from research import *
s=begin(1173,'State the domain of compatible row moves','When is a two-operation row transformation a valid nonnegative biography calculation?',{},['C1152','Strategy §§5B,5C,5G'])
data={'state':'b>=0,r>=0,L=b+r','endpoint_after_Rd_Ae':['b+d>=0','r-d+e>=0'],'R_then_A_intermediate':'r-d>=0 in addition to endpoint conditions','A_then_R_intermediate':'r+e>=0 in addition to endpoint conditions','formal_composition':'R_d A_e = A_e R_d on unrestricted compatible coordinates','source_admission':'Nonnegative intermediate coordinates do not make an unlisted source biography admitted.'}
a=artifact('model/row_operation_domains.json',json.dumps(data,indent=2)+'\n')
finish(s,{'row_domains':a},'The normal form is an integer-coordinate identity, but nonnegative intermediate biographies impose order-sensitive domains. Source admission is an additional requirement beyond those inequalities.','Exhibit a complete positive endpoint for which one formal order leaves the nonnegative domain.',{'compatibility_symbolic':'L=b+r' in data['state'],'domain_separation':len(data['endpoint_after_Rd_Ae'])==2})