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GAP 4.8.9 installation with standard packages -- copy to your CoCalc project to get it

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LoadPackage( "homalg" );

ZZ := HomalgRingOfIntegers( );
R := ZZ / 2^8;

r := (1/3*One(R)+1/5)+3/7;

s := (1/3*One(R)+2/5)+3/7;