Summon

Summons are among the most well known and most powerful abilities in the Golden Sun series. A summon allows the player to call upon a powerful spirit to assist them in battle.

Mechanics
Like Psynergy and Unleashes, Summons are aligned with one of the four elements: Venus, Jupiter, Mars and Mercury. Unlike Psynergy, Summons can not be used at will. Instead, the summon is fueled by the usage of Djinn that have been placed in Standby mode. Typically, the element of most of the necessary Djinn will match the elemental alignment of the summon, though some summons also require Djinn of other elements as well. The power of a summon generally correlates with the amount of Djinn needed to fuel the summon. After a Djinni has been used to fuel a summon, it will enter Recovery for a set period of time. Further summons require that the player return Djinn to standby mode.

Each summon, with the major exception of Coatlicue, which heals the party rather than attacking the enemy, has a specific base damage associated with it. However, the total damage potential of a summon also depends on the elemental Power of the summoner and the elemental Resistance and Hit Points of the targets. Summons typically have an unlimited range.

After a successful summon, the elemental power of the summoner will be increased by a specified amount. The amount of increase depends on the number and element of the Djinn used to fuel the summon. Typically, using 1 Djinn will increase the matching Elemental Power by 10. Likewise, 2 Djinn result in a 30 point increase, 3 Djinn result in a 60 point increase, and 4 or more result in a 100 point increase. However, this increase is only given the first time a summoner uses the summon in a particular battle, barring the summoner being targeted by Break.

Damage Calculation
The damage from a summon is calculated as follows:

$$\mathrm{damage = \left \lfloor \left( \frac{\left \lfloor 256 \cdot dimRatio \right \rfloor}{256}\right) \left(base + \frac{\left \lfloor 256 \cdot multiplier \cdot hp \right \rfloor}{256}\right)\left(1 + \frac{\left \lfloor 256 \cdot \left( \frac{power - resistance}{200} \right)\right \rfloor}{256}\right) \right \rfloor + randDamage}$$


 * damage: final damage.
 * $$\lfloor x \rfloor$$ is the greatest integer less than or equal to $$x$$.
 * dimRatio: This is always 1, 0.7, 0.4, 0.3, 0.2, or 0.1 for summons. Its value depends on the location of the enemy of interest relative to the main target. For example, the main target will take 100% of the damage, the enemies next to him will take 70%, and so on.
 * base: base damage of the attack. The value depends on the summon; see the list below.
 * hp: HP of the target.
 * multiplier: the HP multiplier of the summon. This factor is what makes summons so effective against bosses; the more HP the target has, the more damage a summon will deal. For the party's summons, the HP multiplier is usually equal to $$(3 \cdot \text{number of Djinn used})/100$$. The only exceptions are the multipliers for Iris and Daedalus.
 * power: the user's elemental power in the relevant element.
 * resistance: the target's resistance to the relevant element.
 * randDamage: a randomly generated integer between 0 and 3, inclusive.

In Golden Sun
Golden Sun features a total of sixteen summons, with each element having four summons. These summons use one to four Djinn of a single element and are available as soon as the party has enough Djinn to use them. However, these summons have no secondary effects.

In The Lost Age
Golden Sun: The Lost Age includes the sixteen regular summons from Golden Sun. However, the game also introduced thirteen new summons, which needed to be specifically acquired by encountering special stone tablets. These summons use Djinn of two different elements and each summon has a special secondary effect. Furthermore, 4 of these thirteen summons can only be acquired after defeating a special superboss.

In Dark Dawn
In Golden Sun: Dark Dawn, all 29 summon spirits from the first two games return, in addition to one new summon spirit, known as Crystallux. The older summon sequences underwent visual changes of varying degrees. Some spirits, such as Moloch remain relatively unchanged, while others, like Ulysses, are radically different to the versions seen in the first two games. When Dark Dawn was first announced, trailers showing some of the summon spirits' animation sequences were released to the public. Many of these clips featured animation sequences that were later altered when the game was released. For instance, the Neptune summon was initially shown to be a whale almost identical in appearance to the whale seen in the first two games, but was later altered to have a darker color and sport horns and markings that were not present on the original version.

For a video exhibition of all 30 summon sequences in the game in sequential order, visit this link.