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, e, i, one, pi, subtract, three, 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(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, three)]))

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(\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, 3\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
4	Literal
5	ExprTuple	9
6	Operation	operator: 13 operands: 10
7	Operation	operator: 11 operands: 12
8	Operation	operator: 13 operands: 14
9	ExprRange	lambda_map: 15 start_index: 52 end_index: 16
10	ExprTuple	17, 18
11	Literal
12	ExprTuple	19, 20
13	Literal
14	ExprTuple	56, 21
15	Lambda	parameter: 32 body: 32
16	Literal
17	Operation	operator: 49 operands: 23
18	Operation	operator: 24 operands: 25
19	Operation	operator: 26 operands: 27
20	Operation	operator: 28 operands: 29
21	Operation	operator: 30 operands: 31
22	ExprTuple	32
23	ExprTuple	41, 56
24	Literal
25	ExprTuple	37, 33
26	Literal
27	ExprTuple	34, 36
28	Literal
29	ExprTuple	35, 36
30	Literal
31	ExprTuple	37, 52
32	Variable
33	Operation	operator: 38 operands: 39
34	Variable
35	Operation	operator: 45 operands: 40
36	Variable
37	Literal
38	Literal
39	ExprTuple	41, 42
40	ExprTuple	43, 44
41	Operation	operator: 45 operands: 46
42	Operation	operator: 47 operand: 52
43	Literal
44	Operation	operator: 49 operands: 50
45	Literal
46	ExprTuple	53, 51
47	Literal
48	ExprTuple	52
49	Literal
50	ExprTuple	53, 54, 55, 56
51	Variable
52	Literal
53	Literal
54	Literal
55	Literal
56	Variable