Lines Matching refs:subs
19 e = e.subs({x: n3})
24 e = e.subs({x: n3})
32 e = e.subs({x: n3})
37 e = e.subs({sin(x): cos(x)})
41 assert tan(x).subs({x: pi/2}) is zoo
42 assert cot(x).subs({x: pi}) is zoo
43 assert cot(i*x).subs({x: pi}) is zoo
44 assert tan(i*x).subs({x: pi/2}) == tan(i*pi/2)
45 assert tan(i*x).subs({x: pi/2}).subs({i: 1}) is zoo
47 assert tan(o*x).subs({x: pi/2}) == tan(o*pi/2)
51 assert sqrt(1 - sqrt(x)).subs({x: 4}) == I
52 assert (sqrt(1 - x**2)**3).subs({x: 2}) == - 3*I*sqrt(3)
53 assert cbrt(x).subs({x: 27}) == 3
54 assert cbrt(x).subs({x: -27}) == 3*cbrt(-1)
55 assert cbrt(-x).subs({x: 27}) == 3*cbrt(-1)
57 assert (x**n).subs({x: 0}) is zoo
58 assert exp(-1).subs({E: 0}) is zoo
59 assert (x**(4.0*y)).subs({x**(2.0*y): n}) == n**2.0
60 assert (2**(x + 2)).subs({2: 3}) == 3**(x + 3)
63 assert (4**x).subs({2**x: y}) == y**2
64 assert (9**x).subs({3**x: y}) == y**2
67 assert (-2*x*sqrt(2)).subs({2*x: y}) == -sqrt(2)*y
74 assert e.subs({2**x: w}) != e
75 assert e.subs({exp(x*log(2)): w}) != e
82 assert y.subs({x1: Float(3.0)}) == Float(3.0)*x2
87 (x**x).subs({x: 1})
88 (x**x).subs({x: 1.0})
93 assert Float(7.7).epsilon_eq(abs(x).subs({x: -7.7}))
103 assert e.subs(r) == r[a]/r[b]*sin(r[b]*x)
104 assert e.subs(r) == 3*sin(4*x) / 4
106 assert e.subs(s) == r[a]/r[b]*sin(r[b]*x)
107 assert e.subs(s) == 3*sin(4*x) / 4
109 assert e.subs(r) == r[a]/r[b]*sin(r[b]*x)
110 assert e.subs(r) == 3*sin(4*x) / 4
111 assert x.subs(Dict((x, 1))) == 1
124 assert f.subs(df) == y**2
125 assert g.subs(dg) == y**2
128 assert f.subs({x: y}).subs({exp(x): y}) == y*exp(y)
129 assert f.subs({exp(x): y}).subs({x: y}) == y**2
136 assert e.subs({x: y, y: 2}) == 5
139 assert exp(x/2 + y).subs({exp(y + 1): 2, x: 2}) == exp(y + 1)
146 assert pat.subs({y: y**2}) == Derivative(f(x), x, x)
147 assert pat.subs({y: y**2}) != Derivative(f(x), x)
155 assert eq.subs({f(x): 4}) == res
162 assert bool(eq.subs({f(x): 3})) is False
163 assert bool(eq.subs({f(x): 4})) is True
170 assert e.subs({sqrt(x): 1}) == exp(y)
174 assert (1 + x*y).subs({x: pi}) == 1 + pi*y
175 assert (1 + x*y).subs({x: pi, y: 2}) == 1 + 2*pi
180 assert (test.subs({c1**2: 1 - s1**2, c2**2: 1 - s2**2, c3**3: 1 - s3**2})
187 assert (x*y*z).subs({z*x: y}) == y**2
188 assert (z*x).subs({1/x: z}) == z*x
189 assert (x*y/z).subs({1/z: a}) == a*x*y
190 assert (x*y/z).subs({x/z: a}) == a*y
191 assert (x*y/z).subs({y/z: a}) == a*x
192 assert (x*y/z).subs({x/z: 1/a}) == y/a
193 assert (x*y/z).subs({x: 1/a}) == y/(z*a)
194 assert (2*x*y).subs({5*x*y: z}) != 2*z/5
195 assert (x*y*A).subs({x*y: a}) == a*A
197 assert (x**2*y**(3*x/2)).subs({x*y**(x/2): 2}) == 4*y**(x/2)
198 assert (x*exp(x*2)).subs({x*exp(x): 2}) == 2*exp(x)
