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İt's easy to solve coupled systems of differential equations in the form d/dt (X,y,z) = (X, y, z)*A where A is a 3x3 matrix with constants as elements. Now, what if A is not just constants but functions of t? Below is my investigation into this: The idea is as follows: 1. Write the dependent variables into a vector, do the same for the derivatives as well as their non constant coefficients, so that we can apply linear algebra. 2. Map the solution vector X into another vector space U in which the matrix relating the vector and it's derivatives becomes easily diagonalisable. Achieve this by a linear map L acting on the original solution vector. X = L U 3. Now we need to find L and decouple the relationship. 4. Solve the decoupled equations row by row 5. Map back into X space from U space to obtain the desired solutions.

Let's model the trajectory of a self-propelled rocket! I have made a start here, now it's up to you diligent people to solve the equations numerically

Hello there! In anticipation of my (also Mediterranean) vacation in Italy I want to publish the last map I mainly built in November to December 2021. As new Aegean textures came out in Alpha 25 the summer a year ago I tried to make some map out of them (I can remember @wowgetoffyourcellphone of wishing my Map "Metropolis" having used the new terrains ). After my maps "The Legend of Avilava" and "Metropolis" (both scenarios) I decided to resort to the Skirmish type of map giving the player more individuality by choosing their own civ. Thus, there are no starting structures / little cities besides the original headquaters each player beginns with. Maybe I'm too generous in the assumption everyone playing 0ad has a proper gaming PC. I just like these huge maps (even beyond "giant" would be great) with gigantic battles and stuff, hence I've decided it's scale being "giant". The map generally is arranged to have a 4 vs 4 setting. Each player starts near his own team; far from enemy players. Relatively the same amount of starting resources near the headquaters accompany each player; every team should have land more or less equally distributed to gain resources from, to build and / or to expand on. Having let some simulations with bots go their way, I've had a lot of fun watching them. Through this I've been able to correct some little flaws and some features that would hinder the game's fluency. It's likely this map isn't perfect or "fine" anyway (others have to say so), thus I imagine that I'll maybe make some further versions. And if others like to do so, you're granted permission to of course. You guys feel free to use this map in which way you want, it's yours! But I think now it's time to show you some screenshots to get a better understanding of what I'm talking about. Best to show you the type of Mediterranean landscape that I love so much (regarding this I sadly live in Austria :D) and which I hope I've been able to properly reconstruct here: Also a look onto the starting positions of each player (screenshot follows player number): (Team 1: Player 1 - Player 4; Team 2: Player 5 - Player 8) Looking back, I'm happy enough with what came out of my conception of a Mediterranean "holyday-like" map. It's too good I'm now starting with feeling it all myself in my vacation in Italy! As for you guys, as I said - The map is all yours. Thank the 0ad programmers for having made this aweseome game and featuring the forum to have the gamers able to communicate and exchange with each other - and to publish self made maps! Cya soon, this Saturday I'm out in Italy now yooooo! Aegean Archipelago.xmlAegean Archipelago.pmp Edit on 13.8.2022: The edited versions should be preferred I hope there are no problems with downloading them? Aegean Archipelago First Edit.pmpAegean Archipelago First Edit.xml (When a number in front of the map file's name occur, you have to delete this part of the file name. For example, after downloading, you may get the files with a certain number, like: "678349583_AegeanArchipelagoFirstEdit.pmp" and "678349583_AegeanArchipelagoFirstEdit.xml" - you have to delete "678349583_" of the file names to be able to play on the map)

It was in response to Stan's question about the reasoning about the current behavior. Commit archaeology suggests its a bug introduced during one of the large rewrites at some point.

We need to find our L matrix and it must satisfy L°AL-L°L' = a diagonal matrix. L° represents the inverse of L and L' represents derivative of L with respect to time. This is the difficult part; for L with constant coefficients, the second term will be 0 which would lead to just the diagonalised A, but if A is not constant then there is a second term containing a derivative of L and inverse L. Normally L will be the matrix of eigenvalues of A, in our case and my exampled I forced some eigenvalues and eigenvectors out of A which do contain t. İn the particular exame I used, I was able to satisfy this equation with just the eigenvalues matrix, but I am not sure if the result will still be diagonal if my A was different. I would like some help here, for example proving whether the conditions are always satisfiable. İt would also be great if you can find some alternative methods to calculate L. The example worked perfectly but it was a very simple matrix.

