Expression of type Conditional ¶

from the theory of proveit.physics.quantum.algebra ¶

import proveit
# Automation is not needed when building an expression:
proveit.defaults.automation = False # This will speed things up.
proveit.defaults.inline_pngs = False # Makes files smaller.
%load_expr # Load the stored expression as 'stored_expr'
# import Expression classes needed to build the expression
from proveit import Conditional, U, alpha, n
from proveit.linear_algebra import Norm, Unitary
from proveit.logic import CartExp, Equals, Forall, InSet
from proveit.numbers import Complex, NaturalPos, RealNonNeg
from proveit.physics.quantum import Qmult, var_ket_psi

# build up the expression from sub-expressions
expr = Conditional(Forall(instance_param_or_params = [U], instance_expr = Forall(instance_param_or_params = [alpha], instance_expr = Forall(instance_param_or_params = [var_ket_psi], instance_expr = Equals(Norm(Qmult(U, var_ket_psi)), alpha), domain = CartExp(Complex, n), condition = Equals(Norm(var_ket_psi), alpha)), domain = RealNonNeg), domain = Unitary(n)), InSet(n, NaturalPos))

# check that the built expression is the same as the stored expression
assert expr == stored_expr
assert expr._style_id == stored_expr._style_id
print("Passed sanity check: expr matches stored_expr")

Passed sanity check: expr matches stored_expr

# Show the LaTeX representation of the expression for convenience if you need it.
print(stored_expr.latex())

\left\{\forall_{U \in \textrm{U}\left(n\right)}~\left[\forall_{\alpha \in \mathbb{R}^{\ge 0}}~\left[\forall_{\lvert \psi \rangle \in \mathbb{C}^{n}~|~\left \|\lvert \psi \rangle\right \| = \alpha}~\left(\left \|U \thinspace \lvert \psi \rangle\right \| = \alpha\right)\right]\right] \textrm{ if } n \in \mathbb{N}^+\right..

stored_expr.style_options()

# display the expression information
stored_expr.expr_info()

	core type	sub-expressions
0	Conditional	value: 1 condition: 2
1	Operation	operator: 21 operand: 5
2	Operation	operator: 36 operands: 4
3	ExprTuple	5
4	ExprTuple	52, 6
5	Lambda	parameter: 50 body: 8
6	Literal
7	ExprTuple	50
8	Conditional	value: 9 condition: 10
9	Operation	operator: 21 operand: 13
10	Operation	operator: 36 operands: 12
11	ExprTuple	13
12	ExprTuple	50, 14
13	Lambda	parameter: 43 body: 16
14	Operation	operator: 17 operand: 52
15	ExprTuple	43
16	Conditional	value: 19 condition: 20
17	Literal
18	ExprTuple	52
19	Operation	operator: 21 operand: 24
20	Operation	operator: 36 operands: 23
21	Literal
22	ExprTuple	24
23	ExprTuple	43, 25
24	Lambda	parameter: 53 body: 26
25	Literal
26	Conditional	value: 27 condition: 28
27	Operation	operator: 38 operands: 29
28	Operation	operator: 30 operands: 31
29	ExprTuple	32, 43
30	Literal
31	ExprTuple	33, 34
32	Operation	operator: 48 operand: 40
33	Operation	operator: 36 operands: 37
34	Operation	operator: 38 operands: 39
35	ExprTuple	40
36	Literal
37	ExprTuple	53, 41
38	Literal
39	ExprTuple	42, 43
40	Operation	operator: 44 operands: 45
41	Operation	operator: 46 operands: 47
42	Operation	operator: 48 operand: 53
43	Variable
44	Literal
45	ExprTuple	50, 53
46	Literal
47	ExprTuple	51, 52
48	Literal
49	ExprTuple	53
50	Variable
51	Literal
52	Variable
53	Variable

Expression of type Conditional¶

from the theory of proveit.physics.quantum.algebra¶

Expression of type Conditional ¶

from the theory of proveit.physics.quantum.algebra ¶