199 assert ((x**(2*y))**3).subs({x**y: 2}) == 64
200 assert (x*A*B).subs({x*A: y}) == y*B
201 assert (x*y*(1 + x)*(1 + x*y)).subs({x*y: 2}) == 6*(1 + x)
202 assert ((1 + A*B)*A*B).subs({A*B: x*A*B})
203 assert (x*a/z).subs({x/z: A}) == a*A
205 assert (x**3*A).subs({x**2*A: a}) == a*x
206 assert (x**2*A*B).subs({x**2*B: a}) == a*A
207 assert (x**2*A*B).subs({x**2*A: a}) == a*B
208 assert (b*A**3/(a**3*c**3)).subs({a**4*c**3*A**3/b**4: z}) == \
210 assert (6*x).subs({2*x: y}) == 3*y
211 assert (y*exp(3*x/2)).subs({y*exp(x): 2}) == 2*exp(x/2)
212 assert (y*exp(3*x/2)).subs({y*exp(x): 2}) == 2*exp(x/2)
213 assert (A**2*B*A**2*B*A**2).subs({A*B*A: C}) == A*C**2*A
214 assert (x*A**3).subs({x*A: y}) == y*A**2
215 assert (x**2*A**3).subs({x*A: y}) == y**2*A
216 assert (x*A**3).subs({x*A: B}) == B*A**2
217 assert (x*A*B*A*exp(x*A*B)).subs({x*A: B}) == B**2*A*exp(B*B)
218 assert (x**2*A*B*A*exp(x*A*B)).subs({x*A: B}) == B**3*exp(B**2)
219 assert (x**3*A*exp(x*A*B)*A*exp(x*A*B)).subs({x*A: B}) == \
221 assert (x*A*B*C*A*B).subs({x*A*B: C}) == C**2*A*B
222 assert (-I*a*b).subs({a*b: 2}) == -2*I
225 assert (-8*I*a).subs({-2*a: 1}) == 4*I
226 assert (-I*a).subs({-a: 1}) == I
229 assert (4*x**2).subs({2*x: y}) == y**2
230 assert (2*4*x**2).subs({2*x: y}) == 2*y**2
231 assert (-x**3/9).subs({-x/3: z}) == -z**2*x
232 assert (-x**3/9).subs({x/3: z}) == -z**2*x
233 assert (-2*x**3/9).subs({x/3: z}) == -2*x*z**2
234 assert (-2*x**3/9).subs({-x/3: z}) == -2*x*z**2
235 assert (-2*x**3/9).subs({-2*x: z}) == z*x**2/9
236 assert (-2*x**3/9).subs({2*x: z}) == -z*x**2/9
237 assert (2*(3*x/5/7)**2).subs({3*x/5: z}) == 2*Rational(1, 7)**2*z**2
238 assert (4*x).subs({-2*x: z}) == 4*x # try keep subs literal
240 assert (A**2*B**2).subs({A*B**3: C}) == A**2*B**2
241 assert (A**Rational(5, 3)*B**3).subs({sqrt(A)*B: C}) == A**Rational(5, 3)*B**3
242 assert (A**2*B**2*A).subs({A**2*B*A: C}) == A**2*B**2*A
249 assert (2*a).subs({1: 3}) == 2*a
250 assert (2*a).subs({2: 3}) == 3*a
251 assert (2*a).subs({a: 3}) == 6
252 assert sin(2).subs({1: 3}) == sin(2)
253 assert sin(2).subs({2: 3}) == sin(3)
254 assert sin(a).subs({a: 3}) == sin(3)
256 assert (2*x).subs({1: 3}) == 2*x
257 assert (2*x).subs({2: 3}) == 3*x
258 assert (2*x).subs({x: 3}) == 6
259 assert sin(x).subs({x: 3}) == sin(3)
266 assert (a*b).subs({2*a: 1}) == a*b
267 assert (1.5*a*b).subs({a: 1}) == 1.5*b
268 assert (2*a*b).subs({2*a: 1}) == b
269 assert (2*a*b).subs({4*a: 1}) == 2*a*b
271 assert (x*y).subs({2*x: 1}) == x*y
272 assert (1.5*x*y).subs({x: 1}) == 1.5*y
273 assert (2*x*y).subs({2*x: 1}) == y
274 assert (2*x*y).subs({4*x: 1}) == 2*x*y
280 assert (a*b).subs({a*b: K}) == K
281 assert (a*b*a*b).subs({a*b: K}) == K**2
