@@ -2273,10 +2273,8 @@ cdef class Expression(CommutativeRingElement):
22732273 False
22742274 sage: SR(1).__nonzero__()
22752275 True
2276- sage: bool(abs(x))
2277- True
2278- sage: bool(x/x - 1)
2279- False
2276+ sage: assert(abs(x))
2277+ sage: assert(not x/x - 1)
22802278
22812279 This is called by :meth:`is_zero`::
22822280
@@ -2295,67 +2293,41 @@ cdef class Expression(CommutativeRingElement):
22952293 for symbolic relations::
22962294
22972295 sage: x = var('x')
2298- sage: bool((x-1)^2 == x^2 - 2*x + 1)
2299- True
2300- sage: bool(((x-1)^2 == x^2 - 2*x + 1).expand())
2301- True
2302- sage: bool(((x-1)^2 == x^2 - 2*x + 3).expand())
2303- False
2304- sage: bool(2 + x < 3 + x)
2305- True
2306- sage: bool(2 + x < 1 + x)
2307- False
2308- sage: bool(2 + x > 1 + x)
2309- True
2310- sage: bool(1 + x > 1 + x)
2311- False
2312- sage: bool(1 + x >= 1 + x)
2313- True
2314- sage: bool(1 + x < 1 + x)
2315- False
2316- sage: bool(1 + x <= 1 + x)
2317- True
2318- sage: bool(1 + x^2 != 1 + x*x)
2319- False
2320- sage: bool(1 + x^2 != 2 + x*x)
2321- True
2322- sage: bool(SR(oo) == SR(oo))
2323- True
2324- sage: bool(-SR(oo) == SR(oo))
2325- False
2326- sage: bool(-SR(oo) != SR(oo))
2327- True
2296+ sage: assert((x-1)^2 == x^2 - 2*x + 1)
2297+ sage: assert(((x-1)^2 == x^2 - 2*x + 1).expand())
2298+ sage: assert(not ((x-1)^2 == x^2 - 2*x + 3).expand())
2299+ sage: assert(2 + x < 3 + x)
2300+ sage: assert(not 2 + x < 1 + x)
2301+ sage: assert(2 + x > 1 + x)
2302+ sage: assert(not 1 + x > 1 + x)
2303+ sage: assert(1 + x >= 1 + x)
2304+ sage: assert(not 1 + x < 1 + x)
2305+ sage: assert(1 + x <= 1 + x)
2306+ sage: assert(not 1 + x^2 != 1 + x*x)
2307+ sage: assert(1 + x^2 != 2 + x*x)
2308+ sage: assert(SR(oo) == SR(oo))
2309+ sage: assert(not -SR(oo) == SR(oo))
2310+ sage: assert(-SR(oo) != SR(oo))
23282311
23292312 Next, tests to ensure assumptions are correctly used::
23302313
23312314 sage: x, y, z = var('x, y, z')
2332- sage: assume(x>=y,y>=z,z>=x)
2333- sage: bool(x==z)
2334- True
2335- sage: bool(z<x)
2336- False
2337- sage: bool(z>y)
2338- False
2339- sage: bool(y==z)
2340- True
2341- sage: bool(y<=z)
2342- True
2315+ sage: assume(x >= y, y >= z, z >= x)
2316+ sage: assert(x == z)
2317+ sage: assert(not z < x)
2318+ sage: assert(not z > y)
2319+ sage: assert(y == z)
2320+ sage: assert(y <= z)
23432321 sage: forget()
2344- sage: assume(x>=1,x<=1)
2345- sage: bool(x==1)
2346- True
2347- sage: bool(x != 1)
2348- False
2349- sage: bool(x>1)
2350- False
2322+ sage: assume(x >= 1, x <= 1)
2323+ sage: assert(x == 1)
2324+ sage: assert(not x != 1)
2325+ sage: assert(not x > 1)
23512326 sage: forget()
2352- sage: assume(x>0)
2353- sage: bool(x==0)
2354- False
2355- sage: bool(x != 0)
2356- True
2357- sage: bool(x == 1)
2358- False
2327+ sage: assume(x > 0)
2328+ sage: assert(not x == 0)
2329+ sage: assert(x != 0)
2330+ sage: assert(not x == 1)
23592331
23602332 The following must be true, even though we do not
23612333 know for sure that x is not 1, as symbolic comparisons
@@ -2365,16 +2337,12 @@ cdef class Expression(CommutativeRingElement):
23652337
23662338 ::
23672339
2368- sage: bool(x != 1)
2369- True
2340+ sage: assert(x != 1)
23702341 sage: forget()
23712342 sage: assume(x>y)
2372- sage: bool(x==y)
2373- False
2374- sage: bool(x != y)
2375- True
2376- sage: bool(x != y) # The same comment as above applies here as well
2377- True
2343+ sage: assert(not x==y)
2344+ sage: assert(x != y)
2345+ sage: assert(x != y) # The same comment as above applies here as well
23782346 sage: forget()
23792347
23802348 Comparisons of infinities::
@@ -2405,30 +2373,29 @@ cdef class Expression(CommutativeRingElement):
24052373
24062374 Check that :trac:`13326` is fixed::
24072375
2408- sage: bool(log(2)*Infinity == Infinity)
2409- True
2376+ sage: assert(log(2)*Infinity == Infinity)
24102377
24112378 More checks for comparisons with infinity (see :trac:`12967`)::
24122379
2413- sage: assert(bool( SR(oo) > 5) )
2414- sage: assert(bool( 5 < SR(oo) ))
2415- sage: assert(bool( SR(2) < Infinity) )
2416- sage: assert(bool( pi < Infinity) )
2417- sage: assert(not bool( pi>Infinity) )
2418- sage: assert(bool( 2*pi < Infinity) )
2419- sage: assert(bool( SR(pi) < SR(Infinity) ))
2420- sage: assert(bool( sqrt(2) < oo) )
2421- sage: assert(bool( log(2) < oo) )
2422- sage: assert(bool( e < oo) )
2423- sage: assert(bool( e+pi < oo) )
2424- sage: assert(bool( e^pi < oo) )
2425- sage: assert(not bool( SR(2) < -oo) )
2426- sage: assert(bool( SR(2) > -oo) )
2427- sage: assert(bool( exp(2) > -oo) )
2428- sage: assert(bool( SR(oo) > sqrt(2) ))
2429- sage: assert(bool( sqrt(2) < SR(oo) ))
2430- sage: assert(bool( SR(-oo) < sqrt(2) ))
2431- sage: assert(bool( sqrt(2) > SR(-oo) ))
2380+ sage: assert(SR(oo) > 5)
2381+ sage: assert(5 < SR(oo))
2382+ sage: assert(SR(2) < Infinity)
2383+ sage: assert(pi < Infinity)
2384+ sage: assert(not pi>Infinity)
2385+ sage: assert(2*pi < Infinity)
2386+ sage: assert(SR(pi) < SR(Infinity))
2387+ sage: assert(sqrt(2) < oo)
2388+ sage: assert(log(2) < oo)
2389+ sage: assert(e < oo)
2390+ sage: assert(e+pi < oo)
2391+ sage: assert(e^pi < oo)
2392+ sage: assert(not SR(2) < -oo)
2393+ sage: assert(SR(2) > -oo)
2394+ sage: assert(exp(2) > -oo)
2395+ sage: assert(SR(oo) > sqrt(2))
2396+ sage: assert(sqrt(2) < SR(oo))
2397+ sage: assert(SR(-oo) < sqrt(2))
2398+ sage: assert(sqrt(2) > SR(-oo))
24322399
24332400 Check that :trac:`18360` is fixed::
24342401
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