ImproviseImprovise is a static ability that functions while the spell with improvise is on the stack. “Improvise” means “For each generic mana in this spell’s total cost, you may tap an untapped artifact you control rather than pay that mana.”
The improvise ability isn’t an additional or alternative cost and applies only after the total cost of the spell with improvise is determined.
Multiple instances of improvise on the same spell are redundant. (CR 702.126) (Your artifacts can help
castTo cast a spell is to take it from the zone it’s in (usually the hand), put it on the stack, and pay its costs, so that it will eventually resolve and have its effect. A player may cast a spell if they have priority. See rule 601, “Casting Spells.”
To cast a card is to cast it as a spell. (CR 701.5) this spell. Each artifact you
tapTo tap a permanent, turn it sideways from an upright position. Only untapped permanents can be tapped. (CR 701.26) after you're done activating mana abilities pays for
.)
HexproofHexproof is a static ability.
“Hexproof” on a permanent means “This permanent can’t be the target of spells or abilities your opponents control.”
“Hexproof” on a player means “You can’t be the target of spells or abilities your opponents control.”
“Hexproof from [quality]” is a variant of the hexproof ability. “Hexproof from [quality]” on a permanent means “This permanent can’t be the target of [quality] spells your opponents control or abilities your opponents control from [quality] sources.” A “hexproof from [quality]” ability is a hexproof ability.
Any effect that causes an object to lose hexproof will cause an object to lose all “hexproof from [quality]” abilities. Any effect that allows a player to choose a creature with hexproof as a target as though it didn’t have hexproof will allow a player to choose a creature with a “hexproof from [quality]” ability. Any effect that looks for a card with hexproof will find a card with a “hexproof from [quality]” ability.
“Hexproof from [quality A] and from [quality B]” is shorthand for “hexproof from [quality A]” and “hexproof from [quality B]”; it behaves as two separate hexproof abilities.
“Hexproof from each [characteristic]” is shorthand for “hexproof from [quality A],” “hexproof from [quality B],” and so on for each possible quality the listed characteristic could have; it behaves as multiple separate hexproof abilities.
Multiple instances of the same hexproof ability on the same permanent or player are redundant. (CR 702.11) (This creature can't be the target of spells or abilities your opponents control.)