282 assert (a*a*b*b).subs({a*b: K}) == K**2
283 assert (a*b*c*d).subs({a*b*c: K}) == d*K
284 assert (a*b**c).subs({a: K}) == K*b**c
285 assert (a*b**c).subs({b: K}) == a*K**c
286 assert (a*b**c).subs({c: K}) == a*b**K
287 assert (a*b*c*b*a).subs({a*b: K}) == c*K**2
288 assert (a**3*b**2*a).subs({a*b: K}) == a**2*K**2
294 assert (x*y).subs({x*y: L}) == L
295 assert (w*y*x).subs({x*y: L}) == w*y*x
296 assert (w*x*y*z).subs({x*y: L}) == w*L*z
297 assert (x*y*x*y).subs({x*y: L}) == L**2
298 assert (x*x*y).subs({x*y: L}) == x*L
299 assert (x*x*y*y).subs({x*y: L}) == x*L*y
300 assert (w*x*y).subs({x*y*z: L}) == w*x*y
301 assert (x*y**z).subs({x: L}) == L*y**z
302 assert (x*y**z).subs({y: L}) == x*L**z
303 assert (x*y**z).subs({z: L}) == x*y**L
304 assert (w*x*y*z*x*y).subs({x*y*z: L}) == w*L*x*y
305 assert (w*x*y*y*w*x*x*y*x*y*y*x*y).subs({x*y: L}) == w*L*y*w*x*L**2*y*L
310 assert (x*A).subs({x**2*A: B}) == x*A
311 assert (A**2).subs({A**3: B}) == A**2
312 assert (A**6).subs({A**3: B}) == B**2
319 assert (x + y).subs({x + y: L}) == L
320 assert (x - y).subs({x - y: L}) == L
321 assert (x/y).subs({x: L}) == L/y
322 assert (x**y).subs({x: L}) == L**y
323 assert (x**y).subs({y: L}) == x**L
324 assert ((a - c)/b).subs({b: K}) == (a - c)/K
325 assert (exp(x*y - z)).subs({x*y: L}) == exp(L - z)
326 assert (a*exp(x*y - w*z) + b*exp(x*y + w*z)).subs({z: 0}) == \
328 assert ((a - b)/(c*d - a*b)).subs({c*d - a*b: K}) == (a - b)/K
329 assert (w*exp(a*b - c)*x*y/4).subs({x*y: L}) == w*exp(a*b - c)*L/4
335 assert (R*S).subs({R*S: T}) == T
336 assert (S*R).subs({R*S: T}) == T
337 assert (R + S).subs({R + S: T}) == T
338 assert (R**S).subs({R: T}) == T**S
339 assert (R**S).subs({S: T}) == R**T
340 assert (R*S**T).subs({R: U}) == U*S**T
341 assert (R*S**T).subs({S: U}) == R*U**T
342 assert (R*S**T).subs({T: U}) == R*S**U
350 assert (a*x*y).subs({x*y: L}) == a*L
351 assert (a*b*x*y*x).subs({x*y: L}) == a*b*L*x
352 assert (R*x*y*exp(x*y)).subs({x*y: L}) == R*L*exp(L)
353 assert (a*x*y*y*x - x*y*z*exp(a*b)).subs({x*y: L}) == a*L*y*x - L*z*exp(a*b)
355 assert e.subs({x*y: L}).subs({a*b: K}).subs({R*S: U}) == \
363 assert (1/a).subs({a: c}) == 1/c
364 assert (1/a**2).subs({a: c}) == 1/c**2
365 assert (1/a**2).subs({a: -2}) == Rational(1, 4)
366 assert (-(1/a**2)).subs({a: -2}) == -Rational(1, 4)
368 assert (1/x).subs({x: z}) == 1/z
369 assert (1/x**2).subs({x: z}) == 1/z**2
370 assert (1/x**2).subs({x: -2}) == Rational(1, 4)
371 assert (-(1/x**2)).subs({x: -2}) == -Rational(1, 4)
374 assert (1/x).subs({x: 0}) == 1/Integer(0)
378 assert (a**2 - b - c).subs({a**2 - b: d}) in [d - c, a**2 - b - c]
379 assert (a**2 - c).subs({a**2 - c: d}) == d
380 assert (a**2 - b - c).subs({a**2 - c: d}) in [d - b, a**2 - b - c]