I am just trying to copy this from https://www.moddb.com/mods/hyrule-conquest/news/rolling-ridge-and-wizzrobes A look at two of the Minor Factions you can recruit. Posted by The_Undying_Nephalim on Aug 16th, 2022 Today we'll look at the two last Minor Factions that will appear in the next release of Hyrule Conquest. Gorons of Rolling Ridge In the mountain ranges of Labrynna rest the Gorons of Rolling Ridge. Shy, reclusive, and a myth to many in Hyrule, this particular race of rockmen was quite distinct from their mineral-eating, lava-bathing brethren. Although it was quite easy to make friends with the passive fellows, finding them in the first place was a daunting task in itself. Rolling Ridge provides players with a set of durable and high-armor value units, many which have Camouflage. Factions that lack in durable unit options, such as the Kokiri and Fairies of Tarm, are prime factions to seek out the aid of Rolling Ridge. Their unique building is the Talus Mine, which can endlessly harvest Material from the ground to use for building new structures. Bracer - These smaller Goron warriors spend most of their time dancing and eating between the Talus Peaks and Mount Ebon. Despite their shy but friendly personalities, they are more than capable of defending their homes with fists of solid rock. Pebblit - Like the larger Stone Talus, Pebblits spend a vast majority of time laying on the ground as harmless rocks. They can be stirred into aggression and provoked to chase hostiles, and indeed many on the Talus peaks do. Bastion - A giant Goron of Rolling Ridge, the Bastions defend their homelands from would be miners and gem seekers. Using their two massive stone arms, a Bastion can pummel anything smaller than itself into rubble. Buster - High on the mountaintops of Rolling Ridge these Gorons perch themselves, tossing giant boulders from above onto invaders down below. These skilled Gorons are sometimes known for causing "boulderstorms" when bored. Stone Talus - These massive stone creatures seem to spend most of their time as dormant rocks and boulders on the mountainsides of the Talus Peaks. For reasons unknown, they will occasionally spring to life and violently attack anything that moves around their resting place. The Stone Talus on Rolling Ridge are particularly powerful, and the native Gorons have taken the effort to somewhat domesticate these giant lumbering monsters. Smog - The Elder of Rolling Ridge and his tribe of Gorons, Smog advises his people with his centuries of experience from the top of Crown Ridge. He spends most of his day in communion with the Goron spirits, ingesting all manner of smokey incense to aid his connection. When threatened he's able to turn his mastery over the smoke against his attackers. Wizzrobe A truly ancient people that once ruled much of Hyrule, legends say that the Wizzrobe undermined and destroyed their own civilization with their powerful sorcery. Their cities sunk beneath the earth, and for centuries they have maintined a shadow cult-like culture in the darkness of Hyrule's mountainous catacombs. Occasionally these dark magicians make their way to the surface, using their wizardry to raise their ruined cities from beneath the earth. The Wizzrobe provides players with a powerful selection of Mages. Factions that are lacking in any kind of magic damage and defense, such as Moblins and Gorons, would be foolish to not consider establishing an Embassy with the Wizzrobe. Their unique building is the Magic Circle which will not function in the next release, but once completed will be able to teleport your armies anywhere within your territory. Fire Wizzrobe - Perhaps the most common spellcaster in the Wizzrobe ranks, control over fire seems to have been the easiest form of magic to master. These pyromancers use their magic to create and unleash steady streams of flames at their enemies, incinerating just about anything in seconds. Ice Wizzrobe - Wizzrobes skilled in the arts of frost, these icy magicians could halt enemies in place with their cold magics. Earth Wizzrobe - These magicians could will the mineral earth to their command, creating barriers and projectiles out of rocks. Some of these geomancers could hurl boulders large enough to rival catapults and other siege weaponry, crushing multiple enemies in an explosive blast of rubble and dirt. Illusion Wizzrobe - The art of Illusion was one of the most difficult schools of magic for a Wizzrobe to master, and certainly one of the most dangerous. An Illusionist faced the danger of losing all touch with reality, becoming lost in their own creations and mirages, and developing crippling paranoia and mistrust of anything. Those that mastered the art could use it to terrifying effect on their enemies in battle. Conjurer - Conjurers were select Wizzrobe that had devoted their study to the creation and summoning of arcane and magical creatures to do their bidding. A powerful Conjurer could materialize an entire army of loyal minions under his command. In the next release of Hyrule Conquest they will be able to summon Mad Scrubs, Armos Statues, and Twilight Zora. Carock - Carock is among the most powerful of the known Wizzrobe, and there is little other information other than that. He has been tied to many assassinations and overthrowing of monarchs, making him one of the Sheikah's prime enemies.

#4661 -> See comment:1. rP18806 -> Related fix D2483 -> See Chapter 13

Just because teams aren't locked doesn't mean there can't be defaults. Looks like a bug.

