Expression of type ExprTuple

from the theory of proveit.physics.quantum.QPE

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 ExprTuple, U
from proveit.linear_algebra import MatrixMult, ScalarMult, Unitary
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, IntervalCO, Mult, Real, e, i, one, pi, two, zero
from proveit.physics.quantum import normalized_var_ket_u, var_ket_u
from proveit.physics.quantum.QPE import phase, s_ket_domain, two_pow_s

# build up the expression from sub-expressions
expr = ExprTuple(InSet(U, Unitary(two_pow_s)), InSet(var_ket_u, s_ket_domain), InSet(phase, Real), InSet(phase, IntervalCO(zero, one)), normalized_var_ket_u, Equals(MatrixMult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, phase)), var_ket_u)))

expr:

# 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(U \in \textrm{U}\left(2^{s}\right), \lvert u \rangle \in \mathbb{C}^{2^{s}}, \varphi \in \mathbb{R}, \varphi \in \left[0,1\right), \left \|\lvert u \rangle\right \| = 1, \left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right)\right)

stored_expr.style_options()

name	description	default	current value	related methods
wrap_positions	position(s) at which wrapping is to occur; 'n' is after the nth comma.	()	()	('with_wrapping_at',)
justification	if any wrap positions are set, justify to the 'left', 'center', or 'right'	left	left	('with_justification',)

# display the expression information
stored_expr.expr_info()

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