381 assert (a**2 - x - c).subs({a**2 - c: d}) in [d - x, a**2 - x - c]
382 assert (a**2 - b - sqrt(a)).subs({a**2 - sqrt(a): c}) == c - b
383 assert (a + b + exp(a + b)).subs({a + b: c}) == c + exp(c)
384 assert (c + b + exp(c + b)).subs({c + b: a}) == a + exp(a)
385 assert (a + b + c + d).subs({b + c: x}) == a + d + x
386 assert (a + b + c + d).subs({-b - c: x}) == a + d - x
387 assert ((x + 1)*y).subs({x + 1: t}) == t*y
388 assert ((-x - 1)*y).subs({x + 1: t}) == -t*y
389 assert ((x - 1)*y).subs({x + 1: t}) == y*(t - 2)
390 assert ((-x + 1)*y).subs({x + 1: t}) == y*(-t + 2)
394 assert e.subs({Add(*e.args[:2]): d}) == d + e.args[2]
395 assert e.subs({a**2 - c: d}) == d - b
400 assert (0.1 + a).subs({0.1: Rational(1, 10)}) == Rational(1, 10) + a
404 assert e.subs({-y + 1: x}) == ans
408 assert (I*Symbol('a')).subs({1: 2}) == I*Symbol('a')
414 assert (g(y, x) + cos(x)).subs({g: l}) == sin(y) + x + cos(x)
415 assert (f(x)**2).subs({f: sin}) == sin(x)**2
416 assert (f(x, y)).subs({f: log}) == log(x, y)
417 assert (f(x, y)).subs({f: sin}) == f(x, y)
418 assert (sin(x) + atan2(x, y)).subs({atan2: f, sin: g}) == \
420 assert (g(f(x + y, x))).subs({f: l, g: Lambda(x, exp(x))}) == exp(x + sin(x + y))
426 assert Derivative(f(x), x).subs({f(x): y}) != 0
427 assert Derivative(f(x), x).subs({f(x): y}).subs({y: f(x)}) == \
438 assert Derivative(f, x, y).subs({Derivative(f, x, y): g}) == g
439 assert Derivative(f, y, x).subs({Derivative(f, x, y): g}) == g
440 assert Derivative(f, x, y).subs({Derivative(f, x): g}) == Derivative(g, y)
441 assert Derivative(f, x, y).subs({Derivative(f, y): g}) == Derivative(g, x)
442 assert (Derivative(f, x, y, z).subs({Derivative(f, x, z): g}) == Derivative(g, y))
443 assert (Derivative(f, x, y, z).subs({Derivative(f, z, y): g}) == Derivative(g, x))
444 assert Derivative(f, x, y, z).subs({Derivative(f, z, y, x): g}) == g
445 assert (Derivative(sin(x), (x, 2)).subs({Derivative(sin(x), f_func(x)): g_func}) ==
449 assert (Derivative(f, x, x, y).subs({Derivative(f, y, y): g}) == Derivative(f, x, x, y))
450 …assert (Derivative(f, x, y, y, z).subs({Derivative(f, x, y, y, y): g}) == Derivative(f, x, y, y, z…
452 assert Derivative(f, x, y).subs({Derivative(f_func(x), x, y): g}) == Derivative(f, x, y)
458 assert Derivative(dex, x).subs({dex: exp(x)}) == dex
459 assert dex.subs({exp(x): dex}) == Derivative(exp(x), x, x)
463 assert x.subs(reversed([[x, y]])) == y
465 assert x.subs(it) == y
466 assert x.subs(Tuple((x, y))) == y
470 assert (2*x + y + z).subs({x: 1, y: 2}) == 4 + z
473 assert (sin(x)).subs(l) == \
474 (sin(x)).subs(dict(l)) == 2
475 assert sin(x).subs(reversed(l)) == sin(1)
480 assert expr.subs(reps) == c + a*b*sin(d*e)