I am just trying to copy this from https://www.moddb.com/mods/hyrule-conquest/news/zuna-and-tokay A look at two of the Minor Factions you can recruit. Posted by The_Undying_Nephalim on Aug 11th, 2022 Today we'll look at two other Minor Factions that you can employ in Hyrule Conquest. Zuna Perhaps one of the oldest races native to the Gerudo Desert, the Zuna are an isolated culture of reptilian builders and weapon crafters. Though they seem fairly cordial with the Darknut Legion, the Zuna will rarely make contact with anyone outside of weapon dealings. The skill with which the Zuna make their weapons is legendary, so legendary that the Darknut Legion employs them to create incredibly ornate swords for their soldiers. Despite their famous profession, the Zuna rarely ever engage in warfare and their mercantile army usually only operates out of defense. The Zuna provide players with an excellent assortment of siege weaponry. Factions that lack many good options for destroying bases will want to consider setting up an Embassy with the Zuna. Their unique building is the Oasis, which can quickly heal organic units inside of a Zuna base. Tridenteer - Wielding their iconic tridents in hand, these Zuna soldiers patrol the confines and borders of the Merchantmen capital, Zunayus. While technically no more than police, these Zuna are sufficiently trained to defend against a full-scale invasion of their homeland. Tribowmen - Along the terraced walls of Zunayus, scores of these deadly archers defended the capital for many generations. The strange design of the Zuna's crossbow allowed it to hold and store up to three bolts instead of one, giving them the chance to fire several shots before reloading. Devalant - Devalants are giant, burrowing creatures with large snapping pincers that can be found in the far western reaches of the Gerudo Desert. They create sinkholes in the sand as they burrow underneath, drawing in their prey. When a suitable target is near, the Devalant will vomit a burning fireball onto its victim. The Zuna were known to occasionally domesticate these creatures, using them as a sort of guard dog for their villages. Triballista - Much like their handheld crossbow, the Zuna Triballista allowed its crew to load up to three giant bolts at a time instead of one. A single Triballista could hurl these bolts at multiple targets, potentially breaking open multiple holes in an enemy's defense. Siege Tower - A giant and mighty battering ram that the Zuna once used to destroy many a castle, they were perhaps most well known from history in the battle against Baral's Stand, where they managed to break into the mighty Darknut fortress. The Siege Tower can effortlessly destroy the heaviest of fortifications and garrison troops inside. Visier Vorday - The wealthiest and most powerful Zuna to have lived, Master Vorday amassed his assets by being a suck-up and yes-man to the various empires of the Gerudo Desert. While he may be seen as a total coward by outsiders, his habit of selling out to foreigners has lead to the Zuna becoming a giant merchant empire and biggest arms dealer in all of Hyrule. Tokay Hailing from Crescent Island just south of Labrynna, the Tokay were, at first glance, a tribal and primitive collection of people. Their odd manner of speaking, awkward behavior, and obsession with mundane items such as clothing over rupees gave them a reputation for being backward and outright stupid. Despite their quirky demeanor, the Tokay proved to be more than a pushover tribe of spear-wielding reptile barbarians. The Tokay provide players with cheap and affordable fodder units, as well as aquatic options. Goron and Darknut players might be drawn to using the Tokay to supplement their expensive units and give them a fighting force on the water. Their unique building is the Big Boss Hut, which provides a large boost to Population Cap and spawns a free Battalion of Tokay Hunters. Hunter - Armed with a spear in hand, Tokay Hunters would skim along the coast of Crescent Island and hunt the many large fish that roamed the sea. When threatened on land they could easily hold their ground as well. Slinger - Tokay Slingers were the defenders of their island homeland, knocking out and tripping up anyone who invaded. Large groups of Slingers could unleash a huge storm of stones with terrifying speed. Bonker - Donning a coconut shell on their heads, Tokay Bonkers were sent skull first into enemy lines. They would ram into targets much larger than themselves, more often than not sending themselves and their foes staggering in opposite directions. Aquadongo Jockey - Riding on top of a breed of Dodongo native to the Crescent Islands, these mounted jockeys can cross through harsh waters where ships cannot. On land they can halt enemy cavalry with their spears while in the water they can keep sea creatures at bay. Guerrilla - These sneaky bands of Tokay have mastered the art of not drawing attention to themselves, something not hard to pull off since most dismiss the Tokay in general. The Guerrilla can hide in open view and sneak explosives into an enemy base, sabotaging their buildings and bringing them down to rubble. Big Boss Otaylo - Otaylo became Boss of the Tokay not because of power, intellect, or bloodlines... but because she bought a blue shirt to wear from Labrynna. With a spear in arms and Coconut on her head, the Big Boss clumsily leads the Tokay on hunting parties and raids against merchants for new and shiny trinkets. Next time we'll take a lot at two more Minor Factions that will make it into the next release, the Gorons of Rolling Ridge and the Wizzrobe.

I have only one wish - to see 27-th alpha before "Mushroom War". (Just kidding! ) (Or not... )

It worked, thank you! Here's the current progress if you all are wondering what's new.