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 ExprRange, ExprTuple, U, Variable
from proveit.core_expr_types import Len
from proveit.linear_algebra import MatrixMult, ScalarMult
from proveit.logic import Equals, InSet
from proveit.numbers import Exp, Interval, IntervalCO, Mult, Real, e, four, i, one, pi, subtract, two, zero
from proveit.physics.quantum import var_ket_u
from proveit.physics.quantum.QPE import phase, two_pow_t

# build up the expression from sub-expressions
sub_expr1 = Variable("_a", latex_format = r"{_{-}a}")
expr = ExprTuple(Len(operands = [InSet(phase, Real), InSet(Mult(two_pow_t, phase), Interval(zero, subtract(two_pow_t, one))), Equals(MatrixMult(U, var_ket_u), ScalarMult(Exp(e, Mult(two, pi, i, phase)), var_ket_u)), InSet(phase, IntervalCO(zero, one))]), Len(operands = [ExprRange(sub_expr1, sub_expr1, one, four)]))

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(|\left(\varphi \in \mathbb{R}, \left(2^{t} \cdot \varphi\right) \in \{0~\ldotp \ldotp~2^{t} - 1\}, \left(U \thinspace \lvert u \rangle\right) = \left(\mathsf{e}^{2 \cdot \pi \cdot \mathsf{i} \cdot \varphi} \cdot \lvert u \rangle\right), \varphi \in \left[0,1\right)\right)|, |\left(1, 2, \ldots, 4\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
1	Operation	operator: 4 operands: 3
2	Operation	operator: 4 operands: 5
3	ExprTuple	6, 7, 8, 9
4	Literal
5	ExprTuple	10
6	Operation	operator: 15 operands: 11
7	Operation	operator: 15 operands: 12
8	Operation	operator: 13 operands: 14
9	Operation	operator: 15 operands: 16
10	ExprRange	lambda_map: 17 start_index: 55 end_index: 18
11	ExprTuple	59, 19
12	ExprTuple	20, 21
13	Literal
14	ExprTuple	22, 23
15	Literal
16	ExprTuple	59, 24
17	Lambda	parameter: 35 body: 35
18	Literal
19	Literal
20	Operation	operator: 52 operands: 26
21	Operation	operator: 27 operands: 28
22	Operation	operator: 29 operands: 30
23	Operation	operator: 31 operands: 32
24	Operation	operator: 33 operands: 34
25	ExprTuple	35
26	ExprTuple	44, 59
27	Literal
28	ExprTuple	40, 36
29	Literal
30	ExprTuple	37, 39
31	Literal
32	ExprTuple	38, 39
33	Literal
34	ExprTuple	40, 55
35	Variable
36	Operation	operator: 41 operands: 42
37	Variable
38	Operation	operator: 48 operands: 43
39	Variable
40	Literal
41	Literal
42	ExprTuple	44, 45
43	ExprTuple	46, 47
44	Operation	operator: 48 operands: 49
45	Operation	operator: 50 operand: 55
46	Literal
47	Operation	operator: 52 operands: 53
48	Literal
49	ExprTuple	56, 54
50	Literal
51	ExprTuple	55
52	Literal
53	ExprTuple	56, 57, 58, 59
54	Variable
55	Literal
56	Literal
57	Literal
58	Literal
59	Variable