483 assert (x + y).subs(l) == 3 + x**2
484 assert (x + y).subs(reversed(l)) == 12
490 assert (y - 1 + 3*x).subs(l) == 5 + 3*x
492 assert (y - 2).subs(l) == 3
496 assert (x + 3).subs({x + 3: a}) == a
497 assert (x + 3).subs({x + 2: a}) == a + 1
499 assert (x + y + 3).subs({x + 3: a}) == a + y
500 assert (x + y + 3).subs({x + 2: a}) == a + y + 1
502 assert (x + 3.0).subs({x + 3.0: a}) == a
503 assert (x + 3.0).subs({x + 2.0: a}) == x + 3.0
505 assert (x + y + 3.0).subs({x + 3.0: a}) == a + y
506 assert (x + y + 3.0).subs({x + 2.0: a}) == x + y + 3.0
511 assert (a/(b*c)).subs({b*c: K}) == a/K
512 assert (a/(b**2*c**3)).subs({b*c: K}) == a/(c*K**2)
513 assert (1/(x*y)).subs({x*y: 2}) == Rational(1, 2)
514 assert ((1 + x*y)/(x*y)).subs({x*y: 1}) == 2
515 assert (x*y*z).subs({x*y: 2}) == 2*z
516 assert ((1 + x*y)/(x*y)/z).subs({x*y: 1}) == 2/z
520 assert Tuple(1, True).subs({1: 2}) == Tuple(2, True)
525 assert _aresame((x + 2.0).subs({2: 3}), x + 2.0)
526 assert _aresame((x + 2.0).subs({2.0: 3}), x + 3)
536 assert N.subs({N: 3}) == 3
540 assert (x - 1).subs({1: y}) == x - y
541 assert (x - 1).subs({-1: y}) == x + y
542 assert (x - oo).subs({oo: y}) == x - y
543 assert (x - oo).subs({-oo: y}) == x + y
549 assert p.subs({g: h}) == Piecewise((h(f(x, y)), x < -1), (h(x), x <= 1))
550 assert (f(y) + g(x)).subs({f: h, g: i}) == i(x) + h(y)
555 assert (x/y).subs(reps) != (y/x).subs(reps)
556 assert (x/y).subs(reps, simultaneous=True) == \
557 (y/x).subs(reps, simultaneous=True)
559 assert (x/y).subs(reps) != (y/x).subs(reps)
560 assert (x/y).subs(reps, simultaneous=True) == \
561 (y/x).subs(reps, simultaneous=True)
562 assert Derivative(x, y, z).subs(reps, simultaneous=True) == \
567 assert (1/(1 + x/y)).subs({x/y: x}) == 1/(1 + x)
568 assert (-2*I).subs({2*I: x}) == -x
569 assert (-I*x).subs({I*x: x}) == -x
570 assert (-3*I*y**4).subs({3*I*y**2: x}) == -x*y**2
574 assert (-12*x + y).subs({-x: 1}) == 12 + y
586 assert exp(e).subs({exp(x): y}) == y**I
587 assert (2**e).subs({2**x: y}) == y**I
589 assert eq.subs({(-2)**x: y}) == eq
604 assert (x*y*x).subs({x: x*y, y: x}, simultaneous=True) == (x*y*x**2*y)
609 assert (x + f).subs({f: 2}) == x + 2
619 assert (1/(1 - t)).subs({t: 1}) == zoo
622 assert (n/d).subs({t: 1}) == zoo
623 assert (-n/-d).subs({t: 1}) == zoo
632 assert w.subs(sub) == 1 + s
633 assert z.subs(sub) == 1 - s
635 assert q.subs(sub) == 2*y**2*s
645 result = s.subs({sqrt(x**2): y})
651 assert exp(n*x).subs({exp(x): x}) == x**n
657 assert exp0.subs({exp1: exp0}) == E**4
664 assert (x < r).subs({x: r}) is false
669 assert (1/x).subs({x**2: 1}) != 1
677 assert (x*e1).subs({e2: y}) == x*y
679 assert e3.subs({e2: y}) == e3
681 assert e4.subs({e2: y}) == e4
687 assert e.subs(s) == 3