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First problem i can see: when you write a= K.gens(), you overwrite the Python name a, hence in further commands, a is a list, it is not the first undeterminate of the ring S anymore.

There might be other issues, but you should start with fixing that one.

First problem i can see: when you write a= K.gens(), you overwrite the Python name a, hence in further commands, a is a list, it is not the first undeterminate of the ring S anymore.anymore, so when you write a[1]*a you try to multipliy an element of K with a list, which Sage is not able to give a meaning.

There might be other issues, but you should start with fixing that one.

First problem i can see: when you write a= K.gens(), you overwrite the Python name a, hence in further commands, a is a list, it is not the first undeterminate of the ring S anymore, so when you write a[1]*a you try to multipliy an element of K with a list, which Sage is not able to give a meaning.

There might be other issues, issues (like how K and S are related), but you should start with fixing that one.