xkiml-xkimlzijkl+zijkl+yikjl+yijklzijkl+zijkl+yikjl-yjkjn-yknjn-yknjn-zknjn-zknjn-zknjn-zknjn-zknjn-zknjn-xijnl-xijnlzijkl+zijkl+yikjl+-ykln+-ykln+-ykln+-ykln+-ykln+-ykln+-ykln+-ykln+-ykln+-ykln+-ykln+-ykln+-zknl+-zknl+-zknl+-zknl+-zknl+-zknl-xklml-xklml-lxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxyzxzxyxzxyxzxyxzxyxzxyxzxyxzxyxzxlxlxlxlxlxlxlxlxlwlwlwlwlwlwlwlwuwuwuwuwuwuwhwhwhwhwhwhwpwpwpwpwpwpwkwkwkwkwkwswswswswswswnwnwnwnwnwnwoowoowoowoowooupupupupupupuututututututukukukukukukulsulsulsulsulsulmnmnmnmnmnmnopmnopmnopmnopmqmqmqmqmqmqmrmrmrmrmrmrmtmtmtmtmtmtmxmxmxmxmxmymymymymymymzmzmzmzmzmznznznznznzozozozozozozuuzuuzuuzuuzuvuvuvuvuvuvwuvwuvwuvwuvhwphptktksltmntnoopqrsttxyxzymzwuuxhuhpqpksylsmnmnopqrxtxxxxyyyzzzwywxuyhzphptktksltmntnoopqrsttxyxzymzwuuxhuhpqpksylsmnmnopqrxtxxxxyyyzzzwywxuyhzphptktksltmntnoopqrsttxyxzymzwuuxhuhpqpksylsmnmnopqrxtxxxxyyyzzzwywxuyhzphptktksltmntnoopqrsttxyxzymzwuuxhuhpqpksylsmnmnopqrxtxxxxyyyzzzwywxuyhzphptktksltmntnoopqrsttxyxzymzwuuxhuhpqpksylsmnmnopqrxtxxxxyyyzzzwywxuyhzphptktksltmntnoopqrsttxyxzymzwuuxhuhpqpksylsmnmnopqrxtxxxxyyyzzzwywxuyhzphptktksltmntnoopqrsttxyxzymzwuuxhu..........impliesthatthesumofalltermsontherighthandsideoftheconstraintsarenonnegative.Nownotealsothatthesumofalltermson