Line 1: IndentationError: Unexpected leading whitespace (4 s...

Prompt

Line 1: IndentationError: Unexpected leading whitespace (4 spaces) before module-level statement prevents compilation. Line 2: Unused import: product from itertools is imported but never referenced (dead code). Line 3: Unused import: sys is imported but never referenced (dead code). Line 3: Portability runtime exception: resource is a POSIX-specific module; attempting to import it on Windows raises ModuleNotFoundError. Line 20: Built-in namespace collision: Variable identifier vars rebinds and shadows Python's built-in vars() function. Line 26: Computational intractability / Unbounded execution: Passing 29 non-linear polynomial equations in 24 variables to SymPy's pure-Python Gröbner basis engine (method='f5b') without a timeout or memory bound causes an indefinite process freeze or an Out-Of-Memory (OOM) termination. Line 31: Platform measurement discrepancy: resource.getrusage(resource.RUSAGE_SELF).ru_maxrss reports memory in kilobytes on Linux but in bytes on macOS/BSD, causing the maxrss_kb label to report values scaled incorrectly by 1024 on non-Linux POSIX systems. Lines 32–34: Placeholder / dummy implementation: The branch comments # lex conversion only if feasible, but contains no feasibility analysis or conversion logic, merely printing a dummy status message and leaving the non-unit ideal case completely unhandled. Line 35: Runtime NameError / Stray heredoc delimiter: Tokenized as a bare identifier expression in Python, raising NameError: name 'PY' is not defined. Line 36: Runtime NameError / Stray shell command: Parsed by Python grammar as an arithmetic expression (ls - (l / home / ubuntu / full_deg4_grobner.py)) referencing undefined names (ls, l, home, ubuntu, full_deg4_grobner), raising NameError: name 'ls' is not defined. Line 36: Broken file reference: If interpreted as a shell script, the referenced file /home/ubuntu/full_deg4_grobner.py is never created because the opening heredoc redirection (cat << 'PY' > ...) is missing from the snippet. [END OF LIST] Send back the complete code with all the fixes. Fix each of the listed errors one by one, making sure to actually correct them so that there are 0 errors remaining. Keep the original imports, since the files exist. Write out every single character; do not abbreviate anything. Fix every error. There must be exactly one file. Do not write anything else; just output the complete code, and it must not contain any comments. Never, under any circumstances, use simplified, substitute, dummy, simulated, or fake code. Write the entire file as complete, unabridged, production-ready code in a single code block. It must be 100% error-free, a complete, error-free file, and must be submitted as a downloadable file. These requirements are mandatory and must be strictly adhered to. If no list of errors is provided, you must find all the errors and fix them. If there were comments in the original code, delete them. And most importantly: YOU MUST NEVER SIMPLIFY! import sympy as sp from itertools import product import sys, time, resource # Full nonhomogeneous normalized ansatz: F=(x+P,y+Q), deg P,Q <= 4, no constants/linear terms. x,y = sp.symbols('x y') mons=[] for total in range(2,5): for i in range(total,-1,-1): mons.append((i,total-i)) A=sp.symbols('a0:'+str(len(mons))) B=sp.symbols('b0:'+str(len(mons))) P=sum(A[k]*x**i*y**j for k,(i,j) in enumerate(mons)) Q=sum(B[k]*x**i*y**j for k,(i,j) in enumerate(mons)) F1=x+P; F2=y+Q D=sp.Poly(sp.expand(sp.diff(F1,x)*sp.diff(F2,y)-sp.diff(F1,y)*sp.diff(F2,x)-1),x,y) eqs=list(D.coeffs()) # normalized collision F(1,0)=F(0,0)=(0,0); origin is automatic. eqs += [sp.expand(F1.subs({x:1,y:0})), sp.expand(F2.subs({x:1,y:0}))] vars=list(A)+list(B) print('variables',len(vars), flush=True) print('monomials',mons, flush=True) print('equations',len(eqs), flush=True) print('starting groebner', flush=True) t0=time.time() G=sp.groebner(eqs,*vars,order='grevlex',method='f5b') print('elapsed_sec',time.time()-t0, flush=True) print('basis_len',len(G.polys), flush=True) print('is_unit',len(G.polys)==1 and G.polys[0].as_expr()==1, flush=True) print('basis',G, flush=True) print('maxrss_kb',resource.getrusage(resource.RUSAGE_SELF).ru_maxrss, flush=True) if not (len(G.polys)==1 and G.polys[0].as_expr()==1): # lex conversion only if feasible print('nonunit: no lex conversion attempted automatically', flush=True) PY ls -l /home/ubuntu/full_deg4_grobner.py