4208.sagews

factor(1311)

3 * 19 * 23

1311/2451

23/43

f(x)=abs(x)

f(-10)

10

solve([f(x)<=3], x)

#0: solve_rat_ineq(ineq=abs(x) <= 3) [[x == 3], [x == -3], [-3 < x, x < 3]]

factor (10989)

3^3 * 11 * 37

factor (12177)

3^3 * 11 * 41

10989/12

37/41

g(x)=abs(x)

g(-1)=([abs(x-3)+3],x)

Traceback (most recent call last): File "<stdin>", line 1, in <module> File "_sage_input_13.py", line 10, in <module> exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("ZygtMSk9KFthYnMoeC0zKSszXSx4KQ=="),globals())+"\\n"); execfile(os.path.abspath("___code___.py"))' + '\n', '', 'single') File "", line 1, in <module> File "/tmp/tmpuKN56F/___code___.py", line 3, in <module> exec compile(u'__tmp__=var("-_sage_const_1"); g = symbolic_expression(([abs(x-_sage_const_3 )+_sage_const_3 ],x)).function(-_sage_const_1)' + '\n', '', 'single') File "", line 1, in <module> File "var.pyx", line 108, in sage.calculus.var.var (sage/calculus/var.c:687) File "ring.pyx", line 521, in sage.symbolic.ring.SymbolicRing.var (sage/symbolic/ring.cpp:6342) File "ring.pyx", line 560, in sage.symbolic.ring.SymbolicRing.var (sage/symbolic/ring.cpp:6069) ValueError: The name "-_sage_const_1" is not a valid Python identifier.

solve ([abs(x-3)+3>=5],x)

#0: solve_rat_ineq(ineq=abs(x-3)+3 >= 5) [[x == 5], [x == 1], [5 < x], [x < 1]]